AuroraMiddleware/glibc
1
0
Fork 0
mirror of https://sourceware.org/git/glibc.git synced 2024-11-08 22:30:07 +00:00
Code Issues Packages Projects Releases Wiki Activity

2006-01-27 Dwayne Grant McConnell <decimal@us.ibm.com>

Browse Source 
Jakub Jelinek  <jakub@redhat.com>
	    Roland McGrath  <roland@redhat.com>
	    Steven Munroe  <sjmunroe@us.ibm.com>
	    Alan Modra  <amodra@bigpond.net.au>

	* sysdeps/powerpc/powerpc64/fpu/s_truncf.S: Comment fix.
	* sysdeps/powerpc/powerpc32/fpu/s_truncf.S: Likewise.
	* sysdeps/powerpc/powerpc64/fpu/s_llroundf.S: Likewise.

	* sysdeps/powerpc/fpu/libm-test-ulps: Update.

	* math/libm-test.inc (check_float_internal): Allow ulp <= 0.5.
	(erfc_test): Don't run erfcl (27.0L) test if erfcl (27.0L) is
	denormal.
	[TEST_LDOUBLE] (ceil_test, floor_test, llrint_test, llround_test,
	rint_test, round_test, trunc_test): Add new tests.

	* sysdeps/powerpc/powerpc32/fpu/s_copysignl.S: New file.
	* sysdeps/powerpc/powerpc32/fpu/s_fabs.S: New file.
	* sysdeps/powerpc/powerpc32/fpu/s_fabsl.S: New file.
	* sysdeps/powerpc/powerpc32/fpu/s_fdim.c: New file.
	* sysdeps/powerpc/powerpc32/fpu/s_fmax.S: New file.
	* sysdeps/powerpc/powerpc32/fpu/s_fmin.S: New file.
	* sysdeps/powerpc/powerpc32/fpu/s_isnan.c: New file.

	* sysdeps/powerpc/powerpc64/fpu/s_ceill.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_copysignl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_fabs.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_fabsl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_fdim.c: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_floorl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_fmax.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_fmin.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_isnan.c: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_llrintl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_llroundl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_lrintl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_lroundl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_nearbyintl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_rintl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_roundl.S: New file.
	* sysdeps/powerpc/powerpc64/fpu/s_truncl.S: New file.

	* sysdeps/unix/sysv/linux/powerpc/Implies: New file.
	* sysdeps/unix/sysv/linux/powerpc/powerpc64/fpu/Implies: New file.
	* sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/Implies: New file.
	* sysdeps/unix/sysv/linux/powerpc/configure.in: New file.
	* sysdeps/unix/sysv/linux/powerpc/configure: New file.
	* sysdeps/unix/sysv/linux/powerpc/bits/wordsize.h
	(__LONG_DOUBLE_MATH_OPTIONAL): Define.
	(__NO_LONG_DOUBLE_MATH): Define.
	* sysdeps/unix/sysv/linux/powerpc/nldbl-abi.h: New file.
	* sysdeps/powerpc/fpu/s_isnan.c: Include math_ldbl_opt.h.
	* sysdeps/powerpc/powerpc64/fpu/s_ceil.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols.
	* sysdeps/powerpc/powerpc64/fpu/s_copysign.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc64/fpu/s_floor.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc64/fpu/s_llrint.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (llrintl, lrintl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc64/fpu/s_llround.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (llroundl, lroundl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc64/fpu/s_rint.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc64/fpu/s_round.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc64/fpu/s_trunc.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_ceil.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_copysign.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_floor.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_lrint.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (lrintl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_llrint.c: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (llrintl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_lround.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (lroundl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_rint.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_round.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols.
	* sysdeps/powerpc/powerpc32/fpu/s_trunc.S: Include math_ldbl_opt.h.
	[LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols.

	* misc/qefgcvt_r.c [LDBL_MIN_10_EXP == -291] (FLOAT_MIN_10_NORM): New.

	* sysdeps/powerpc/fpu/bits/mathdef.h (__NO_LONG_DOUBLE_MATH): Remove.
	* sysdeps/powerpc/Implies: Add ieee754/ldbl-128ibm.
	* sysdeps/powerpc/powerpc32/Implies: Remove powerpc/soft-fp.
	* sysdeps/ieee754/ldbl-128ibm/Makefile: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_acoshl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_acosl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_asinl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_atan2l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_coshl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_expl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_fmodl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_j0l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_j1l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_log10l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_log2l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_logl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_powl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_remainderl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_sinhl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/ieee754.h: New file.
	* sysdeps/ieee754/ldbl-128ibm/k_cosl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/k_sincosl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/k_sinl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/k_tanl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/math_ldbl.h: New file.
	* sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/printf_fphex.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_atanl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_cosl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_erfl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_expm1l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_fabsl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_finitel.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_frexpl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_ilogbl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_isinfl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_isnanl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_log1pl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_logbl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_modfl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_remquol.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_rintl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_signbitl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_sincosl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_sinl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_tanhl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_tanl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_truncl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/strtold_l.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/t_sincosl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/w_expl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_copysignl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_floorl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_llrintl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_llroundl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_roundl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_ceill.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_lrintl.c: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_lroundl.c: New file.

	* sysdeps/ieee754/ldbl-128/e_powl.c: Fix old comment.
This commit is contained in:
Roland McGrath 2006-01-28 00:15:15 +00:00
parent d421a7801d
commit f964490f3c
133 changed files with 12670 additions and 136 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

170
ChangeLog
View File

@ -1,3 +1,173 @@
2006-01-27 Dwayne Grant McConnell <decimal@us.ibm.com>
Jakub Jelinek <jakub@redhat.com>
Roland McGrath <roland@redhat.com>
Steven Munroe <sjmunroe@us.ibm.com>
Alan Modra <amodra@bigpond.net.au>
* sysdeps/powerpc/powerpc64/fpu/s_truncf.S: Comment fix.
* sysdeps/powerpc/powerpc32/fpu/s_truncf.S: Likewise.
* sysdeps/powerpc/powerpc64/fpu/s_llroundf.S: Likewise.
* sysdeps/powerpc/fpu/libm-test-ulps: Update.
* math/libm-test.inc (check_float_internal): Allow ulp <= 0.5.
(erfc_test): Don't run erfcl (27.0L) test if erfcl (27.0L) is
denormal.
[TEST_LDOUBLE] (ceil_test, floor_test, llrint_test, llround_test,
rint_test, round_test, trunc_test): Add new tests.
* sysdeps/powerpc/powerpc32/fpu/s_copysignl.S: New file.
* sysdeps/powerpc/powerpc32/fpu/s_fabs.S: New file.
* sysdeps/powerpc/powerpc32/fpu/s_fabsl.S: New file.
* sysdeps/powerpc/powerpc32/fpu/s_fdim.c: New file.
* sysdeps/powerpc/powerpc32/fpu/s_fmax.S: New file.
* sysdeps/powerpc/powerpc32/fpu/s_fmin.S: New file.
* sysdeps/powerpc/powerpc32/fpu/s_isnan.c: New file.
* sysdeps/powerpc/powerpc64/fpu/s_ceill.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_copysignl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_fabs.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_fabsl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_fdim.c: New file.
* sysdeps/powerpc/powerpc64/fpu/s_floorl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_fmax.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_fmin.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_isnan.c: New file.
* sysdeps/powerpc/powerpc64/fpu/s_llrintl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_llroundl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_lrintl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_lroundl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_nearbyintl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_rintl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_roundl.S: New file.
* sysdeps/powerpc/powerpc64/fpu/s_truncl.S: New file.
* sysdeps/unix/sysv/linux/powerpc/Implies: New file.
* sysdeps/unix/sysv/linux/powerpc/powerpc64/fpu/Implies: New file.
* sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/Implies: New file.
* sysdeps/unix/sysv/linux/powerpc/configure.in: New file.
* sysdeps/unix/sysv/linux/powerpc/configure: New file.
* sysdeps/unix/sysv/linux/powerpc/bits/wordsize.h
(__LONG_DOUBLE_MATH_OPTIONAL): Define.
(__NO_LONG_DOUBLE_MATH): Define.
* sysdeps/unix/sysv/linux/powerpc/nldbl-abi.h: New file.
* sysdeps/powerpc/fpu/s_isnan.c: Include math_ldbl_opt.h.
* sysdeps/powerpc/powerpc64/fpu/s_ceil.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols.
* sysdeps/powerpc/powerpc64/fpu/s_copysign.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols.
* sysdeps/powerpc/powerpc64/fpu/s_floor.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols.
* sysdeps/powerpc/powerpc64/fpu/s_llrint.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (llrintl, lrintl): Add compatibility symbols.
* sysdeps/powerpc/powerpc64/fpu/s_llround.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (llroundl, lroundl): Add compatibility symbols.
* sysdeps/powerpc/powerpc64/fpu/s_rint.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols.
* sysdeps/powerpc/powerpc64/fpu/s_round.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols.
* sysdeps/powerpc/powerpc64/fpu/s_trunc.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_ceil.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_copysign.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_floor.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_lrint.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (lrintl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_llrint.c: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (llrintl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_lround.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (lroundl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_rint.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_round.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols.
* sysdeps/powerpc/powerpc32/fpu/s_trunc.S: Include math_ldbl_opt.h.
[LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols.
* misc/qefgcvt_r.c [LDBL_MIN_10_EXP == -291] (FLOAT_MIN_10_NORM): New.
* sysdeps/powerpc/fpu/bits/mathdef.h (__NO_LONG_DOUBLE_MATH): Remove.
* sysdeps/powerpc/Implies: Add ieee754/ldbl-128ibm.
* sysdeps/powerpc/powerpc32/Implies: Remove powerpc/soft-fp.
* sysdeps/ieee754/ldbl-128ibm/Makefile: New file.
* sysdeps/ieee754/ldbl-128ibm/e_acoshl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_acosl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_asinl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_atan2l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_coshl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_expl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_fmodl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_hypotl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_j0l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_j1l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_jnl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_log10l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_log2l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_logl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_powl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_remainderl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_sinhl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/ieee754.h: New file.
* sysdeps/ieee754/ldbl-128ibm/k_cosl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/k_sincosl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/k_sinl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/k_tanl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c: New file.
* sysdeps/ieee754/ldbl-128ibm/math_ldbl.h: New file.
* sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/printf_fphex.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_atanl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_cosl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_erfl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_expm1l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_fabsl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_finitel.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_frexpl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_ilogbl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_isinfl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_isnanl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_log1pl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_logbl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_modfl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_remquol.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_rintl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_signbitl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_sincosl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_sinl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_tanhl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_tanl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_truncl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/strtold_l.c: New file.
* sysdeps/ieee754/ldbl-128ibm/t_sincosl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/w_expl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_copysignl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_floorl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_llrintl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_llroundl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_roundl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_ceill.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_lrintl.c: New file.
* sysdeps/ieee754/ldbl-128ibm/s_lroundl.c: New file.
* sysdeps/ieee754/ldbl-128/e_powl.c: Fix old comment.
2006-01-22 Aurelien Jarno <aurelien@aurel32.net>
* sysdeps/gnu/errlist-compat.awk: Reduce required number of symbols in

307
math/libm-test.inc
View File

@ -22,7 +22,7 @@
This file is processed by a perl script. The resulting file has to
be included by a master file that defines:
Makros:
Macros:
FUNC(function): converts general function name (like cos) to
name with correct suffix (e.g. cosl or cosf)
MATHCONST(x): like FUNC but for constants (e.g convert 0.0 to 0.0L)
@ -498,7 +498,7 @@ check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
&& computed == 0.0 && expected == 0.0
&& signbit(computed) != signbit (expected))
ok = 0;
else if (ulp == 0.0 || (ulp <= max_ulp && !ignore_max_ulp))
else if (ulp <= 0.5 || (ulp <= max_ulp && !ignore_max_ulp))
ok = 1;
else
{
@ -1631,6 +1631,51 @@ ceil_test (void)
TEST_f_f (ceil, 0.25, 1.0);
TEST_f_f (ceil, -0.25, minus_zero);
#ifdef TEST_LDOUBLE
/* The result can only be represented in long double. */
TEST_f_f (ceil, 4503599627370495.5L, 4503599627370496.0L);
TEST_f_f (ceil, 4503599627370496.25L, 4503599627370497.0L);
TEST_f_f (ceil, 4503599627370496.5L, 4503599627370497.0L);
TEST_f_f (ceil, 4503599627370496.75L, 4503599627370497.0L);
TEST_f_f (ceil, 4503599627370497.5L, 4503599627370498.0L);
TEST_f_f (ceil, -4503599627370495.5L, -4503599627370495.0L);
TEST_f_f (ceil, -4503599627370496.25L, -4503599627370496.0L);
TEST_f_f (ceil, -4503599627370496.5L, -4503599627370496.0L);
TEST_f_f (ceil, -4503599627370496.75L, -4503599627370496.0L);
TEST_f_f (ceil, -4503599627370497.5L, -4503599627370497.0L);
TEST_f_f (ceil, 9007199254740991.5L, 9007199254740992.0L);
TEST_f_f (ceil, 9007199254740992.25L, 9007199254740993.0L);
TEST_f_f (ceil, 9007199254740992.5L, 9007199254740993.0L);
TEST_f_f (ceil, 9007199254740992.75L, 9007199254740993.0L);
TEST_f_f (ceil, 9007199254740993.5L, 9007199254740994.0L);
TEST_f_f (ceil, -9007199254740991.5L, -9007199254740991.0L);
TEST_f_f (ceil, -9007199254740992.25L, -9007199254740992.0L);
TEST_f_f (ceil, -9007199254740992.5L, -9007199254740992.0L);
TEST_f_f (ceil, -9007199254740992.75L, -9007199254740992.0L);
TEST_f_f (ceil, -9007199254740993.5L, -9007199254740993.0L);
TEST_f_f (ceil, 72057594037927935.5L, 72057594037927936.0L);
TEST_f_f (ceil, 72057594037927936.25L, 72057594037927937.0L);
TEST_f_f (ceil, 72057594037927936.5L, 72057594037927937.0L);
TEST_f_f (ceil, 72057594037927936.75L, 72057594037927937.0L);
TEST_f_f (ceil, 72057594037927937.5L, 72057594037927938.0L);
TEST_f_f (ceil, -72057594037927935.5L, -72057594037927935.0L);
TEST_f_f (ceil, -72057594037927936.25L, -72057594037927936.0L);
TEST_f_f (ceil, -72057594037927936.5L, -72057594037927936.0L);
TEST_f_f (ceil, -72057594037927936.75L, -72057594037927936.0L);
TEST_f_f (ceil, -72057594037927937.5L, -72057594037927937.0L);
TEST_f_f (ceil, 10141204801825835211973625643007.5L, 10141204801825835211973625643008.0L);
TEST_f_f (ceil, 10141204801825835211973625643008.25L, 10141204801825835211973625643009.0L);
TEST_f_f (ceil, 10141204801825835211973625643008.5L, 10141204801825835211973625643009.0L);
TEST_f_f (ceil, 10141204801825835211973625643008.75L, 10141204801825835211973625643009.0L);
TEST_f_f (ceil, 10141204801825835211973625643009.5L, 10141204801825835211973625643010.0L);
#endif
END (ceil);
}
@ -2389,7 +2434,9 @@ erfc_test (void)
TEST_f_f (erfc, 4.125L, 0.542340079956506600531223408575531062e-8L);
#ifdef TEST_LDOUBLE
/* The result can only be represented in long double. */
# if LDBL_MIN_10_EXP < -319
TEST_f_f (erfc, 27.0L, 0.523704892378925568501606768284954709e-318L);
# endif
#endif
END (erfc);
@ -2584,6 +2631,52 @@ floor_test (void)
TEST_f_f (floor, 0.25, 0.0);
TEST_f_f (floor, -0.25, -1.0);
#ifdef TEST_LDOUBLE
/* The result can only be represented in long double. */
TEST_f_f (floor, 4503599627370495.5L, 4503599627370495.0L);
TEST_f_f (floor, 4503599627370496.25L, 4503599627370496.0L);
TEST_f_f (floor, 4503599627370496.5L, 4503599627370496.0L);
TEST_f_f (floor, 4503599627370496.75L, 4503599627370496.0L);
TEST_f_f (floor, 4503599627370497.5L, 4503599627370497.0L);
TEST_f_f (floor, -4503599627370495.5L, -4503599627370496.0L);
TEST_f_f (floor, -4503599627370496.25L, -4503599627370497.0L);
TEST_f_f (floor, -4503599627370496.5L, -4503599627370497.0L);
TEST_f_f (floor, -4503599627370496.75L, -4503599627370497.0L);
TEST_f_f (floor, -4503599627370497.5L, -4503599627370498.0L);
TEST_f_f (floor, 9007199254740991.5L, 9007199254740991.0L);
TEST_f_f (floor, 9007199254740992.25L, 9007199254740992.0L);
TEST_f_f (floor, 9007199254740992.5L, 9007199254740992.0L);
TEST_f_f (floor, 9007199254740992.75L, 9007199254740992.0L);
TEST_f_f (floor, 9007199254740993.5L, 9007199254740993.0L);
TEST_f_f (floor, -9007199254740991.5L, -9007199254740992.0L);
TEST_f_f (floor, -9007199254740992.25L, -9007199254740993.0L);
TEST_f_f (floor, -9007199254740992.5L, -9007199254740993.0L);
TEST_f_f (floor, -9007199254740992.75L, -9007199254740993.0L);
TEST_f_f (floor, -9007199254740993.5L, -9007199254740994.0L);
TEST_f_f (floor, 72057594037927935.5L, 72057594037927935.0L);
TEST_f_f (floor, 72057594037927936.25L, 72057594037927936.0L);
TEST_f_f (floor, 72057594037927936.5L, 72057594037927936.0L);
TEST_f_f (floor, 72057594037927936.75L, 72057594037927936.0L);
TEST_f_f (floor, 72057594037927937.5L, 72057594037927937.0L);
TEST_f_f (floor, -72057594037927935.5L, -72057594037927936.0L);
TEST_f_f (floor, -72057594037927936.25L, -72057594037927937.0L);
TEST_f_f (floor, -72057594037927936.5L, -72057594037927937.0L);
TEST_f_f (floor, -72057594037927936.75L, -72057594037927937.0L);
TEST_f_f (floor, -72057594037927937.5L, -72057594037927938.0L);
TEST_f_f (floor, 10141204801825835211973625643007.5L, 10141204801825835211973625643007.0L);
TEST_f_f (floor, 10141204801825835211973625643008.25L, 10141204801825835211973625643008.0L);
TEST_f_f (floor, 10141204801825835211973625643008.5L, 10141204801825835211973625643008.0L);
TEST_f_f (floor, 10141204801825835211973625643008.75L, 10141204801825835211973625643008.0L);
TEST_f_f (floor, 10141204801825835211973625643009.5L, 10141204801825835211973625643009.0L);
#endif
END (floor);
}
@ -3164,6 +3257,44 @@ llrint_test (void)
TEST_f_L (llrint, 36028797018963968.0, 36028797018963968LL);
/* 0x100000000000000 */
TEST_f_L (llrint, 72057594037927936.0, 72057594037927936LL);
#ifdef TEST_LDOUBLE
/* The input can only be represented in long double. */
TEST_f_L (llrint, 4503599627370495.5L, 4503599627370496LL);
TEST_f_L (llrint, 4503599627370496.25L, 4503599627370496LL);
TEST_f_L (llrint, 4503599627370496.5L, 4503599627370496LL);
TEST_f_L (llrint, 4503599627370496.75L, 4503599627370497LL);
TEST_f_L (llrint, 4503599627370497.5L, 4503599627370498LL);
TEST_f_L (llrint, -4503599627370495.5L, -4503599627370496LL);
TEST_f_L (llrint, -4503599627370496.25L, -4503599627370496LL);
TEST_f_L (llrint, -4503599627370496.5L, -4503599627370496LL);
TEST_f_L (llrint, -4503599627370496.75L, -4503599627370497LL);
TEST_f_L (llrint, -4503599627370497.5L, -4503599627370498LL);
TEST_f_L (llrint, 9007199254740991.5L, 9007199254740992LL);
TEST_f_L (llrint, 9007199254740992.25L, 9007199254740992LL);
TEST_f_L (llrint, 9007199254740992.5L, 9007199254740992LL);
TEST_f_L (llrint, 9007199254740992.75L, 9007199254740993LL);
TEST_f_L (llrint, 9007199254740993.5L, 9007199254740994LL);
TEST_f_L (llrint, -9007199254740991.5L, -9007199254740992LL);
TEST_f_L (llrint, -9007199254740992.25L, -9007199254740992LL);
TEST_f_L (llrint, -9007199254740992.5L, -9007199254740992LL);
TEST_f_L (llrint, -9007199254740992.75L, -9007199254740993LL);
TEST_f_L (llrint, -9007199254740993.5L, -9007199254740994LL);
TEST_f_L (llrint, 72057594037927935.5L, 72057594037927936LL);
TEST_f_L (llrint, 72057594037927936.25L, 72057594037927936LL);
TEST_f_L (llrint, 72057594037927936.5L, 72057594037927936LL);
TEST_f_L (llrint, 72057594037927936.75L, 72057594037927937LL);
TEST_f_L (llrint, 72057594037927937.5L, 72057594037927938LL);
TEST_f_L (llrint, -72057594037927935.5L, -72057594037927936LL);
TEST_f_L (llrint, -72057594037927936.25L, -72057594037927936LL);
TEST_f_L (llrint, -72057594037927936.5L, -72057594037927936LL);
TEST_f_L (llrint, -72057594037927936.75L, -72057594037927937LL);
TEST_f_L (llrint, -72057594037927937.5L, -72057594037927938LL);
#endif
END (llrint);
}
@ -3398,6 +3529,45 @@ llround_test (void)
TEST_f_L (llround, 8589934591.5, 8589934592LL);
#endif
#ifdef TEST_LDOUBLE
/* The input can only be represented in long double. */
TEST_f_L (llround, 4503599627370495.5L, 4503599627370496LL);
TEST_f_L (llround, 4503599627370496.25L, 4503599627370496LL);
TEST_f_L (llround, 4503599627370496.5L, 4503599627370497LL);
TEST_f_L (llround, 4503599627370496.75L, 4503599627370497LL);
TEST_f_L (llround, 4503599627370497.5L, 4503599627370498LL);
TEST_f_L (llround, -4503599627370495.5L, -4503599627370496LL);
TEST_f_L (llround, -4503599627370496.25L, -4503599627370496LL);
TEST_f_L (llround, -4503599627370496.5L, -4503599627370497LL);
TEST_f_L (llround, -4503599627370496.75L, -4503599627370497LL);
TEST_f_L (llround, -4503599627370497.5L, -4503599627370498LL);
TEST_f_L (llround, 9007199254740991.5L, 9007199254740992LL);
TEST_f_L (llround, 9007199254740992.25L, 9007199254740992LL);
TEST_f_L (llround, 9007199254740992.5L, 9007199254740993LL);
TEST_f_L (llround, 9007199254740992.75L, 9007199254740993LL);
TEST_f_L (llround, 9007199254740993.5L, 9007199254740994LL);
TEST_f_L (llround, -9007199254740991.5L, -9007199254740992LL);
TEST_f_L (llround, -9007199254740992.25L, -9007199254740992LL);
TEST_f_L (llround, -9007199254740992.5L, -9007199254740993LL);
TEST_f_L (llround, -9007199254740992.75L, -9007199254740993LL);
TEST_f_L (llround, -9007199254740993.5L, -9007199254740994LL);
TEST_f_L (llround, 72057594037927935.5L, 72057594037927936LL);
TEST_f_L (llround, 72057594037927936.25L, 72057594037927936LL);
TEST_f_L (llround, 72057594037927936.5L, 72057594037927937LL);
TEST_f_L (llround, 72057594037927936.75L, 72057594037927937LL);
TEST_f_L (llround, 72057594037927937.5L, 72057594037927938LL);
TEST_f_L (llround, -72057594037927935.5L, -72057594037927936LL);
TEST_f_L (llround, -72057594037927936.25L, -72057594037927936LL);
TEST_f_L (llround, -72057594037927936.5L, -72057594037927937LL);
TEST_f_L (llround, -72057594037927936.75L, -72057594037927937LL);
TEST_f_L (llround, -72057594037927937.5L, -72057594037927938LL);
#endif
END (llround);
}
@ -3794,6 +3964,50 @@ rint_test (void)
TEST_f_f (rint, -2.5, -2.0);
TEST_f_f (rint, -3.5, -4.0);
TEST_f_f (rint, -4.5, -4.0);
#ifdef TEST_LDOUBLE
/* The result can only be represented in long double. */
TEST_f_f (rint, 4503599627370495.5L, 4503599627370496.0L);
TEST_f_f (rint, 4503599627370496.25L, 4503599627370496.0L);
TEST_f_f (rint, 4503599627370496.5L, 4503599627370496.0L);
TEST_f_f (rint, 4503599627370496.75L, 4503599627370497.0L);
TEST_f_f (rint, 4503599627370497.5L, 4503599627370498.0L);
TEST_f_f (rint, -4503599627370495.5L, -4503599627370496.0L);
TEST_f_f (rint, -4503599627370496.25L, -4503599627370496.0L);
TEST_f_f (rint, -4503599627370496.5L, -4503599627370496.0L);
TEST_f_f (rint, -4503599627370496.75L, -4503599627370497.0L);
TEST_f_f (rint, -4503599627370497.5L, -4503599627370498.0L);
TEST_f_f (rint, 9007199254740991.5L, 9007199254740992.0L);
TEST_f_f (rint, 9007199254740992.25L, 9007199254740992.0L);
TEST_f_f (rint, 9007199254740992.5L, 9007199254740992.0L);
TEST_f_f (rint, 9007199254740992.75L, 9007199254740993.0L);
TEST_f_f (rint, 9007199254740993.5L, 9007199254740994.0L);
TEST_f_f (rint, -9007199254740991.5L, -9007199254740992.0L);
TEST_f_f (rint, -9007199254740992.25L, -9007199254740992.0L);
TEST_f_f (rint, -9007199254740992.5L, -9007199254740992.0L);
TEST_f_f (rint, -9007199254740992.75L, -9007199254740993.0L);
TEST_f_f (rint, -9007199254740993.5L, -9007199254740994.0L);
TEST_f_f (rint, 72057594037927935.5L, 72057594037927936.0L);
TEST_f_f (rint, 72057594037927936.25L, 72057594037927936.0L);
TEST_f_f (rint, 72057594037927936.5L, 72057594037927936.0L);
TEST_f_f (rint, 72057594037927936.75L, 72057594037927937.0L);
TEST_f_f (rint, 72057594037927937.5L, 72057594037927938.0L);
TEST_f_f (rint, -72057594037927935.5L, -72057594037927936.0L);
TEST_f_f (rint, -72057594037927936.25L, -72057594037927936.0L);
TEST_f_f (rint, -72057594037927936.5L, -72057594037927936.0L);
TEST_f_f (rint, -72057594037927936.75L, -72057594037927937.0L);
TEST_f_f (rint, -72057594037927937.5L, -72057594037927938.0L);
TEST_f_f (rint, 10141204801825835211973625643007.5L, 10141204801825835211973625643008.0L);
TEST_f_f (rint, 10141204801825835211973625643008.25L, 10141204801825835211973625643008.0L);
TEST_f_f (rint, 10141204801825835211973625643008.5L, 10141204801825835211973625643008.0L);
TEST_f_f (rint, 10141204801825835211973625643008.75L, 10141204801825835211973625643009.0L);
TEST_f_f (rint, 10141204801825835211973625643009.5L, 10141204801825835211973625643010.0L);
#endif
END (rint);
}
@ -3924,6 +4138,51 @@ round_test (void)
TEST_f_f (round, 2097152.5, 2097153);
TEST_f_f (round, -2097152.5, -2097153);
#ifdef TEST_LDOUBLE
/* The result can only be represented in long double. */
TEST_f_f (round, 4503599627370495.5L, 4503599627370496.0L);
TEST_f_f (round, 4503599627370496.25L, 4503599627370496.0L);
TEST_f_f (round, 4503599627370496.5L, 4503599627370497.0L);
TEST_f_f (round, 4503599627370496.75L, 4503599627370497.0L);
TEST_f_f (round, 4503599627370497.5L, 4503599627370498.0L);
TEST_f_f (round, -4503599627370495.5L, -4503599627370496.0L);
TEST_f_f (round, -4503599627370496.25L, -4503599627370496.0L);
TEST_f_f (round, -4503599627370496.5L, -4503599627370497.0L);
TEST_f_f (round, -4503599627370496.75L, -4503599627370497.0L);
TEST_f_f (round, -4503599627370497.5L, -4503599627370498.0L);
TEST_f_f (round, 9007199254740991.5L, 9007199254740992.0L);
TEST_f_f (round, 9007199254740992.25L, 9007199254740992.0L);
TEST_f_f (round, 9007199254740992.5L, 9007199254740993.0L);
TEST_f_f (round, 9007199254740992.75L, 9007199254740993.0L);
TEST_f_f (round, 9007199254740993.5L, 9007199254740994.0L);
TEST_f_f (round, -9007199254740991.5L, -9007199254740992.0L);
TEST_f_f (round, -9007199254740992.25L, -9007199254740992.0L);
TEST_f_f (round, -9007199254740992.5L, -9007199254740993.0L);
TEST_f_f (round, -9007199254740992.75L, -9007199254740993.0L);
TEST_f_f (round, -9007199254740993.5L, -9007199254740994.0L);
TEST_f_f (round, 72057594037927935.5L, 72057594037927936.0L);
TEST_f_f (round, 72057594037927936.25L, 72057594037927936.0L);
TEST_f_f (round, 72057594037927936.5L, 72057594037927937.0L);
TEST_f_f (round, 72057594037927936.75L, 72057594037927937.0L);
TEST_f_f (round, 72057594037927937.5L, 72057594037927938.0L);
TEST_f_f (round, -72057594037927935.5L, -72057594037927936.0L);
TEST_f_f (round, -72057594037927936.25L, -72057594037927936.0L);
TEST_f_f (round, -72057594037927936.5L, -72057594037927937.0L);
TEST_f_f (round, -72057594037927936.75L, -72057594037927937.0L);
TEST_f_f (round, -72057594037927937.5L, -72057594037927938.0L);
TEST_f_f (round, 10141204801825835211973625643007.5L, 10141204801825835211973625643008.0L);
TEST_f_f (round, 10141204801825835211973625643008.25L, 10141204801825835211973625643008.0L);
TEST_f_f (round, 10141204801825835211973625643008.5L, 10141204801825835211973625643009.0L);
TEST_f_f (round, 10141204801825835211973625643008.75L, 10141204801825835211973625643009.0L);
TEST_f_f (round, 10141204801825835211973625643009.5L, 10141204801825835211973625643010.0L);
#endif
END (round);
}
@ -4291,6 +4550,50 @@ trunc_test (void)
TEST_f_f (trunc, 4294967296.625L, 4294967296.0L);
TEST_f_f (trunc, -4294967296.625L, -4294967296.0L);
#ifdef TEST_LDOUBLE
/* The result can only be represented in long double. */
TEST_f_f (trunc, 4503599627370495.5L, 4503599627370495.0L);
TEST_f_f (trunc, 4503599627370496.25L, 4503599627370496.0L);
TEST_f_f (trunc, 4503599627370496.5L, 4503599627370496.0L);
TEST_f_f (trunc, 4503599627370496.75L, 4503599627370496.0L);
TEST_f_f (trunc, 4503599627370497.5L, 4503599627370497.0L);
TEST_f_f (trunc, -4503599627370495.5L, -4503599627370495.0L);
TEST_f_f (trunc, -4503599627370496.25L, -4503599627370496.0L);
TEST_f_f (trunc, -4503599627370496.5L, -4503599627370496.0L);
TEST_f_f (trunc, -4503599627370496.75L, -4503599627370496.0L);
TEST_f_f (trunc, -4503599627370497.5L, -4503599627370497.0L);
TEST_f_f (trunc, 9007199254740991.5L, 9007199254740991.0L);
TEST_f_f (trunc, 9007199254740992.25L, 9007199254740992.0L);
TEST_f_f (trunc, 9007199254740992.5L, 9007199254740992.0L);
TEST_f_f (trunc, 9007199254740992.75L, 9007199254740992.0L);
TEST_f_f (trunc, 9007199254740993.5L, 9007199254740993.0L);
TEST_f_f (trunc, -9007199254740991.5L, -9007199254740991.0L);
TEST_f_f (trunc, -9007199254740992.25L, -9007199254740992.0L);
TEST_f_f (trunc, -9007199254740992.5L, -9007199254740992.0L);
TEST_f_f (trunc, -9007199254740992.75L, -9007199254740992.0L);
TEST_f_f (trunc, -9007199254740993.5L, -9007199254740993.0L);
TEST_f_f (trunc, 72057594037927935.5L, 72057594037927935.0L);
TEST_f_f (trunc, 72057594037927936.25L, 72057594037927936.0L);
TEST_f_f (trunc, 72057594037927936.5L, 72057594037927936.0L);
TEST_f_f (trunc, 72057594037927936.75L, 72057594037927936.0L);
TEST_f_f (trunc, 72057594037927937.5L, 72057594037927937.0L);
TEST_f_f (trunc, -72057594037927935.5L, -72057594037927935.0L);
TEST_f_f (trunc, -72057594037927936.25L, -72057594037927936.0L);
TEST_f_f (trunc, -72057594037927936.5L, -72057594037927936.0L);
TEST_f_f (trunc, -72057594037927936.75L, -72057594037927936.0L);
TEST_f_f (trunc, -72057594037927937.5L, -72057594037927937.0L);
TEST_f_f (trunc, 10141204801825835211973625643007.5L, 10141204801825835211973625643007.0L);
TEST_f_f (trunc, 10141204801825835211973625643008.25L, 10141204801825835211973625643008.0L);
TEST_f_f (trunc, 10141204801825835211973625643008.5L, 10141204801825835211973625643008.0L);
TEST_f_f (trunc, 10141204801825835211973625643008.75L, 10141204801825835211973625643008.0L);
TEST_f_f (trunc, 10141204801825835211973625643009.5L, 10141204801825835211973625643009.0L);
#endif
END (trunc);
}

2
misc/qefgcvt_r.c
View File

@ -43,6 +43,8 @@
#endif
#if LDBL_MIN_10_EXP == -37
# define FLOAT_MIN_10_NORM 1.0e-37L
#elif LDBL_MIN_10_EXP == -291
# define FLOAT_MIN_10_NORM 1.0e-291L
#elif LDBL_MIN_10_EXP == -307
# define FLOAT_MIN_10_NORM 1.0e-307L
#elif LDBL_MIN_10_EXP == -4931

2
sysdeps/ieee754/ldbl-128/e_powl.c
View File

@ -220,7 +220,7 @@ __ieee754_powl (x, y)
{
if (((ix - 0x3fff0000) | p.parts32.w1 | p.parts32.w2 | p.parts32.w3)
== 0)
return y - y; /* inf**+-1 is NaN */
return y - y; /* +-1**inf is NaN */
else if (ix >= 0x3fff0000) /* (|x|>1)**+-inf = inf,0 */
return (hy >= 0) ? y : zero;
else /* (|x|<1)**-,+inf = inf,0 */

5
sysdeps/ieee754/ldbl-128ibm/Makefile Normal file
View File

@ -0,0 +1,5 @@
# The`long double' type is a distinct type we support if
# -mlong-double-128 option is used (or when it becomes a default
# when -mlong-double-64 is not used).
long-double-fcts = yes
sysdep-CFLAGS += -mlong-double-128

69
sysdeps/ieee754/ldbl-128ibm/e_acoshl.c Normal file
View File

@ -0,0 +1,69 @@
/* @(#)e_acosh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $";
#endif
/* __ieee754_acosh(x)
* Method :
* Based on
* acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
* acosh(x) := log(x)+ln2, if x is large; else
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acosh(x) is NaN with signal if x<1.
* acosh(NaN) is NaN without signal.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double
#else
static long double
#endif
one = 1.0L,
ln2 = 6.93147180559945286227e-01L; /* 0x3FE62E42, 0xFEFA39EF */
#ifdef __STDC__
long double __ieee754_acoshl(long double x)
#else
long double __ieee754_acoshl(x)
long double x;
#endif
{
long double t;
int64_t hx;
u_int64_t lx;
GET_LDOUBLE_WORDS64(hx,lx,x);
if(hx<0x3ff0000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
} else if(hx >=0x41b0000000000000LL) { /* x > 2**28 */
if(hx >=0x7ff0000000000000LL) { /* x is inf of NaN */
return x+x;
} else
return __ieee754_logl(x)+ln2; /* acosh(huge)=log(2x) */
} else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
t=x*x;
return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
} else { /* 1<x<2 */
t = x-one;
return __log1p(t+__sqrtl(2.0*t+t*t));
}
}

328
sysdeps/ieee754/ldbl-128ibm/e_acosl.c Normal file
View File

@ -0,0 +1,328 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
Long double expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* __ieee754_acosl(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x| <= 0.375
* acos(x) = pi/2 - asin(x)
* Between .375 and .5 the approximation is
* acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
* Between .5 and .625 the approximation is
* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
* For x > 0.625,
* acos(x) = 2 asin(sqrt((1-x)/2))
* computed with an extended precision square root in the leading term.
* For x < -0.625
* acos(x) = pi - 2 asin(sqrt((1-|x|)/2))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Functions needed: __ieee754_sqrtl.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double
#else
static long double
#endif
one = 1.0L,
pio2_hi = 1.5707963267948966192313216916397514420986L,
pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
/* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
-0.0625 <= x <= 0.0625
peak relative error 3.3e-35 */
rS0 = 5.619049346208901520945464704848780243887E0L,
rS1 = -4.460504162777731472539175700169871920352E1L,
rS2 = 1.317669505315409261479577040530751477488E2L,
rS3 = -1.626532582423661989632442410808596009227E2L,
rS4 = 3.144806644195158614904369445440583873264E1L,
rS5 = 9.806674443470740708765165604769099559553E1L,
rS6 = -5.708468492052010816555762842394927806920E1L,
rS7 = -1.396540499232262112248553357962639431922E1L,
rS8 = 1.126243289311910363001762058295832610344E1L,
rS9 = 4.956179821329901954211277873774472383512E-1L,
rS10 = -3.313227657082367169241333738391762525780E-1L,
sS0 = -4.645814742084009935700221277307007679325E0L,
sS1 = 3.879074822457694323970438316317961918430E1L,
sS2 = -1.221986588013474694623973554726201001066E2L,
sS3 = 1.658821150347718105012079876756201905822E2L,
sS4 = -4.804379630977558197953176474426239748977E1L,
sS5 = -1.004296417397316948114344573811562952793E2L,
sS6 = 7.530281592861320234941101403870010111138E1L,
sS7 = 1.270735595411673647119592092304357226607E1L,
sS8 = -1.815144839646376500705105967064792930282E1L,
sS9 = -7.821597334910963922204235247786840828217E-2L,
/* 1.000000000000000000000000000000000000000E0 */
acosr5625 = 9.7338991014954640492751132535550279812151E-1L,
pimacosr5625 = 2.1682027434402468335351320579240000860757E0L,
/* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
-0.0625 <= x <= 0.0625
peak relative error 2.1e-35 */
P0 = 2.177690192235413635229046633751390484892E0L,
P1 = -2.848698225706605746657192566166142909573E1L,
P2 = 1.040076477655245590871244795403659880304E2L,
P3 = -1.400087608918906358323551402881238180553E2L,
P4 = 2.221047917671449176051896400503615543757E1L,
P5 = 9.643714856395587663736110523917499638702E1L,
P6 = -5.158406639829833829027457284942389079196E1L,
P7 = -1.578651828337585944715290382181219741813E1L,
P8 = 1.093632715903802870546857764647931045906E1L,
P9 = 5.448925479898460003048760932274085300103E-1L,
P10 = -3.315886001095605268470690485170092986337E-1L,
Q0 = -1.958219113487162405143608843774587557016E0L,
Q1 = 2.614577866876185080678907676023269360520E1L,
Q2 = -9.990858606464150981009763389881793660938E1L,
Q3 = 1.443958741356995763628660823395334281596E2L,
Q4 = -3.206441012484232867657763518369723873129E1L,
Q5 = -1.048560885341833443564920145642588991492E2L,
Q6 = 6.745883931909770880159915641984874746358E1L,
Q7 = 1.806809656342804436118449982647641392951E1L,
Q8 = -1.770150690652438294290020775359580915464E1L,
Q9 = -5.659156469628629327045433069052560211164E-1L,
/* 1.000000000000000000000000000000000000000E0 */
acosr4375 = 1.1179797320499710475919903296900511518755E0L,
pimacosr4375 = 2.0236129215398221908706530535894517323217E0L,
/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
0 <= x <= 0.5
peak relative error 1.9e-35 */
pS0 = -8.358099012470680544198472400254596543711E2L,
pS1 = 3.674973957689619490312782828051860366493E3L,
pS2 = -6.730729094812979665807581609853656623219E3L,
pS3 = 6.643843795209060298375552684423454077633E3L,
pS4 = -3.817341990928606692235481812252049415993E3L,
pS5 = 1.284635388402653715636722822195716476156E3L,
pS6 = -2.410736125231549204856567737329112037867E2L,
pS7 = 2.219191969382402856557594215833622156220E1L,
pS8 = -7.249056260830627156600112195061001036533E-1L,
pS9 = 1.055923570937755300061509030361395604448E-3L,
qS0 = -5.014859407482408326519083440151745519205E3L,
qS1 = 2.430653047950480068881028451580393430537E4L,
qS2 = -4.997904737193653607449250593976069726962E4L,
qS3 = 5.675712336110456923807959930107347511086E4L,
qS4 = -3.881523118339661268482937768522572588022E4L,
qS5 = 1.634202194895541569749717032234510811216E4L,
qS6 = -4.151452662440709301601820849901296953752E3L,
qS7 = 5.956050864057192019085175976175695342168E2L,
qS8 = -4.175375777334867025769346564600396877176E1L;
/* 1.000000000000000000000000000000000000000E0 */
#ifdef __STDC__
long double
__ieee754_acosl (long double x)
#else
long double
__ieee754_acosl (x)
long double x;
#endif
{
long double z, r, w, p, q, s, t, f2;
int32_t ix, sign;
ieee854_long_double_shape_type u;
u.value = x;
sign = u.parts32.w0;
ix = sign & 0x7fffffff;
u.parts32.w0 = ix; /* |x| */
if (ix >= 0x3ff00000) /* |x| >= 1 */
{
if (ix == 0x3ff00000
&& (u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0)
{ /* |x| == 1 */
if ((sign & 0x80000000) == 0)
return 0.0; /* acos(1) = 0 */
else
return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */
}
return (x - x) / (x - x); /* acos(|x| > 1) is NaN */
}
else if (ix < 0x3fe00000) /* |x| < 0.5 */
{
if (ix < 0x3c600000) /* |x| < 2**-57 */
return pio2_hi + pio2_lo;
if (ix < 0x3fde0000) /* |x| < .4375 */
{
/* Arcsine of x. */
z = x * x;
p = (((((((((pS9 * z
+ pS8) * z
+ pS7) * z
+ pS6) * z
+ pS5) * z
+ pS4) * z
+ pS3) * z
+ pS2) * z
+ pS1) * z
+ pS0) * z;
q = (((((((( z
+ qS8) * z
+ qS7) * z
+ qS6) * z
+ qS5) * z
+ qS4) * z
+ qS3) * z
+ qS2) * z
+ qS1) * z
+ qS0;
r = x + x * p / q;
z = pio2_hi - (r - pio2_lo);
return z;
}
/* .4375 <= |x| < .5 */
t = u.value - 0.4375L;
p = ((((((((((P10 * t
+ P9) * t
+ P8) * t
+ P7) * t
+ P6) * t
+ P5) * t
+ P4) * t
+ P3) * t
+ P2) * t
+ P1) * t
+ P0) * t;
q = (((((((((t
+ Q9) * t
+ Q8) * t
+ Q7) * t
+ Q6) * t
+ Q5) * t
+ Q4) * t
+ Q3) * t
+ Q2) * t
+ Q1) * t
+ Q0;
r = p / q;
if (sign & 0x80000000)
r = pimacosr4375 - r;
else
r = acosr4375 + r;
return r;
}
else if (ix < 0x3fe40000) /* |x| < 0.625 */
{
t = u.value - 0.5625L;
p = ((((((((((rS10 * t
+ rS9) * t
+ rS8) * t
+ rS7) * t
+ rS6) * t
+ rS5) * t
+ rS4) * t
+ rS3) * t
+ rS2) * t
+ rS1) * t
+ rS0) * t;
q = (((((((((t
+ sS9) * t
+ sS8) * t
+ sS7) * t
+ sS6) * t
+ sS5) * t
+ sS4) * t
+ sS3) * t
+ sS2) * t
+ sS1) * t
+ sS0;
if (sign & 0x80000000)
r = pimacosr5625 - p / q;
else
r = acosr5625 + p / q;
return r;
}
else
{ /* |x| >= .625 */
z = (one - u.value) * 0.5;
s = __ieee754_sqrtl (z);
/* Compute an extended precision square root from
the Newton iteration s -> 0.5 * (s + z / s).
The change w from s to the improved value is
w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s.
Express s = f1 + f2 where f1 * f1 is exactly representable.
w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
s + w has extended precision. */
u.value = s;
u.parts32.w2 = 0;
u.parts32.w3 = 0;
f2 = s - u.value;
w = z - u.value * u.value;
w = w - 2.0 * u.value * f2;
w = w - f2 * f2;
w = w / (2.0 * s);
/* Arcsine of s. */
p = (((((((((pS9 * z
+ pS8) * z
+ pS7) * z
+ pS6) * z
+ pS5) * z
+ pS4) * z
+ pS3) * z
+ pS2) * z
+ pS1) * z
+ pS0) * z;
q = (((((((( z
+ qS8) * z
+ qS7) * z
+ qS6) * z
+ qS5) * z
+ qS4) * z
+ qS3) * z
+ qS2) * z
+ qS1) * z
+ qS0;
r = s + (w + s * p / q);
if (sign & 0x80000000)
w = pio2_hi + (pio2_lo - r);
else
w = r;
return 2.0 * w;
}
}

265
sysdeps/ieee754/ldbl-128ibm/e_asinl.c Normal file
View File

@ -0,0 +1,265 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
Long double expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under the
following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* __ieee754_asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* Between .5 and .625 the approximation is
* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
* For x in [0.625,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
* then for x>0.98
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
* For x<=0.98, let pio4_hi = pio2_hi/2, then
* f = hi part of s;
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
* and
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
#include "math.h"
#include "math_private.h"
long double sqrtl (long double);
#ifdef __STDC__
static const long double
#else
static long double
#endif
one = 1.0L,
huge = 1.0e+300L,
pio2_hi = 1.5707963267948966192313216916397514420986L,
pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
/* coefficient for R(x^2) */
/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
0 <= x <= 0.5
peak relative error 1.9e-35 */
pS0 = -8.358099012470680544198472400254596543711E2L,
pS1 = 3.674973957689619490312782828051860366493E3L,
pS2 = -6.730729094812979665807581609853656623219E3L,
pS3 = 6.643843795209060298375552684423454077633E3L,
pS4 = -3.817341990928606692235481812252049415993E3L,
pS5 = 1.284635388402653715636722822195716476156E3L,
pS6 = -2.410736125231549204856567737329112037867E2L,
pS7 = 2.219191969382402856557594215833622156220E1L,
pS8 = -7.249056260830627156600112195061001036533E-1L,
pS9 = 1.055923570937755300061509030361395604448E-3L,
qS0 = -5.014859407482408326519083440151745519205E3L,
qS1 = 2.430653047950480068881028451580393430537E4L,
qS2 = -4.997904737193653607449250593976069726962E4L,
qS3 = 5.675712336110456923807959930107347511086E4L,
qS4 = -3.881523118339661268482937768522572588022E4L,
qS5 = 1.634202194895541569749717032234510811216E4L,
qS6 = -4.151452662440709301601820849901296953752E3L,
qS7 = 5.956050864057192019085175976175695342168E2L,
qS8 = -4.175375777334867025769346564600396877176E1L,
/* 1.000000000000000000000000000000000000000E0 */
/* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
-0.0625 <= x <= 0.0625
peak relative error 3.3e-35 */
rS0 = -5.619049346208901520945464704848780243887E0L,
rS1 = 4.460504162777731472539175700169871920352E1L,
rS2 = -1.317669505315409261479577040530751477488E2L,
rS3 = 1.626532582423661989632442410808596009227E2L,
rS4 = -3.144806644195158614904369445440583873264E1L,
rS5 = -9.806674443470740708765165604769099559553E1L,
rS6 = 5.708468492052010816555762842394927806920E1L,
rS7 = 1.396540499232262112248553357962639431922E1L,
rS8 = -1.126243289311910363001762058295832610344E1L,
rS9 = -4.956179821329901954211277873774472383512E-1L,
rS10 = 3.313227657082367169241333738391762525780E-1L,
sS0 = -4.645814742084009935700221277307007679325E0L,
sS1 = 3.879074822457694323970438316317961918430E1L,
sS2 = -1.221986588013474694623973554726201001066E2L,
sS3 = 1.658821150347718105012079876756201905822E2L,
sS4 = -4.804379630977558197953176474426239748977E1L,
sS5 = -1.004296417397316948114344573811562952793E2L,
sS6 = 7.530281592861320234941101403870010111138E1L,
sS7 = 1.270735595411673647119592092304357226607E1L,
sS8 = -1.815144839646376500705105967064792930282E1L,
sS9 = -7.821597334910963922204235247786840828217E-2L,
/* 1.000000000000000000000000000000000000000E0 */
asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
#ifdef __STDC__
long double
__ieee754_asinl (long double x)
#else
double
__ieee754_asinl (x)
long double x;
#endif
{
long double t, w, p, q, c, r, s;
int32_t ix, sign, flag;
ieee854_long_double_shape_type u;
flag = 0;
u.value = x;
sign = u.parts32.w0;
ix = sign & 0x7fffffff;
u.parts32.w0 = ix; /* |x| */
if (ix >= 0x3ff00000) /* |x|>= 1 */
{
if (ix == 0x3ff00000
&& (u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3) == 0)
/* asin(1)=+-pi/2 with inexact */
return x * pio2_hi + x * pio2_lo;
return (x - x) / (x - x); /* asin(|x|>1) is NaN */
}
else if (ix < 0x3fe00000) /* |x| < 0.5 */
{
if (ix < 0x3c600000) /* |x| < 2**-57 */
{
if (huge + x > one)
return x; /* return x with inexact if x!=0 */
}
else
{
t = x * x;
/* Mark to use pS, qS later on. */
flag = 1;
}
}
else if (ix < 0x3fe40000) /* 0.625 */
{
t = u.value - 0.5625;
p = ((((((((((rS10 * t
+ rS9) * t
+ rS8) * t
+ rS7) * t
+ rS6) * t
+ rS5) * t
+ rS4) * t
+ rS3) * t
+ rS2) * t
+ rS1) * t
+ rS0) * t;
q = ((((((((( t
+ sS9) * t
+ sS8) * t
+ sS7) * t
+ sS6) * t
+ sS5) * t
+ sS4) * t
+ sS3) * t
+ sS2) * t
+ sS1) * t
+ sS0;
t = asinr5625 + p / q;
if ((sign & 0x80000000) == 0)
return t;
else
return -t;
}
else
{
/* 1 > |x| >= 0.625 */
w = one - u.value;
t = w * 0.5;
}
p = (((((((((pS9 * t
+ pS8) * t
+ pS7) * t
+ pS6) * t
+ pS5) * t
+ pS4) * t
+ pS3) * t
+ pS2) * t
+ pS1) * t
+ pS0) * t;
q = (((((((( t
+ qS8) * t
+ qS7) * t
+ qS6) * t
+ qS5) * t
+ qS4) * t
+ qS3) * t
+ qS2) * t
+ qS1) * t
+ qS0;
if (flag) /* 2^-57 < |x| < 0.5 */
{
w = p / q;
return x + x * w;
}
s = __ieee754_sqrtl (t);
if (ix >= 0x3fef3333) /* |x| > 0.975 */
{
w = p / q;
t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
}
else
{
u.value = s;
u.parts32.w3 = 0;
u.parts32.w2 = 0;
w = u.value;
c = (t - w * w) / (s + w);
r = p / q;
p = 2.0 * s * r - (pio2_lo - 2.0 * c);
q = pio4_hi - 2.0 * w;
t = pio4_hi - (p - q);
}
if ((sign & 0x80000000) == 0)
return t;
else
return -t;
}

124
sysdeps/ieee754/ldbl-128ibm/e_atan2l.c Normal file
View File

@ -0,0 +1,124 @@
/* e_atan2l.c -- long double version of e_atan2.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_atan2l(y,x)
* Method :
* 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double
#else
static long double
#endif
tiny = 1.0e-300L,
zero = 0.0,
pi_o_4 = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */
pi_o_2 = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */
pi = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */
pi_lo = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */
#ifdef __STDC__
long double __ieee754_atan2l(long double y, long double x)
#else
long double __ieee754_atan2l(y,x)
long double y,x;
#endif
{
long double z;
int64_t k,m,hx,hy,ix,iy;
u_int64_t lx,ly;
GET_LDOUBLE_WORDS64(hx,lx,x);
ix = hx&0x7fffffffffffffffLL;
GET_LDOUBLE_WORDS64(hy,ly,y);
iy = hy&0x7fffffffffffffffLL;
if(((ix)>0x7ff0000000000000LL)||
((iy)>0x7ff0000000000000LL)) /* x or y is NaN */
return x+y;
if(((hx-0x3ff0000000000000LL))==0) return __atanl(y); /* x=1.0L */
m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if((iy|(ly&0x7fffffffffffffffLL))==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if((ix|(lx&0x7fffffffffffffff))==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7ff0000000000000LL) {
if(iy==0x7ff0000000000000LL) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return 3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy==0x7ff0000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* compute y/x */
k = (iy-ix)>>52;
if(k > 120) z=pi_o_2+0.5L*pi_lo; /* |y/x| > 2**120 */
else if(hx<0&&k<-120) z=0.0L; /* |y|/x < -2**120 */
else z=__atanl(fabsl(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: return -z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}

79
sysdeps/ieee754/ldbl-128ibm/e_atanhl.c Normal file
View File

@ -0,0 +1,79 @@
/* @(#)e_atanh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $";
#endif
/* __ieee754_atanh(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
*
* Special cases:
* atanh(x) is NaN if |x| > 1 with signal;
* atanh(NaN) is that NaN with no signal;
* atanh(+-1) is +-INF with signal.
*
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double one = 1.0L, huge = 1e300L;
#else
static long double one = 1.0L, huge = 1e300L;
#endif
#ifdef __STDC__
static const long double zero = 0.0L;
#else
static long double zero = 0.0L;
#endif
#ifdef __STDC__
long double __ieee754_atanhl(long double x)
#else
long double __ieee754_atanhl(x)
long double x;
#endif
{
long double t;
int64_t hx,ix;
u_int64_t lx;
GET_LDOUBLE_WORDS64(hx,lx,x);
ix = hx&0x7fffffffffffffffLL;
if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */
if (ix > 0x3ff0000000000000LL)
return (x-x)/(x-x);
t = fabsl (x);
if (t > one)
return (x-x)/(x-x);
if (t == one)
return x/zero;
}
if(ix<0x3e20000000000000LL&&(huge+x)>zero) return x; /* x<2**-29 */
x = fabsl (x);
if(ix<0x3fe0000000000000LL) { /* x < 0.5 */
t = x+x;
t = 0.5*__log1pl(t+t*x/(one-x));
} else
t = 0.5*__log1pl((x+x)/(one-x));
if(hx>=0) return t; else return -t;
}

90
sysdeps/ieee754/ldbl-128ibm/e_coshl.c Normal file
View File

@ -0,0 +1,90 @@
/* @(#)e_cosh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";
#endif
/* __ieee754_cosh(x)
* Method :
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : cosh(x) := -------------------
* 2
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double one = 1.0L, half=0.5L, huge = 1.0e300L;
#else
static long double one = 1.0L, half=0.5L, huge = 1.0e300L;
#endif
#ifdef __STDC__
long double __ieee754_coshl(long double x)
#else
long double __ieee754_coshl(x)
long double x;
#endif
{
long double t,w;
int64_t ix;
/* High word of |x|. */
GET_LDOUBLE_MSW64(ix,x);
ix &= 0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) return x*x;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e42fefa39efLL) {
t = __expm1l(fabsl(x));
w = one+t;
if (ix<0x3c80000000000000LL) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x4036000000000000LL) {
t = __ieee754_expl(fabsl(x));
return half*t+half/t;
}
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix < 0x408633ce8fb9f87dLL) {
w = __ieee754_expl(half*fabsl(x));
t = half*w;
return t*w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}

257
sysdeps/ieee754/ldbl-128ibm/e_expl.c Normal file
View File

@ -0,0 +1,257 @@
/* Quad-precision floating point e^x.
Copyright (C) 1999,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
Partly based on double-precision code
by Geoffrey Keating <geoffk@ozemail.com.au>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* The basic design here is from
Abraham Ziv, "Fast Evaluation of Elementary Mathematical Functions with
Correctly Rounded Last Bit", ACM Trans. Math. Soft., 17 (3), September 1991,
pp. 410-423.
We work with number pairs where the first number is the high part and
the second one is the low part. Arithmetic with the high part numbers must
be exact, without any roundoff errors.
The input value, X, is written as
X = n * ln(2)_0 + arg1[t1]_0 + arg2[t2]_0 + x
- n * ln(2)_1 + arg1[t1]_1 + arg2[t2]_1 + xl
where:
- n is an integer, 16384 >= n >= -16495;
- ln(2)_0 is the first 93 bits of ln(2), and |ln(2)_0-ln(2)-ln(2)_1| < 2^-205
- t1 is an integer, 89 >= t1 >= -89
- t2 is an integer, 65 >= t2 >= -65
- |arg1[t1]-t1/256.0| < 2^-53
- |arg2[t2]-t2/32768.0| < 2^-53
- x + xl is whatever is left, |x + xl| < 2^-16 + 2^-53
Then e^x is approximated as
e^x = 2^n_1 ( 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1)
+ 2^n_0 e^(arg1[t1]_0 + arg1[t1]_1) e^(arg2[t2]_0 + arg2[t2]_1)
* p (x + xl + n * ln(2)_1))
where:
- p(x) is a polynomial approximating e(x)-1
- e^(arg1[t1]_0 + arg1[t1]_1) is obtained from a table
- e^(arg2[t2]_0 + arg2[t2]_1) likewise
- n_1 + n_0 = n, so that |n_0| < -LDBL_MIN_EXP-1.
If it happens that n_1 == 0 (this is the usual case), that multiplication
is omitted.
*/
#ifndef _GNU_SOURCE
#define _GNU_SOURCE
#endif
#include <float.h>
#include <ieee754.h>
#include <math.h>
#include <fenv.h>
#include <inttypes.h>
#include <math_private.h>
#include <sysdeps/ieee754/ldbl-128/t_expl.h>
static const long double C[] = {
/* Smallest integer x for which e^x overflows. */
#define himark C[0]
709.08956571282405153382846025171462914L,
/* Largest integer x for which e^x underflows. */
#define lomark C[1]
-709.08956571282405153382846025171462914L,
/* 3x2^96 */
#define THREEp96 C[2]
59421121885698253195157962752.0L,
/* 3x2^103 */
#define THREEp103 C[3]
30423614405477505635920876929024.0L,
/* 3x2^111 */
#define THREEp111 C[4]
7788445287802241442795744493830144.0L,
/* 1/ln(2) */
#define M_1_LN2 C[5]
1.44269504088896340735992468100189204L,
/* first 93 bits of ln(2) */
#define M_LN2_0 C[6]
0.693147180559945309417232121457981864L,
/* ln2_0 - ln(2) */
#define M_LN2_1 C[7]
-1.94704509238074995158795957333327386E-31L,
/* very small number */
#define TINY C[8]
1.0e-308L,
/* 2^16383 */
#define TWO1023 C[9]
8.988465674311579538646525953945123668E+307L,
/* 256 */
#define TWO8 C[10]
256.0L,
/* 32768 */
#define TWO15 C[11]
32768.0L,
/* Chebyshev polynom coeficients for (exp(x)-1)/x */
#define P1 C[12]
#define P2 C[13]
#define P3 C[14]
#define P4 C[15]
#define P5 C[16]
#define P6 C[17]
0.5L,
1.66666666666666666666666666666666683E-01L,
4.16666666666666666666654902320001674E-02L,
8.33333333333333333333314659767198461E-03L,
1.38888888889899438565058018857254025E-03L,
1.98412698413981650382436541785404286E-04L,
};
long double
__ieee754_expl (long double x)
{
/* Check for usual case. */
if (isless (x, himark) && isgreater (x, lomark))
{
int tval1, tval2, unsafe, n_i, exponent2;
long double x22, n, result, xl;
union ibm_extended_long_double ex2_u, scale_u;
fenv_t oldenv;
feholdexcept (&oldenv);
#ifdef FE_TONEAREST
fesetround (FE_TONEAREST);
#endif
n = roundl(x*M_1_LN2);
x = x-n*M_LN2_0;
xl = n*M_LN2_1;
tval1 = roundl(x*TWO8);
x -= __expl_table[T_EXPL_ARG1+2*tval1];
xl -= __expl_table[T_EXPL_ARG1+2*tval1+1];
tval2 = roundl(x*TWO15);
x -= __expl_table[T_EXPL_ARG2+2*tval2];
xl -= __expl_table[T_EXPL_ARG2+2*tval2+1];
x = x + xl;
/* Compute ex2 = 2^n_0 e^(argtable[tval1]) e^(argtable[tval2]). */
ex2_u.d = __expl_table[T_EXPL_RES1 + tval1]
* __expl_table[T_EXPL_RES2 + tval2];
n_i = (int)n;
/* 'unsafe' is 1 iff n_1 != 0. */
unsafe = fabsl(n_i) >= -LDBL_MIN_EXP - 1;
ex2_u.ieee.exponent += n_i >> unsafe;
/* Fortunately, there are no subnormal lowpart doubles in
__expl_table, only normal values and zeros.
But after scaling it can be subnormal. */
exponent2 = ex2_u.ieee.exponent2 + (n_i >> unsafe);
if (ex2_u.ieee.exponent2 == 0)
/* assert ((ex2_u.ieee.mantissa2|ex2_u.ieee.mantissa3) == 0) */;
else if (exponent2 > 0)
ex2_u.ieee.exponent2 = exponent2;
else if (exponent2 <= -54)
{
ex2_u.ieee.exponent2 = 0;
ex2_u.ieee.mantissa2 = 0;
ex2_u.ieee.mantissa3 = 0;
}
else
{
static const double
two54 = 1.80143985094819840000e+16, /* 4350000000000000 */
twom54 = 5.55111512312578270212e-17; /* 3C90000000000000 */
ex2_u.dd[1] *= two54;
ex2_u.ieee.exponent2 += n_i >> unsafe;
ex2_u.dd[1] *= twom54;
}
/* Compute scale = 2^n_1. */
scale_u.d = 1.0L;
scale_u.ieee.exponent += n_i - (n_i >> unsafe);
/* Approximate e^x2 - 1, using a seventh-degree polynomial,
with maximum error in [-2^-16-2^-53,2^-16+2^-53]
less than 4.8e-39. */
x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));
/* Return result. */
fesetenv (&oldenv);
result = x22 * ex2_u.d + ex2_u.d;
/* Now we can test whether the result is ultimate or if we are unsure.
In the later case we should probably call a mpn based routine to give
the ultimate result.
Empirically, this routine is already ultimate in about 99.9986% of
cases, the test below for the round to nearest case will be false
in ~ 99.9963% of cases.
Without proc2 routine maximum error which has been seen is
0.5000262 ulp.
union ieee854_long_double ex3_u;
#ifdef FE_TONEAREST
fesetround (FE_TONEAREST);
#endif
ex3_u.d = (result - ex2_u.d) - x22 * ex2_u.d;
ex2_u.d = result;
ex3_u.ieee.exponent += LDBL_MANT_DIG + 15 + IEEE854_LONG_DOUBLE_BIAS
- ex2_u.ieee.exponent;
n_i = abs (ex3_u.d);
n_i = (n_i + 1) / 2;
fesetenv (&oldenv);
#ifdef FE_TONEAREST
if (fegetround () == FE_TONEAREST)
n_i -= 0x4000;
#endif
if (!n_i) {
return __ieee754_expl_proc2 (origx);
}
*/
if (!unsafe)
return result;
else
return result * scale_u.d;
}
/* Exceptional cases: */
else if (isless (x, himark))
{
if (__isinfl (x))
/* e^-inf == 0, with no error. */
return 0;
else
/* Underflow */
return TINY * TINY;
}
else
/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
return TWO1023*x;
}

145
sysdeps/ieee754/ldbl-128ibm/e_fmodl.c Normal file
View File

@ -0,0 +1,145 @@
/* e_fmodl.c -- long double version of e_fmod.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __ieee754_fmodl(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include "math.h"
#include "math_private.h"
#include <ieee754.h>
#ifdef __STDC__
static const long double one = 1.0, Zero[] = {0.0, -0.0,};
#else
static long double one = 1.0, Zero[] = {0.0, -0.0,};
#endif
#ifdef __STDC__
long double __ieee754_fmodl(long double x, long double y)
#else
long double __ieee754_fmodl(x,y)
long double x,y;
#endif
{
int64_t n,hx,hy,hz,ix,iy,sx,i;
u_int64_t lx,ly,lz;
int temp;
GET_LDOUBLE_WORDS64(hx,lx,x);
GET_LDOUBLE_WORDS64(hy,ly,y);
sx = hx&0x8000000000000000ULL; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffffffffffffLL; /* |y| */
/* purge off exception values */
if((hy|(ly&0x7fffffffffffffff))==0||(hx>=0x7ff0000000000000LL)|| /* y=0,or x not finite */
(hy>0x7ff0000000000000LL)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<=hy) {
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
if(lx==ly)
return Zero[(u_int64_t)sx>>63]; /* |x|=|y| return x*0*/
}
/* determine ix = ilogb(x) */
if(hx<0x0010000000000000LL) { /* subnormal x */
if(hx==0) {
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
} else {
for (ix = -1022, i=hx<<19; i>0; i<<=1) ix -=1;
}
} else ix = (hx>>52)-0x3ff;
/* determine iy = ilogb(y) */
if(hy<0x0010000000000000LL) { /* subnormal y */
if(hy==0) {
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
} else {
for (iy = -1022, i=hy<<19; i>0; i<<=1) iy -=1;
}
} else iy = (hy>>52)-0x3ff;
/* Make the IBM extended format 105 bit mantissa look like the ieee854 112
bit mantissa so the following operatations will give the correct
result. */
EXTRACT_IBM_EXTENDED_MANTISSA(hx, lx, temp, x);
EXTRACT_IBM_EXTENDED_MANTISSA(hy, ly, temp, y);
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -1022)
hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx);
else { /* subnormal x, shift x to normal */
n = -1022-ix;
if(n<=63) {
hx = (hx<<n)|(lx>>(64-n));
lx <<= n;
} else {
hx = lx<<(n-64);
lx = 0;
}
}
if(iy >= -1022)
hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy);
else { /* subnormal y, shift y to normal */
n = -1022-iy;
if(n<=63) {
hy = (hy<<n)|(ly>>(64-n));
ly <<= n;
} else {
hy = ly<<(n-64);
ly = 0;
}
}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;}
else {
if((hz|(lz&0x7fffffffffffffff))==0) /* return sign(x)*0 */
return Zero[(u_int64_t)sx>>63];
hx = hz+hz+(lz>>63); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
/* convert back to floating value and restore the sign */
if((hx|(lx&0x7fffffffffffffff))==0) /* return sign(x)*0 */
return Zero[(u_int64_t)sx>>63];
while(hx<0x0001000000000000LL) { /* normalize x */
hx = hx+hx+(lx>>63); lx = lx+lx;
iy -= 1;
}
if(iy>= -1022) { /* normalize output */
INSERT_IBM_EXTENDED_MANTISSA(x, (sx>>63), iy, hx, lx);
} else { /* subnormal output */
n = -1022 - iy;
if(n<=48) {
lx = (lx>>n)|((u_int64_t)hx<<(64-n));
hx >>= n;
} else if (n<=63) {
lx = (hx<<(64-n))|(lx>>n); hx = sx;
} else {
lx = hx>>(n-64); hx = sx;
}
INSERT_IBM_EXTENDED_MANTISSA(x, (sx>>63), iy, hx, lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}

58
sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c Normal file
View File

@ -0,0 +1,58 @@
/* Implementation of gamma function according to ISO C.
Copyright (C) 1997,1999,2002,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz, 1999.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <math.h>
#include <math_private.h>
long double
__ieee754_gammal_r (long double x, int *signgamp)
{
/* We don't have a real gamma implementation now. We'll use lgamma
and the exp function. But due to the required boundary
conditions we must check some values separately. */
int64_t hx;
u_int64_t lx;
GET_LDOUBLE_WORDS64 (hx, lx, x);
if (((hx | lx) & 0x7fffffffffffffffLL) == 0)
{
/* Return value for x == 0 is Inf with divide by zero exception. */
*signgamp = 0;
return 1.0 / x;
}
if (hx < 0 && (u_int64_t) hx < 0xfff0000000000000ULL && __rintl (x) == x)
{
/* Return value for integer x < 0 is NaN with invalid exception. */
*signgamp = 0;
return (x - x) / (x - x);
}
if (hx == 0xfff0000000000000ULL)
{
/* x == -Inf. According to ISO this is NaN. */
*signgamp = 0;
return x - x;
}
/* XXX FIXME. */
return __ieee754_expl (__ieee754_lgammal_r (x, signgamp));
}

131
sysdeps/ieee754/ldbl-128ibm/e_hypotl.c Normal file
View File

@ -0,0 +1,131 @@
/* @(#)e_hypotl.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_hypotl.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
#endif
/* __ieee754_hypotl(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrtl(2)/2 ulp, than
* sqrtl(z) has error less than 1 ulp (exercise).
*
* So, compute sqrtl(x*x+y*y) with some care as
* follows to get the error below 1 ulp:
*
* Assume x>y>0;
* (if possible, set rounding to round-to-nearest)
* 1. if x > 2y use
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
* where x1 = x with lower 53 bits cleared, x2 = x-x1; else
* 2. if x <= 2y use
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
* where t1 = 2x with lower 53 bits cleared, t2 = 2x-t1,
* y1= y with lower 53 bits chopped, y2 = y-y1.
*
* NOTE: scaling may be necessary if some argument is too
* large or too tiny
*
* Special cases:
* hypotl(x,y) is INF if x or y is +INF or -INF; else
* hypotl(x,y) is NAN if x or y is NAN.
*
* Accuracy:
* hypotl(x,y) returns sqrtl(x^2+y^2) with error less
* than 1 ulps (units in the last place)
*/
#include "math.h"
#include "math_private.h"
static const long double two600 = 0x1.0p+600L;
static const long double two1022 = 0x1.0p+1022L;
#ifdef __STDC__
long double __ieee754_hypotl(long double x, long double y)
#else
long double __ieee754_hypotl(x,y)
long double x, y;
#endif
{
long double a,b,t1,t2,y1,y2,w,kld;
int64_t j,k,ha,hb;
GET_LDOUBLE_MSW64(ha,x);
ha &= 0x7fffffffffffffffLL;
GET_LDOUBLE_MSW64(hb,y);
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
a = fabsl(a); /* a <- |a| */
b = fabsl(b); /* b <- |b| */
if((ha-hb)>0x3c0000000000000LL) {return a+b;} /* x/y > 2**60 */
k=0;
kld = 1.0L;
if(ha > 0x5f30000000000000LL) { /* a>2**500 */
if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */
u_int64_t low;
w = a+b; /* for sNaN */
GET_LDOUBLE_LSW64(low,a);
if(((ha&0xfffffffffffffLL)|(low&0x7fffffffffffffffLL))==0)
w = a;
GET_LDOUBLE_LSW64(low,b);
if(((hb^0x7ff0000000000000LL)|(low&0x7fffffffffffffffLL))==0)
w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x2580000000000000LL; hb -= 0x2580000000000000LL; k += 600;
a /= two600;
b /= two600;
k += 600;
kld = two600;
}
if(hb < 0x20b0000000000000LL) { /* b < 2**-500 */
if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */
u_int64_t low;
GET_LDOUBLE_LSW64(low,b);
if((hb|(low&0x7fffffffffffffffLL))==0) return a;
t1=two1022; /* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
kld = kld / two1022;
} else { /* scale a and b by 2^600 */
ha += 0x2580000000000000LL; /* a *= 2^600 */
hb += 0x2580000000000000LL; /* b *= 2^600 */
k -= 600;
a *= two600;
b *= two600;
kld = kld / two600;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
SET_LDOUBLE_WORDS64(t1,ha,0);
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
SET_LDOUBLE_WORDS64(y1,hb,0);
y2 = b - y1;
SET_LDOUBLE_WORDS64(t1,ha+0x0010000000000000LL,0);
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0)
return w*kld;
else
return w;
}

3
sysdeps/ieee754/ldbl-128ibm/e_j0l.c Normal file
View File

@ -0,0 +1,3 @@
/* Looks like we can use ieee854 e_j0l.c as is for IBM extended format. */
#include <sysdeps/ieee754/ldbl-128/e_j0l.c>

2
sysdeps/ieee754/ldbl-128ibm/e_j1l.c Normal file
View File

@ -0,0 +1,2 @@
/* Looks like we can use ieee854 e_j1l.c as is for IBM extended format. */
#include <sysdeps/ieee754/ldbl-128/e_j1l.c>

402
sysdeps/ieee754/ldbl-128ibm/e_jnl.c Normal file
View File

@ -0,0 +1,402 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* Modifications for 128-bit long double are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/*
* __ieee754_jn(n, x), __ieee754_yn(n, x)
* floating point Bessel's function of the 1st and 2nd kind
* of order n
*
* Special cases:
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
* Note 2. About jn(n,x), yn(n,x)
* For n=0, j0(x) is called,
* for n=1, j1(x) is called,
* for n<x, forward recursion us used starting
* from values of j0(x) and j1(x).
* for n>x, a continued fraction approximation to
* j(n,x)/j(n-1,x) is evaluated and then backward
* recursion is used starting from a supposed value
* for j(n,x). The resulting value of j(0,x) is
* compared with the actual value to correct the
* supposed value of j(n,x).
*
* yn(n,x) is similar in all respects, except
* that forward recursion is used for all
* values of n>1.
*
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double
#else
static long double
#endif
invsqrtpi = 5.6418958354775628694807945156077258584405E-1L,
two = 2.0e0L,
one = 1.0e0L,
zero = 0.0L;
#ifdef __STDC__
long double
__ieee754_jnl (int n, long double x)
#else
long double
__ieee754_jnl (n, x)
int n;
long double x;
#endif
{
u_int32_t se;
int32_t i, ix, sgn;
long double a, b, temp, di;
long double z, w;
ieee854_long_double_shape_type u;
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
* Thus, J(-n,x) = J(n,-x)
*/
u.value = x;
se = u.parts32.w0;
ix = se & 0x7fffffff;
/* if J(n,NaN) is NaN */
if (ix >= 0x7ff00000)
{
if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
| (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
return x + x;
}
if (n < 0)
{
n = -n;
x = -x;
se ^= 0x80000000;
}
if (n == 0)
return (__ieee754_j0l (x));
if (n == 1)
return (__ieee754_j1l (x));
sgn = (n & 1) & (se >> 31); /* even n -- 0, odd n -- sign(x) */
x = fabsl (x);
if (x == 0.0L || ix >= 0x7ff00000) /* if x is 0 or inf */
b = zero;
else if ((long double) n <= x)
{
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
if (ix >= 0x52d00000)
{ /* x > 2**302 */
/* ??? Could use an expansion for large x here. */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
long double s;
long double c;
__sincosl (x, &s, &c);
switch (n & 3)
{
case 0:
temp = c + s;
break;
case 1:
temp = -c + s;
break;
case 2:
temp = -c - s;
break;
case 3:
temp = c - s;
break;
}
b = invsqrtpi * temp / __ieee754_sqrtl (x);
}
else
{
a = __ieee754_j0l (x);
b = __ieee754_j1l (x);
for (i = 1; i < n; i++)
{
temp = b;
b = b * ((long double) (i + i) / x) - a; /* avoid underflow */
a = temp;
}
}
}
else
{
if (ix < 0x3e100000)
{ /* x < 2**-29 */
/* x is tiny, return the first Taylor expansion of J(n,x)
* J(n,x) = 1/n!*(x/2)^n - ...
*/
if (n >= 33) /* underflow, result < 10^-300 */
b = zero;
else
{
temp = x * 0.5;
b = temp;
for (a = one, i = 2; i <= n; i++)
{
a *= (long double) i; /* a = n! */
b *= temp; /* b = (x/2)^n */
}
b = b / a;
}
}
else
{
/* use backward recurrence */
/* x x^2 x^2
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
* 2n - 2(n+1) - 2(n+2)
*
* 1 1 1
* (for large x) = ---- ------ ------ .....
* 2n 2(n+1) 2(n+2)
* -- - ------ - ------ -
* x x x
*
* Let w = 2n/x and h=2/x, then the above quotient
* is equal to the continued fraction:
* 1
* = -----------------------
* 1
* w - -----------------
* 1
* w+h - ---------
* w+2h - ...
*
* To determine how many terms needed, let
* Q(0) = w, Q(1) = w(w+h) - 1,
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
* When Q(k) > 1e4 good for single
* When Q(k) > 1e9 good for double
* When Q(k) > 1e17 good for quadruple
*/
/* determine k */
long double t, v;
long double q0, q1, h, tmp;
int32_t k, m;
w = (n + n) / (long double) x;
h = 2.0L / (long double) x;
q0 = w;
z = w + h;
q1 = w * z - 1.0L;
k = 1;
while (q1 < 1.0e17L)
{
k += 1;
z += h;
tmp = z * q1 - q0;
q0 = q1;
q1 = tmp;
}
m = n + n;
for (t = zero, i = 2 * (n + k); i >= m; i -= 2)
t = one / (i / x - t);
a = t;
b = one;
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
* Hence, if n*(log(2n/x)) > ...
* single 8.8722839355e+01
* double 7.09782712893383973096e+02
* long double 1.1356523406294143949491931077970765006170e+04
* then recurrent value may overflow and the result is
* likely underflow to zero
*/
tmp = n;
v = two / x;
tmp = tmp * __ieee754_logl (fabsl (v * tmp));
if (tmp < 1.1356523406294143949491931077970765006170e+04L)
{
for (i = n - 1, di = (long double) (i + i); i > 0; i--)
{
temp = b;
b *= di;
b = b / x - a;
a = temp;
di -= two;
}
}
else
{
for (i = n - 1, di = (long double) (i + i); i > 0; i--)
{
temp = b;
b *= di;
b = b / x - a;
a = temp;
di -= two;
/* scale b to avoid spurious overflow */
if (b > 1e100L)
{
a /= b;
t /= b;
b = one;
}
}
}
b = (t * __ieee754_j0l (x) / b);
}
}
if (sgn == 1)
return -b;
else
return b;
}
#ifdef __STDC__
long double
__ieee754_ynl (int n, long double x)
#else
long double
__ieee754_ynl (n, x)
int n;
long double x;
#endif
{
u_int32_t se;
int32_t i, ix;
int32_t sign;
long double a, b, temp;
ieee854_long_double_shape_type u;
u.value = x;
se = u.parts32.w0;
ix = se & 0x7fffffff;
/* if Y(n,NaN) is NaN */
if (ix >= 0x7ff00000)
{
if ((u.parts32.w0 & 0xfffff) | u.parts32.w1
| (u.parts32.w2 & 0x7fffffff) | u.parts32.w3)
return x + x;
}
if (x <= 0.0L)
{
if (x == 0.0L)
return -HUGE_VALL + x;
if (se & 0x80000000)
return zero / (zero * x);
}
sign = 1;
if (n < 0)
{
n = -n;
sign = 1 - ((n & 1) << 1);
}
if (n == 0)
return (__ieee754_y0l (x));
if (n == 1)
return (sign * __ieee754_y1l (x));
if (ix >= 0x7ff00000)
return zero;
if (ix >= 0x52D00000)
{ /* x > 2**302 */
/* ??? See comment above on the possible futility of this. */
/* (x >> n**2)
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
* Let s=sin(x), c=cos(x),
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
*
* n sin(xn)*sqt2 cos(xn)*sqt2
* ----------------------------------
* 0 s-c c+s
* 1 -s-c -c+s
* 2 -s+c -c-s
* 3 s+c c-s
*/
long double s;
long double c;
__sincosl (x, &s, &c);
switch (n & 3)
{
case 0:
temp = s - c;
break;
case 1:
temp = -s - c;
break;
case 2:
temp = -s + c;
break;
case 3:
temp = s + c;
break;
}
b = invsqrtpi * temp / __ieee754_sqrtl (x);
}
else
{
a = __ieee754_y0l (x);
b = __ieee754_y1l (x);
/* quit if b is -inf */
u.value = b;
se = u.parts32.w0 & 0xfff00000;
for (i = 1; i < n && se != 0xfff00000; i++)
{
temp = b;
b = ((long double) (i + i) / x) * b - a;
u.value = b;
se = u.parts32.w0 & 0xfff00000;
a = temp;
}
}
if (sign > 0)
return b;
else
return -b;
}

3
sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c Normal file
View File

@ -0,0 +1,3 @@
/* Looks like we can use ieee854 e_lgammal_r.c as is for IBM extended format. */
#include <sysdeps/ieee754/ldbl-128/e_lgammal_r.c>

258
sysdeps/ieee754/ldbl-128ibm/e_log10l.c Normal file
View File

@ -0,0 +1,258 @@
/* log10l.c
*
* Common logarithm, 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, log10l();
*
* y = log10l( x );
*
*
*
* DESCRIPTION:
*
* Returns the base 10 logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the logarithm
* of the fraction is approximated by
*
* log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
*
* Otherwise, setting z = 2(x-1)/x+1),
*
* log(x) = z + z^3 P(z)/Q(z).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.5, 2.0 30000 2.3e-34 4.9e-35
* IEEE exp(+-10000) 30000 1.0e-34 4.1e-35
*
* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
*
*/
/*
Cephes Math Library Release 2.2: January, 1991
Copyright 1984, 1991 by Stephen L. Moshier
Adapted for glibc November, 2001
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "math.h"
#include "math_private.h"
/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 5.3e-37,
* relative peak error spread = 2.3e-14
*/
static const long double P[13] =
{
1.313572404063446165910279910527789794488E4L,
7.771154681358524243729929227226708890930E4L,
2.014652742082537582487669938141683759923E5L,
3.007007295140399532324943111654767187848E5L,
2.854829159639697837788887080758954924001E5L,
1.797628303815655343403735250238293741397E5L,
7.594356839258970405033155585486712125861E4L,
2.128857716871515081352991964243375186031E4L,
3.824952356185897735160588078446136783779E3L,
4.114517881637811823002128927449878962058E2L,
2.321125933898420063925789532045674660756E1L,
4.998469661968096229986658302195402690910E-1L,
1.538612243596254322971797716843006400388E-6L
};
static const long double Q[12] =
{
3.940717212190338497730839731583397586124E4L,
2.626900195321832660448791748036714883242E5L,
7.777690340007566932935753241556479363645E5L,
1.347518538384329112529391120390701166528E6L,
1.514882452993549494932585972882995548426E6L,
1.158019977462989115839826904108208787040E6L,
6.132189329546557743179177159925690841200E5L,
2.248234257620569139969141618556349415120E5L,
5.605842085972455027590989944010492125825E4L,
9.147150349299596453976674231612674085381E3L,
9.104928120962988414618126155557301584078E2L,
4.839208193348159620282142911143429644326E1L
/* 1.000000000000000000000000000000000000000E0L, */
};
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 1.1e-35,
* relative peak error spread 1.1e-9
*/
static const long double R[6] =
{
1.418134209872192732479751274970992665513E5L,
-8.977257995689735303686582344659576526998E4L,
2.048819892795278657810231591630928516206E4L,
-2.024301798136027039250415126250455056397E3L,
8.057002716646055371965756206836056074715E1L,
-8.828896441624934385266096344596648080902E-1L
};
static const long double S[6] =
{
1.701761051846631278975701529965589676574E6L,
-1.332535117259762928288745111081235577029E6L,
4.001557694070773974936904547424676279307E5L,
-5.748542087379434595104154610899551484314E4L,
3.998526750980007367835804959888064681098E3L,
-1.186359407982897997337150403816839480438E2L
/* 1.000000000000000000000000000000000000000E0L, */
};
static const long double
/* log10(2) */
L102A = 0.3125L,
L102B = -1.14700043360188047862611052755069732318101185E-2L,
/* log10(e) */
L10EA = 0.5L,
L10EB = -6.570551809674817234887108108339491770560299E-2L,
/* sqrt(2)/2 */
SQRTH = 7.071067811865475244008443621048490392848359E-1L;
/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
static long double
neval (long double x, const long double *p, int n)
{
long double y;
p += n;
y = *p--;
do
{
y = y * x + *p--;
}
while (--n > 0);
return y;
}
/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
static long double
deval (long double x, const long double *p, int n)
{
long double y;
p += n;
y = x + *p--;
do
{
y = y * x + *p--;
}
while (--n > 0);
return y;
}
long double
__ieee754_log10l (x)
long double x;
{
long double z;
long double y;
int e;
int64_t hx, lx;
/* Test for domain */
GET_LDOUBLE_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | (lx & 0x7fffffffffffffffLL)) == 0)
return (-1.0L / (x - x));
if (hx < 0)
return (x - x) / (x - x);
if (hx >= 0x7ff0000000000000LL)
return (x + x);
/* separate mantissa from exponent */
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = __frexpl (x, &e);
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if ((e > 2) || (e < -2))
{
if (x < SQRTH)
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5L;
y = 0.5L * z + 0.5L;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5L;
z -= 0.5L;
y = 0.5L * x + 0.5L;
}
x = z / y;
z = x * x;
y = x * (z * neval (z, R, 5) / deval (z, S, 5));
goto done;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH)
{
e -= 1;
x = 2.0 * x - 1.0L; /* 2x - 1 */
}
else
{
x = x - 1.0L;
}
z = x * x;
y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
y = y - 0.5 * z;
done:
/* Multiply log of fraction by log10(e)
* and base 2 exponent by log10(2).
*/
z = y * L10EB;
z += x * L10EB;
z += e * L102B;
z += y * L10EA;
z += x * L10EA;
z += e * L102A;
return (z);
}

250
sysdeps/ieee754/ldbl-128ibm/e_log2l.c Normal file
View File

@ -0,0 +1,250 @@
/* log2l.c
* Base 2 logarithm, 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, log2l();
*
* y = log2l( x );
*
*
*
* DESCRIPTION:
*
* Returns the base 2 logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the (natural)
* logarithm of the fraction is approximated by
*
* log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
*
* Otherwise, setting z = 2(x-1)/x+1),
*
* log(x) = z + z^3 P(z)/Q(z).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.5, 2.0 100,000 2.6e-34 4.9e-35
* IEEE exp(+-10000) 100,000 9.6e-35 4.0e-35
*
* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
*
*/
/*
Cephes Math Library Release 2.2: January, 1991
Copyright 1984, 1991 by Stephen L. Moshier
Adapted for glibc November, 2001
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "math.h"
#include "math_private.h"
/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 5.3e-37,
* relative peak error spread = 2.3e-14
*/
static const long double P[13] =
{
1.313572404063446165910279910527789794488E4L,
7.771154681358524243729929227226708890930E4L,
2.014652742082537582487669938141683759923E5L,
3.007007295140399532324943111654767187848E5L,
2.854829159639697837788887080758954924001E5L,
1.797628303815655343403735250238293741397E5L,
7.594356839258970405033155585486712125861E4L,
2.128857716871515081352991964243375186031E4L,
3.824952356185897735160588078446136783779E3L,
4.114517881637811823002128927449878962058E2L,
2.321125933898420063925789532045674660756E1L,
4.998469661968096229986658302195402690910E-1L,
1.538612243596254322971797716843006400388E-6L
};
static const long double Q[12] =
{
3.940717212190338497730839731583397586124E4L,
2.626900195321832660448791748036714883242E5L,
7.777690340007566932935753241556479363645E5L,
1.347518538384329112529391120390701166528E6L,
1.514882452993549494932585972882995548426E6L,
1.158019977462989115839826904108208787040E6L,
6.132189329546557743179177159925690841200E5L,
2.248234257620569139969141618556349415120E5L,
5.605842085972455027590989944010492125825E4L,
9.147150349299596453976674231612674085381E3L,
9.104928120962988414618126155557301584078E2L,
4.839208193348159620282142911143429644326E1L
/* 1.000000000000000000000000000000000000000E0L, */
};
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 1.1e-35,
* relative peak error spread 1.1e-9
*/
static const long double R[6] =
{
1.418134209872192732479751274970992665513E5L,
-8.977257995689735303686582344659576526998E4L,
2.048819892795278657810231591630928516206E4L,
-2.024301798136027039250415126250455056397E3L,
8.057002716646055371965756206836056074715E1L,
-8.828896441624934385266096344596648080902E-1L
};
static const long double S[6] =
{
1.701761051846631278975701529965589676574E6L,
-1.332535117259762928288745111081235577029E6L,
4.001557694070773974936904547424676279307E5L,
-5.748542087379434595104154610899551484314E4L,
3.998526750980007367835804959888064681098E3L,
-1.186359407982897997337150403816839480438E2L
/* 1.000000000000000000000000000000000000000E0L, */
};
static const long double
/* log2(e) - 1 */
LOG2EA = 4.4269504088896340735992468100189213742664595E-1L,
/* sqrt(2)/2 */
SQRTH = 7.071067811865475244008443621048490392848359E-1L;
/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
static long double
neval (long double x, const long double *p, int n)
{
long double y;
p += n;
y = *p--;
do
{
y = y * x + *p--;
}
while (--n > 0);
return y;
}
/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
static long double
deval (long double x, const long double *p, int n)
{
long double y;
p += n;
y = x + *p--;
do
{
y = y * x + *p--;
}
while (--n > 0);
return y;
}
long double
__ieee754_log2l (x)
long double x;
{
long double z;
long double y;
int e;
int64_t hx, lx;
/* Test for domain */
GET_LDOUBLE_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | (lx & 0x7fffffffffffffffLL)) == 0)
return (-1.0L / (x - x));
if (hx < 0)
return (x - x) / (x - x);
if (hx >= 0x7ff0000000000000LL)
return (x + x);
/* separate mantissa from exponent */
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = __frexpl (x, &e);
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if ((e > 2) || (e < -2))
{
if (x < SQRTH)
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5L;
y = 0.5L * z + 0.5L;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5L;
z -= 0.5L;
y = 0.5L * x + 0.5L;
}
x = z / y;
z = x * x;
y = x * (z * neval (z, R, 5) / deval (z, S, 5));
goto done;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH)
{
e -= 1;
x = 2.0 * x - 1.0L; /* 2x - 1 */
}
else
{
x = x - 1.0L;
}
z = x * x;
y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
y = y - 0.5 * z;
done:
/* Multiply log of fraction by log2(e)
* and base 2 exponent by 1
*/
z = y * LOG2EA;
z += x * LOG2EA;
z += y;
z += x;
z += e;
return (z);
}

281
sysdeps/ieee754/ldbl-128ibm/e_logl.c Normal file
View File

@ -0,0 +1,281 @@
/* logll.c
*
* Natural logarithm for 128-bit long double precision.
*
*
*
* SYNOPSIS:
*
* long double x, y, logl();
*
* y = logl( x );
*
*
*
* DESCRIPTION:
*
* Returns the base e (2.718...) logarithm of x.
*
* The argument is separated into its exponent and fractional
* parts. Use of a lookup table increases the speed of the routine.
* The program uses logarithms tabulated at intervals of 1/128 to
* cover the domain from approximately 0.7 to 1.4.
*
* On the interval [-1/128, +1/128] the logarithm of 1+x is approximated by
* log(1+x) = x - 0.5 x^2 + x^3 P(x) .
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0.875, 1.125 100000 1.2e-34 4.1e-35
* IEEE 0.125, 8 100000 1.2e-34 4.1e-35
*
*
* WARNING:
*
* This program uses integer operations on bit fields of floating-point
* numbers. It does not work with data structures other than the
* structure assumed.
*
*/
/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
#include "math_private.h"
/* log(1+x) = x - .5 x^2 + x^3 l(x)
-.0078125 <= x <= +.0078125
peak relative error 1.2e-37 */
static const long double
l3 = 3.333333333333333333333333333333336096926E-1L,
l4 = -2.499999999999999999999999999486853077002E-1L,
l5 = 1.999999999999999999999999998515277861905E-1L,
l6 = -1.666666666666666666666798448356171665678E-1L,
l7 = 1.428571428571428571428808945895490721564E-1L,
l8 = -1.249999999999999987884655626377588149000E-1L,
l9 = 1.111111111111111093947834982832456459186E-1L,
l10 = -1.000000000000532974938900317952530453248E-1L,
l11 = 9.090909090915566247008015301349979892689E-2L,
l12 = -8.333333211818065121250921925397567745734E-2L,
l13 = 7.692307559897661630807048686258659316091E-2L,
l14 = -7.144242754190814657241902218399056829264E-2L,
l15 = 6.668057591071739754844678883223432347481E-2L;
/* Lookup table of ln(t) - (t-1)
t = 0.5 + (k+26)/128)
k = 0, ..., 91 */
static const long double logtbl[92] = {
-5.5345593589352099112142921677820359632418E-2L,
-5.2108257402767124761784665198737642086148E-2L,
-4.8991686870576856279407775480686721935120E-2L,
-4.5993270766361228596215288742353061431071E-2L,
-4.3110481649613269682442058976885699556950E-2L,
-4.0340872319076331310838085093194799765520E-2L,
-3.7682072451780927439219005993827431503510E-2L,
-3.5131785416234343803903228503274262719586E-2L,
-3.2687785249045246292687241862699949178831E-2L,
-3.0347913785027239068190798397055267411813E-2L,
-2.8110077931525797884641940838507561326298E-2L,
-2.5972247078357715036426583294246819637618E-2L,
-2.3932450635346084858612873953407168217307E-2L,
-2.1988775689981395152022535153795155900240E-2L,
-2.0139364778244501615441044267387667496733E-2L,
-1.8382413762093794819267536615342902718324E-2L,
-1.6716169807550022358923589720001638093023E-2L,
-1.5138929457710992616226033183958974965355E-2L,
-1.3649036795397472900424896523305726435029E-2L,
-1.2244881690473465543308397998034325468152E-2L,
-1.0924898127200937840689817557742469105693E-2L,
-9.6875626072830301572839422532631079809328E-3L,
-8.5313926245226231463436209313499745894157E-3L,
-7.4549452072765973384933565912143044991706E-3L,
-6.4568155251217050991200599386801665681310E-3L,
-5.5356355563671005131126851708522185605193E-3L,
-4.6900728132525199028885749289712348829878E-3L,
-3.9188291218610470766469347968659624282519E-3L,
-3.2206394539524058873423550293617843896540E-3L,
-2.5942708080877805657374888909297113032132E-3L,
-2.0385211375711716729239156839929281289086E-3L,
-1.5522183228760777967376942769773768850872E-3L,
-1.1342191863606077520036253234446621373191E-3L,
-7.8340854719967065861624024730268350459991E-4L,
-4.9869831458030115699628274852562992756174E-4L,
-2.7902661731604211834685052867305795169688E-4L,
-1.2335696813916860754951146082826952093496E-4L,
-3.0677461025892873184042490943581654591817E-5L,
#define ZERO logtbl[38]
0.0000000000000000000000000000000000000000E0L,
-3.0359557945051052537099938863236321874198E-5L,
-1.2081346403474584914595395755316412213151E-4L,
-2.7044071846562177120083903771008342059094E-4L,
-4.7834133324631162897179240322783590830326E-4L,
-7.4363569786340080624467487620270965403695E-4L,
-1.0654639687057968333207323853366578860679E-3L,
-1.4429854811877171341298062134712230604279E-3L,
-1.8753781835651574193938679595797367137975E-3L,
-2.3618380914922506054347222273705859653658E-3L,
-2.9015787624124743013946600163375853631299E-3L,
-3.4938307889254087318399313316921940859043E-3L,
-4.1378413103128673800485306215154712148146E-3L,
-4.8328735414488877044289435125365629849599E-3L,
-5.5782063183564351739381962360253116934243E-3L,
-6.3731336597098858051938306767880719015261E-3L,
-7.2169643436165454612058905294782949315193E-3L,
-8.1090214990427641365934846191367315083867E-3L,
-9.0486422112807274112838713105168375482480E-3L,
-1.0035177140880864314674126398350812606841E-2L,
-1.1067990155502102718064936259435676477423E-2L,
-1.2146457974158024928196575103115488672416E-2L,
-1.3269969823361415906628825374158424754308E-2L,
-1.4437927104692837124388550722759686270765E-2L,
-1.5649743073340777659901053944852735064621E-2L,
-1.6904842527181702880599758489058031645317E-2L,
-1.8202661505988007336096407340750378994209E-2L,
-1.9542647000370545390701192438691126552961E-2L,
-2.0924256670080119637427928803038530924742E-2L,
-2.2346958571309108496179613803760727786257E-2L,
-2.3810230892650362330447187267648486279460E-2L,
-2.5313561699385640380910474255652501521033E-2L,
-2.6856448685790244233704909690165496625399E-2L,
-2.8438398935154170008519274953860128449036E-2L,
-3.0058928687233090922411781058956589863039E-2L,
-3.1717563112854831855692484086486099896614E-2L,
-3.3413836095418743219397234253475252001090E-2L,
-3.5147290019036555862676702093393332533702E-2L,
-3.6917475563073933027920505457688955423688E-2L,
-3.8723951502862058660874073462456610731178E-2L,
-4.0566284516358241168330505467000838017425E-2L,
-4.2444048996543693813649967076598766917965E-2L,
-4.4356826869355401653098777649745233339196E-2L,
-4.6304207416957323121106944474331029996141E-2L,
-4.8285787106164123613318093945035804818364E-2L,
-5.0301169421838218987124461766244507342648E-2L,
-5.2349964705088137924875459464622098310997E-2L,
-5.4431789996103111613753440311680967840214E-2L,
-5.6546268881465384189752786409400404404794E-2L,
-5.8693031345788023909329239565012647817664E-2L,
-6.0871713627532018185577188079210189048340E-2L,
-6.3081958078862169742820420185833800925568E-2L,
-6.5323413029406789694910800219643791556918E-2L,
-6.7595732653791419081537811574227049288168E-2L
};
/* ln(2) = ln2a + ln2b with extended precision. */
static const long double
ln2a = 6.93145751953125e-1L,
ln2b = 1.4286068203094172321214581765680755001344E-6L;
long double
__ieee754_logl(long double x)
{
long double z, y, w;
ieee854_long_double_shape_type u, t;
unsigned int m;
int k, e;
u.value = x;
m = u.parts32.w0;
/* Check for IEEE special cases. */
k = m & 0x7fffffff;
/* log(0) = -infinity. */
if ((k | u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3) == 0)
{
return -0.5L / ZERO;
}
/* log ( x < 0 ) = NaN */
if (m & 0x80000000)
{
return (x - x) / ZERO;
}
/* log (infinity or NaN) */
if (k >= 0x7ff00000)
{
return x + x;
}
/* On this interval the table is not used due to cancellation error. */
if ((x <= 1.0078125L) && (x >= 0.9921875L))
{
z = x - 1.0L;
k = 64;
t.value = 1.0L;
e = 0;
}
else
{
/* Extract exponent and reduce domain to 0.703125 <= u < 1.40625 */
unsigned int w0;
e = (int) (m >> 20) - (int) 0x3fe;
m &= 0xfffff;
w0 = m | 0x3fe00000;
m |= 0x100000;
/* Find lookup table index k from high order bits of the significand. */
if (m < 0x168000)
{
k = (m - 0xff000) >> 13;
/* t is the argument 0.5 + (k+26)/128
of the nearest item to u in the lookup table. */
t.parts32.w0 = 0x3ff00000 + (k << 13);
t.parts32.w1 = 0;
t.parts32.w2 = 0;
t.parts32.w3 = 0;
w0 += 0x100000;
e -= 1;
k += 64;
}
else
{
k = (m - 0xfe000) >> 14;
t.parts32.w0 = 0x3fe00000 + (k << 14);
t.parts32.w1 = 0;
t.parts32.w2 = 0;
t.parts32.w3 = 0;
}
u.value = __scalbnl (u.value, ((int) ((w0 - u.parts32.w0) * 2)) >> 21);
/* log(u) = log( t u/t ) = log(t) + log(u/t)
log(t) is tabulated in the lookup table.
Express log(u/t) = log(1+z), where z = u/t - 1 = (u-t)/t.
cf. Cody & Waite. */
z = (u.value - t.value) / t.value;
}
/* Series expansion of log(1+z). */
w = z * z;
y = ((((((((((((l15 * z
+ l14) * z
+ l13) * z
+ l12) * z
+ l11) * z
+ l10) * z
+ l9) * z
+ l8) * z
+ l7) * z
+ l6) * z
+ l5) * z
+ l4) * z
+ l3) * z * w;
y -= 0.5 * w;
y += e * ln2b; /* Base 2 exponent offset times ln(2). */
y += z;
y += logtbl[k-26]; /* log(t) - (t-1) */
y += (t.value - 1.0L);
y += e * ln2a;
return y;
}

441
sysdeps/ieee754/ldbl-128ibm/e_powl.c Normal file
View File

@ -0,0 +1,441 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* Expansions and modifications for 128-bit long double are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* __ieee754_powl(x,y) return x**y
*
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 113-53 = 60 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
* 3. (anything) ** NAN is NAN
* 4. NAN ** (anything except 0) is NAN
* 5. +-(|x| > 1) ** +INF is +INF
* 6. +-(|x| > 1) ** -INF is +0
* 7. +-(|x| < 1) ** +INF is +0
* 8. +-(|x| < 1) ** -INF is +INF
* 9. +-1 ** +-INF is NAN
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
* 12. +0 ** (-anything except 0, NAN) is +INF
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
* 15. +INF ** (+anything except 0,NAN) is +INF
* 16. +INF ** (-anything except 0,NAN) is +0
* 17. -INF ** (anything) = -0 ** (-anything)
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
*
*/
#include "math.h"
#include "math_private.h"
static const long double bp[] = {
1.0L,
1.5L,
};
/* log_2(1.5) */
static const long double dp_h[] = {
0.0,
5.8496250072115607565592654282227158546448E-1L
};
/* Low part of log_2(1.5) */
static const long double dp_l[] = {
0.0,
1.0579781240112554492329533686862998106046E-16L
};
static const long double zero = 0.0L,
one = 1.0L,
two = 2.0L,
two113 = 1.0384593717069655257060992658440192E34L,
huge = 1.0e3000L,
tiny = 1.0e-3000L;
/* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2))
z = (x-1)/(x+1)
1 <= x <= 1.25
Peak relative error 2.3e-37 */
static const long double LN[] =
{
-3.0779177200290054398792536829702930623200E1L,
6.5135778082209159921251824580292116201640E1L,
-4.6312921812152436921591152809994014413540E1L,
1.2510208195629420304615674658258363295208E1L,
-9.9266909031921425609179910128531667336670E-1L
};
static const long double LD[] =
{
-5.129862866715009066465422805058933131960E1L,
1.452015077564081884387441590064272782044E2L,
-1.524043275549860505277434040464085593165E2L,
7.236063513651544224319663428634139768808E1L,
-1.494198912340228235853027849917095580053E1L
/* 1.0E0 */
};
/* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2)))
0 <= x <= 0.5
Peak relative error 5.7e-38 */
static const long double PN[] =
{
5.081801691915377692446852383385968225675E8L,
9.360895299872484512023336636427675327355E6L,
4.213701282274196030811629773097579432957E4L,
5.201006511142748908655720086041570288182E1L,
9.088368420359444263703202925095675982530E-3L,
};
static const long double PD[] =
{
3.049081015149226615468111430031590411682E9L,
1.069833887183886839966085436512368982758E8L,
8.259257717868875207333991924545445705394E5L,
1.872583833284143212651746812884298360922E3L,
/* 1.0E0 */
};
static const long double
/* ln 2 */
lg2 = 6.9314718055994530941723212145817656807550E-1L,
lg2_h = 6.9314718055994528622676398299518041312695E-1L,
lg2_l = 2.3190468138462996154948554638754786504121E-17L,
ovt = 8.0085662595372944372e-0017L,
/* 2/(3*log(2)) */
cp = 9.6179669392597560490661645400126142495110E-1L,
cp_h = 9.6179669392597555432899980587535537779331E-1L,
cp_l = 5.0577616648125906047157785230014751039424E-17L;
#ifdef __STDC__
long double
__ieee754_powl (long double x, long double y)
#else
long double
__ieee754_powl (x, y)
long double x, y;
#endif
{
long double z, ax, z_h, z_l, p_h, p_l;
long double y1, t1, t2, r, s, t, u, v, w;
long double s2, s_h, s_l, t_h, t_l;
int32_t i, j, k, yisint, n;
u_int32_t ix, iy;
int32_t hx, hy;
ieee854_long_double_shape_type o, p, q;
p.value = x;
hx = p.parts32.w0;
ix = hx & 0x7fffffff;
q.value = y;
hy = q.parts32.w0;
iy = hy & 0x7fffffff;
/* y==zero: x**0 = 1 */
if ((iy | q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
return one;
/* 1.0**y = 1; -1.0**+-Inf = 1 */
if (x == one)
return one;
if (x == -1.0L && iy == 0x7ff00000
&& (q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
return one;
/* +-NaN return x+y */
if ((ix > 0x7ff00000)
|| ((ix == 0x7ff00000)
&& ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) != 0))
|| (iy > 0x7ff00000)
|| ((iy == 0x7ff00000)
&& ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) != 0)))
return x + y;
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if (hx < 0)
{
if ((q.parts32.w2 & 0x7fffffff) >= 0x43400000) /* Low part >= 2^53 */
yisint = 2; /* even integer y */
else if (iy >= 0x3ff00000) /* 1.0 */
{
if (__floorl (y) == y)
{
z = 0.5 * y;
if (__floorl (z) == z)
yisint = 2;
else
yisint = 1;
}
}
}
/* special value of y */
if ((q.parts32.w1 | (q.parts32.w2 & 0x7fffffff) | q.parts32.w3) == 0)
{
if (iy == 0x7ff00000 && q.parts32.w1 == 0) /* y is +-inf */
{
if (((ix - 0x3ff00000) | p.parts32.w1
| (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0)
return y - y; /* inf**+-1 is NaN */
else if (ix > 0x3ff00000 || fabsl (x) > 1.0L)
/* (|x|>1)**+-inf = inf,0 */
return (hy >= 0) ? y : zero;
else
/* (|x|<1)**-,+inf = inf,0 */
return (hy < 0) ? -y : zero;
}
if (iy == 0x3ff00000)
{ /* y is +-1 */
if (hy < 0)
return one / x;
else
return x;
}
if (hy == 0x40000000)
return x * x; /* y is 2 */
if (hy == 0x3fe00000)
{ /* y is 0.5 */
if (hx >= 0) /* x >= +0 */
return __ieee754_sqrtl (x);
}
}
ax = fabsl (x);
/* special value of x */
if ((p.parts32.w1 | (p.parts32.w2 & 0x7fffffff) | p.parts32.w3) == 0)
{
if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000)
{
z = ax; /*x is +-0,+-inf,+-1 */
if (hy < 0)
z = one / z; /* z = (1/|x|) */
if (hx < 0)
{
if (((ix - 0x3ff00000) | yisint) == 0)
{
z = (z - z) / (z - z); /* (-1)**non-int is NaN */
}
else if (yisint == 1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
/* (x<0)**(non-int) is NaN */
if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0)
return (x - x) / (x - x);
/* |y| is huge.
2^-16495 = 1/2 of smallest representable value.
If (1 - 1/131072)^y underflows, y > 1.4986e9 */
if (iy > 0x41d654b0)
{
/* if (1 - 2^-113)^y underflows, y > 1.1873e38 */
if (iy > 0x47d654b0)
{
if (ix <= 0x3fefffff)
return (hy < 0) ? huge * huge : tiny * tiny;
if (ix >= 0x3ff00000)
return (hy > 0) ? huge * huge : tiny * tiny;
}
/* over/underflow if x is not close to one */
if (ix < 0x3fefffff)
return (hy < 0) ? huge * huge : tiny * tiny;
if (ix > 0x3ff00000)
return (hy > 0) ? huge * huge : tiny * tiny;
}
n = 0;
/* take care subnormal number */
if (ix < 0x00100000)
{
ax *= two113;
n -= 113;
o.value = ax;
ix = o.parts32.w0;
}
n += ((ix) >> 20) - 0x3ff;
j = ix & 0x000fffff;
/* determine interval */
ix = j | 0x3ff00000; /* normalize ix */
if (j <= 0x39880)
k = 0; /* |x|<sqrt(3/2) */
else if (j < 0xbb670)
k = 1; /* |x|<sqrt(3) */
else
{
k = 0;
n += 1;
ix -= 0x00100000;
}
o.value = ax;
o.value = __scalbnl (o.value, ((int) ((ix - o.parts32.w0) * 2)) >> 21);
ax = o.value;
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one / (ax + bp[k]);
s = u * v;
s_h = s;
o.value = s_h;
o.parts32.w3 = 0;
o.parts32.w2 &= 0xffff8000;
s_h = o.value;
/* t_h=ax+bp[k] High */
t_h = ax + bp[k];
o.value = t_h;
o.parts32.w3 = 0;
o.parts32.w2 &= 0xffff8000;
t_h = o.value;
t_l = ax - (t_h - bp[k]);
s_l = v * ((u - s_h * t_h) - s_h * t_l);
/* compute log(ax) */
s2 = s * s;
u = LN[0] + s2 * (LN[1] + s2 * (LN[2] + s2 * (LN[3] + s2 * LN[4])));
v = LD[0] + s2 * (LD[1] + s2 * (LD[2] + s2 * (LD[3] + s2 * (LD[4] + s2))));
r = s2 * s2 * u / v;
r += s_l * (s_h + s);
s2 = s_h * s_h;
t_h = 3.0 + s2 + r;
o.value = t_h;
o.parts32.w3 = 0;
o.parts32.w2 &= 0xffff8000;
t_h = o.value;
t_l = r - ((t_h - 3.0) - s2);
/* u+v = s*(1+...) */
u = s_h * t_h;
v = s_l * t_h + t_l * s;
/* 2/(3log2)*(s+...) */
p_h = u + v;
o.value = p_h;
o.parts32.w3 = 0;
o.parts32.w2 &= 0xffff8000;
p_h = o.value;
p_l = v - (p_h - u);
z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l * p_h + p_l * cp + dp_l[k];
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (long double) n;
t1 = (((z_h + z_l) + dp_h[k]) + t);
o.value = t1;
o.parts32.w3 = 0;
o.parts32.w2 &= 0xffff8000;
t1 = o.value;
t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
/* s (sign of result -ve**odd) = -1 else = 1 */
s = one;
if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
s = -one; /* (-ve)**(odd int) */
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
o.value = y1;
o.parts32.w3 = 0;
o.parts32.w2 &= 0xffff8000;
y1 = o.value;
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
o.value = z;
j = o.parts32.w0;
if (j >= 0x40d00000) /* z >= 16384 */
{
/* if z > 16384 */
if (((j - 0x40d00000) | o.parts32.w1
| (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0)
return s * huge * huge; /* overflow */
else
{
if (p_l + ovt > z - p_h)
return s * huge * huge; /* overflow */
}
}
else if ((j & 0x7fffffff) >= 0x40d01b90) /* z <= -16495 */
{
/* z < -16495 */
if (((j - 0xc0d01bc0) | o.parts32.w1
| (o.parts32.w2 & 0x7fffffff) | o.parts32.w3) != 0)
return s * tiny * tiny; /* underflow */
else
{
if (p_l <= z - p_h)
return s * tiny * tiny; /* underflow */
}
}
/* compute 2**(p_h+p_l) */
i = j & 0x7fffffff;
k = (i >> 20) - 0x3ff;
n = 0;
if (i > 0x3fe00000)
{ /* if |z| > 0.5, set n = [z+0.5] */
n = __floorl (z + 0.5L);
t = n;
p_h -= t;
}
t = p_l + p_h;
o.value = t;
o.parts32.w3 = 0;
o.parts32.w2 &= 0xffff8000;
t = o.value;
u = t * lg2_h;
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
z = u + v;
w = v - (z - u);
/* exp(z) */
t = z * z;
u = PN[0] + t * (PN[1] + t * (PN[2] + t * (PN[3] + t * PN[4])));
v = PD[0] + t * (PD[1] + t * (PD[2] + t * (PD[3] + t)));
t1 = z - t * u / v;
r = (z * t1) / (t1 - two) - (w + z * w);
z = one - (r - z);
z = __scalbnl (z, n);
return s * z;
}

277
sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c Normal file
View File

@ -0,0 +1,277 @@
/* Quad-precision floating point argument reduction.
Copyright (C) 1999,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include "math.h"
#include "math_private.h"
#include <ieee754.h>
/*
* Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi
*/
static const int32_t two_over_pi[] = {
0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62,
0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a,
0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129,
0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41,
0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8,
0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf,
0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5,
0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08,
0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3,
0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880,
0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b,
0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6,
0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2,
0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35,
0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30,
0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c,
0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4,
0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770,
0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7,
0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19,
0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522,
0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16,
0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6,
0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e,
0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48,
0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3,
0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf,
0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55,
0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612,
0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929,
0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec,
0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b,
0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c,
0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4,
0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb,
0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc,
0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c,
0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f,
0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5,
0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437,
0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b,
0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea,
0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad,
0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3,
0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3,
0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717,
0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f,
0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61,
0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db,
0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51,
0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0,
0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c,
0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6,
0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc,
0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed,
0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328,
0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d,
0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0,
0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b,
0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4,
0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3,
0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f,
0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad,
0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b,
0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4,
0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761,
0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31,
0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30,
0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262,
0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e,
0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1,
0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c,
0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4,
0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08,
0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196,
0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9,
0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4,
0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc,
0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c,
0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0,
0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c,
0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0,
0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac,
0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22,
0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893,
0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7,
0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5,
0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f,
0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4,
0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf,
0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b,
0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2,
0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138,
0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e,
0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569,
0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34,
0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9,
0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d,
0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f,
0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855,
0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569,
0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b,
0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe,
0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41,
0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49,
0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f,
0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110,
0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8,
0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365,
0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a,
0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270,
0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5,
0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616,
0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b,
0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0,
0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb,
0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a,
0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e,
0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa,
0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5,
0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0,
0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2,
0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886,
0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142,
0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba,
0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4,
0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708,
0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555,
0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3,
0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55,
0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58,
0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5,
0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c,
0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe,
0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b,
0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8,
0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005,
0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7,
0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50,
0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604,
0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643,
0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485,
0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d,
0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6,
0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2,
0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02,
0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3,
0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412,
0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274,
0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755,
0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849,
0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce,
0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5,
0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba,
0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6,
0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d,
0x7b7b89, 0x483d38,
};
static const long double c[] = {
/* 93 bits of pi/2 */
#define PI_2_1 c[0]
1.57079632679489661923132169155131424e+00L, /* 3fff921fb54442d18469898cc5100000 */
/* pi/2 - PI_2_1 */
#define PI_2_1t c[1]
8.84372056613570112025531863263659260e-29L, /* 3fa1c06e0e68948127044533e63a0106 */
};
int32_t __ieee754_rem_pio2l(long double x, long double *y)
{
long double z, w, t;
double tx[8];
int64_t exp, n, ix, hx, ixd;
u_int64_t lx, lxd;
GET_LDOUBLE_WORDS64 (hx, lx, x);
ix = hx & 0x7fffffffffffffffLL;
if (ix <= 0x3fe921fb54442d10LL) /* x in <-pi/4, pi/4> */
{
y[0] = x;
y[1] = 0;
return 0;
}
if (ix < 0x4002d97c7f3321d0LL) /* |x| in <pi/4, 3pi/4) */
{
if (hx > 0)
{
/* 113 + 93 bit PI is ok */
z = x - PI_2_1;
y[0] = z - PI_2_1t;
y[1] = (z - y[0]) - PI_2_1t;
return 1;
}
else
{
/* 113 + 93 bit PI is ok */
z = x + PI_2_1;
y[0] = z + PI_2_1t;
y[1] = (z - y[0]) + PI_2_1t;
return -1;
}
}
if (ix >= 0x7ff0000000000000LL) /* x is +=oo or NaN */
{
y[0] = x - x;
y[1] = y[0];
return 0;
}
/* Handle large arguments.
We split the 113 bits of the mantissa into 5 24bit integers
stored in a double array. */
/* Make the IBM extended format 105 bit mantissa look like the ieee854 112
bit mantissa so the next operatation will give the correct result. */
EXTRACT_IBM_EXTENDED_MANTISSA (ixd, lxd, exp, x);
exp = exp - 23;
/* This is faster than doing this in floating point, because we
have to convert it to integers anyway and like this we can keep
both integer and floating point units busy. */
tx [0] = (double)(((ixd >> 25) & 0x7fffff) | 0x800000);
tx [1] = (double)((ixd >> 1) & 0xffffff);
tx [2] = (double)(((ixd << 23) | (lxd >> 41)) & 0xffffff);
tx [3] = (double)((lxd >> 17) & 0xffffff);
tx [4] = (double)((lxd << 7) & 0xffffff);
n = __kernel_rem_pio2 (tx, tx + 5, exp, ((lxd << 7) & 0xffffff) ? 5 : 4,
3, two_over_pi);
/* The result is now stored in 3 double values, we need to convert it into
two long double values. */
t = (long double) tx [6] + (long double) tx [7];
w = (long double) tx [5];
if (hx >= 0)
{
y[0] = w + t;
y[1] = t - (y[0] - w);
return n;
}
else
{
y[0] = -(w + t);
y[1] = -t - (y[0] + w);
return -n;
}
}

78
sysdeps/ieee754/ldbl-128ibm/e_remainderl.c Normal file
View File

@ -0,0 +1,78 @@
/* e_fmodl.c -- long double version of e_fmod.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_remainderl(x,p)
* Return :
* returns x REM p = x - [x/p]*p as if in infinite
* precise arithmetic, where [x/p] is the (infinite bit)
* integer nearest x/p (in half way case choose the even one).
* Method :
* Based on fmodl() return x-[x/p]chopped*p exactlp.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double zero = 0.0L;
#else
static long double zero = 0.0L;
#endif
#ifdef __STDC__
long double __ieee754_remainderl(long double x, long double p)
#else
long double __ieee754_remainderl(x,p)
long double x,p;
#endif
{
int64_t hx,hp;
u_int64_t sx,lx,lp;
long double p_half;
GET_LDOUBLE_WORDS64(hx,lx,x);
GET_LDOUBLE_WORDS64(hp,lp,p);
sx = hx&0x8000000000000000ULL;
hp &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* purge off exception values */
if((hp|(lp&0x7fffffffffffffff))==0) return (x*p)/(x*p); /* p = 0 */
if((hx>=0x7ff0000000000000LL)|| /* x not finite */
((hp>=0x7ff0000000000000LL)&& /* p is NaN */
(((hp-0x7ff0000000000000LL)|lp)!=0)))
return (x*p)/(x*p);
if (hp<=0x7fdfffffffffffffLL) x = __ieee754_fmodl(x,p+p); /* now x < 2p */
if (((hx-hp)|(lx-lp))==0) return zero*x;
x = fabsl(x);
p = fabsl(p);
if (hp<0x0020000000000000LL) {
if(x+x>p) {
x-=p;
if(x+x>=p) x -= p;
}
} else {
p_half = 0.5L*p;
if(x>p_half) {
x-=p;
if(x>=p_half) x -= p;
}
}
GET_LDOUBLE_MSW64(hx,x);
SET_LDOUBLE_MSW64(x,hx^sx);
return x;
}

84
sysdeps/ieee754/ldbl-128ibm/e_sinhl.c Normal file
View File

@ -0,0 +1,84 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
#endif
/* __ieee754_sinh(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
* 2
*
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : sinh(x) := x*shuge (overflow)
*
* Special cases:
* sinh(x) is |x| if x is +INF, -INF, or NaN.
* only sinh(0)=0 is exact for finite x.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double one = 1.0, shuge = 1.0e307;
#else
static long double one = 1.0, shuge = 1.0e307;
#endif
#ifdef __STDC__
long double __ieee754_sinhl(long double x)
#else
long double __ieee754_sinhl(x)
long double x;
#endif
{
long double t,w,h;
int64_t ix,jx;
/* High word of |x|. */
GET_LDOUBLE_MSW64(jx,x);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) return x+x;
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x4036000000000000LL) { /* |x|<22 */
if (ix<0x3e20000000000000LL) /* |x|<2**-29 */
if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
t = __expm1l(fabsl(x));
if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
return h*(t+t/(t+one));
}
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= 0x408633ce8fb9f87dLL) {
w = __ieee754_expl(0.5*fabsl(x));
t = h*w;
return t*w;
}
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}

109
sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c Normal file
View File

@ -0,0 +1,109 @@
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001, 2004, 2006 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/*********************************************************************/
/* MODULE_NAME: uroot.c */
/* */
/* FUNCTION: usqrt */
/* */
/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
/* uroot.tbl */
/* */
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include <math_private.h>
typedef unsigned int int4;
typedef union {int4 i[4]; long double x; double d[2]; } mynumber;
static const mynumber
t512 = {{0x5ff00000, 0x00000000, 0x00000000, 0x00000000 }}, /* 2^512 */
tm256 = {{0x2ff00000, 0x00000000, 0x00000000, 0x00000000 }}; /* 2^-256 */
static const double
two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */
/*********************************************************************/
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/*********************************************************************/
long double __ieee754_sqrtl(long double x)
{
static const long double big = 134217728.0, big1 = 134217729.0;
long double t,s,i;
mynumber a,c;
int4 k, l, m;
int n;
double d;
a.x=x;
k=a.i[0] & 0x7fffffff;
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
if (k>0x000fffff && k<0x7ff00000) {
if (x < 0) return (big1-big1)/(big-big);
l = (k&0x001fffff)|0x3fe00000;
if (((a.i[2] & 0x7fffffff) | a.i[3]) != 0) {
n = (int) ((l - k) * 2) >> 21;
m = (a.i[2] >> 20) & 0x7ff;
if (m == 0) {
a.d[1] *= two54;
m = ((a.i[2] >> 20) & 0x7ff) - 54;
}
m += n;
if (m > 0)
a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
else if (m <= -54) {
a.i[2] &= 0x80000000;
a.i[3] = 0;
} else {
m += 54;
a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
a.d[1] *= twom54;
}
}
a.i[0] = l;
s = a.x;
d = __ieee754_sqrt (a.d[0]);
c.i[0] = 0x20000000+((k&0x7fe00000)>>1);
c.i[1] = 0;
c.i[2] = 0;
c.i[3] = 0;
i = d;
t = 0.5L * (i + s / i);
i = 0.5L * (t + s / t);
return c.x * i;
}
else {
if (k>=0x7ff00000) {
if (a.i[0] == 0xfff00000 && a.i[1] == 0)
return (big1-big1)/(big-big); /* sqrt (-Inf) = NaN. */
return x; /* sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */
}
if (x == 0) return x;
if (x < 0) return (big1-big1)/(big-big);
return tm256.x*__ieee754_sqrtl(x*t512.x);
}
}

210
sysdeps/ieee754/ldbl-128ibm/ieee754.h Normal file
View File

@ -0,0 +1,210 @@
/* Copyright (C) 1992, 1995, 1996, 1999, 2004, 2006
Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#ifndef _IEEE754_H
#define _IEEE754_H 1
#include <features.h>
#include <endian.h>
__BEGIN_DECLS
union ieee754_float
{
float f;
/* This is the IEEE 754 single-precision format. */
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned int negative:1;
unsigned int exponent:8;
unsigned int mantissa:23;
#endif /* Big endian. */
#if __BYTE_ORDER == __LITTLE_ENDIAN
unsigned int mantissa:23;
unsigned int exponent:8;
unsigned int negative:1;
#endif /* Little endian. */
} ieee;
/* This format makes it easier to see if a NaN is a signalling NaN. */
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned int negative:1;
unsigned int exponent:8;
unsigned int quiet_nan:1;
unsigned int mantissa:22;
#endif /* Big endian. */
#if __BYTE_ORDER == __LITTLE_ENDIAN
unsigned int mantissa:22;
unsigned int quiet_nan:1;
unsigned int exponent:8;
unsigned int negative:1;
#endif /* Little endian. */
} ieee_nan;
};
#define IEEE754_FLOAT_BIAS 0x7f /* Added to exponent. */
union ieee754_double
{
double d;
/* This is the IEEE 754 double-precision format. */
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned int negative:1;
unsigned int exponent:11;
/* Together these comprise the mantissa. */
unsigned int mantissa0:20;
unsigned int mantissa1:32;
#endif /* Big endian. */
#if __BYTE_ORDER == __LITTLE_ENDIAN
/* Together these comprise the mantissa. */
unsigned int mantissa1:32;
unsigned int mantissa0:20;
unsigned int exponent:11;
unsigned int negative:1;
#endif /* Little endian. */
} ieee;
/* This format makes it easier to see if a NaN is a signalling NaN. */
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned int negative:1;
unsigned int exponent:11;
unsigned int quiet_nan:1;
/* Together these comprise the mantissa. */
unsigned int mantissa0:19;
unsigned int mantissa1:32;
#else
/* Together these comprise the mantissa. */
unsigned int mantissa1:32;
unsigned int mantissa0:19;
unsigned int quiet_nan:1;
unsigned int exponent:11;
unsigned int negative:1;
#endif
} ieee_nan;
};
#define IEEE754_DOUBLE_BIAS 0x3ff /* Added to exponent. */
union ieee854_long_double
{
long double d;
/* This is the IEEE 854 quad-precision format. */
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned int negative:1;
unsigned int exponent:15;
/* Together these comprise the mantissa. */
unsigned int mantissa0:16;
unsigned int mantissa1:32;
unsigned int mantissa2:32;
unsigned int mantissa3:32;
#endif /* Big endian. */
#if __BYTE_ORDER == __LITTLE_ENDIAN
/* Together these comprise the mantissa. */
unsigned int mantissa3:32;
unsigned int mantissa2:32;
unsigned int mantissa1:32;
unsigned int mantissa0:16;
unsigned int exponent:15;
unsigned int negative:1;
#endif /* Little endian. */
} ieee;
/* This format makes it easier to see if a NaN is a signalling NaN. */
struct
{
#if __BYTE_ORDER == __BIG_ENDIAN
unsigned int negative:1;
unsigned int exponent:15;
unsigned int quiet_nan:1;
/* Together these comprise the mantissa. */
unsigned int mantissa0:15;
unsigned int mantissa1:32;
unsigned int mantissa2:32;
unsigned int mantissa3:32;
#else
/* Together these comprise the mantissa. */
unsigned int mantissa3:32;
unsigned int mantissa2:32;
unsigned int mantissa1:32;
unsigned int mantissa0:15;
unsigned int quiet_nan:1;
unsigned int exponent:15;
unsigned int negative:1;
#endif
} ieee_nan;
};
#define IEEE854_LONG_DOUBLE_BIAS 0x3fff /* Added to exponent. */
/* IBM extended format for long double.
Each long double is made up of two IEEE doubles. The value of the
long double is the sum of the values of the two parts. The most
significant part is required to be the value of the long double
rounded to the nearest double, as specified by IEEE. For Inf
values, the least significant part is required to be one of +0.0 or
-0.0. No other requirements are made; so, for example, 1.0 may be
represented as (1.0, +0.0) or (1.0, -0.0), and the low part of a
NaN is don't-care. */
union ibm_extended_long_double
{
long double d;
double dd[2];
/* This is the IBM extended format long double. */
struct
{ /* Big endian. There is no other. */
unsigned int negative:1;
unsigned int exponent:11;
/* Together Mantissa0-3 comprise the mantissa. */
unsigned int mantissa0:20;
unsigned int mantissa1:32;
unsigned int negative2:1;
unsigned int exponent2:11;
/* There is an implied 1 here? */
/* Together these comprise the mantissa. */
unsigned int mantissa2:20;
unsigned int mantissa3:32;
} ieee;
};
#define IBM_EXTENDED_LONG_DOUBLE_BIAS 0x3ff /* Added to exponent. */
__END_DECLS
#endif /* ieee754.h */

128
sysdeps/ieee754/ldbl-128ibm/k_cosl.c Normal file
View File

@ -0,0 +1,128 @@
/* Quad-precision floating point cosine on <-pi/4,pi/4>.
Copyright (C) 1999,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include "math.h"
#include "math_private.h"
static const long double c[] = {
#define ONE c[0]
1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
x in <0,1/256> */
#define SCOS1 c[1]
#define SCOS2 c[2]
#define SCOS3 c[3]
#define SCOS4 c[4]
#define SCOS5 c[5]
-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
x in <0,0.1484375> */
#define COS1 c[6]
#define COS2 c[7]
#define COS3 c[8]
#define COS4 c[9]
#define COS5 c[10]
#define COS6 c[11]
#define COS7 c[12]
#define COS8 c[13]
-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
x in <0,1/256> */
#define SSIN1 c[14]
#define SSIN2 c[15]
#define SSIN3 c[16]
#define SSIN4 c[17]
#define SSIN5 c[18]
-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
};
#define SINCOSL_COS_HI 0
#define SINCOSL_COS_LO 1
#define SINCOSL_SIN_HI 2
#define SINCOSL_SIN_LO 3
extern const long double __sincosl_table[];
long double
__kernel_cosl(long double x, long double y)
{
long double h, l, z, sin_l, cos_l_m1;
int64_t ix;
u_int32_t tix, hix, index;
GET_LDOUBLE_MSW64 (ix, x);
tix = ((u_int64_t)ix) >> 32;
tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
if (tix < 0x3fc30000) /* |x| < 0.1484375 */
{
/* Argument is small enough to approximate it by a Chebyshev
polynomial of degree 16. */
if (tix < 0x3c600000) /* |x| < 2^-57 */
if (!((int)x)) return ONE; /* generate inexact */
z = x * x;
return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
}
else
{
/* So that we don't have to use too large polynomial, we find
l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
possible values for h. We look up cosl(h) and sinl(h) in
pre-computed tables, compute cosl(l) and sinl(l) using a
Chebyshev polynomial of degree 10(11) and compute
cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
index = 0x3fe - (tix >> 20);
hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
x = fabsl (x);
switch (index)
{
case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
default:
case 2: index = (hix - 0x3fc30000) >> 14; break;
}
SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
l = y - (h - x);
z = l * l;
sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
return __sincosl_table [index + SINCOSL_COS_HI]
+ (__sincosl_table [index + SINCOSL_COS_LO]
- (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
- __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
}
}

163
sysdeps/ieee754/ldbl-128ibm/k_sincosl.c Normal file
View File

@ -0,0 +1,163 @@
/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
Copyright (C) 1999,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include "math.h"
#include "math_private.h"
static const long double c[] = {
#define ONE c[0]
1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
x in <0,1/256> */
#define SCOS1 c[1]
#define SCOS2 c[2]
#define SCOS3 c[3]
#define SCOS4 c[4]
#define SCOS5 c[5]
-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
x in <0,0.1484375> */
#define COS1 c[6]
#define COS2 c[7]
#define COS3 c[8]
#define COS4 c[9]
#define COS5 c[10]
#define COS6 c[11]
#define COS7 c[12]
#define COS8 c[13]
-4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */
4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */
-1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */
2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
-2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */
2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */
-1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */
4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
x in <0,1/256> */
#define SSIN1 c[14]
#define SSIN2 c[15]
#define SSIN3 c[16]
#define SSIN4 c[17]
#define SSIN5 c[18]
-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
x in <0,0.1484375> */
#define SIN1 c[19]
#define SIN2 c[20]
#define SIN3 c[21]
#define SIN4 c[22]
#define SIN5 c[23]
#define SIN6 c[24]
#define SIN7 c[25]
#define SIN8 c[26]
-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
};
#define SINCOSL_COS_HI 0
#define SINCOSL_COS_LO 1
#define SINCOSL_SIN_HI 2
#define SINCOSL_SIN_LO 3
extern const long double __sincosl_table[];
void
__kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy)
{
long double h, l, z, sin_l, cos_l_m1;
int64_t ix;
u_int32_t tix, hix, index;
GET_LDOUBLE_MSW64 (ix, x);
tix = ((u_int64_t)ix) >> 32;
tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
if (tix < 0x3fc30000) /* |x| < 0.1484375 */
{
/* Argument is small enough to approximate it by a Chebyshev
polynomial of degree 16(17). */
if (tix < 0x3c600000) /* |x| < 2^-57 */
if (!((int)x)) /* generate inexact */
{
*sinx = x;
*cosx = ONE;
return;
}
z = x * x;
*sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
*cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
}
else
{
/* So that we don't have to use too large polynomial, we find
l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
possible values for h. We look up cosl(h) and sinl(h) in
pre-computed tables, compute cosl(l) and sinl(l) using a
Chebyshev polynomial of degree 10(11) and compute
sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l). */
index = 0x3fe - (tix >> 20);
hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
x = fabsl (x);
switch (index)
{
case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
default:
case 2: index = (hix - 0x3fc30000) >> 14; break;
}
SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
if (iy)
l = y - (h - x);
else
l = x - h;
z = l * l;
sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
z = __sincosl_table [index + SINCOSL_SIN_HI]
+ (__sincosl_table [index + SINCOSL_SIN_LO]
+ (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
+ (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
*sinx = (ix < 0) ? -z : z;
*cosx = __sincosl_table [index + SINCOSL_COS_HI]
+ (__sincosl_table [index + SINCOSL_COS_LO]
- (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
- __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
}
}

132
sysdeps/ieee754/ldbl-128ibm/k_sinl.c Normal file
View File

@ -0,0 +1,132 @@
/* Quad-precision floating point sine on <-pi/4,pi/4>.
Copyright (C) 1999,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include "math.h"
#include "math_private.h"
static const long double c[] = {
#define ONE c[0]
1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */
/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
x in <0,1/256> */
#define SCOS1 c[1]
#define SCOS2 c[2]
#define SCOS3 c[3]
#define SCOS4 c[4]
#define SCOS5 c[5]
-5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */
4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */
-1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */
2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
-2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */
/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
x in <0,0.1484375> */
#define SIN1 c[6]
#define SIN2 c[7]
#define SIN3 c[8]
#define SIN4 c[9]
#define SIN5 c[10]
#define SIN6 c[11]
#define SIN7 c[12]
#define SIN8 c[13]
-1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */
8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */
-1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */
2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */
-2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */
1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */
-7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */
/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
x in <0,1/256> */
#define SSIN1 c[14]
#define SSIN2 c[15]
#define SSIN3 c[16]
#define SSIN4 c[17]
#define SSIN5 c[18]
-1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */
8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */
-1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */
2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */
-2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */
};
#define SINCOSL_COS_HI 0
#define SINCOSL_COS_LO 1
#define SINCOSL_SIN_HI 2
#define SINCOSL_SIN_LO 3
extern const long double __sincosl_table[];
long double
__kernel_sinl(long double x, long double y, int iy)
{
long double h, l, z, sin_l, cos_l_m1;
int64_t ix;
u_int32_t tix, hix, index;
GET_LDOUBLE_MSW64 (ix, x);
tix = ((u_int64_t)ix) >> 32;
tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
if (tix < 0x3fc30000) /* |x| < 0.1484375 */
{
/* Argument is small enough to approximate it by a Chebyshev
polynomial of degree 17. */
if (tix < 0x3c600000) /* |x| < 2^-57 */
if (!((int)x)) return x; /* generate inexact */
z = x * x;
return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
}
else
{
/* So that we don't have to use too large polynomial, we find
l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
possible values for h. We look up cosl(h) and sinl(h) in
pre-computed tables, compute cosl(l) and sinl(l) using a
Chebyshev polynomial of degree 10(11) and compute
sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
index = 0x3fe - (tix >> 20);
hix = (tix + (0x2000 << index)) & (0xffffc000 << index);
x = fabsl (x);
switch (index)
{
case 0: index = ((45 << 14) + hix - 0x3fe00000) >> 12; break;
case 1: index = ((13 << 15) + hix - 0x3fd00000) >> 13; break;
default:
case 2: index = (hix - 0x3fc30000) >> 14; break;
}
SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0);
if (iy)
l = y - (h - x);
else
l = x - h;
z = l * l;
sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
z = __sincosl_table [index + SINCOSL_SIN_HI]
+ (__sincosl_table [index + SINCOSL_SIN_LO]
+ (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
+ (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
return (ix < 0) ? -z : z;
}
}

164
sysdeps/ieee754/ldbl-128ibm/k_tanl.c Normal file
View File

@ -0,0 +1,164 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
Long double expansions are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* __kernel_tanl( x, y, k )
* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
* Input k indicates whether tan (if k=1) or
* -1/tan (if k= -1) is returned.
*
* Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
* 2. if x < 2^-57, return x with inexact if x!=0.
* 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
* on [0,0.67433].
*
* Note: tan(x+y) = tan(x) + tan'(x)*y
* ~ tan(x) + (1+x*x)*y
* Therefore, for better accuracy in computing tan(x+y), let
* r = x^3 * R(x^2)
* then
* tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
*
* 4. For x in [0.67433,pi/4], let y = pi/4 - x, then
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double
#else
static long double
#endif
one = 1.0L,
pio4hi = 7.8539816339744830961566084581987569936977E-1L,
pio4lo = 2.1679525325309452561992610065108379921906E-35L,
/* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
0 <= x <= 0.6743316650390625
Peak relative error 8.0e-36 */
TH = 3.333333333333333333333333333333333333333E-1L,
T0 = -1.813014711743583437742363284336855889393E7L,
T1 = 1.320767960008972224312740075083259247618E6L,
T2 = -2.626775478255838182468651821863299023956E4L,
T3 = 1.764573356488504935415411383687150199315E2L,
T4 = -3.333267763822178690794678978979803526092E-1L,
U0 = -1.359761033807687578306772463253710042010E8L,
U1 = 6.494370630656893175666729313065113194784E7L,
U2 = -4.180787672237927475505536849168729386782E6L,
U3 = 8.031643765106170040139966622980914621521E4L,
U4 = -5.323131271912475695157127875560667378597E2L;
/* 1.000000000000000000000000000000000000000E0 */
#ifdef __STDC__
long double
__kernel_tanl (long double x, long double y, int iy)
#else
long double
__kernel_tanl (x, y, iy)
long double x, y;
int iy;
#endif
{
long double z, r, v, w, s;
int32_t ix, sign;
ieee854_long_double_shape_type u, u1;
u.value = x;
ix = u.parts32.w0 & 0x7fffffff;
if (ix < 0x3c600000) /* x < 2**-57 */
{
if ((int) x == 0)
{ /* generate inexact */
if ((ix | u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3
| (iy + 1)) == 0)
return one / fabs (x);
else
return (iy == 1) ? x : -one / x;
}
}
if (ix >= 0x3fe59420) /* |x| >= 0.6743316650390625 */
{
if ((u.parts32.w0 & 0x80000000) != 0)
{
x = -x;
y = -y;
sign = -1;
}
else
sign = 1;
z = pio4hi - x;
w = pio4lo - y;
x = z + w;
y = 0.0;
}
z = x * x;
r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
r = r / v;
s = z * x;
r = y + z * (s * r + y);
r += TH * s;
w = x + r;
if (ix >= 0x3fe59420)
{
v = (long double) iy;
w = (v - 2.0 * (x - (w * w / (w + v) - r)));
if (sign < 0)
w = -w;
return w;
}
if (iy == 1)
return w;
else
{ /* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
u1.value = w;
u1.parts32.w2 = 0;
u1.parts32.w3 = 0;
v = r - (u1.value - x); /* u1+v = r+x */
z = -1.0 / w;
u.value = z;
u.parts32.w2 = 0;
u.parts32.w3 = 0;
s = 1.0 + u.value * u1.value;
return u.value + z * (s + u.value * v);
}
}

175
sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c Normal file
View File

@ -0,0 +1,175 @@
/* Copyright (C) 1995,1996,1997,1998,1999,2002,2003,2006
Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include <ieee754.h>
#include <float.h>
#include <math.h>
#include <stdlib.h>
/* Convert a `long double' in IBM extended format to a multi-precision
integer representing the significand scaled up by its number of
bits (106 for long double) and an integral power of two (MPN
frexpl). */
mp_size_t
__mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size,
int *expt, int *is_neg,
long double value)
{
union ibm_extended_long_double u;
unsigned long long hi, lo;
int ediff;
u.d = value;
*is_neg = u.ieee.negative;
*expt = (int) u.ieee.exponent - IBM_EXTENDED_LONG_DOUBLE_BIAS;
lo = ((long long) u.ieee.mantissa2 << 32) | u.ieee.mantissa3;
hi = ((long long) u.ieee.mantissa0 << 32) | u.ieee.mantissa1;
/* If the lower double is not a denomal or zero then set the hidden
53rd bit. */
if (u.ieee.exponent2 > 0)
{
lo |= 1LL << 52;
/* The lower double is normalized separately from the upper. We may
need to adjust the lower manitissa to reflect this. */
ediff = u.ieee.exponent - u.ieee.exponent2;
if (ediff > 53)
lo = lo >> (ediff-53);
}
/* The high double may be rounded and the low double reflects the
difference between the long double and the rounded high double
value. This is indicated by a differnce between the signs of the
high and low doubles. */
if ((u.ieee.negative != u.ieee.negative2)
&& ((u.ieee.exponent2 != 0) && (lo != 0L)))
{
lo = (1ULL << 53) - lo;
if (hi == 0LL)
{
/* we have a borrow from the hidden bit, so shift left 1. */
hi = 0x0ffffffffffffeLL | (lo >> 51);
lo = 0x1fffffffffffffLL & (lo << 1);
(*expt)--;
}
else
hi--;
}
#if BITS_PER_MP_LIMB == 32
/* Combine the mantissas to be contiguous. */
res_ptr[0] = lo;
res_ptr[1] = (hi << (53 - 32)) | (lo >> 32);
res_ptr[2] = hi >> 11;
res_ptr[3] = hi >> (32 + 11);
#define N 4
#elif BITS_PER_MP_LIMB == 64
/* Combine the two mantissas to be contiguous. */
res_ptr[0] = (hi << 53) | lo;
res_ptr[1] = hi >> 11;
#define N 2
#else
#error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
#endif
/* The format does not fill the last limb. There are some zeros. */
#define NUM_LEADING_ZEROS (BITS_PER_MP_LIMB \
- (LDBL_MANT_DIG - ((N - 1) * BITS_PER_MP_LIMB)))
if (u.ieee.exponent == 0)
{
/* A biased exponent of zero is a special case.
Either it is a zero or it is a denormal number. */
if (res_ptr[0] == 0 && res_ptr[1] == 0
&& res_ptr[N - 2] == 0 && res_ptr[N - 1] == 0) /* Assumes N<=4. */
/* It's zero. */
*expt = 0;
else
{
/* It is a denormal number, meaning it has no implicit leading
one bit, and its exponent is in fact the format minimum. */
int cnt;
#if N == 2
if (res_ptr[N - 1] != 0)
{
count_leading_zeros (cnt, res_ptr[N - 1]);
cnt -= NUM_LEADING_ZEROS;
res_ptr[N - 1] = res_ptr[N - 1] << cnt
| (res_ptr[0] >> (BITS_PER_MP_LIMB - cnt));
res_ptr[0] <<= cnt;
*expt = LDBL_MIN_EXP - 1 - cnt;
}
else
{
count_leading_zeros (cnt, res_ptr[0]);
if (cnt >= NUM_LEADING_ZEROS)
{
res_ptr[N - 1] = res_ptr[0] << (cnt - NUM_LEADING_ZEROS);
res_ptr[0] = 0;
}
else
{
res_ptr[N - 1] = res_ptr[0] >> (NUM_LEADING_ZEROS - cnt);
res_ptr[0] <<= BITS_PER_MP_LIMB - (NUM_LEADING_ZEROS - cnt);
}
*expt = LDBL_MIN_EXP - 1
- (BITS_PER_MP_LIMB - NUM_LEADING_ZEROS) - cnt;
}
#else
int j, k, l;
for (j = N - 1; j > 0; j--)
if (res_ptr[j] != 0)
break;
count_leading_zeros (cnt, res_ptr[j]);
cnt -= NUM_LEADING_ZEROS;
l = N - 1 - j;
if (cnt < 0)
{
cnt += BITS_PER_MP_LIMB;
l--;
}
if (!cnt)
for (k = N - 1; k >= l; k--)
res_ptr[k] = res_ptr[k-l];
else
{
for (k = N - 1; k > l; k--)
res_ptr[k] = res_ptr[k-l] << cnt
| res_ptr[k-l-1] >> (BITS_PER_MP_LIMB - cnt);
res_ptr[k--] = res_ptr[0] << cnt;
}
for (; k >= 0; k--)
res_ptr[k] = 0;
*expt = LDBL_MIN_EXP - 1 - l * BITS_PER_MP_LIMB - cnt;
#endif
}
}
else
/* Add the implicit leading one bit for a normalized number. */
res_ptr[N - 1] |= (mp_limb_t) 1 << (LDBL_MANT_DIG - 1
- ((N - 1) * BITS_PER_MP_LIMB));
return N;
}

124
sysdeps/ieee754/ldbl-128ibm/math_ldbl.h Normal file
View File

@ -0,0 +1,124 @@
#ifndef _MATH_PRIVATE_H_
#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
#endif
#include <sysdeps/ieee754/ldbl-128/math_ldbl.h>
#define EXTRACT_IBM_EXTENDED_MANTISSA(hi64, lo64, expnt, ibm_ext_ldbl) \
do \
{ \
/* We have 105 bits of mantissa plus one implicit digit. Since \
106 bits are representable without the rest using hexadecimal \
digits we use only the implicit digits for the number before \
the decimal point. */ \
unsigned long long hi, lo; \
int ediff; \
union ibm_extended_long_double eldbl; \
eldbl.d = ibm_ext_ldbl; \
expnt = eldbl.ieee.exponent - IBM_EXTENDED_LONG_DOUBLE_BIAS; \
\
lo = ((long long)eldbl.ieee.mantissa2 << 32) | eldbl.ieee.mantissa3; \
hi = ((long long)eldbl.ieee.mantissa0 << 32) | eldbl.ieee.mantissa1; \
/* If the lower double is not a denomal or zero then set the hidden \
53rd bit. */ \
if (eldbl.ieee.exponent2 > 0x001) \
{ \
lo |= (1ULL << 52); \
lo = lo << 7; /* pre-shift lo to match ieee854. */ \
/* The lower double is normalized separately from the upper. We \
may need to adjust the lower manitissa to reflect this. */ \
ediff = eldbl.ieee.exponent - eldbl.ieee.exponent2; \
if (ediff > 53) \
lo = lo >> (ediff-53); \
} \
hi |= (1ULL << 52); \
\
if ((eldbl.ieee.negative != eldbl.ieee.negative2) \
&& ((eldbl.ieee.exponent2 != 0) && (lo != 0LL))) \
{ \
hi--; \
lo = (1ULL << 60) - lo; \
if (hi < (1ULL << 52)) \
{ \
/* we have a borrow from the hidden bit, so shift left 1. */ \
hi = (hi << 1) | (lo >> 59); \
lo = 0xfffffffffffffffLL & (lo << 1); \
expnt--; \
} \
} \
lo64 = (hi << 60) | lo; \
hi64 = hi >> 4; \
} \
while (0)
#define INSERT_IBM_EXTENDED_MANTISSA(ibm_ext_ldbl, sign, expnt, hi64, lo64) \
do \
{ \
union ibm_extended_long_double u; \
unsigned long hidden2, lzcount; \
unsigned long long hi, lo; \
\
u.ieee.negative = sign; \
u.ieee.negative2 = sign; \
u.ieee.exponent = expnt + IBM_EXTENDED_LONG_DOUBLE_BIAS; \
u.ieee.exponent2 = expnt-53 + IBM_EXTENDED_LONG_DOUBLE_BIAS; \
/* Expect 113 bits (112 bits + hidden) right justified in two longs. \
The low order 53 bits (52 + hidden) go into the lower double */ \
lo = (lo64 >> 7)& ((1ULL << 53) - 1); \
hidden2 = (lo64 >> 59) & 1ULL; \
/* The high order 53 bits (52 + hidden) go into the upper double */ \
hi = (lo64 >> 60) & ((1ULL << 11) - 1); \
hi |= (hi64 << 4); \
\
if (lo != 0LL) \
{ \
/* hidden2 bit of low double controls rounding of the high double. \
If hidden2 is '1' then round up hi and adjust lo (2nd mantissa) \
plus change the sign of the low double to compensate. */ \
if (hidden2) \
{ \
hi++; \
u.ieee.negative2 = !sign; \
lo = (1ULL << 53) - lo; \
} \
/* The hidden bit of the lo mantissa is zero so we need to \
normalize the it for the low double. Shift it left until the \
hidden bit is '1' then adjust the 2nd exponent accordingly. */ \
\
if (sizeof (lo) == sizeof (long)) \
lzcount = __builtin_clzl (lo); \
else if ((lo >> 32) != 0) \
lzcount = __builtin_clzl ((long) (lo >> 32)); \
else \
lzcount = __builtin_clzl ((long) lo) + 32; \
lzcount = lzcount - 11; \
if (lzcount > 0) \
{ \
int expnt2 = u.ieee.exponent2 - lzcount; \
if (expnt2 >= 1) \
{ \
/* Not denormal. Normalize and set low exponent. */ \
lo = lo << lzcount; \
u.ieee.exponent2 = expnt2; \
} \
else \
{ \
/* Is denormal. */ \
lo = lo << (lzcount + expnt2); \
u.ieee.exponent2 = 0; \
} \
} \
} \
else \
{ \
u.ieee.negative2 = 0; \
u.ieee.exponent2 = 0; \
} \
\
u.ieee.mantissa3 = lo & ((1ULL << 32) - 1); \
u.ieee.mantissa2 = (lo >> 32) & ((1ULL << 20) - 1); \
u.ieee.mantissa1 = hi & ((1ULL << 32) - 1); \
u.ieee.mantissa0 = (hi >> 32) & ((1ULL << 20) - 1); \
ibm_ext_ldbl = u.d; \
} \
while (0)

103
sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c Normal file
View File

@ -0,0 +1,103 @@
/* Copyright (C) 1995, 1996, 1997, 1998, 1999, 2002, 2003, 2004, 2006
Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include "gmp.h"
#include "gmp-impl.h"
#include <ieee754.h>
#include <float.h>
#include <math.h>
/* Convert a multi-precision integer of the needed number of bits (106
for long double) and an integral power of two to a `long double' in
IBM extended format. */
long double
__mpn_construct_long_double (mp_srcptr frac_ptr, int expt, int sign)
{
union ibm_extended_long_double u;
unsigned long hidden2, lzcount;
unsigned long long hi, lo;
u.ieee.negative = sign;
u.ieee.negative2 = sign;
u.ieee.exponent = expt + IBM_EXTENDED_LONG_DOUBLE_BIAS;
u.ieee.exponent2 = expt - 53 + IBM_EXTENDED_LONG_DOUBLE_BIAS;
#if BITS_PER_MP_LIMB == 32
/* The low order 53 bits (52 + hidden) go into the lower double */
lo = frac_ptr[0];
lo |= (frac_ptr[1] & ((1LL << (53 - 32)) - 1)) << 32;
hidden2 = (frac_ptr[1] >> (52 - 32)) & ((mp_limb_t) 1);
/* The high order 53 bits (52 + hidden) go into the upper double */
hi = (frac_ptr[1] >> (53 - 32)) & ((1 << 11) - 1);
hi |= ((unsigned long long) frac_ptr[2]) << 11;
hi |= ((unsigned long long) frac_ptr[3]) << (32 + 11);
#elif BITS_PER_MP_LIMB == 64
/* The low order 53 bits (52 + hidden) go into the lower double */
lo = frac_ptr[0] & (((mp_limb_t) 1 << 53) - 1);
hidden2 = (frac_ptr[0] >> 52) & ((mp_limb_t) 1);
/* The high order 53 bits (52 + hidden) go into the upper double */
hi = (frac_ptr[0] >> 53) & (((mp_limb_t) 1 << 11) - 1);
hi |= (frac_ptr[1] << 11);
#else
#error "mp_limb size " BITS_PER_MP_LIMB "not accounted for"
#endif
if (lo != 0L)
{
/* hidden2 bit of low double controls rounding of the high double.
If hidden2 is '1' then round up hi and adjust lo (2nd mantissa)
plus change the sign of the low double to compensate. */
if (hidden2)
{
hi++;
u.ieee.negative2 = !sign;
lo = (1LL << 53) - lo;
}
/* The hidden bit of the lo mantissa is zero so we need to normalize
it for the low double. Shift it left until the hidden bit is '1'
then adjust the 2nd exponent accordingly. */
if (sizeof (lo) == sizeof (long))
lzcount = __builtin_clzl (lo);
else if ((lo >> 32) != 0)
lzcount = __builtin_clzl ((long) (lo >> 32));
else
lzcount = __builtin_clzl ((long) lo) + 32;
lzcount = lzcount - 11;
if (lzcount > 0)
{
lo = lo << lzcount;
u.ieee.exponent2 = u.ieee.exponent2 - lzcount;
}
}
else
{
u.ieee.negative2 = 0;
u.ieee.exponent2 = 0;
}
u.ieee.mantissa3 = lo & 0xffffffffLL;
u.ieee.mantissa2 = (lo >> 32) & 0xffffff;
u.ieee.mantissa1 = hi & 0xffffffffLL;
u.ieee.mantissa0 = (hi >> 32) & ((1LL << (LDBL_MANT_DIG - 86)) - 1);
return u.d;
}

138
sysdeps/ieee754/ldbl-128ibm/printf_fphex.c Normal file
View File

@ -0,0 +1,138 @@
/* Print floating point number in hexadecimal notation according to ISO C99.
Copyright (C) 1997,1998,1999,2000,2001,2002,2004,2006
Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#define PRINT_FPHEX_LONG_DOUBLE \
do { \
/* We have 105 bits of mantissa plus one implicit digit. Since \
106 bits are representable without rest using hexadecimal \
digits we use only the implicit digits for the number before \
the decimal point. */ \
unsigned long long int num0, num1; \
unsigned long long hi, lo; \
int ediff; \
union ibm_extended_long_double eldbl; \
eldbl.d = fpnum.ldbl.d; \
\
assert (sizeof (long double) == 16); \
\
lo = ((long long)eldbl.ieee.mantissa2 << 32) | eldbl.ieee.mantissa3; \
hi = ((long long)eldbl.ieee.mantissa0 << 32) | eldbl.ieee.mantissa1; \
/* If the lower double is not a denomal or zero then set the hidden \
53rd bit. */ \
if (eldbl.ieee.exponent2 > 0x001) \
{ \
lo |= (1ULL << 52); \
lo = lo << 7; /* pre-shift lo to match ieee854. */ \
/* The lower double is normalized separately from the upper. We \
may need to adjust the lower manitissa to reflect this. */ \
ediff = eldbl.ieee.exponent - eldbl.ieee.exponent2; \
if (ediff > 53) \
lo = lo >> (ediff-53); \
} \
\
if ((eldbl.ieee.negative != eldbl.ieee.negative2) \
&& ((eldbl.ieee.exponent2 != 0) && (lo != 0L))) \
{ \
lo = (1ULL << 60) - lo; \
if (hi == 0L) \
{ \
/* we have a borrow from the hidden bit, so shift left 1. */ \
hi = 0xffffffffffffeLL | (lo >> 59); \
lo = 0xfffffffffffffffLL & (lo << 1); \
eldbl.ieee.exponent--; \
} \
else \
hi--; \
} \
num1 = (hi << 60) | lo; \
num0 = hi >> 4; \
\
zero_mantissa = (num0|num1) == 0; \
\
if (sizeof (unsigned long int) > 6) \
{ \
numstr = _itoa_word (num1, numbuf + sizeof numbuf, 16, \
info->spec == 'A'); \
wnumstr = _itowa_word (num1, \
wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t),\
16, info->spec == 'A'); \
} \
else \
{ \
numstr = _itoa (num1, numbuf + sizeof numbuf, 16, \
info->spec == 'A'); \
wnumstr = _itowa (num1, \
wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t), \
16, info->spec == 'A'); \
} \
\
while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \
{ \
*--numstr = '0'; \
*--wnumstr = L'0'; \
} \
\
if (sizeof (unsigned long int) > 6) \
{ \
numstr = _itoa_word (num0, numstr, 16, info->spec == 'A'); \
wnumstr = _itowa_word (num0, wnumstr, 16, info->spec == 'A'); \
} \
else \
{ \
numstr = _itoa (num0, numstr, 16, info->spec == 'A'); \
wnumstr = _itowa (num0, wnumstr, 16, info->spec == 'A'); \
} \
\
/* Fill with zeroes. */ \
while (numstr > numbuf + (sizeof numbuf - 112 / 4)) \
{ \
*--numstr = '0'; \
*--wnumstr = L'0'; \
} \
\
leading = eldbl.ieee.exponent == 0 ? '0' : '1'; \
\
exponent = eldbl.ieee.exponent; \
\
if (exponent == 0) \
{ \
if (zero_mantissa) \
expnegative = 0; \
else \
{ \
/* This is a denormalized number. */ \
expnegative = 1; \
exponent = IBM_EXTENDED_LONG_DOUBLE_BIAS - 1; \
} \
} \
else if (exponent >= IBM_EXTENDED_LONG_DOUBLE_BIAS) \
{ \
expnegative = 0; \
exponent -= IBM_EXTENDED_LONG_DOUBLE_BIAS; \
} \
else \
{ \
expnegative = 1; \
exponent = -(exponent - IBM_EXTENDED_LONG_DOUBLE_BIAS); \
} \
} while (0)
#include <stdio-common/printf_fphex.c>

67
sysdeps/ieee754/ldbl-128ibm/s_asinhl.c Normal file
View File

@ -0,0 +1,67 @@
/* @(#)s_asinh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
#endif
/* asinh(x)
* Method :
* Based on
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
* we have
* asinh(x) := x if 1+x*x=1,
* := sign(x)*(log(x)+ln2)) for large |x|, else
* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
static const long double
#else
static long double
#endif
one = 1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */
ln2 = 0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */
huge= 1.00000000000000000000e+300L;
#ifdef __STDC__
long double __asinhl(long double x)
#else
long double __asinhl(x)
long double x;
#endif
{
long double t,w;
int64_t hx,ix;
GET_LDOUBLE_MSW64(hx,x);
ix = hx&0x7fffffffffffffffLL;
if(ix>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */
if(ix< 0x3e20000000000000LL) { /* |x|<2**-29 */
if(huge+x>one) return x; /* return x inexact except 0 */
}
if(ix>0x41b0000000000000LL) { /* |x| > 2**28 */
w = __ieee754_logl(fabs(x))+ln2;
} else if (ix>0x4000000000000000LL) { /* 2**28 > |x| > 2.0 */
t = fabs(x);
w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
} else { /* 2.0 > |x| > 2**-29 */
t = x*x;
w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
}
if(hx>0) return w; else return -w;
}
long_double_symbol (libm, __asinhl, asinhl);

234
sysdeps/ieee754/ldbl-128ibm/s_atanl.c Normal file
View File

@ -0,0 +1,234 @@
/* s_atanl.c
*
* Inverse circular tangent for 128-bit long double precision
* (arctangent)
*
*
*
* SYNOPSIS:
*
* long double x, y, atanl();
*
* y = atanl( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between -pi/2 and +pi/2 whose tangent is x.
*
* The function uses a rational approximation of the form
* t + t^3 P(t^2)/Q(t^2), optimized for |t| < 0.09375.
*
* The argument is reduced using the identity
* arctan x - arctan u = arctan ((x-u)/(1 + ux))
* and an 83-entry lookup table for arctan u, with u = 0, 1/8, ..., 10.25.
* Use of the table improves the execution speed of the routine.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -19, 19 4e5 1.7e-34 5.4e-35
*
*
* WARNING:
*
* This program uses integer operations on bit fields of floating-point
* numbers. It does not work with data structures other than the
* structure assumed.
*
*/
/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
#include "math_private.h"
#include <math_ldbl_opt.h>
/* arctan(k/8), k = 0, ..., 82 */
static const long double atantbl[84] = {
0.0000000000000000000000000000000000000000E0L,
1.2435499454676143503135484916387102557317E-1L, /* arctan(0.125) */
2.4497866312686415417208248121127581091414E-1L,
3.5877067027057222039592006392646049977698E-1L,
4.6364760900080611621425623146121440202854E-1L,
5.5859931534356243597150821640166127034645E-1L,
6.4350110879328438680280922871732263804151E-1L,
7.1882999962162450541701415152590465395142E-1L,
7.8539816339744830961566084581987572104929E-1L,
8.4415398611317100251784414827164750652594E-1L,
8.9605538457134395617480071802993782702458E-1L,
9.4200004037946366473793717053459358607166E-1L,
9.8279372324732906798571061101466601449688E-1L,
1.0191413442663497346383429170230636487744E0L,
1.0516502125483736674598673120862998296302E0L,
1.0808390005411683108871567292171998202703E0L,
1.1071487177940905030170654601785370400700E0L,
1.1309537439791604464709335155363278047493E0L,
1.1525719972156675180401498626127513797495E0L,
1.1722738811284763866005949441337046149712E0L,
1.1902899496825317329277337748293183376012E0L,
1.2068173702852525303955115800565576303133E0L,
1.2220253232109896370417417439225704908830E0L,
1.2360594894780819419094519711090786987027E0L,
1.2490457723982544258299170772810901230778E0L,
1.2610933822524404193139408812473357720101E0L,
1.2722973952087173412961937498224804940684E0L,
1.2827408797442707473628852511364955306249E0L,
1.2924966677897852679030914214070816845853E0L,
1.3016288340091961438047858503666855921414E0L,
1.3101939350475556342564376891719053122733E0L,
1.3182420510168370498593302023271362531155E0L,
1.3258176636680324650592392104284756311844E0L,
1.3329603993374458675538498697331558093700E0L,
1.3397056595989995393283037525895557411039E0L,
1.3460851583802539310489409282517796256512E0L,
1.3521273809209546571891479413898128509842E0L,
1.3578579772154994751124898859640585287459E0L,
1.3633001003596939542892985278250991189943E0L,
1.3684746984165928776366381936948529556191E0L,
1.3734007669450158608612719264449611486510E0L,
1.3780955681325110444536609641291551522494E0L,
1.3825748214901258580599674177685685125566E0L,
1.3868528702577214543289381097042486034883E0L,
1.3909428270024183486427686943836432060856E0L,
1.3948567013423687823948122092044222644895E0L,
1.3986055122719575950126700816114282335732E0L,
1.4021993871854670105330304794336492676944E0L,
1.4056476493802697809521934019958079881002E0L,
1.4089588955564736949699075250792569287156E0L,
1.4121410646084952153676136718584891599630E0L,
1.4152014988178669079462550975833894394929E0L,
1.4181469983996314594038603039700989523716E0L,
1.4209838702219992566633046424614466661176E0L,
1.4237179714064941189018190466107297503086E0L,
1.4263547484202526397918060597281265695725E0L,
1.4288992721907326964184700745371983590908E0L,
1.4313562697035588982240194668401779312122E0L,
1.4337301524847089866404719096698873648610E0L,
1.4360250423171655234964275337155008780675E0L,
1.4382447944982225979614042479354815855386E0L,
1.4403930189057632173997301031392126865694E0L,
1.4424730991091018200252920599377292525125E0L,
1.4444882097316563655148453598508037025938E0L,
1.4464413322481351841999668424758804165254E0L,
1.4483352693775551917970437843145232637695E0L,
1.4501726582147939000905940595923466567576E0L,
1.4519559822271314199339700039142990228105E0L,
1.4536875822280323362423034480994649820285E0L,
1.4553696664279718992423082296859928222270E0L,
1.4570043196511885530074841089245667532358E0L,
1.4585935117976422128825857356750737658039E0L,
1.4601391056210009726721818194296893361233E0L,
1.4616428638860188872060496086383008594310E0L,
1.4631064559620759326975975316301202111560E0L,
1.4645314639038178118428450961503371619177E0L,
1.4659193880646627234129855241049975398470E0L,
1.4672716522843522691530527207287398276197E0L,
1.4685896086876430842559640450619880951144E0L,
1.4698745421276027686510391411132998919794E0L,
1.4711276743037345918528755717617308518553E0L,
1.4723501675822635384916444186631899205983E0L,
1.4735431285433308455179928682541563973416E0L, /* arctan(10.25) */
1.5707963267948966192313216916397514420986E0L /* pi/2 */
};
/* arctan t = t + t^3 p(t^2) / q(t^2)
|t| <= 0.09375
peak relative error 5.3e-37 */
static const long double
p0 = -4.283708356338736809269381409828726405572E1L,
p1 = -8.636132499244548540964557273544599863825E1L,
p2 = -5.713554848244551350855604111031839613216E1L,
p3 = -1.371405711877433266573835355036413750118E1L,
p4 = -8.638214309119210906997318946650189640184E-1L,
q0 = 1.285112506901621042780814422948906537959E2L,
q1 = 3.361907253914337187957855834229672347089E2L,
q2 = 3.180448303864130128268191635189365331680E2L,
q3 = 1.307244136980865800160844625025280344686E2L,
q4 = 2.173623741810414221251136181221172551416E1L;
/* q5 = 1.000000000000000000000000000000000000000E0 */
long double
__atanl (long double x)
{
int k, sign;
long double t, u, p, q;
ieee854_long_double_shape_type s;
s.value = x;
k = s.parts32.w0;
if (k & 0x80000000)
sign = 1;
else
sign = 0;
/* Check for IEEE special cases. */
k &= 0x7fffffff;
if (k >= 0x7ff00000)
{
/* NaN. */
if ((k & 0xfffff) | s.parts32.w1 )
return (x + x);
/* Infinity. */
if (sign)
return -atantbl[83];
else
return atantbl[83];
}
if (sign)
x = -x;
if (k >= 0x40248000) /* 10.25 */
{
k = 83;
t = -1.0/x;
}
else
{
/* Index of nearest table element.
Roundoff to integer is asymmetrical to avoid cancellation when t < 0
(cf. fdlibm). */
k = 8.0 * x + 0.25;
u = 0.125 * k;
/* Small arctan argument. */
t = (x - u) / (1.0 + x * u);
}
/* Arctan of small argument t. */
u = t * t;
p = ((((p4 * u) + p3) * u + p2) * u + p1) * u + p0;
q = ((((u + q4) * u + q3) * u + q2) * u + q1) * u + q0;
u = t * u * p / q + t;
/* arctan x = arctan u + arctan t */
u = atantbl[k] + u;
if (sign)
return (-u);
else
return u;
}
long_double_symbol (libm, __atanl, atanl);

6
sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c Normal file
View File

@ -0,0 +1,6 @@
/* Looks like we can use ieee854 s_cbrtl.c as is for IBM extended format. */
#include <math_ldbl_opt.h>
#undef weak_alias
#define weak_alias(n,a)
#include <sysdeps/ieee754/ldbl-128/s_cbrtl.c>
long_double_symbol (libm, __cbrtl, cbrtl);

119
sysdeps/ieee754/ldbl-128ibm/s_ceill.c Normal file
View File

@ -0,0 +1,119 @@
/* Ceil (round to +inf) long double floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <fenv.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long double
__ceill (long double x)
#else
long double
__ceill (x)
long double x;
#endif
{
static const double TWO52 = 4503599627370496.0L;
int mode = fegetround();
union ibm_extended_long_double u;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
fesetround(FE_UPWARD);
if (u.dd[0] > 0.0)
{
u.dd[0] += TWO52;
u.dd[0] -= TWO52;
}
else if (u.dd[0] < 0.0)
{
u.dd[0] -= TWO52;
u.dd[0] += TWO52;
}
u.dd[1] = 0.0;
fesetround(mode);
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_UPWARD);
low += TWO52;
low -= TWO52;
fesetround(mode);
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_UPWARD);
low -= TWO52;
low += TWO52;
fesetround(mode);
}
u.dd[0] = high + low;
u.dd[1] = high - u.dd[0] + low;
}
return u.d;
}
long_double_symbol (libm, __ceill, ceill);

45
sysdeps/ieee754/ldbl-128ibm/s_copysignl.c Normal file
View File

@ -0,0 +1,45 @@
/* s_copysignl.c -- long double version of s_copysign.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* copysignl(long double x, long double y)
* copysignl(x,y) returns a value with the magnitude of x and
* with the sign bit of y.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
long double __copysignl(long double x, long double y)
#else
long double __copysignl(x,y)
long double x,y;
#endif
{
if (y < 0.0)
{
if (x >= 0.0)
x = -x;
}
else if (x < 0.0)
x = -x;
return x;
}
weak_alias (__copysignl, copysignl)

88
sysdeps/ieee754/ldbl-128ibm/s_cosl.c Normal file
View File

@ -0,0 +1,88 @@
/* s_cosl.c -- long double version of s_cos.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* cosl(x)
* Return cosine function of x.
*
* kernel function:
* __kernel_sinl ... sine function on [-pi/4,pi/4]
* __kernel_cosl ... cosine function on [-pi/4,pi/4]
* __ieee754_rem_pio2l ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
long double __cosl(long double x)
#else
long double __cosl(x)
long double x;
#endif
{
long double y[2],z=0.0L;
int64_t n, ix;
/* High word of x. */
GET_LDOUBLE_MSW64(ix,x);
/* |x| ~< pi/4 */
ix &= 0x7fffffffffffffffLL;
if(ix <= 0x3fe921fb54442d18LL)
return __kernel_cosl(x,z);
/* cos(Inf or NaN) is NaN */
else if (ix>=0x7ff0000000000000LL)
return x-x;
/* argument reduction needed */
else {
n = __ieee754_rem_pio2l(x,y);
switch(n&3) {
case 0:
return __kernel_cosl(y[0],y[1]);
case 1:
return -__kernel_sinl(y[0],y[1],1);
case 2:
return -__kernel_cosl(y[0],y[1]);
default:
return __kernel_sinl(y[0],y[1],1);
}
}
}
long_double_symbol (libm, __cosl, cosl);

958
sysdeps/ieee754/ldbl-128ibm/s_erfl.c Normal file
View File

@ -0,0 +1,958 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* Modifications and expansions for 128-bit long double are
Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
and are incorporated herein by permission of the author. The author
reserves the right to distribute this material elsewhere under different
copying permissions. These modifications are distributed here under
the following terms:
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* double erf(double x)
* double erfc(double x)
* x
* 2 |\
* erf(x) = --------- | exp(-t*t)dt
* sqrt(pi) \|
* 0
*
* erfc(x) = 1-erf(x)
* Note that
* erf(-x) = -erf(x)
* erfc(-x) = 2 - erfc(x)
*
* Method:
* 1. erf(x) = x + x*R(x^2) for |x| in [0, 7/8]
* Remark. The formula is derived by noting
* erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....)
* and that
* 2/sqrt(pi) = 1.128379167095512573896158903121545171688
* is close to one.
*
* 1a. erf(x) = 1 - erfc(x), for |x| > 1.0
* erfc(x) = 1 - erf(x) if |x| < 1/4
*
* 2. For |x| in [7/8, 1], let s = |x| - 1, and
* c = 0.84506291151 rounded to single (24 bits)
* erf(s + c) = sign(x) * (c + P1(s)/Q1(s))
* Remark: here we use the taylor series expansion at x=1.
* erf(1+s) = erf(1) + s*Poly(s)
* = 0.845.. + P1(s)/Q1(s)
* Note that |P1/Q1|< 0.078 for x in [0.84375,1.25]
*
* 3. For x in [1/4, 5/4],
* erfc(s + const) = erfc(const) + s P1(s)/Q1(s)
* for const = 1/4, 3/8, ..., 9/8
* and 0 <= s <= 1/8 .
*
* 4. For x in [5/4, 107],
* erfc(x) = (1/x)*exp(-x*x-0.5625 + R(z))
* z=1/x^2
* The interval is partitioned into several segments
* of width 1/8 in 1/x.
*
* Note1:
* To compute exp(-x*x-0.5625+R/S), let s be a single
* precision number and s := x; then
* -x*x = -s*s + (s-x)*(s+x)
* exp(-x*x-0.5626+R/S) =
* exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S);
* Note2:
* Here 4 and 5 make use of the asymptotic series
* exp(-x*x)
* erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) )
* x*sqrt(pi)
*
* 5. For inf > x >= 107
* erf(x) = sign(x) *(1 - tiny) (raise inexact)
* erfc(x) = tiny*tiny (raise underflow) if x > 0
* = 2 - tiny if x<0
*
* 7. Special case:
* erf(0) = 0, erf(inf) = 1, erf(-inf) = -1,
* erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2,
* erfc/erf(NaN) is NaN
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
static long double
neval (long double x, const long double *p, int n)
{
long double y;
p += n;
y = *p--;
do
{
y = y * x + *p--;
}
while (--n > 0);
return y;
}
/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
static long double
deval (long double x, const long double *p, int n)
{
long double y;
p += n;
y = x + *p--;
do
{
y = y * x + *p--;
}
while (--n > 0);
return y;
}
#ifdef __STDC__
static const long double
#else
static long double
#endif
tiny = 1e-300L,
half = 0.5L,
one = 1.0L,
two = 2.0L,
/* 2/sqrt(pi) - 1 */
efx = 1.2837916709551257389615890312154517168810E-1L,
/* 8 * (2/sqrt(pi) - 1) */
efx8 = 1.0270333367641005911692712249723613735048E0L;
/* erf(x) = x + x R(x^2)
0 <= x <= 7/8
Peak relative error 1.8e-35 */
#define NTN1 8
static const long double TN1[NTN1 + 1] =
{
-3.858252324254637124543172907442106422373E10L,
9.580319248590464682316366876952214879858E10L,
1.302170519734879977595901236693040544854E10L,
2.922956950426397417800321486727032845006E9L,
1.764317520783319397868923218385468729799E8L,
1.573436014601118630105796794840834145120E7L,
4.028077380105721388745632295157816229289E5L,
1.644056806467289066852135096352853491530E4L,
3.390868480059991640235675479463287886081E1L
};
#define NTD1 8
static const long double TD1[NTD1 + 1] =
{
-3.005357030696532927149885530689529032152E11L,
-1.342602283126282827411658673839982164042E11L,
-2.777153893355340961288511024443668743399E10L,
-3.483826391033531996955620074072768276974E9L,
-2.906321047071299585682722511260895227921E8L,
-1.653347985722154162439387878512427542691E7L,
-6.245520581562848778466500301865173123136E5L,
-1.402124304177498828590239373389110545142E4L,
-1.209368072473510674493129989468348633579E2L
/* 1.0E0 */
};
/* erf(z+1) = erf_const + P(z)/Q(z)
-.125 <= z <= 0
Peak relative error 7.3e-36 */
static const long double erf_const = 0.845062911510467529296875L;
#define NTN2 8
static const long double TN2[NTN2 + 1] =
{
-4.088889697077485301010486931817357000235E1L,
7.157046430681808553842307502826960051036E3L,
-2.191561912574409865550015485451373731780E3L,
2.180174916555316874988981177654057337219E3L,
2.848578658049670668231333682379720943455E2L,
1.630362490952512836762810462174798925274E2L,
6.317712353961866974143739396865293596895E0L,
2.450441034183492434655586496522857578066E1L,
5.127662277706787664956025545897050896203E-1L
};
#define NTD2 8
static const long double TD2[NTD2 + 1] =
{
1.731026445926834008273768924015161048885E4L,
1.209682239007990370796112604286048173750E4L,
1.160950290217993641320602282462976163857E4L,
5.394294645127126577825507169061355698157E3L,
2.791239340533632669442158497532521776093E3L,
8.989365571337319032943005387378993827684E2L,
2.974016493766349409725385710897298069677E2L,
6.148192754590376378740261072533527271947E1L,
1.178502892490738445655468927408440847480E1L
/* 1.0E0 */
};
/* erfc(x + 0.25) = erfc(0.25) + x R(x)
0 <= x < 0.125
Peak relative error 1.4e-35 */
#define NRNr13 8
static const long double RNr13[NRNr13 + 1] =
{
-2.353707097641280550282633036456457014829E3L,
3.871159656228743599994116143079870279866E2L,
-3.888105134258266192210485617504098426679E2L,
-2.129998539120061668038806696199343094971E1L,
-8.125462263594034672468446317145384108734E1L,
8.151549093983505810118308635926270319660E0L,
-5.033362032729207310462422357772568553670E0L,
-4.253956621135136090295893547735851168471E-2L,
-8.098602878463854789780108161581050357814E-2L
};
#define NRDr13 7
static const long double RDr13[NRDr13 + 1] =
{
2.220448796306693503549505450626652881752E3L,
1.899133258779578688791041599040951431383E2L,
1.061906712284961110196427571557149268454E3L,
7.497086072306967965180978101974566760042E1L,
2.146796115662672795876463568170441327274E2L,
1.120156008362573736664338015952284925592E1L,
2.211014952075052616409845051695042741074E1L,
6.469655675326150785692908453094054988938E-1L
/* 1.0E0 */
};
/* erfc(0.25) = C13a + C13b to extra precision. */
static const long double C13a = 0.723663330078125L;
static const long double C13b = 1.0279753638067014931732235184287934646022E-5L;
/* erfc(x + 0.375) = erfc(0.375) + x R(x)
0 <= x < 0.125
Peak relative error 1.2e-35 */
#define NRNr14 8
static const long double RNr14[NRNr14 + 1] =
{
-2.446164016404426277577283038988918202456E3L,
6.718753324496563913392217011618096698140E2L,
-4.581631138049836157425391886957389240794E2L,
-2.382844088987092233033215402335026078208E1L,
-7.119237852400600507927038680970936336458E1L,
1.313609646108420136332418282286454287146E1L,
-6.188608702082264389155862490056401365834E0L,
-2.787116601106678287277373011101132659279E-2L,
-2.230395570574153963203348263549700967918E-2L
};
#define NRDr14 7
static const long double RDr14[NRDr14 + 1] =
{
2.495187439241869732696223349840963702875E3L,
2.503549449872925580011284635695738412162E2L,
1.159033560988895481698051531263861842461E3L,
9.493751466542304491261487998684383688622E1L,
2.276214929562354328261422263078480321204E2L,
1.367697521219069280358984081407807931847E1L,
2.276988395995528495055594829206582732682E1L,
7.647745753648996559837591812375456641163E-1L
/* 1.0E0 */
};
/* erfc(0.375) = C14a + C14b to extra precision. */
static const long double C14a = 0.5958709716796875L;
static const long double C14b = 1.2118885490201676174914080878232469565953E-5L;
/* erfc(x + 0.5) = erfc(0.5) + x R(x)
0 <= x < 0.125
Peak relative error 4.7e-36 */
#define NRNr15 8
static const long double RNr15[NRNr15 + 1] =
{
-2.624212418011181487924855581955853461925E3L,
8.473828904647825181073831556439301342756E2L,
-5.286207458628380765099405359607331669027E2L,
-3.895781234155315729088407259045269652318E1L,
-6.200857908065163618041240848728398496256E1L,
1.469324610346924001393137895116129204737E1L,
-6.961356525370658572800674953305625578903E0L,
5.145724386641163809595512876629030548495E-3L,
1.990253655948179713415957791776180406812E-2L
};
#define NRDr15 7
static const long double RDr15[NRDr15 + 1] =
{
2.986190760847974943034021764693341524962E3L,
5.288262758961073066335410218650047725985E2L,
1.363649178071006978355113026427856008978E3L,
1.921707975649915894241864988942255320833E2L,
2.588651100651029023069013885900085533226E2L,
2.628752920321455606558942309396855629459E1L,
2.455649035885114308978333741080991380610E1L,
1.378826653595128464383127836412100939126E0L
/* 1.0E0 */
};
/* erfc(0.5) = C15a + C15b to extra precision. */
static const long double C15a = 0.4794921875L;
static const long double C15b = 7.9346869534623172533461080354712635484242E-6L;
/* erfc(x + 0.625) = erfc(0.625) + x R(x)
0 <= x < 0.125
Peak relative error 5.1e-36 */
#define NRNr16 8
static const long double RNr16[NRNr16 + 1] =
{
-2.347887943200680563784690094002722906820E3L,
8.008590660692105004780722726421020136482E2L,
-5.257363310384119728760181252132311447963E2L,
-4.471737717857801230450290232600243795637E1L,
-4.849540386452573306708795324759300320304E1L,
1.140885264677134679275986782978655952843E1L,
-6.731591085460269447926746876983786152300E0L,
1.370831653033047440345050025876085121231E-1L,
2.022958279982138755020825717073966576670E-2L,
};
#define NRDr16 7
static const long double RDr16[NRDr16 + 1] =
{
3.075166170024837215399323264868308087281E3L,
8.730468942160798031608053127270430036627E2L,
1.458472799166340479742581949088453244767E3L,
3.230423687568019709453130785873540386217E2L,
2.804009872719893612081109617983169474655E2L,
4.465334221323222943418085830026979293091E1L,
2.612723259683205928103787842214809134746E1L,
2.341526751185244109722204018543276124997E0L,
/* 1.0E0 */
};
/* erfc(0.625) = C16a + C16b to extra precision. */
static const long double C16a = 0.3767547607421875L;
static const long double C16b = 4.3570693945275513594941232097252997287766E-6L;
/* erfc(x + 0.75) = erfc(0.75) + x R(x)
0 <= x < 0.125
Peak relative error 1.7e-35 */
#define NRNr17 8
static const long double RNr17[NRNr17 + 1] =
{
-1.767068734220277728233364375724380366826E3L,
6.693746645665242832426891888805363898707E2L,
-4.746224241837275958126060307406616817753E2L,
-2.274160637728782675145666064841883803196E1L,
-3.541232266140939050094370552538987982637E1L,
6.988950514747052676394491563585179503865E0L,
-5.807687216836540830881352383529281215100E0L,
3.631915988567346438830283503729569443642E-1L,
-1.488945487149634820537348176770282391202E-2L
};
#define NRDr17 7
static const long double RDr17[NRDr17 + 1] =
{
2.748457523498150741964464942246913394647E3L,
1.020213390713477686776037331757871252652E3L,
1.388857635935432621972601695296561952738E3L,
3.903363681143817750895999579637315491087E2L,
2.784568344378139499217928969529219886578E2L,
5.555800830216764702779238020065345401144E1L,
2.646215470959050279430447295801291168941E1L,
2.984905282103517497081766758550112011265E0L,
/* 1.0E0 */
};
/* erfc(0.75) = C17a + C17b to extra precision. */
static const long double C17a = 0.2888336181640625L;
static const long double C17b = 1.0748182422368401062165408589222625794046E-5L;
/* erfc(x + 0.875) = erfc(0.875) + x R(x)
0 <= x < 0.125
Peak relative error 2.2e-35 */
#define NRNr18 8
static const long double RNr18[NRNr18 + 1] =
{
-1.342044899087593397419622771847219619588E3L,
6.127221294229172997509252330961641850598E2L,
-4.519821356522291185621206350470820610727E2L,
1.223275177825128732497510264197915160235E1L,
-2.730789571382971355625020710543532867692E1L,
4.045181204921538886880171727755445395862E0L,
-4.925146477876592723401384464691452700539E0L,
5.933878036611279244654299924101068088582E-1L,
-5.557645435858916025452563379795159124753E-2L
};
#define NRDr18 7
static const long double RDr18[NRDr18 + 1] =
{
2.557518000661700588758505116291983092951E3L,
1.070171433382888994954602511991940418588E3L,
1.344842834423493081054489613250688918709E3L,
4.161144478449381901208660598266288188426E2L,
2.763670252219855198052378138756906980422E2L,
5.998153487868943708236273854747564557632E1L,
2.657695108438628847733050476209037025318E1L,
3.252140524394421868923289114410336976512E0L,
/* 1.0E0 */
};
/* erfc(0.875) = C18a + C18b to extra precision. */
static const long double C18a = 0.215911865234375L;
static const long double C18b = 1.3073705765341685464282101150637224028267E-5L;
/* erfc(x + 1.0) = erfc(1.0) + x R(x)
0 <= x < 0.125
Peak relative error 1.6e-35 */
#define NRNr19 8
static const long double RNr19[NRNr19 + 1] =
{
-1.139180936454157193495882956565663294826E3L,
6.134903129086899737514712477207945973616E2L,
-4.628909024715329562325555164720732868263E2L,
4.165702387210732352564932347500364010833E1L,
-2.286979913515229747204101330405771801610E1L,
1.870695256449872743066783202326943667722E0L,
-4.177486601273105752879868187237000032364E0L,
7.533980372789646140112424811291782526263E-1L,
-8.629945436917752003058064731308767664446E-2L
};
#define NRDr19 7
static const long double RDr19[NRDr19 + 1] =
{
2.744303447981132701432716278363418643778E3L,
1.266396359526187065222528050591302171471E3L,
1.466739461422073351497972255511919814273E3L,
4.868710570759693955597496520298058147162E2L,
2.993694301559756046478189634131722579643E2L,
6.868976819510254139741559102693828237440E1L,
2.801505816247677193480190483913753613630E1L,
3.604439909194350263552750347742663954481E0L,
/* 1.0E0 */
};
/* erfc(1.0) = C19a + C19b to extra precision. */
static const long double C19a = 0.15728759765625L;
static const long double C19b = 1.1609394035130658779364917390740703933002E-5L;
/* erfc(x + 1.125) = erfc(1.125) + x R(x)
0 <= x < 0.125
Peak relative error 3.6e-36 */
#define NRNr20 8
static const long double RNr20[NRNr20 + 1] =
{
-9.652706916457973956366721379612508047640E2L,
5.577066396050932776683469951773643880634E2L,
-4.406335508848496713572223098693575485978E2L,
5.202893466490242733570232680736966655434E1L,
-1.931311847665757913322495948705563937159E1L,
-9.364318268748287664267341457164918090611E-2L,
-3.306390351286352764891355375882586201069E0L,
7.573806045289044647727613003096916516475E-1L,
-9.611744011489092894027478899545635991213E-2L
};
#define NRDr20 7
static const long double RDr20[NRDr20 + 1] =
{
3.032829629520142564106649167182428189014E3L,
1.659648470721967719961167083684972196891E3L,
1.703545128657284619402511356932569292535E3L,
6.393465677731598872500200253155257708763E2L,
3.489131397281030947405287112726059221934E2L,
8.848641738570783406484348434387611713070E1L,
3.132269062552392974833215844236160958502E1L,
4.430131663290563523933419966185230513168E0L
/* 1.0E0 */
};
/* erfc(1.125) = C20a + C20b to extra precision. */
static const long double C20a = 0.111602783203125L;
static const long double C20b = 8.9850951672359304215530728365232161564636E-6L;
/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2))
7/8 <= 1/x < 1
Peak relative error 1.4e-35 */
#define NRNr8 9
static const long double RNr8[NRNr8 + 1] =
{
3.587451489255356250759834295199296936784E1L,
5.406249749087340431871378009874875889602E2L,
2.931301290625250886238822286506381194157E3L,
7.359254185241795584113047248898753470923E3L,
9.201031849810636104112101947312492532314E3L,
5.749697096193191467751650366613289284777E3L,
1.710415234419860825710780802678697889231E3L,
2.150753982543378580859546706243022719599E2L,
8.740953582272147335100537849981160931197E0L,
4.876422978828717219629814794707963640913E-2L
};
#define NRDr8 8
static const long double RDr8[NRDr8 + 1] =
{
6.358593134096908350929496535931630140282E1L,
9.900253816552450073757174323424051765523E2L,
5.642928777856801020545245437089490805186E3L,
1.524195375199570868195152698617273739609E4L,
2.113829644500006749947332935305800887345E4L,
1.526438562626465706267943737310282977138E4L,
5.561370922149241457131421914140039411782E3L,
9.394035530179705051609070428036834496942E2L,
6.147019596150394577984175188032707343615E1L
/* 1.0E0 */
};
/* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2))
0.75 <= 1/x <= 0.875
Peak relative error 2.0e-36 */
#define NRNr7 9
static const long double RNr7[NRNr7 + 1] =
{
1.686222193385987690785945787708644476545E1L,
1.178224543567604215602418571310612066594E3L,
1.764550584290149466653899886088166091093E4L,
1.073758321890334822002849369898232811561E5L,
3.132840749205943137619839114451290324371E5L,
4.607864939974100224615527007793867585915E5L,
3.389781820105852303125270837910972384510E5L,
1.174042187110565202875011358512564753399E5L,
1.660013606011167144046604892622504338313E4L,
6.700393957480661937695573729183733234400E2L
};
#define NRDr7 9
static const long double RDr7[NRDr7 + 1] =
{
-1.709305024718358874701575813642933561169E3L,
-3.280033887481333199580464617020514788369E4L,
-2.345284228022521885093072363418750835214E5L,
-8.086758123097763971926711729242327554917E5L,
-1.456900414510108718402423999575992450138E6L,
-1.391654264881255068392389037292702041855E6L,
-6.842360801869939983674527468509852583855E5L,
-1.597430214446573566179675395199807533371E5L,
-1.488876130609876681421645314851760773480E4L,
-3.511762950935060301403599443436465645703E2L
/* 1.0E0 */
};
/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
5/8 <= 1/x < 3/4
Peak relative error 1.9e-35 */
#define NRNr6 9
static const long double RNr6[NRNr6 + 1] =
{
1.642076876176834390623842732352935761108E0L,
1.207150003611117689000664385596211076662E2L,
2.119260779316389904742873816462800103939E3L,
1.562942227734663441801452930916044224174E4L,
5.656779189549710079988084081145693580479E4L,
1.052166241021481691922831746350942786299E5L,
9.949798524786000595621602790068349165758E4L,
4.491790734080265043407035220188849562856E4L,
8.377074098301530326270432059434791287601E3L,
4.506934806567986810091824791963991057083E2L
};
#define NRDr6 9
static const long double RDr6[NRDr6 + 1] =
{
-1.664557643928263091879301304019826629067E2L,
-3.800035902507656624590531122291160668452E3L,
-3.277028191591734928360050685359277076056E4L,
-1.381359471502885446400589109566587443987E5L,
-3.082204287382581873532528989283748656546E5L,
-3.691071488256738343008271448234631037095E5L,
-2.300482443038349815750714219117566715043E5L,
-6.873955300927636236692803579555752171530E4L,
-8.262158817978334142081581542749986845399E3L,
-2.517122254384430859629423488157361983661E2L
/* 1.00 */
};
/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
1/2 <= 1/x < 5/8
Peak relative error 4.6e-36 */
#define NRNr5 10
static const long double RNr5[NRNr5 + 1] =
{
-3.332258927455285458355550878136506961608E-3L,
-2.697100758900280402659586595884478660721E-1L,
-6.083328551139621521416618424949137195536E0L,
-6.119863528983308012970821226810162441263E1L,
-3.176535282475593173248810678636522589861E2L,
-8.933395175080560925809992467187963260693E2L,
-1.360019508488475978060917477620199499560E3L,
-1.075075579828188621541398761300910213280E3L,
-4.017346561586014822824459436695197089916E2L,
-5.857581368145266249509589726077645791341E1L,
-2.077715925587834606379119585995758954399E0L
};
#define NRDr5 9
static const long double RDr5[NRDr5 + 1] =
{
3.377879570417399341550710467744693125385E-1L,
1.021963322742390735430008860602594456187E1L,
1.200847646592942095192766255154827011939E2L,
7.118915528142927104078182863387116942836E2L,
2.318159380062066469386544552429625026238E3L,
4.238729853534009221025582008928765281620E3L,
4.279114907284825886266493994833515580782E3L,
2.257277186663261531053293222591851737504E3L,
5.570475501285054293371908382916063822957E2L,
5.142189243856288981145786492585432443560E1L
/* 1.0E0 */
};
/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
3/8 <= 1/x < 1/2
Peak relative error 2.0e-36 */
#define NRNr4 10
static const long double RNr4[NRNr4 + 1] =
{
3.258530712024527835089319075288494524465E-3L,
2.987056016877277929720231688689431056567E-1L,
8.738729089340199750734409156830371528862E0L,
1.207211160148647782396337792426311125923E2L,
8.997558632489032902250523945248208224445E2L,
3.798025197699757225978410230530640879762E3L,
9.113203668683080975637043118209210146846E3L,
1.203285891339933238608683715194034900149E4L,
8.100647057919140328536743641735339740855E3L,
2.383888249907144945837976899822927411769E3L,
2.127493573166454249221983582495245662319E2L
};
#define NRDr4 10
static const long double RDr4[NRDr4 + 1] =
{
-3.303141981514540274165450687270180479586E-1L,
-1.353768629363605300707949368917687066724E1L,
-2.206127630303621521950193783894598987033E2L,
-1.861800338758066696514480386180875607204E3L,
-8.889048775872605708249140016201753255599E3L,
-2.465888106627948210478692168261494857089E4L,
-3.934642211710774494879042116768390014289E4L,
-3.455077258242252974937480623730228841003E4L,
-1.524083977439690284820586063729912653196E4L,
-2.810541887397984804237552337349093953857E3L,
-1.343929553541159933824901621702567066156E2L
/* 1.0E0 */
};
/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
1/4 <= 1/x < 3/8
Peak relative error 8.4e-37 */
#define NRNr3 11
static const long double RNr3[NRNr3 + 1] =
{
-1.952401126551202208698629992497306292987E-6L,
-2.130881743066372952515162564941682716125E-4L,
-8.376493958090190943737529486107282224387E-3L,
-1.650592646560987700661598877522831234791E-1L,
-1.839290818933317338111364667708678163199E0L,
-1.216278715570882422410442318517814388470E1L,
-4.818759344462360427612133632533779091386E1L,
-1.120994661297476876804405329172164436784E2L,
-1.452850765662319264191141091859300126931E2L,
-9.485207851128957108648038238656777241333E1L,
-2.563663855025796641216191848818620020073E1L,
-1.787995944187565676837847610706317833247E0L
};
#define NRDr3 10
static const long double RDr3[NRDr3 + 1] =
{
1.979130686770349481460559711878399476903E-4L,
1.156941716128488266238105813374635099057E-2L,
2.752657634309886336431266395637285974292E-1L,
3.482245457248318787349778336603569327521E0L,
2.569347069372696358578399521203959253162E1L,
1.142279000180457419740314694631879921561E2L,
3.056503977190564294341422623108332700840E2L,
4.780844020923794821656358157128719184422E2L,
4.105972727212554277496256802312730410518E2L,
1.724072188063746970865027817017067646246E2L,
2.815939183464818198705278118326590370435E1L
/* 1.0E0 */
};
/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
1/8 <= 1/x < 1/4
Peak relative error 1.5e-36 */
#define NRNr2 11
static const long double RNr2[NRNr2 + 1] =
{
-2.638914383420287212401687401284326363787E-8L,
-3.479198370260633977258201271399116766619E-6L,
-1.783985295335697686382487087502222519983E-4L,
-4.777876933122576014266349277217559356276E-3L,
-7.450634738987325004070761301045014986520E-2L,
-7.068318854874733315971973707247467326619E-1L,
-4.113919921935944795764071670806867038732E0L,
-1.440447573226906222417767283691888875082E1L,
-2.883484031530718428417168042141288943905E1L,
-2.990886974328476387277797361464279931446E1L,
-1.325283914915104866248279787536128997331E1L,
-1.572436106228070195510230310658206154374E0L
};
#define NRDr2 10
static const long double RDr2[NRDr2 + 1] =
{
2.675042728136731923554119302571867799673E-6L,
2.170997868451812708585443282998329996268E-4L,
7.249969752687540289422684951196241427445E-3L,
1.302040375859768674620410563307838448508E-1L,
1.380202483082910888897654537144485285549E0L,
8.926594113174165352623847870299170069350E0L,
3.521089584782616472372909095331572607185E1L,
8.233547427533181375185259050330809105570E1L,
1.072971579885803033079469639073292840135E2L,
6.943803113337964469736022094105143158033E1L,
1.775695341031607738233608307835017282662E1L
/* 1.0E0 */
};
/* erfc(1/x) = 1/x exp(-1/x^2 - 0.5625 + R(1/x^2))
1/128 <= 1/x < 1/8
Peak relative error 2.2e-36 */
#define NRNr1 9
static const long double RNr1[NRNr1 + 1] =
{
-4.250780883202361946697751475473042685782E-8L,
-5.375777053288612282487696975623206383019E-6L,
-2.573645949220896816208565944117382460452E-4L,
-6.199032928113542080263152610799113086319E-3L,
-8.262721198693404060380104048479916247786E-2L,
-6.242615227257324746371284637695778043982E-1L,
-2.609874739199595400225113299437099626386E0L,
-5.581967563336676737146358534602770006970E0L,
-5.124398923356022609707490956634280573882E0L,
-1.290865243944292370661544030414667556649E0L
};
#define NRDr1 8
static const long double RDr1[NRDr1 + 1] =
{
4.308976661749509034845251315983612976224E-6L,
3.265390126432780184125233455960049294580E-4L,
9.811328839187040701901866531796570418691E-3L,
1.511222515036021033410078631914783519649E-1L,
1.289264341917429958858379585970225092274E0L,
6.147640356182230769548007536914983522270E0L,
1.573966871337739784518246317003956180750E1L,
1.955534123435095067199574045529218238263E1L,
9.472613121363135472247929109615785855865E0L
/* 1.0E0 */
};
#ifdef __STDC__
long double
__erfl (long double x)
#else
double
__erfl (x)
long double x;
#endif
{
long double a, y, z;
int32_t i, ix, sign;
ieee854_long_double_shape_type u;
u.value = x;
sign = u.parts32.w0;
ix = sign & 0x7fffffff;
if (ix >= 0x7ff00000)
{ /* erf(nan)=nan */
i = ((sign & 0xfff00000) >> 31) << 1;
return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */
}
if (ix >= 0x3ff00000) /* |x| >= 1.0 */
{
y = __erfcl (x);
return (one - y);
/* return (one - __erfcl (x)); */
}
u.parts32.w0 = ix;
a = u.value;
z = x * x;
if (ix < 0x3fec0000) /* a < 0.875 */
{
if (ix < 0x3c600000) /* |x|<2**-57 */
{
if (ix < 0x00800000)
{
/* erf (-0) = -0. Unfortunately, for IBM extended double
0.125 * (8.0 * x + efx8 * x) for x = -0 evaluates to 0. */
if (x == 0)
return x;
return 0.125 * (8.0 * x + efx8 * x); /*avoid underflow */
}
return x + efx * x;
}
y = a + a * neval (z, TN1, NTN1) / deval (z, TD1, NTD1);
}
else
{
a = a - one;
y = erf_const + neval (a, TN2, NTN2) / deval (a, TD2, NTD2);
}
if (sign & 0x80000000) /* x < 0 */
y = -y;
return( y );
}
long_double_symbol (libm, __erfl, erfl);
#ifdef __STDC__
long double
__erfcl (long double x)
#else
long double
__erfcl (x)
double
x;
#endif
{
long double y, z, p, r;
int32_t i, ix, sign;
ieee854_long_double_shape_type u;
u.value = x;
sign = u.parts32.w0;
ix = sign & 0x7fffffff;
u.parts32.w0 = ix;
if (ix >= 0x7ff00000)
{ /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
return (long double) (((u_int32_t) sign >> 31) << 1) + one / x;
}
if (ix < 0x3fd00000) /* |x| <1/4 */
{
if (ix < 0x38d00000) /* |x|<2**-114 */
return one - x;
return one - __erfl (x);
}
if (ix < 0x3ff40000) /* 1.25 */
{
x = u.value;
i = 8.0 * x;
switch (i)
{
case 2:
z = x - 0.25L;
y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13);
y += C13a;
break;
case 3:
z = x - 0.375L;
y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14);
y += C14a;
break;
case 4:
z = x - 0.5L;
y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15);
y += C15a;
break;
case 5:
z = x - 0.625L;
y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16);
y += C16a;
break;
case 6:
z = x - 0.75L;
y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17);
y += C17a;
break;
case 7:
z = x - 0.875L;
y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18);
y += C18a;
break;
case 8:
z = x - 1.0L;
y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19);
y += C19a;
break;
case 9:
z = x - 1.125L;
y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20);
y += C20a;
break;
}
if (sign & 0x80000000)
y = 2.0L - y;
return y;
}
/* 1.25 < |x| < 107 */
if (ix < 0x405ac000)
{
/* x < -9 */
if ((ix >= 0x40220000) && (sign & 0x80000000))
return two - tiny;
x = fabsl (x);
z = one / (x * x);
i = 8.0 / x;
switch (i)
{
default:
case 0:
p = neval (z, RNr1, NRNr1) / deval (z, RDr1, NRDr1);
break;
case 1:
p = neval (z, RNr2, NRNr2) / deval (z, RDr2, NRDr2);
break;
case 2:
p = neval (z, RNr3, NRNr3) / deval (z, RDr3, NRDr3);
break;
case 3:
p = neval (z, RNr4, NRNr4) / deval (z, RDr4, NRDr4);
break;
case 4:
p = neval (z, RNr5, NRNr5) / deval (z, RDr5, NRDr5);
break;
case 5:
p = neval (z, RNr6, NRNr6) / deval (z, RDr6, NRDr6);
break;
case 6:
p = neval (z, RNr7, NRNr7) / deval (z, RDr7, NRDr7);
break;
case 7:
p = neval (z, RNr8, NRNr8) / deval (z, RDr8, NRDr8);
break;
}
u.value = x;
u.parts32.w3 = 0;
u.parts32.w2 &= 0xffffe000;
z = u.value;
r = __ieee754_expl (-z * z - 0.5625) *
__ieee754_expl ((z - x) * (z + x) + p);
if ((sign & 0x80000000) == 0)
return r / x;
else
return two - r / x;
}
else
{
if ((sign & 0x80000000) == 0)
return tiny * tiny;
else
return two - tiny;
}
}
long_double_symbol (libm, __erfcl, erfcl);

160
sysdeps/ieee754/ldbl-128ibm/s_expm1l.c Normal file
View File

@ -0,0 +1,160 @@
/* expm1l.c
*
* Exponential function, minus 1
* 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, expm1l();
*
* y = expm1l( x );
*
*
*
* DESCRIPTION:
*
* Returns e (2.71828...) raised to the x power, minus one.
*
* Range reduction is accomplished by separating the argument
* into an integer k and fraction f such that
*
* x k f
* e = 2 e.
*
* An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1
* in the basic range [-0.5 ln 2, 0.5 ln 2].
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -79,+MAXLOG 100,000 1.7e-34 4.5e-35
*
*/
/* Copyright 2001 by Stephen L. Moshier
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x)
-.5 ln 2 < x < .5 ln 2
Theoretical peak relative error = 8.1e-36 */
static const long double
P0 = 2.943520915569954073888921213330863757240E8L,
P1 = -5.722847283900608941516165725053359168840E7L,
P2 = 8.944630806357575461578107295909719817253E6L,
P3 = -7.212432713558031519943281748462837065308E5L,
P4 = 4.578962475841642634225390068461943438441E4L,
P5 = -1.716772506388927649032068540558788106762E3L,
P6 = 4.401308817383362136048032038528753151144E1L,
P7 = -4.888737542888633647784737721812546636240E-1L,
Q0 = 1.766112549341972444333352727998584753865E9L,
Q1 = -7.848989743695296475743081255027098295771E8L,
Q2 = 1.615869009634292424463780387327037251069E8L,
Q3 = -2.019684072836541751428967854947019415698E7L,
Q4 = 1.682912729190313538934190635536631941751E6L,
Q5 = -9.615511549171441430850103489315371768998E4L,
Q6 = 3.697714952261803935521187272204485251835E3L,
Q7 = -8.802340681794263968892934703309274564037E1L,
/* Q8 = 1.000000000000000000000000000000000000000E0 */
/* C1 + C2 = ln 2 */
C1 = 6.93145751953125E-1L,
C2 = 1.428606820309417232121458176568075500134E-6L,
/* ln (2^16384 * (1 - 2^-113)) */
maxlog = 1.1356523406294143949491931077970764891253E4L,
/* ln 2^-114 */
minarg = -7.9018778583833765273564461846232128760607E1L, big = 2e307L;
long double
__expm1l (long double x)
{
long double px, qx, xx;
int32_t ix, sign;
ieee854_long_double_shape_type u;
int k;
/* Detect infinity and NaN. */
u.value = x;
ix = u.parts32.w0;
sign = ix & 0x80000000;
ix &= 0x7fffffff;
if (ix >= 0x7ff00000)
{
/* Infinity. */
if (((ix & 0xfffff) | u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0)
{
if (sign)
return -1.0L;
else
return x;
}
/* NaN. No invalid exception. */
return x;
}
/* expm1(+- 0) = +- 0. */
if ((ix == 0) && (u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0)
return x;
/* Overflow. */
if (x > maxlog)
return (big * big);
/* Minimum value. */
if (x < minarg)
return (4.0/big - 1.0L);
/* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */
xx = C1 + C2; /* ln 2. */
px = __floorl (0.5 + x / xx);
k = px;
/* remainder times ln 2 */
x -= px * C1;
x -= px * C2;
/* Approximate exp(remainder ln 2). */
px = (((((((P7 * x
+ P6) * x
+ P5) * x + P4) * x + P3) * x + P2) * x + P1) * x + P0) * x;
qx = (((((((x
+ Q7) * x
+ Q6) * x + Q5) * x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0;
xx = x * x;
qx = x + (0.5 * xx + xx * px / qx);
/* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2).
We have qx = exp(remainder ln 2) - 1, so
exp(x) - 1 = 2^k (qx + 1) - 1
= 2^k qx + 2^k - 1. */
px = ldexpl (1.0L, k);
x = px * qx + (px - 1.0);
return x;
}
libm_hidden_def (__expm1l)
long_double_symbol (libm, __expm1l, expm1l);

43
sysdeps/ieee754/ldbl-128ibm/s_fabsl.c Normal file
View File

@ -0,0 +1,43 @@
/* s_fabsl.c -- long double version of s_fabs.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* fabsl(x) returns the absolute value of x.
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
long double __fabsl(long double x)
#else
long double __fabsl(x)
long double x;
#endif
{
u_int64_t hx, lx;
GET_LDOUBLE_WORDS64(hx,lx,x);
lx = lx ^ ( hx & 0x8000000000000000LL );
hx = hx & 0x7fffffffffffffffLL;
SET_LDOUBLE_WORDS64(hx,lx,x);
return x;
}
long_double_symbol (libm, __fabsl, fabsl);

42
sysdeps/ieee754/ldbl-128ibm/s_finitel.c Normal file
View File

@ -0,0 +1,42 @@
/* s_finitel.c -- long double version of s_finite.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* finitel(x) returns 1 is x is finite, else 0;
* no branching!
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
int
___finitel (long double x)
{
int64_t hx;
GET_LDOUBLE_MSW64(hx,x);
return (int)((u_int64_t)((hx&0x7fffffffffffffffLL)
-0x7ff0000000000000LL)>>63);
}
hidden_ver (___finitel, __finitel)
#ifndef IS_IN_libm
weak_alias (___finitel, ____finitel)
long_double_symbol (libc, ___finitel, finitel);
long_double_symbol (libc, ____finitel, __finitel);
#endif

118
sysdeps/ieee754/ldbl-128ibm/s_floorl.c Normal file
View File

@ -0,0 +1,118 @@
/* Round to int long double floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <fenv.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long double
__floorl (long double x)
#else
long double
__floorl (x)
long double x;
#endif
{
static const double TWO52 = 4503599627370496.0L;
int mode = fegetround();
union ibm_extended_long_double u;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
fesetround(FE_DOWNWARD);
if (u.dd[0] > 0.0)
{
u.dd[0] += TWO52;
u.dd[0] -= TWO52;
}
else if (u.dd[0] < 0.0)
{
u.dd[0] -= TWO52;
u.dd[0] += TWO52;
}
u.dd[1] = 0.0;
fesetround(mode);
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_DOWNWARD);
low += TWO52;
low -= TWO52;
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_DOWNWARD);
low -= TWO52;
low += TWO52;
}
fesetround(mode);
u.dd[0] = high + low;
u.dd[1] = high - u.dd[0] + low;
}
return u.d;
}
long_double_symbol (libm, __floorl, floorl);

82
sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c Normal file
View File

@ -0,0 +1,82 @@
/* Return classification value corresponding to argument.
Copyright (C) 1997,1999,2002,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <math.h>
#include "math_private.h"
#include <math_ldbl_opt.h>
/*
* hx lx
* +NaN 7ffn nnnn nnnn nnnn xxxx xxxx xxxx xxxx
* -NaN fffn nnnn nnnn nnnn xxxx xxxx xxxx xxxx
* +Inf 7ff0 0000 0000 0000 xxxx xxxx xxxx xxxx
* -Inf fff0 0000 0000 0000 xxxx xxxx xxxx xxxx
* +0 0000 0000 0000 0000
* -0 8000 0000 0000 0000
* +normal 001n nnnn nnnn nnnn (smallest)
* -normal 801n nnnn nnnn nnnn (smallest)
* +normal 7fen nnnn nnnn nnnn (largest)
* -normal ffen nnnn nnnn nnnn (largest)
* +denorm 000n nnnn nnnn nnnn
* -denorm 800n nnnn nnnn nnnn
*/
int
___fpclassifyl (long double x)
{
u_int64_t hx, lx;
int retval = FP_NORMAL;
GET_LDOUBLE_WORDS64 (hx, lx, x);
if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL) {
/* +/-NaN or +/-Inf */
if (hx & 0x000fffffffffffffULL) {
/* +/-NaN */
retval = FP_NAN;
} else {
retval = FP_INFINITE;
}
} else {
/* +/-zero or +/- normal or +/- denormal */
if (hx & 0x7fffffffffffffffULL) {
/* +/- normal or +/- denormal */
if ((hx & 0x7ff0000000000000ULL) >= 0x0360000000000000ULL) {
/* +/- normal */
retval = FP_NORMAL;
} else {
/* +/- denormal */
retval = FP_SUBNORMAL;
}
} else {
/* +/- zero */
retval = FP_ZERO;
}
}
return retval;
}
long_double_symbol (libm, ___fpclassifyl, __fpclassifyl);
#ifdef __LONG_DOUBLE_MATH_OPTIONAL
libm_hidden_ver (___fpclassifyl, __fpclassifyl)
#else
libm_hidden_def (__fpclassifyl)
#endif

92
sysdeps/ieee754/ldbl-128ibm/s_frexpl.c Normal file
View File

@ -0,0 +1,92 @@
/* s_frexpl.c -- long double version of s_frexp.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* for non-zero x
* x = frexpl(arg,&exp);
* return a long double fp quantity x such that 0.5 <= |x| <1.0
* and the corresponding binary exponent "exp". That is
* arg = x*2^exp.
* If arg is inf, 0.0, or NaN, then frexpl(arg,&exp) returns arg
* with *exp=0.
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
static const long double
#else
static long double
#endif
two107 = 162259276829213363391578010288128.0; /* 0x4670000000000000, 0 */
#ifdef __STDC__
long double __frexpl(long double x, int *eptr)
#else
long double __frexpl(x, eptr)
long double x; int *eptr;
#endif
{
u_int64_t hx, lx, ix, ixl;
int64_t explo;
GET_LDOUBLE_WORDS64(hx,lx,x);
ixl = 0x7fffffffffffffffULL&lx;
ix = 0x7fffffffffffffffULL&hx;
*eptr = 0;
if(ix>=0x7ff0000000000000ULL||((ix|ixl)==0)) return x; /* 0,inf,nan */
if (ix<0x0010000000000000ULL) { /* subnormal */
x *= two107;
GET_LDOUBLE_MSW64(hx,x);
ix = hx&0x7fffffffffffffffULL;
*eptr = -107;
}
*eptr += (ix>>52)-1022;
if (ixl != 0ULL) {
explo = (ixl>>52) - (ix>>52) + 0x3fe;
if ((ixl&0x7ff0000000000000ULL) == 0LL) {
/* the lower double is a denomal so we need to correct its
mantissa and perhaps its exponent. */
int cnt;
if (sizeof (ixl) == sizeof (long))
cnt = __builtin_clzl (ixl);
else if ((ixl >> 32) != 0)
cnt = __builtin_clzl ((long) (ixl >> 32));
else
cnt = __builtin_clzl ((long) ixl) + 32;
cnt = cnt - 12;
lx = (lx&0x8000000000000000ULL) | ((explo-cnt)<<52)
| ((ixl<<(cnt+1))&0x000fffffffffffffULL);
} else
lx = (lx&0x800fffffffffffffULL) | (explo<<52);
} else
lx = 0ULL;
hx = (hx&0x800fffffffffffffULL) | 0x3fe0000000000000ULL;
SET_LDOUBLE_WORDS64(x,hx,lx);
return x;
}
#ifdef IS_IN_libm
long_double_symbol (libm, __frexpl, frexpl);
#else
long_double_symbol (libc, __frexpl, frexpl);
#endif

63
sysdeps/ieee754/ldbl-128ibm/s_ilogbl.c Normal file
View File

@ -0,0 +1,63 @@
/* s_ilogbl.c -- long double version of s_ilogb.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/* ilogbl(long double x)
* return the binary exponent of non-zero x
* ilogbl(0) = FP_ILOGB0
* ilogbl(NaN) = FP_ILOGBNAN (no signal is raised)
* ilogbl(+-Inf) = INT_MAX (no signal is raised)
*/
#include <limits.h>
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
int __ilogbl(long double x)
#else
int __ilogbl(x)
long double x;
#endif
{
int64_t hx,lx;
int ix;
GET_LDOUBLE_WORDS64(hx,lx,x);
hx &= 0x7fffffffffffffffLL;
if(hx <= 0x0010000000000000LL) {
if((hx|(lx&0x7fffffffffffffffLL))==0)
return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */
else /* subnormal x */
if(hx==0) {
for (ix = -1043; lx>0; lx<<=1) ix -=1;
} else {
for (ix = -1022, hx<<=11; hx>0; hx<<=1) ix -=1;
}
return ix;
}
else if (hx<0x7ff0000000000000LL) return (hx>>52)-0x3ff;
else if (FP_ILOGBNAN != INT_MAX) {
/* ISO C99 requires ilogbl(+-Inf) == INT_MAX. */
if (((hx^0x7ff0000000000000LL)|lx) == 0)
return INT_MAX;
}
return FP_ILOGBNAN;
}
long_double_symbol (libm, __ilogbl, ilogbl);

35
sysdeps/ieee754/ldbl-128ibm/s_isinfl.c Normal file
View File

@ -0,0 +1,35 @@
/*
* Written by J.T. Conklin <jtc@netbsd.org>.
* Change for long double by Jakub Jelinek <jj@ultra.linux.cz>
* Public domain.
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* isinfl(x) returns 1 if x is inf, -1 if x is -inf, else 0;
* no branching!
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
int
___isinfl (long double x)
{
int64_t hx,lx;
GET_LDOUBLE_WORDS64(hx,lx,x);
lx = (lx & 0x7fffffffffffffffLL);
lx |= (hx & 0x7fffffffffffffffLL) ^ 0x7ff0000000000000LL;
lx |= -lx;
return ~(lx >> 63) & (hx >> 62);
}
hidden_ver (___isinfl, __isinfl)
#ifndef IS_IN_libm
weak_alias (___isinfl, ____isinfl)
long_double_symbol (libc, ___isinfl, isinfl);
long_double_symbol (libc, ____isinfl, __isinfl);
#endif

43
sysdeps/ieee754/ldbl-128ibm/s_isnanl.c Normal file
View File

@ -0,0 +1,43 @@
/* s_isnanl.c -- long double version of s_isnan.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* isnanl(x) returns 1 is x is nan, else 0;
* no branching!
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
int
___isnanl (long double x)
{
int64_t hx,lx;
GET_LDOUBLE_WORDS64(hx,lx,x);
hx &= 0x7fffffffffffffffLL;
hx = 0x7ff0000000000000LL - hx;
return (int)((u_int64_t)hx>>63);
}
hidden_ver (___isnanl, __isnanl)
#ifndef IS_IN_libm
weak_alias (___isnanl, ____isnanl)
long_double_symbol (libc, ___isnanl, isnanl);
long_double_symbol (libc, ____isnanl, __isnanl);
#endif

124
sysdeps/ieee754/ldbl-128ibm/s_llrintl.c Normal file
View File

@ -0,0 +1,124 @@
/* Round to int long double floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long long
__llrintl (long double x)
#else
long long
__llrintl (x)
long double x;
#endif
{
static const double TWO52 = 4503599627370496.0L;
union ibm_extended_long_double u;
long long result = __LONG_LONG_MAX__;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
double high = u.dd[0];
if (high > 0.0)
{
high += TWO52;
high -= TWO52;
if (high == -0.0) high = 0.0;
}
else if (high < 0.0)
{
high -= TWO52;
high += TWO52;
if (high == 0.0) high = -0.0;
}
result = high;
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low, tau;
long long lowint;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
tau = nextafter (u.dd[0], 0.0);
tau = (u.dd[0] - tau) * 2.0;
high = u.dd[0] - tau;
low = u.dd[1] + tau;
}
low += TWO52;
low -= TWO52;
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
tau = nextafter (u.dd[0], 0.0);
tau = (u.dd[0] - tau) * 2.0;
high = u.dd[0] - tau;
low = u.dd[1] + tau;
}
low = TWO52 - low;
low = -(low - TWO52);
}
lowint = low;
result = high;
result += lowint;
}
else
result = u.dd[0];
return result;
}
long_double_symbol (libm, __llrintl, llrintl);

128
sysdeps/ieee754/ldbl-128ibm/s_llroundl.c Normal file
View File

@ -0,0 +1,128 @@
/* Round to long long, long double floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <fenv.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long long
__llroundl (long double x)
#else
long long
__llroundl (x)
long double x;
#endif
{
static const double TWO52 = 4503599627370496.0;
static const double HALF = 0.5;
int mode = fegetround();
union ibm_extended_long_double u;
long long result = __LONG_LONG_MAX__;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
fesetround(FE_TOWARDZERO);
if (u.dd[0] > 0.0)
{
u.dd[0] += HALF;
u.dd[0] += TWO52;
u.dd[0] -= TWO52;
}
else if (u.dd[0] < 0.0)
{
u.dd[0] = TWO52 - (u.dd[0] - HALF);
u.dd[0] = -(u.dd[0] - TWO52);
}
fesetround(mode);
result = u.dd[0];
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low;
long long lowint;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_TOWARDZERO);
low += HALF;
low += TWO52;
low -= TWO52;
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_TOWARDZERO);
low -= HALF;
low = TWO52 - low;
low = -(low - TWO52);
}
fesetround(mode);
lowint = low;
result = high;
result += lowint;
}
else
{
result = u.dd[0];
}
return result;
}
long_double_symbol (libm, __llroundl, llroundl);

257
sysdeps/ieee754/ldbl-128ibm/s_log1pl.c Normal file
View File

@ -0,0 +1,257 @@
/* log1pl.c
*
* Relative error logarithm
* Natural logarithm of 1+x, 128-bit long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, log1pl();
*
* y = log1pl( x );
*
*
*
* DESCRIPTION:
*
* Returns the base e (2.718...) logarithm of 1+x.
*
* The argument 1+x is separated into its exponent and fractional
* parts. If the exponent is between -1 and +1, the logarithm
* of the fraction is approximated by
*
* log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
*
* Otherwise, setting z = 2(w-1)/(w+1),
*
* log(w) = z + z^3 P(z)/Q(z).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -1, 8 100000 1.9e-34 4.3e-35
*/
/* Copyright 2001 by Stephen L. Moshier
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x)
* 1/sqrt(2) <= 1+x < sqrt(2)
* Theoretical peak relative error = 5.3e-37,
* relative peak error spread = 2.3e-14
*/
static const long double
P12 = 1.538612243596254322971797716843006400388E-6L,
P11 = 4.998469661968096229986658302195402690910E-1L,
P10 = 2.321125933898420063925789532045674660756E1L,
P9 = 4.114517881637811823002128927449878962058E2L,
P8 = 3.824952356185897735160588078446136783779E3L,
P7 = 2.128857716871515081352991964243375186031E4L,
P6 = 7.594356839258970405033155585486712125861E4L,
P5 = 1.797628303815655343403735250238293741397E5L,
P4 = 2.854829159639697837788887080758954924001E5L,
P3 = 3.007007295140399532324943111654767187848E5L,
P2 = 2.014652742082537582487669938141683759923E5L,
P1 = 7.771154681358524243729929227226708890930E4L,
P0 = 1.313572404063446165910279910527789794488E4L,
/* Q12 = 1.000000000000000000000000000000000000000E0L, */
Q11 = 4.839208193348159620282142911143429644326E1L,
Q10 = 9.104928120962988414618126155557301584078E2L,
Q9 = 9.147150349299596453976674231612674085381E3L,
Q8 = 5.605842085972455027590989944010492125825E4L,
Q7 = 2.248234257620569139969141618556349415120E5L,
Q6 = 6.132189329546557743179177159925690841200E5L,
Q5 = 1.158019977462989115839826904108208787040E6L,
Q4 = 1.514882452993549494932585972882995548426E6L,
Q3 = 1.347518538384329112529391120390701166528E6L,
Q2 = 7.777690340007566932935753241556479363645E5L,
Q1 = 2.626900195321832660448791748036714883242E5L,
Q0 = 3.940717212190338497730839731583397586124E4L;
/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 1.1e-35,
* relative peak error spread 1.1e-9
*/
static const long double
R5 = -8.828896441624934385266096344596648080902E-1L,
R4 = 8.057002716646055371965756206836056074715E1L,
R3 = -2.024301798136027039250415126250455056397E3L,
R2 = 2.048819892795278657810231591630928516206E4L,
R1 = -8.977257995689735303686582344659576526998E4L,
R0 = 1.418134209872192732479751274970992665513E5L,
/* S6 = 1.000000000000000000000000000000000000000E0L, */
S5 = -1.186359407982897997337150403816839480438E2L,
S4 = 3.998526750980007367835804959888064681098E3L,
S3 = -5.748542087379434595104154610899551484314E4L,
S2 = 4.001557694070773974936904547424676279307E5L,
S1 = -1.332535117259762928288745111081235577029E6L,
S0 = 1.701761051846631278975701529965589676574E6L;
/* C1 + C2 = ln 2 */
static const long double C1 = 6.93145751953125E-1L;
static const long double C2 = 1.428606820309417232121458176568075500134E-6L;
static const long double sqrth = 0.7071067811865475244008443621048490392848L;
/* ln (2^16384 * (1 - 2^-113)) */
static const long double maxlog = 1.1356523406294143949491931077970764891253E4L;
static const long double big = 2e300L;
static const long double zero = 0.0L;
#if 1
/* Make sure these are prototyped. */
long double frexpl (long double, int *);
long double ldexpl (long double, int);
#endif
long double
__log1pl (long double xm1)
{
long double x, y, z, r, s;
ieee854_long_double_shape_type u;
int32_t hx;
int e;
/* Test for NaN or infinity input. */
u.value = xm1;
hx = u.parts32.w0;
if (hx >= 0x7ff00000)
return xm1;
/* log1p(+- 0) = +- 0. */
if (((hx & 0x7fffffff) == 0)
&& (u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3) == 0)
return xm1;
x = xm1 + 1.0L;
/* log1p(-1) = -inf */
if (x <= 0.0L)
{
if (x == 0.0L)
return (-1.0L / (x - x));
else
return (zero / (x - x));
}
/* Separate mantissa from exponent. */
/* Use frexp used so that denormal numbers will be handled properly. */
x = frexpl (x, &e);
/* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2),
where z = 2(x-1)/x+1). */
if ((e > 2) || (e < -2))
{
if (x < sqrth)
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5L;
y = 0.5L * z + 0.5L;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5L;
z -= 0.5L;
y = 0.5L * x + 0.5L;
}
x = z / y;
z = x * x;
r = ((((R5 * z
+ R4) * z
+ R3) * z
+ R2) * z
+ R1) * z
+ R0;
s = (((((z
+ S5) * z
+ S4) * z
+ S3) * z
+ S2) * z
+ S1) * z
+ S0;
z = x * (z * r / s);
z = z + e * C2;
z = z + x;
z = z + e * C1;
return (z);
}
/* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */
if (x < sqrth)
{
e -= 1;
if (e != 0)
x = 2.0L * x - 1.0L; /* 2x - 1 */
else
x = xm1;
}
else
{
if (e != 0)
x = x - 1.0L;
else
x = xm1;
}
z = x * x;
r = (((((((((((P12 * x
+ P11) * x
+ P10) * x
+ P9) * x
+ P8) * x
+ P7) * x
+ P6) * x
+ P5) * x
+ P4) * x
+ P3) * x
+ P2) * x
+ P1) * x
+ P0;
s = (((((((((((x
+ Q11) * x
+ Q10) * x
+ Q9) * x
+ Q8) * x
+ Q7) * x
+ Q6) * x
+ Q5) * x
+ Q4) * x
+ Q3) * x
+ Q2) * x
+ Q1) * x
+ Q0;
y = x * (z * r / s);
y = y + e * C2;
z = y - 0.5L * z;
z = z + x;
z = z + e * C1;
return (z);
}
long_double_symbol (libm, __log1pl, log1pl);

47
sysdeps/ieee754/ldbl-128ibm/s_logbl.c Normal file
View File

@ -0,0 +1,47 @@
/* s_logbl.c -- long double version of s_logb.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* long double logbl(x)
* IEEE 754 logb. Included to pass IEEE test suite. Not recommend.
* Use ilogb instead.
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
long double __logbl(long double x)
#else
long double __logbl(x)
long double x;
#endif
{
int64_t lx,hx;
GET_LDOUBLE_WORDS64(hx,lx,x);
hx &= 0x7fffffffffffffffLL; /* high |x| */
if((hx|(lx&0x7fffffffffffffffLL))==0) return -1.0/fabs(x);
if(hx>=0x7ff0000000000000LL) return x*x;
if((hx>>=52)==0) /* IEEE 754 logb */
return -1022.0;
else
return (long double) (hx-0x3ff);
}
long_double_symbol (libm, __logbl, logbl);

9
sysdeps/ieee754/ldbl-128ibm/s_lrintl.c Normal file
View File

@ -0,0 +1,9 @@
/* FIXME */
#include <math.h>
#include <math_ldbl_opt.h>
long int __lrintl (long double d)
{
return llrintl (d);
}
long_double_symbol (libm, __lrintl, lrintl);

9
sysdeps/ieee754/ldbl-128ibm/s_lroundl.c Normal file
View File

@ -0,0 +1,9 @@
/* FIXME */
#include <math.h>
#include <math_ldbl_opt.h>
long int __lroundl (long double d)
{
return llroundl (d);
}
long_double_symbol (libm, __lroundl, lroundl);

94
sysdeps/ieee754/ldbl-128ibm/s_modfl.c Normal file
View File

@ -0,0 +1,94 @@
/* s_modfl.c -- long double version of s_modf.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* modfl(long double x, long double *iptr)
* return fraction part of x, and return x's integral part in *iptr.
* Method:
* Bit twiddling.
*
* Exception:
* No exception.
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
static const long double one = 1.0;
#else
static long double one = 1.0;
#endif
#ifdef __STDC__
long double __modfl(long double x, long double *iptr)
#else
long double __modfl(x, iptr)
long double x,*iptr;
#endif
{
int64_t i0,i1,j0;
u_int64_t i;
GET_LDOUBLE_WORDS64(i0,i1,x);
i1 &= 0x000fffffffffffffLL;
j0 = ((i0>>52)&0x7ff)-0x3ff; /* exponent of x */
if(j0<52) { /* integer part in high x */
if(j0<0) { /* |x|<1 */
/* *iptr = +-0 */
SET_LDOUBLE_WORDS64(*iptr,i0&0x8000000000000000ULL,0);
return x;
} else {
i = (0x000fffffffffffffLL)>>j0;
if(((i0&i)|(i1&0x7fffffffffffffffLL))==0) { /* x is integral */
*iptr = x;
/* return +-0 */
SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0);
return x;
} else {
SET_LDOUBLE_WORDS64(*iptr,i0&(~i),0);
return x - *iptr;
}
}
} else if (j0>103) { /* no fraction part */
*iptr = x*one;
/* We must handle NaNs separately. */
if (j0 == 0x400 && ((i0 & 0x000fffffffffffffLL) | i1))
return x*one;
/* return +-0 */
SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0);
return x;
} else { /* fraction part in low x */
i = -1ULL>>(j0-52);
if((i1&i)==0) { /* x is integral */
*iptr = x;
/* return +-0 */
SET_LDOUBLE_WORDS64(x,i0&0x8000000000000000ULL,0);
return x;
} else {
SET_LDOUBLE_WORDS64(*iptr,i0,i1&(~i));
return x - *iptr;
}
}
}
#ifdef IS_IN_libm
long_double_symbol (libm, __modfl, modfl);
#else
long_double_symbol (libc, __modfl, modfl);
#endif

125
sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c Normal file
View File

@ -0,0 +1,125 @@
/* Round to int long double floating-point values without raising inexact.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <fenv.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long double
__nearbyintl (long double x)
#else
long double
__nearbyintl (x)
long double x;
#endif
{
fenv_t env;
static const long double TWO52 = 4503599627370496.0L;
union ibm_extended_long_double u;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
double high = u.dd[0];
feholdexcept (&env);
if (high > 0.0)
{
high += TWO52;
high -= TWO52;
if (high == -0.0) high = 0.0;
}
else if (high < 0.0)
{
high -= TWO52;
high += TWO52;
if (high == 0.0) high = -0.0;
}
u.dd[0] = high;
u.dd[1] = 0.0;
fesetenv (&env);
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low, tau;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
feholdexcept (&env);
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
tau = nextafter (u.dd[0], 0.0);
tau = (u.dd[0] - tau) * 2.0;
high = u.dd[0] - tau;
low = u.dd[1] + tau;
}
low += TWO52;
low -= TWO52;
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
tau = nextafter (u.dd[0], 0.0);
tau = (u.dd[0] - tau) * 2.0;
high = u.dd[0] - tau;
low = u.dd[1] + tau;
}
low = TWO52 - low;
low = -(low - TWO52);
}
u.dd[0] = high + low;
u.dd[1] = high - u.dd[0] + low;
fesetenv (&env);
}
return u.d;
}
long_double_symbol (libm, __nearbyintl, nearbyintl);

108
sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c Normal file
View File

@ -0,0 +1,108 @@
/* s_nextafterl.c -- long double version of s_nextafter.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/* IEEE functions
* nextafterl(x,y)
* return the next machine floating-point number of x in the
* direction toward y.
* Special cases:
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
long double __nextafterl(long double x, long double y)
#else
long double __nextafterl(x,y)
long double x,y;
#endif
{
int64_t hx,hy,ihx,ihy,ilx,ily;
u_int64_t lx,ly;
GET_LDOUBLE_WORDS64(hx,lx,x);
GET_LDOUBLE_WORDS64(hy,ly,y);
ihx = hx&0x7fffffffffffffffLL; /* |hx| */
ilx = lx&0x7fffffffffffffffLL; /* |lx| */
ihy = hy&0x7fffffffffffffffLL; /* |hy| */
ily = ly&0x7fffffffffffffffLL; /* |ly| */
if((((ihx&0x7ff0000000000000LL)==0x7ff0000000000000LL)&&
((ihx&0x000fffffffffffffLL)!=0)) || /* x is nan */
(((ihy&0x7ff0000000000000LL)==0x7ff0000000000000LL)&&
((ihy&0x000fffffffffffffLL)!=0))) /* y is nan */
return x+y; /* signal the nan */
if(x==y)
return y; /* x=y, return y */
if(ihx == 0 && ilx == 0) { /* x == 0 */
SET_LDOUBLE_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */
y = x*x;
if(y==x) return y; else return x; /* raise underflow flag */
}
if(ihx>=0) { /* x > 0 */
if(ihx>ihy||((ihx==ihy)&&(ilx>ily))) { /* x > y, x -= ulp */
if(ilx==0)
hx--;
else
lx--;
} else { /* x < y, x += ulp */
if((hx==0x7fefffffffffffffLL)&&(lx==0x7c8ffffffffffffeLL))
{
SET_LDOUBLE_WORDS64(x,0x7ff0000000000000,0x8000000000000000);
return x;
}
else if((hx==0xffefffffffffffffLL)&&(lx==0xfc8ffffffffffffeLL))
{
SET_LDOUBLE_WORDS64(x,0xfff0000000000000,0x8000000000000000);
return x;
}
else if((lx&0x7fffffffffffffff)==0) hx++;
else
lx++;
}
} else { /* x < 0 */
if(ihy>=0||ihx>ihy||((ihx==ihy)&&(ilx>ily))){/* x < y, x -= ulp */
if((lx&0x7fffffffffffffff)==0)
hx--;
else
lx--;
} else { /* x > y, x += ulp */
if((lx&0x7fffffffffffffff)==0) hx++;
else
lx++;
}
}
hy = hx&0x7ff0000000000000LL;
if(hy==0x7ff0000000000000LL) return x+x;/* overflow */
if(hy==0) { /* underflow */
y = x*x;
if(y!=x) { /* raise underflow flag */
SET_LDOUBLE_WORDS64(y,hx,lx);
return y;
}
}
SET_LDOUBLE_WORDS64(x,hx,lx);
return x;
}
strong_alias (__nextafterl, __nexttowardl)
long_double_symbol (libm, __nextafterl, nextafterl);
long_double_symbol (libm, __nexttowardl, nexttowardl);

106
sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c Normal file
View File

@ -0,0 +1,106 @@
/* s_nexttoward.c
* Conversion from s_nextafter.c by Ulrich Drepper, Cygnus Support,
* drepper@cygnus.com and Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/* IEEE functions
* nexttoward(x,y)
* return the next machine floating-point number of x in the
* direction toward y.
* Special cases:
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#include <float.h>
#ifdef __STDC__
double __nexttoward(double x, long double y)
#else
double __nexttoward(x,y)
double x;
long double y;
#endif
{
int32_t hx,ix;
int64_t hy,iy;
u_int32_t lx;
u_int64_t ly,uly;
EXTRACT_WORDS(hx,lx,x);
GET_LDOUBLE_WORDS64(hy,ly,y);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
uly = ly&0x7fffffffffffffffLL; /* |y| */
if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */
((iy>=0x7ff0000000000000LL)&&((iy-0x7ff0000000000000LL)|uly)!=0))
/* y is nan */
return x+y;
if((long double) x==y) return y; /* x=y, return y */
if((ix|lx)==0) { /* x == 0 */
double x2;
INSERT_WORDS(x,(u_int32_t)((hy>>32)&0x80000000),1);/* return +-minsub */
x2 = x*x;
if(x2==x) return x2; else return x; /* raise underflow flag */
}
if(hx>=0) { /* x > 0 */
if (hy<0||(ix>>20)>(iy>>52)
|| ((ix>>20)==(iy>>52)
&& (((((int64_t)hx)<<32)|(lx))>(hy&0x000fffffffffffffLL)
|| (((((int64_t)hx)<<32)|(lx))==(hy&0x000fffffffffffffLL)
)))) { /* x > y, x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x < y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
} else { /* x < 0 */
if (hy>=0||(ix>>20)>(iy>>52)
|| ((ix>>20)==(iy>>52)
&& (((((int64_t)hx)<<32)|(lx))>(hy&0x000fffffffffffffLL)
|| (((((int64_t)hx)<<32)|(lx))==(hy&0x000fffffffffffffLL)
)))) { /* x < y, x -= ulp */
if(lx==0) hx -= 1;
lx -= 1;
} else { /* x > y, x += ulp */
lx += 1;
if(lx==0) hx += 1;
}
}
hy = hx&0x7ff00000;
if(hy>=0x7ff00000) {
x = x+x; /* overflow */
if (FLT_EVAL_METHOD != 0 && FLT_EVAL_METHOD != 1)
/* Force conversion to float. */
asm ("" : "=m"(x) : "m"(x));
return x;
}
if(hy<0x00100000) { /* underflow */
double x2 = x*x;
if(x2!=x) { /* raise underflow flag */
INSERT_WORDS(x2,hx,lx);
return x2;
}
}
INSERT_WORDS(x,hx,lx);
return x;
}
long_double_symbol (libm, __nexttoward, nexttoward);

83
sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c Normal file
View File

@ -0,0 +1,83 @@
/* s_nexttowardf.c -- float version of s_nextafter.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com
* and Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
float __nexttowardf(float x, long double y)
#else
float __nexttowardf(x,y)
float x;
long double y;
#endif
{
int32_t hx,ix;
int64_t hy,iy;
u_int64_t ly, uly;
GET_FLOAT_WORD(hx,x);
GET_LDOUBLE_WORDS64(hy,ly,y);
ix = hx&0x7fffffff; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
uly = ly&0x7fffffffffffffffLL; /* |y| */
if((ix>0x7f800000) || /* x is nan */
((iy>=0x7ff0000000000000LL)&&((iy-0x7ff0000000000000LL)|uly)!=0))
/* y is nan */
return x+y;
if((long double) x==y) return y; /* x=y, return y */
if(ix==0) { /* x == 0 */
float x2;
SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/
x2 = x*x;
if(x2==x) return x2; else return x; /* raise underflow flag */
}
if(hx>=0) { /* x > 0 */
if(hy<0||(ix>>23)>(iy>>52)-0x380
|| ((ix>>23)==(iy>>52)-0x380
&& (ix&0x7fffff)>((hy>>29)&0x7fffff))) {/* x > y, x -= ulp */
hx -= 1;
} else { /* x < y, x += ulp */
hx += 1;
}
} else { /* x < 0 */
if(hy>=0||(ix>>23)>(iy>>52)-0x380
|| ((ix>>23)==(iy>>52)-0x380
&& (ix&0x7fffff)>((hy>>29)&0x7fffff))) {/* x < y, x -= ulp */
hx -= 1;
} else { /* x > y, x += ulp */
hx += 1;
}
}
hy = hx&0x7f800000;
if(hy>=0x7f800000) return x+x; /* overflow */
if(hy<0x00800000) { /* underflow */
float x2 = x*x;
if(x2!=x) { /* raise underflow flag */
SET_FLOAT_WORD(x2,hx);
return x2;
}
}
SET_FLOAT_WORD(x,hx);
return x;
}
long_double_symbol (libm, __nexttowardf, nexttowardf);

111
sysdeps/ieee754/ldbl-128ibm/s_remquol.c Normal file
View File

@ -0,0 +1,111 @@
/* Compute remainder and a congruent to the quotient.
Copyright (C) 1997,1999,2002,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>, 1999.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <math.h>
#include "math_private.h"
#include <math_ldbl_opt.h>
static const long double zero = 0.0;
long double
__remquol (long double x, long double y, int *quo)
{
int64_t hx,hy;
u_int64_t sx,lx,ly,qs;
int cquo;
GET_LDOUBLE_WORDS64 (hx, lx, x);
GET_LDOUBLE_WORDS64 (hy, ly, y);
sx = hx & 0x8000000000000000ULL;
qs = sx ^ (hy & 0x8000000000000000ULL);
hy &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* Purge off exception values. */
if ((hy | (ly & 0x7fffffffffffffff)) == 0)
return (x * y) / (x * y); /* y = 0 */
if ((hx >= 0x7ff0000000000000LL) /* x not finite */
|| ((hy >= 0x7ff0000000000000LL) /* y is NaN */
&& (((hy - 0x7ff0000000000000LL) | ly) != 0)))
return (x * y) / (x * y);
if (hy <= 0x7fbfffffffffffffLL)
x = __ieee754_fmodl (x, 8 * y); /* now x < 8y */
if (((hx - hy) | (lx - ly)) == 0)
{
*quo = qs ? -1 : 1;
return zero * x;
}
x = fabsl (x);
y = fabsl (y);
cquo = 0;
if (x >= 4 * y)
{
x -= 4 * y;
cquo += 4;
}
if (x >= 2 * y)
{
x -= 2 * y;
cquo += 2;
}
if (hy < 0x0020000000000000LL)
{
if (x + x > y)
{
x -= y;
++cquo;
if (x + x >= y)
{
x -= y;
++cquo;
}
}
}
else
{
long double y_half = 0.5L * y;
if (x > y_half)
{
x -= y;
++cquo;
if (x >= y_half)
{
x -= y;
++cquo;
}
}
}
*quo = qs ? -cquo : cquo;
if (sx)
x = -x;
return x;
}
long_double_symbol (libm, __remquol, remquol);

119
sysdeps/ieee754/ldbl-128ibm/s_rintl.c Normal file
View File

@ -0,0 +1,119 @@
/* Round to int long double floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long double
__rintl (long double x)
#else
long double
__rintl (x)
long double x;
#endif
{
static const long double TWO52 = 4503599627370496.0L;
union ibm_extended_long_double u;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
double high = u.dd[0];
if (high > 0.0)
{
high += TWO52;
high -= TWO52;
if (high == -0.0) high = 0.0;
}
else if (high < 0.0)
{
high -= TWO52;
high += TWO52;
if (high == 0.0) high = -0.0;
}
u.dd[0] = high;
u.dd[1] = 0.0;
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low, tau;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
tau = nextafter (u.dd[0], 0.0);
tau = (u.dd[0] - tau) * 2.0;
high = u.dd[0] - tau;
low = u.dd[1] + tau;
}
low += TWO52;
low -= TWO52;
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
tau = nextafter (u.dd[0], 0.0);
tau = (u.dd[0] - tau) * 2.0;
high = u.dd[0] - tau;
low = u.dd[1] + tau;
}
low = TWO52 - low;
low = -(low - TWO52);
}
u.dd[0] = high + low;
u.dd[1] = high - u.dd[0] + low;
}
return u.d;
}
long_double_symbol (libm, __rintl, rintl);

120
sysdeps/ieee754/ldbl-128ibm/s_roundl.c Normal file
View File

@ -0,0 +1,120 @@
/* Round to int long double floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <fenv.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long double
__roundl (long double x)
#else
long double
__roundl (x)
long double x;
#endif
{
static const double TWO52 = 4503599627370496.0;
static const double HALF = 0.5;
int mode = fegetround();
union ibm_extended_long_double u;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
fesetround(FE_TOWARDZERO);
if (u.dd[0] > 0.0)
{
u.dd[0] += HALF;
u.dd[0] += TWO52;
u.dd[0] -= TWO52;
}
else if (u.dd[0] < 0.0)
{
u.dd[0] = TWO52 - (u.dd[0] - HALF);
u.dd[0] = -(u.dd[0] - TWO52);
}
u.dd[1] = 0.0;
fesetround(mode);
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_TOWARDZERO);
low += HALF;
low += TWO52;
low -= TWO52;
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_TOWARDZERO);
low -= HALF;
low = TWO52 - low;
low = -(low - TWO52);
}
fesetround(mode);
u.dd[0] = high + low;
u.dd[1] = high - u.dd[0] + low;
}
return u.d;
}
long_double_symbol (libm, __roundl, roundl);

105
sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c Normal file
View File

@ -0,0 +1,105 @@
/* s_scalblnl.c -- long double version of s_scalbln.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/* @(#)s_scalbln.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* scalblnl (long double x, long int n)
* scalblnl(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
static const long double
#else
static long double
#endif
twolm54 = 5.55111512312578270212e-17, /* 0x3C90000000000000, 0 */
huge = 1.0E+300L,
tiny = 1.0E-300L;
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */
#ifdef __STDC__
long double __scalblnl (long double x, long int n)
#else
long double __scalblnl (x,n)
long double x; long int n;
#endif
{
int64_t k,l,hx,lx;
union { int64_t i; double d; } u;
GET_LDOUBLE_WORDS64(hx,lx,x);
k = (hx>>52)&0x7ff; /* extract exponent */
l = (lx>>52)&0x7ff;
if (k==0) { /* 0 or subnormal x */
if (((hx|lx)&0x7fffffffffffffffULL)==0) return x; /* +-0 */
u.i = hx;
u.d *= two54;
hx = u.i;
k = ((hx>>52)&0x7ff) - 54;
}
else if (k==0x7ff) return x+x; /* NaN or Inf */
k = k+n;
if (n> 50000 || k > 0x7fe)
return huge*__copysignl(huge,x); /* overflow */
if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow */
if (k > 0) { /* normal result */
hx = (hx&0x800fffffffffffffULL)|(k<<52);
if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */
SET_LDOUBLE_WORDS64(x,hx,lx);
return x;
}
if (l == 0) { /* low part subnormal */
u.i = lx;
u.d *= two54;
lx = u.i;
l = ((lx>>52)&0x7ff) - 54;
}
l = l + n;
if (l > 0)
lx = (lx&0x800fffffffffffffULL)|(l<<52);
else if (l <= -54)
lx = (lx&0x8000000000000000ULL);
else {
l += 54;
u.i = (lx&0x800fffffffffffffULL)|(l<<52);
u.d *= twom54;
lx = u.i;
}
SET_LDOUBLE_WORDS64(x,hx,lx);
return x;
}
if (k <= -54)
return tiny*__copysignl(tiny,x); /*underflow*/
k += 54; /* subnormal result */
lx &= 0x8000000000000000ULL;
SET_LDOUBLE_WORDS64(x,(hx&0x800fffffffffffffULL)|(k<<52),lx);
return x*twolm54;
}
long_double_symbol (libm, __scalblnl, scalblnl);

109
sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c Normal file
View File

@ -0,0 +1,109 @@
/* s_scalbnl.c -- long double version of s_scalbn.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/* @(#)s_scalbn.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/*
* scalbnl (long double x, int n)
* scalbnl(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
static const long double
#else
static long double
#endif
twolm54 = 5.55111512312578270212e-17, /* 0x3C90000000000000, 0 */
huge = 1.0E+300L,
tiny = 1.0E-300L;
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */
#ifdef __STDC__
long double __scalbnl (long double x, int n)
#else
long double __scalbnl (x,n)
long double x; int n;
#endif
{
int64_t k,l,hx,lx;
union { int64_t i; double d; } u;
GET_LDOUBLE_WORDS64(hx,lx,x);
k = (hx>>52)&0x7ff; /* extract exponent */
l = (lx>>52)&0x7ff;
if (k==0) { /* 0 or subnormal x */
if (((hx|lx)&0x7fffffffffffffffULL)==0) return x; /* +-0 */
u.i = hx;
u.d *= two54;
hx = u.i;
k = ((hx>>52)&0x7ff) - 54;
}
else if (k==0x7ff) return x+x; /* NaN or Inf */
k = k+n;
if (n> 50000 || k > 0x7fe)
return huge*__copysignl(huge,x); /* overflow */
if (n< -50000) return tiny*__copysignl(tiny,x); /*underflow */
if (k > 0) { /* normal result */
hx = (hx&0x800fffffffffffffULL)|(k<<52);
if ((lx & 0x7fffffffffffffffULL) == 0) { /* low part +-0 */
SET_LDOUBLE_WORDS64(x,hx,lx);
return x;
}
if (l == 0) { /* low part subnormal */
u.i = lx;
u.d *= two54;
lx = u.i;
l = ((lx>>52)&0x7ff) - 54;
}
l = l + n;
if (l > 0)
lx = (lx&0x800fffffffffffffULL)|(l<<52);
else if (l <= -54)
lx = (lx&0x8000000000000000ULL);
else {
l += 54;
u.i = (lx&0x800fffffffffffffULL)|(l<<52);
u.d *= twom54;
lx = u.i;
}
SET_LDOUBLE_WORDS64(x,hx,lx);
return x;
}
if (k <= -54)
return tiny*__copysignl(tiny,x); /*underflow*/
k += 54; /* subnormal result */
lx &= 0x8000000000000000ULL;
SET_LDOUBLE_WORDS64(x,(hx&0x800fffffffffffffULL)|(k<<52),lx);
return x*twolm54;
}
#ifdef IS_IN_libm
long_double_symbol (libm, __scalbnl, scalbnl);
#else
long_double_symbol (libc, __scalbnl, scalbnl);
#endif

37
sysdeps/ieee754/ldbl-128ibm/s_signbitl.c Normal file
View File

@ -0,0 +1,37 @@
/* Return nonzero value if number is negative.
Copyright (C) 1997,1999,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <math.h>
#include "math_private.h"
#include <math_ldbl_opt.h>
int
___signbitl (long double x)
{
int64_t e;
GET_LDOUBLE_MSW64 (e, x);
return e < 0;
}
#ifdef IS_IN_libm
long_double_symbol (libm, ___signbitl, __signbitl);
#else
long_double_symbol (libc, ___signbitl, __signbitl);
#endif

72
sysdeps/ieee754/ldbl-128ibm/s_sincosl.c Normal file
View File

@ -0,0 +1,72 @@
/* Compute sine and cosine of argument.
Copyright (C) 1997,1999,2004,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and
Jakub Jelinek <jj@ultra.linux.cz>.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <math.h>
#include "math_private.h"
#include <math_ldbl_opt.h>
void
__sincosl (long double x, long double *sinx, long double *cosx)
{
int64_t ix;
/* High word of x. */
GET_LDOUBLE_MSW64 (ix, x);
/* |x| ~< pi/4 */
ix &= 0x7fffffffffffffffLL;
if (ix <= 0x3fe921fb54442d10LL)
__kernel_sincosl (x, 0.0L, sinx, cosx, 0);
else if (ix >= 0x7ff0000000000000LL)
{
/* sin(Inf or NaN) is NaN */
*sinx = *cosx = x - x;
}
else
{
/* Argument reduction needed. */
long double y[2];
int n;
n = __ieee754_rem_pio2l (x, y);
switch (n & 3)
{
case 0:
__kernel_sincosl (y[0], y[1], sinx, cosx, 1);
break;
case 1:
__kernel_sincosl (y[0], y[1], cosx, sinx, 1);
*cosx = -*cosx;
break;
case 2:
__kernel_sincosl (y[0], y[1], sinx, cosx, 1);
*sinx = -*sinx;
*cosx = -*cosx;
break;
default:
__kernel_sincosl (y[0], y[1], cosx, sinx, 1);
*sinx = -*sinx;
break;
}
}
}
long_double_symbol (libm, __sincosl, sincosl);

84
sysdeps/ieee754/ldbl-128ibm/s_sinl.c Normal file
View File

@ -0,0 +1,84 @@
/* s_sinl.c -- long double version of s_sin.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* sinl(x)
* Return sine function of x.
*
* kernel function:
* __kernel_sinl ... sine function on [-pi/4,pi/4]
* __kernel_cosl ... cose function on [-pi/4,pi/4]
* __ieee754_rem_pio2l ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
long double __sinl(long double x)
#else
long double __sinl(x)
long double x;
#endif
{
long double y[2],z=0.0L;
int64_t n, ix;
/* High word of x. */
GET_LDOUBLE_MSW64(ix,x);
/* |x| ~< pi/4 */
ix &= 0x7fffffffffffffffLL;
if(ix <= 0x3fe921fb54442d10LL)
return __kernel_sinl(x,z,0);
/* sin(Inf or NaN) is NaN */
else if (ix>=0x7ff0000000000000LL) return x-x;
/* argument reduction needed */
else {
n = __ieee754_rem_pio2l(x,y);
switch(n&3) {
case 0: return __kernel_sinl(y[0],y[1],1);
case 1: return __kernel_cosl(y[0],y[1]);
case 2: return -__kernel_sinl(y[0],y[1],1);
default:
return -__kernel_cosl(y[0],y[1]);
}
}
}
long_double_symbol (libm, __sinl, sinl);

90
sysdeps/ieee754/ldbl-128ibm/s_tanhl.c Normal file
View File

@ -0,0 +1,90 @@
/* @(#)s_tanh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
#endif
/* Tanh(x)
* Return the Hyperbolic Tangent of x
*
* Method :
* x -x
* e - e
* 0. tanh(x) is defined to be -----------
* x -x
* e + e
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
* 2. 0 <= x <= 2**-57 : tanh(x) := x*(one+x)
* -t
* 2**-57 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
* t + 2
* 2
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
* t + 2
* 22.0 < x <= INF : tanh(x) := 1.
*
* Special cases:
* tanh(NaN) is NaN;
* only tanh(0)=0 is exact for finite argument.
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
#else
static long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
#endif
#ifdef __STDC__
long double __tanhl(long double x)
#else
long double __tanhl(x)
long double x;
#endif
{
long double t,z;
int64_t jx,ix,lx;
/* High word of |x|. */
GET_LDOUBLE_WORDS64(jx,lx,x);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) {
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
else return one/x-one; /* tanh(NaN) = NaN */
}
/* |x| < 22 */
if (ix < 0x4036000000000000LL) { /* |x|<22 */
if ((ix | (lx&0x7fffffffffffffffLL)) == 0)
return x; /* x == +-0 */
if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
return x*(one+x); /* tanh(small) = small */
if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */
t = __expm1l(two*fabsl(x));
z = one - two/(t+two);
} else {
t = __expm1l(-two*fabsl(x));
z= -t/(t+two);
}
/* |x| > 22, return +-1 */
} else {
z = one - tiny; /* raised inexact flag */
}
return (jx>=0)? z: -z;
}
long_double_symbol (libm, __tanhl, tanhl);

78
sysdeps/ieee754/ldbl-128ibm/s_tanl.c Normal file
View File

@ -0,0 +1,78 @@
/* s_tanl.c -- long double version of s_tan.c.
* Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/* @(#)s_tan.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* tanl(x)
* Return tangent function of x.
*
* kernel function:
* __kernel_tanl ... tangent function on [-pi/4,pi/4]
* __ieee754_rem_pio2l ... argument reduction routine
*
* Method.
* Let S,C and T denote the sin, cos and tan respectively on
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
* in [-pi/4 , +pi/4], and let n = k mod 4.
* We have
*
* n sin(x) cos(x) tan(x)
* ----------------------------------------------------------
* 0 S C T
* 1 C -S -1/T
* 2 -S -C T
* 3 -C S -1/T
* ----------------------------------------------------------
*
* Special cases:
* Let trig be any of sin, cos, or tan.
* trig(+-INF) is NaN, with signals;
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
*/
#include "math.h"
#include "math_private.h"
#include <math_ldbl_opt.h>
#ifdef __STDC__
long double __tanl(long double x)
#else
long double __tanl(x)
long double x;
#endif
{
long double y[2],z=0.0L;
int64_t n, ix;
/* High word of x. */
GET_LDOUBLE_MSW64(ix,x);
/* |x| ~< pi/4 */
ix &= 0x7fffffffffffffffLL;
if(ix <= 0x3fe921fb54442d10LL) return __kernel_tanl(x,z,1);
/* tanl(Inf or NaN) is NaN */
else if (ix>=0x7ff0000000000000LL) return x-x; /* NaN */
/* argument reduction needed */
else {
n = __ieee754_rem_pio2l(x,y);
return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
-1 -- n odd */
}
}
long_double_symbol (libm, __tanl, tanl);

119
sysdeps/ieee754/ldbl-128ibm/s_truncl.c Normal file
View File

@ -0,0 +1,119 @@
/* Truncate (toward zero) long double floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* This has been coded in assembler because GCC makes such a mess of it
when it's coded in C. */
#include <math.h>
#include <fenv.h>
#include <math_ldbl_opt.h>
#include <float.h>
#include <ieee754.h>
#ifdef __STDC__
long double
__truncl (long double x)
#else
long double
__truncl (x)
long double x;
#endif
{
static const double TWO52 = 4503599627370496.0L;
int mode = fegetround();
union ibm_extended_long_double u;
u.d = x;
if (fabs (u.dd[0]) < TWO52)
{
fesetround(FE_TOWARDZERO);
if (u.dd[0] > 0.0)
{
u.dd[0] += TWO52;
u.dd[0] -= TWO52;
}
else if (u.dd[0] < 0.0)
{
u.dd[0] = TWO52 - u.dd[0];
u.dd[0] = -(u.dd[0] - TWO52);
}
u.dd[1] = 0.0;
fesetround(mode);
}
else if (fabs (u.dd[1]) < TWO52 && u.dd[1] != 0.0)
{
double high, low;
/* In this case we have to round the low double and handle any
adjustment to the high double that may be caused by rounding
(up). This is complicated by the fact that the high double
may already be rounded and the low double may have the
opposite sign to compensate. */
if (u.dd[0] > 0.0)
{
if (u.dd[1] > 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] < 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_TOWARDZERO);
low += TWO52;
low -= TWO52;
fesetround(mode);
}
else if (u.dd[0] < 0.0)
{
if (u.dd[1] < 0.0)
{
/* If the high/low doubles are the same sign then simply
round the low double. */
high = u.dd[0];
low = u.dd[1];
}
else if (u.dd[1] > 0.0)
{
/* Else the high double is pre rounded and we need to
adjust for that. */
high = nextafter (u.dd[0], 0.0);
low = u.dd[1] + (u.dd[0] - high);
}
fesetround(FE_TOWARDZERO);
low = TWO52 - low;
low = -(low - TWO52);
fesetround(mode);
}
u.dd[0] = high + low;
u.dd[1] = high - u.dd[0] + low;
}
return u.d;
}
long_double_symbol (libm, __truncl, truncl);

63
sysdeps/ieee754/ldbl-128ibm/strtold_l.c Normal file
View File

@ -0,0 +1,63 @@
/* Copyright (C) 1999, 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <math.h>
#include <stdlib.h>
#include <wchar.h>
#include <xlocale.h>
/* The actual implementation for all floating point sizes is in strtod.c.
These macros tell it to produce the `long double' version, `strtold'. */
#define FLOAT long double
#define FLT LDBL
#ifdef USE_WIDE_CHAR
extern long double ____new_wcstold_l (const wchar_t *, wchar_t **, __locale_t);
# define STRTOF __new_wcstold_l
# define __STRTOF ____new_wcstold_l
# define ____STRTOF_INTERNAL ____wcstold_l_internal
#else
extern long double ____new_strtold_l (const char *, char **, __locale_t);
# define STRTOF __new_strtold_l
# define __STRTOF ____new_strtold_l
# define ____STRTOF_INTERNAL ____strtold_l_internal
#endif
#define MPN2FLOAT __mpn_construct_long_double
#define FLOAT_HUGE_VAL HUGE_VALL
# define SET_MANTISSA(flt, mant) \
do { union ibm_extended_long_double u; \
u.d = (flt); \
if ((mant & 0xfffffffffffffULL) == 0) \
mant = 0x8000000000000ULL; \
u.ieee.mantissa0 = ((mant) >> 32) & 0xfffff; \
u.ieee.mantissa1 = (mant) & 0xffffffff; \
(flt) = u.d; \
} while (0)
#include <strtod_l.c>
#ifdef __LONG_DOUBLE_MATH_OPTIONAL
# include <math_ldbl_opt.h>
# ifdef USE_WIDE_CHAR
long_double_symbol (libc, __new_wcstold_l, wcstold_l);
long_double_symbol (libc, ____new_wcstold_l, __wcstold_l);
# else
long_double_symbol (libc, __new_strtold_l, strtold_l);
long_double_symbol (libc, ____new_strtold_l, __strtold_l);
# endif
#endif

694
sysdeps/ieee754/ldbl-128ibm/t_sincosl.c Normal file
View File

@ -0,0 +1,694 @@
/* Quad-precision floating point sine and cosine tables.
Copyright (C) 1999,2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* For 0.1484375 + n/128.0, n=0..82 this table contains
first 113 bits of cosine, then at least 113 additional
bits and the same for sine.
0.1484375+82.0/128.0 is the smallest number among above defined numbers
larger than pi/4.
Computed using gmp.
*/
const long double __sincosl_table[] = {
/* x = 1.48437500000000000000000000000000000e-01L 3ffc3000000000000000000000000000 */
/* cos(x) = 0.fd2f5320e1b790209b4dda2f98 f79caaa7b873aff1014b0fbc52 43766d03cb006bc837c4358 */
0x0.fd2f5320e1b790209b4dda2f98p0L,
0x0.f79caaa7b873aff1014b0fbc52p-104L,
/* sin(x) = 0.25dc50bc95711d0d9787d108fd 438cf5959ee0bfb7a1e36e8b1a 112968f356657420e9cc9ea */
0x0.25dc50bc95711d0d9787d108fdp0L,
0x0.438cf5959ee0bfb7a1e36e8b1ap-104L,
/* x = 1.56250000000000000000000000000000000e-01 3ffc4000000000000000000000000000 */
/* cos(x) = 0.fce1a053e621438b6d60c76e8c 45bf0a9dc71aa16f922acc10e9 5144ec796a249813c9cb649 */
0x0.fce1a053e621438b6d60c76e8cp0L,
0x0.45bf0a9dc71aa16f922acc10e9p-104L,
/* sin(x) = 0.27d66258bacd96a3eb335b365c 87d59438c5142bb56a489e9b8d b9d36234ffdebb6bdc22d8e */
0x0.27d66258bacd96a3eb335b365cp0L,
0x0.87d59438c5142bb56a489e9b8dp-104L,
/* x = 1.64062500000000000000000000000000000e-01 3ffc5000000000000000000000000000 */
/* cos(x) = 0.fc8ffa01ba6807417e05962b0d 9fdf1fddb0cc4c07d22e19e080 19bffa50a6c7acdb40307a3 */
0x0.fc8ffa01ba6807417e05962b0dp0L,
0x0.9fdf1fddb0cc4c07d22e19e080p-104L,
/* sin(x) = 0.29cfd49b8be4f665276cab01cb f0426934906c3dd105473b226e 410b1450f62e53ff7c6cce1 */
0x0.29cfd49b8be4f665276cab01cbp0L,
0x0.f0426934906c3dd105473b226ep-104L,
/* x = 1.71875000000000000000000000000000000e-01 3ffc6000000000000000000000000000 */
/* cos(x) = 0.fc3a6170f767ac735d63d99a9d 439e1db5e59d3ef153a4265d58 55850ed82b536bf361b80e3 */
0x0.fc3a6170f767ac735d63d99a9dp0L,
0x0.439e1db5e59d3ef153a4265d58p-104L,
/* sin(x) = 0.2bc89f9f424de5485de7ce03b2 514952b9faf5648c3244d4736f eb95dbb9da49f3b58a9253b */
0x0.2bc89f9f424de5485de7ce03b2p0L,
0x0.514952b9faf5648c3244d4736fp-104L,
/* x = 1.79687500000000000000000000000000000e-01 3ffc7000000000000000000000000000 */
/* cos(x) = 0.fbe0d7f7fef11e70aa43b8abf4 f6a457cea20c8f3f676b47781f 9821bbe9ce04b3c7b981c0b */
0x0.fbe0d7f7fef11e70aa43b8abf4p0L,
0x0.f6a457cea20c8f3f676b47781fp-104L,
/* sin(x) = 0.2dc0bb80b49a97ffb34e8dd1f8 db9df7af47ed2dcf58b12c8e78 27e048cae929da02c04ecac */
0x0.2dc0bb80b49a97ffb34e8dd1f8p0L,
0x0.db9df7af47ed2dcf58b12c8e78p-104L,
/* x = 1.87500000000000000000000000000000000e-01 3ffc8000000000000000000000000000 */
/* cos(x) = 0.fb835efcf670dd2ce6fe792469 7eea13ea358867e9cdb3899b78 3f4f9f43aa5626e8b67b3bc */
0x0.fb835efcf670dd2ce6fe792469p0L,
0x0.7eea13ea358867e9cdb3899b78p-104L,
/* sin(x) = 0.2fb8205f75e56a2b56a1c4792f 856258769af396e0189ef72c05 e4df59a6b00e4b44a6ea515 */
0x0.2fb8205f75e56a2b56a1c4792fp0L,
0x0.856258769af396e0189ef72c05p-104L,
/* x = 1.95312500000000000000000000000000000e-01 3ffc9000000000000000000000000000 */
/* cos(x) = 0.fb21f7f5c156696b00ac1fe28a c5fd76674a92b4df80d9c8a46c 684399005deccc41386257c */
0x0.fb21f7f5c156696b00ac1fe28ap0L,
0x0.c5fd76674a92b4df80d9c8a46cp-104L,
/* sin(x) = 0.31aec65df552876f82ece9a235 6713246eba6799983d7011b0b3 698d6e1da919c15d57c30c1 */
0x0.31aec65df552876f82ece9a235p0L,
0x0.6713246eba6799983d7011b0b3p-104L,
/* x = 2.03125000000000000000000000000000000e-01 3ffca000000000000000000000000000 */
/* cos(x) = 0.fabca467fb3cb8f1d069f01d8e a33ade5bfd68296ecd1cc9f7b7 609bbcf3676e726c3301334 */
0x0.fabca467fb3cb8f1d069f01d8ep0L,
0x0.a33ade5bfd68296ecd1cc9f7b7p-104L,
/* sin(x) = 0.33a4a5a19d86246710f602c44d f4fa513f4639ce938477aeeabb 82e8e0a7ed583a188879fd4 */
0x0.33a4a5a19d86246710f602c44dp0L,
0x0.f4fa513f4639ce938477aeeabbp-104L,
/* x = 2.10937500000000000000000000000000000e-01 3ffcb000000000000000000000000000 */
/* cos(x) = 0.fa5365e8f1d3ca27be1db5d76a e64d983d7470a4ab0f4ccf65a2 b8c67a380df949953a09bc1 */
0x0.fa5365e8f1d3ca27be1db5d76ap0L,
0x0.e64d983d7470a4ab0f4ccf65a2p-104L,
/* sin(x) = 0.3599b652f40ec999df12a0a4c8 561de159c98d4e54555de518b9 7f48886f715d8df5f4f093e */
0x0.3599b652f40ec999df12a0a4c8p0L,
0x0.561de159c98d4e54555de518b9p-104L,
/* x = 2.18750000000000000000000000000000000e-01 3ffcc000000000000000000000000000 */
/* cos(x) = 0.f9e63e1d9e8b6f6f2e296bae5b 5ed9c11fd7fa2fe11e09fc7bde 901abed24b6365e72f7db4e */
0x0.f9e63e1d9e8b6f6f2e296bae5bp0L,
0x0.5ed9c11fd7fa2fe11e09fc7bdep-104L,
/* sin(x) = 0.378df09db8c332ce0d2b53d865 582e4526ea336c768f68c32b49 6c6d11c1cd241bb9f1da523 */
0x0.378df09db8c332ce0d2b53d865p0L,
0x0.582e4526ea336c768f68c32b49p-104L,
/* x = 2.26562500000000000000000000000000000e-01 3ffcd000000000000000000000000000 */
/* cos(x) = 0.f9752eba9fff6b98842beadab0 54a932fb0f8d5b875ae63d6b22 88d09b148921aeb6e52f61b */
0x0.f9752eba9fff6b98842beadab0p0L,
0x0.54a932fb0f8d5b875ae63d6b22p-104L,
/* sin(x) = 0.39814cb10513453cb97b21bc1c a6a337b150c21a675ab85503bc 09a436a10ab1473934e20c8 */
0x0.39814cb10513453cb97b21bc1cp0L,
0x0.a6a337b150c21a675ab85503bcp-104L,
/* x = 2.34375000000000000000000000000000000e-01 3ffce000000000000000000000000000 */
/* cos(x) = 0.f90039843324f9b940416c1984 b6cbed1fc733d97354d4265788 a86150493ce657cae032674 */
0x0.f90039843324f9b940416c1984p0L,
0x0.b6cbed1fc733d97354d4265788p-104L,
/* sin(x) = 0.3b73c2bf6b4b9f668ef9499c81 f0d965087f1753fa64b086e58c b8470515c18c1412f8c2e02 */
0x0.3b73c2bf6b4b9f668ef9499c81p0L,
0x0.f0d965087f1753fa64b086e58cp-104L,
/* x = 2.42187500000000000000000000000000000e-01 3ffcf000000000000000000000000000 */
/* cos(x) = 0.f887604e2c39dbb20e4ec58250 59a789ffc95b275ad9954078ba 8a28d3fcfe9cc2c1d49697b */
0x0.f887604e2c39dbb20e4ec58250p0L,
0x0.59a789ffc95b275ad9954078bap-104L,
/* sin(x) = 0.3d654aff15cb457a0fca854698 aba33039a8a40626609204472d 9d40309b626eccc6dff0ffa */
0x0.3d654aff15cb457a0fca854698p0L,
0x0.aba33039a8a40626609204472dp-104L,
/* x = 2.50000000000000000000000000000000000e-01 3ffd0000000000000000000000000000 */
/* cos(x) = 0.f80aa4fbef750ba783d33cb95f 94f8a41426dbe79edc4a023ef9 ec13c944551c0795b84fee1 */
0x0.f80aa4fbef750ba783d33cb95fp0L,
0x0.94f8a41426dbe79edc4a023ef9p-104L,
/* sin(x) = 0.3f55dda9e62aed7513bd7b8e6a 3d1635dd5676648d7db525898d 7086af9330f03c7f285442a */
0x0.3f55dda9e62aed7513bd7b8e6ap0L,
0x0.3d1635dd5676648d7db525898dp-104L,
/* x = 2.57812500000000000000000000000000000e-01 3ffd0800000000000000000000000000 */
/* cos(x) = 0.f78a098069792daabc9ee42591 b7c5a68cb1ab822aeb446b3311 b4ba5371b8970e2c1547ad7 */
0x0.f78a098069792daabc9ee42591p0L,
0x0.b7c5a68cb1ab822aeb446b3311p-104L,
/* sin(x) = 0.414572fd94556e6473d6202713 88dd47c0ba050cdb5270112e3e 370e8c4705ae006426fb5d5 */
0x0.414572fd94556e6473d6202713p0L,
0x0.88dd47c0ba050cdb5270112e3ep-104L,
/* x = 2.65625000000000000000000000000000000e-01 3ffd1000000000000000000000000000 */
/* cos(x) = 0.f7058fde0788dfc805b8fe8878 9e4f4253e3c50afe8b22f41159 620ab5940ff7df9557c0d1f */
0x0.f7058fde0788dfc805b8fe8878p0L,
0x0.9e4f4253e3c50afe8b22f41159p-104L,
/* sin(x) = 0.4334033bcd90d6604f5f36c1d4 b84451a87150438275b77470b5 0e5b968fa7962b5ffb379b7 */
0x0.4334033bcd90d6604f5f36c1d4p0L,
0x0.b84451a87150438275b77470b5p-104L,
/* x = 2.73437500000000000000000000000000000e-01 3ffd1800000000000000000000000000 */
/* cos(x) = 0.f67d3a26af7d07aa4bd6d42af8 c0067fefb96d5b46c031eff536 27f215ea3242edc3f2e13eb */
0x0.f67d3a26af7d07aa4bd6d42af8p0L,
0x0.c0067fefb96d5b46c031eff536p-104L,
/* sin(x) = 0.452186aa5377ab20bbf2524f52 e3a06a969f47166ab88cf88c11 1ad12c55941021ef3317a1a */
0x0.452186aa5377ab20bbf2524f52p0L,
0x0.e3a06a969f47166ab88cf88c11p-104L,
/* x = 2.81250000000000000000000000000000000e-01 3ffd2000000000000000000000000000 */
/* cos(x) = 0.f5f10a7bb77d3dfa0c1da8b578 42783280d01ce3c0f82bae3b9d 623c168d2e7c29977994451 */
0x0.f5f10a7bb77d3dfa0c1da8b578p0L,
0x0.42783280d01ce3c0f82bae3b9dp-104L,
/* sin(x) = 0.470df5931ae1d946076fe0dcff 47fe31bb2ede618ebc607821f8 462b639e1f4298b5ae87fd3 */
0x0.470df5931ae1d946076fe0dcffp0L,
0x0.47fe31bb2ede618ebc607821f8p-104L,
/* x = 2.89062500000000000000000000000000000e-01 3ffd2800000000000000000000000000 */
/* cos(x) = 0.f561030ddd7a78960ea9f4a32c 6521554995667f5547bafee9ec 48b3155cdb0f7fd00509713 */
0x0.f561030ddd7a78960ea9f4a32cp0L,
0x0.6521554995667f5547bafee9ecp-104L,
/* sin(x) = 0.48f948446abcd6b0f7fccb100e 7a1b26eccad880b0d24b59948c 7cdd49514d44b933e6985c2 */
0x0.48f948446abcd6b0f7fccb100ep0L,
0x0.7a1b26eccad880b0d24b59948cp-104L,
/* x = 2.96875000000000000000000000000000000e-01 3ffd3000000000000000000000000000 */
/* cos(x) = 0.f4cd261d3e6c15bb369c875863 0d2ac00b7ace2a51c0631bfeb3 9ed158ba924cc91e259c195 */
0x0.f4cd261d3e6c15bb369c875863p0L,
0x0.0d2ac00b7ace2a51c0631bfeb3p-104L,
/* sin(x) = 0.4ae37710fad27c8aa9c4cf96c0 3519b9ce07dc08a1471775499f 05c29f86190aaebaeb9716e */
0x0.4ae37710fad27c8aa9c4cf96c0p0L,
0x0.3519b9ce07dc08a1471775499fp-104L,
/* x = 3.04687500000000000000000000000000000e-01 3ffd3800000000000000000000000000 */
/* cos(x) = 0.f43575f94d4f6b272f5fb76b14 d2a64ab52df1ee8ddf7c651034 e5b2889305a9ea9015d758a */
0x0.f43575f94d4f6b272f5fb76b14p0L,
0x0.d2a64ab52df1ee8ddf7c651034p-104L,
/* sin(x) = 0.4ccc7a50127e1de0cb6b40c302 c651f7bded4f9e7702b0471ae0 288d091a37391950907202f */
0x0.4ccc7a50127e1de0cb6b40c302p0L,
0x0.c651f7bded4f9e7702b0471ae0p-104L,
/* x = 3.12500000000000000000000000000000000e-01 3ffd4000000000000000000000000000 */
/* cos(x) = 0.f399f500c9e9fd37ae9957263d ab8877102beb569f101ee44953 50868e5847d181d50d3cca2 */
0x0.f399f500c9e9fd37ae9957263dp0L,
0x0.ab8877102beb569f101ee44953p-104L,
/* sin(x) = 0.4eb44a5da74f600207aaa090f0 734e288603ffadb3eb2542a469 77b105f8547128036dcf7f0 */
0x0.4eb44a5da74f600207aaa090f0p0L,
0x0.734e288603ffadb3eb2542a469p-104L,
/* x = 3.20312500000000000000000000000000000e-01 3ffd4800000000000000000000000000 */
/* cos(x) = 0.f2faa5a1b74e82fd61fa05f917 7380e8e69b7b15a945e8e5ae11 24bf3d12b0617e03af4fab5 */
0x0.f2faa5a1b74e82fd61fa05f917p0L,
0x0.7380e8e69b7b15a945e8e5ae11p-104L,
/* sin(x) = 0.509adf9a7b9a5a0f638a8fa3a6 0a199418859f18b37169a644fd b986c21ecb00133853bc35b */
0x0.509adf9a7b9a5a0f638a8fa3a6p0L,
0x0.0a199418859f18b37169a644fdp-104L,
/* x = 3.28125000000000000000000000000000000e-01 3ffd5000000000000000000000000000 */
/* cos(x) = 0.f2578a595224dd2e6bfa2eb2f9 9cc674f5ea6f479eae2eb58018 6897ae3f893df1113ca06b8 */
0x0.f2578a595224dd2e6bfa2eb2f9p0L,
0x0.9cc674f5ea6f479eae2eb58018p-104L,
/* sin(x) = 0.5280326c3cf481823ba6bb08ea c82c2093f2bce3c4eb4ee3dec7 df41c92c8a4226098616075 */
0x0.5280326c3cf481823ba6bb08eap0L,
0x0.c82c2093f2bce3c4eb4ee3dec7p-104L,
/* x = 3.35937500000000000000000000000000000e-01 3ffd5800000000000000000000000000 */
/* cos(x) = 0.f1b0a5b406b526d886c55feadc 8d0dcc8eb9ae2ac707051771b4 8e05b25b000009660bdb3e3 */
0x0.f1b0a5b406b526d886c55feadcp0L,
0x0.8d0dcc8eb9ae2ac707051771b4p-104L,
/* sin(x) = 0.54643b3da29de9b357155eef0f 332fb3e66c83bf4dddd9491c5e b8e103ccd92d6175220ed51 */
0x0.54643b3da29de9b357155eef0fp0L,
0x0.332fb3e66c83bf4dddd9491c5ep-104L,
/* x = 3.43750000000000000000000000000000000e-01 3ffd6000000000000000000000000000 */
/* cos(x) = 0.f105fa4d66b607a67d44e04272 5204435142ac8ad54dfb0907a4 f6b56b06d98ee60f19e557a */
0x0.f105fa4d66b607a67d44e04272p0L,
0x0.5204435142ac8ad54dfb0907a4p-104L,
/* sin(x) = 0.5646f27e8bd65cbe3a5d61ff06 572290ee826d9674a00246b05a e26753cdfc90d9ce81a7d02 */
0x0.5646f27e8bd65cbe3a5d61ff06p0L,
0x0.572290ee826d9674a00246b05ap-104L,
/* x = 3.51562500000000000000000000000000000e-01 3ffd6800000000000000000000000000 */
/* cos(x) = 0.f0578ad01ede707fa39c09dc6b 984afef74f3dc8d0efb0f4c5a6 b13771145b3e0446fe33887 */
0x0.f0578ad01ede707fa39c09dc6bp0L,
0x0.984afef74f3dc8d0efb0f4c5a6p-104L,
/* sin(x) = 0.582850a41e1dd46c7f602ea244 cdbbbfcdfa8f3189be794dda42 7ce090b5f85164f1f80ac13 */
0x0.582850a41e1dd46c7f602ea244p0L,
0x0.cdbbbfcdfa8f3189be794dda42p-104L,
/* x = 3.59375000000000000000000000000000000e-01 3ffd7000000000000000000000000000 */
/* cos(x) = 0.efa559f5ec3aec3a4eb0331927 8a2d41fcf9189462261125fe61 47b078f1daa0b06750a1654 */
0x0.efa559f5ec3aec3a4eb0331927p0L,
0x0.8a2d41fcf9189462261125fe61p-104L,
/* sin(x) = 0.5a084e28e35fda2776dfdbbb55 31d74ced2b5d17c0b1afc46475 29d50c295e36d8ceec126c1 */
0x0.5a084e28e35fda2776dfdbbb55p0L,
0x0.31d74ced2b5d17c0b1afc46475p-104L,
/* x = 3.67187500000000000000000000000000000e-01 3ffd7800000000000000000000000000 */
/* cos(x) = 0.eeef6a879146af0bf9b95ea2ea 0ac0d3e2e4d7e15d93f48cbd41 bf8e4fded40bef69e19eafa */
0x0.eeef6a879146af0bf9b95ea2eap0L,
0x0.0ac0d3e2e4d7e15d93f48cbd41p-104L,
/* sin(x) = 0.5be6e38ce8095542bc14ee9da0 d36483e6734bcab2e07624188a f5653f114eeb46738fa899d */
0x0.5be6e38ce8095542bc14ee9da0p0L,
0x0.d36483e6734bcab2e07624188ap-104L,
/* x = 3.75000000000000000000000000000000000e-01 3ffd8000000000000000000000000000 */
/* cos(x) = 0.ee35bf5ccac89052cd91ddb734 d3a47e262e3b609db604e21705 3803be0091e76daf28a89b7 */
0x0.ee35bf5ccac89052cd91ddb734p0L,
0x0.d3a47e262e3b609db604e21705p-104L,
/* sin(x) = 0.5dc40955d9084f48a94675a249 8de5d851320ff5528a6afb3f2e 24de240fce6cbed1ba0ccd6 */
0x0.5dc40955d9084f48a94675a249p0L,
0x0.8de5d851320ff5528a6afb3f2ep-104L,
/* x = 3.82812500000000000000000000000000000e-01 3ffd8800000000000000000000000000 */
/* cos(x) = 0.ed785b5c44741b4493c56bcb9d 338a151c6f6b85d8f8aca658b2 8572c162b199680eb9304da */
0x0.ed785b5c44741b4493c56bcb9dp0L,
0x0.338a151c6f6b85d8f8aca658b2p-104L,
/* sin(x) = 0.5f9fb80f21b53649c432540a50 e22c53057ff42ae0fdf1307760 dc0093f99c8efeb2fbd7073 */
0x0.5f9fb80f21b53649c432540a50p0L,
0x0.e22c53057ff42ae0fdf1307760p-104L,
/* x = 3.90625000000000000000000000000000000e-01 3ffd9000000000000000000000000000 */
/* cos(x) = 0.ecb7417b8d4ee3fec37aba4073 aa48f1f14666006fb431d96713 03c8100d10190ec8179c41d */
0x0.ecb7417b8d4ee3fec37aba4073p0L,
0x0.aa48f1f14666006fb431d96713p-104L,
/* sin(x) = 0.6179e84a09a5258a40e9b5face 03e525f8b5753cd0105d93fe62 98010c3458e84d75fe420e9 */
0x0.6179e84a09a5258a40e9b5facep0L,
0x0.03e525f8b5753cd0105d93fe62p-104L,
/* x = 3.98437500000000000000000000000000000e-01 3ffd9800000000000000000000000000 */
/* cos(x) = 0.ebf274bf0bda4f62447e56a093 626798d3013b5942b1abfd155a acc9dc5c6d0806a20d6b9c1 */
0x0.ebf274bf0bda4f62447e56a093p0L,
0x0.626798d3013b5942b1abfd155ap-104L,
/* sin(x) = 0.6352929dd264bd44a02ea76632 5d8aa8bd9695fc8def3caefba5 b94c9a3c873f7b2d3776ead */
0x0.6352929dd264bd44a02ea76632p0L,
0x0.5d8aa8bd9695fc8def3caefba5p-104L,
/* x = 4.06250000000000000000000000000000000e-01 3ffda000000000000000000000000000 */
/* cos(x) = 0.eb29f839f201fd13b937968279 16a78f15c85230a4e8ea4b2155 8265a14367e1abb4c30695a */
0x0.eb29f839f201fd13b937968279p0L,
0x0.16a78f15c85230a4e8ea4b2155p-104L,
/* sin(x) = 0.6529afa7d51b129631ec197c0a 840a11d7dc5368b0a47956feb2 85caa8371c4637ef17ef01b */
0x0.6529afa7d51b129631ec197c0ap0L,
0x0.840a11d7dc5368b0a47956feb2p-104L,
/* x = 4.14062500000000000000000000000000000e-01 3ffda800000000000000000000000000 */
/* cos(x) = 0.ea5dcf0e30cf03e6976ef0b1ec 26515fba47383855c3b4055a99 b5e86824b2cd1a691fdca7b */
0x0.ea5dcf0e30cf03e6976ef0b1ecp0L,
0x0.26515fba47383855c3b4055a99p-104L,
/* sin(x) = 0.66ff380ba0144109e39a320b0a 3fa5fd65ea0585bcbf9b1a769a 9b0334576c658139e1a1cbe */
0x0.66ff380ba0144109e39a320b0ap0L,
0x0.3fa5fd65ea0585bcbf9b1a769ap-104L,
/* x = 4.21875000000000000000000000000000000e-01 3ffdb000000000000000000000000000 */
/* cos(x) = 0.e98dfc6c6be031e60dd3089cbd d18a75b1f6b2c1e97f79225202 f03dbea45b07a5ec4efc062 */
0x0.e98dfc6c6be031e60dd3089cbdp0L,
0x0.d18a75b1f6b2c1e97f79225202p-104L,
/* sin(x) = 0.68d32473143327973bc712bcc4 ccddc47630d755850c0655243b 205934dc49ffed8eb76adcb */
0x0.68d32473143327973bc712bcc4p0L,
0x0.ccddc47630d755850c0655243bp-104L,
/* x = 4.29687500000000000000000000000000000e-01 3ffdb800000000000000000000000000 */
/* cos(x) = 0.e8ba8393eca7821aa563d83491 b6101189b3b101c3677f73d7ba d7c10f9ee02b7ab4009739a */
0x0.e8ba8393eca7821aa563d83491p0L,
0x0.b6101189b3b101c3677f73d7bap-104L,
/* sin(x) = 0.6aa56d8e8249db4eb60a761fe3 f9e559be456b9e13349ca99b0b fb787f22b95db3b70179615 */
0x0.6aa56d8e8249db4eb60a761fe3p0L,
0x0.f9e559be456b9e13349ca99b0bp-104L,
/* x = 4.37500000000000000000000000000000000e-01 3ffdc000000000000000000000000000 */
/* cos(x) = 0.e7e367d2956cfb16b6aa11e541 9cd0057f5c132a6455bf064297 e6a76fe2b72bb630d6d50ff */
0x0.e7e367d2956cfb16b6aa11e541p0L,
0x0.9cd0057f5c132a6455bf064297p-104L,
/* sin(x) = 0.6c760c14c8585a51dbd34660ae 6c52ac7036a0b40887a0b63724 f8b4414348c3063a637f457 */
0x0.6c760c14c8585a51dbd34660aep0L,
0x0.6c52ac7036a0b40887a0b63724p-104L,
/* x = 4.45312500000000000000000000000000000e-01 3ffdc800000000000000000000000000 */
/* cos(x) = 0.e708ac84d4172a3e2737662213 429e14021074d7e702e77d72a8 f1101a7e70410df8273e9aa */
0x0.e708ac84d4172a3e2737662213p0L,
0x0.429e14021074d7e702e77d72a8p-104L,
/* sin(x) = 0.6e44f8c36eb10a1c752d093c00 f4d47ba446ac4c215d26b03164 42f168459e677d06e7249e3 */
0x0.6e44f8c36eb10a1c752d093c00p0L,
0x0.f4d47ba446ac4c215d26b03164p-104L,
/* x = 4.53125000000000000000000000000000000e-01 3ffdd000000000000000000000000000 */
/* cos(x) = 0.e62a551594b970a770b15d41d4 c0e483e47aca550111df6966f9 e7ac3a94ae49e6a71eb031e */
0x0.e62a551594b970a770b15d41d4p0L,
0x0.c0e483e47aca550111df6966f9p-104L,
/* sin(x) = 0.70122c5ec5028c8cff33abf4fd 340ccc382e038379b09cf04f9a 52692b10b72586060cbb001 */
0x0.70122c5ec5028c8cff33abf4fdp0L,
0x0.340ccc382e038379b09cf04f9ap-104L,
/* x = 4.60937500000000000000000000000000000e-01 3ffdd800000000000000000000000000 */
/* cos(x) = 0.e54864fe33e8575cabf5bd0e5c f1b1a8bc7c0d5f61702450fa6b 6539735820dd2603ae355d5 */
0x0.e54864fe33e8575cabf5bd0e5cp0L,
0x0.f1b1a8bc7c0d5f61702450fa6bp-104L,
/* sin(x) = 0.71dd9fb1ff4677853acb970a9f 6729c6e3aac247b1c57cea66c7 7413f1f98e8b9e98e49d851 */
0x0.71dd9fb1ff4677853acb970a9fp0L,
0x0.6729c6e3aac247b1c57cea66c7p-104L,
/* x = 4.68750000000000000000000000000000000e-01 3ffde000000000000000000000000000 */
/* cos(x) = 0.e462dfc670d421ab3d1a159012 28f146a0547011202bf5ab01f9 14431859aef577966bc4fa4 */
0x0.e462dfc670d421ab3d1a159012p0L,
0x0.28f146a0547011202bf5ab01f9p-104L,
/* sin(x) = 0.73a74b8f52947b681baf6928eb 3fb021769bf4779bad0e3aa9b1 cdb75ec60aad9fc63ff19d5 */
0x0.73a74b8f52947b681baf6928ebp0L,
0x0.3fb021769bf4779bad0e3aa9b1p-104L,
/* x = 4.76562500000000000000000000000000000e-01 3ffde800000000000000000000000000 */
/* cos(x) = 0.e379c9045f29d517c4808aa497 c2057b2b3d109e76c0dc302d4d 0698b36e3f0bdbf33d8e952 */
0x0.e379c9045f29d517c4808aa497p0L,
0x0.c2057b2b3d109e76c0dc302d4dp-104L,
/* sin(x) = 0.756f28d011d98528a44a75fc29 c779bd734ecdfb582fdb74b68a 4c4c4be54cfd0b2d3ad292f */
0x0.756f28d011d98528a44a75fc29p0L,
0x0.c779bd734ecdfb582fdb74b68ap-104L,
/* x = 4.84375000000000000000000000000000000e-01 3ffdf000000000000000000000000000 */
/* cos(x) = 0.e28d245c58baef72225e232abc 003c4366acd9eb4fc2808c2ab7 fe7676cf512ac7f945ae5fb */
0x0.e28d245c58baef72225e232abcp0L,
0x0.003c4366acd9eb4fc2808c2ab7p-104L,
/* sin(x) = 0.77353054ca72690d4c6e171fd9 9e6b39fa8e1ede5f052fd29645 34c75340970a3a9cd3c5c32 */
0x0.77353054ca72690d4c6e171fd9p0L,
0x0.9e6b39fa8e1ede5f052fd29645p-104L,
/* x = 4.92187500000000000000000000000000000e-01 3ffdf800000000000000000000000000 */
/* cos(x) = 0.e19cf580eeec046aa1422fa748 07ecefb2a1911c94e7b5f20a00 f70022d940193691e5bd790 */
0x0.e19cf580eeec046aa1422fa748p0L,
0x0.07ecefb2a1911c94e7b5f20a00p-104L,
/* sin(x) = 0.78f95b0560a9a3bd6df7bd981d c38c61224d08bc20631ea932e6 05e53b579e9e0767dfcbbcb */
0x0.78f95b0560a9a3bd6df7bd981dp0L,
0x0.c38c61224d08bc20631ea932e6p-104L,
/* x = 5.00000000000000000000000000000000000e-01 3ffe0000000000000000000000000000 */
/* cos(x) = 0.e0a94032dbea7cedbddd9da2fa fad98556566b3a89f43eabd723 50af3e8b19e801204d8fe2e */
0x0.e0a94032dbea7cedbddd9da2fap0L,
0x0.fad98556566b3a89f43eabd723p-104L,
/* sin(x) = 0.7abba1d12c17bfa1d92f0d93f6 0ded9992f45b4fcaf13cd58b30 3693d2a0db47db35ae8a3a9 */
0x0.7abba1d12c17bfa1d92f0d93f6p0L,
0x0.0ded9992f45b4fcaf13cd58b30p-104L,
/* x = 5.07812500000000000000000000000000000e-01 3ffe0400000000000000000000000000 */
/* cos(x) = 0.dfb20840f3a9b36f7ae2c51534 2890b5ec583b8366cc2b55029e 95094d31112383f2553498b */
0x0.dfb20840f3a9b36f7ae2c51534p0L,
0x0.2890b5ec583b8366cc2b55029ep-104L,
/* sin(x) = 0.7c7bfdaf13e5ed17212f8a7525 bfb113aba6c0741b5362bb8d59 282a850b63716bca0c910f0 */
0x0.7c7bfdaf13e5ed17212f8a7525p0L,
0x0.bfb113aba6c0741b5362bb8d59p-104L,
/* x = 5.15625000000000000000000000000000000e-01 3ffe0800000000000000000000000000 */
/* cos(x) = 0.deb7518814a7a931bbcc88c109 cd41c50bf8bb48f20ae8c36628 d1d3d57574f7dc58f27d91c */
0x0.deb7518814a7a931bbcc88c109p0L,
0x0.cd41c50bf8bb48f20ae8c36628p-104L,
/* sin(x) = 0.7e3a679daaf25c676542bcb402 8d0964172961c921823a4ef0c3 a9070d886dbd073f6283699 */
0x0.7e3a679daaf25c676542bcb402p0L,
0x0.8d0964172961c921823a4ef0c3p-104L,
/* x = 5.23437500000000000000000000000000000e-01 3ffe0c00000000000000000000000000 */
/* cos(x) = 0.ddb91ff318799172bd2452d0a3 889f5169c64a0094bcf0b8aa7d cf0d7640a2eba68955a80be */
0x0.ddb91ff318799172bd2452d0a3p0L,
0x0.889f5169c64a0094bcf0b8aa7dp-104L,
/* sin(x) = 0.7ff6d8a34bd5e8fa54c97482db 5159df1f24e8038419c0b448b9 eea8939b5d4dfcf40900257 */
0x0.7ff6d8a34bd5e8fa54c97482dbp0L,
0x0.5159df1f24e8038419c0b448b9p-104L,
/* x = 5.31250000000000000000000000000000000e-01 3ffe1000000000000000000000000000 */
/* cos(x) = 0.dcb7777ac420705168f31e3eb7 80ce9c939ecada62843b54522f 5407eb7f21e556059fcd734 */
0x0.dcb7777ac420705168f31e3eb7p0L,
0x0.80ce9c939ecada62843b54522fp-104L,
/* sin(x) = 0.81b149ce34caa5a4e650f8d09f d4d6aa74206c32ca951a93074c 83b2d294d25dbb0f7fdfad2 */
0x0.81b149ce34caa5a4e650f8d09fp0L,
0x0.d4d6aa74206c32ca951a93074cp-104L,
/* x = 5.39062500000000000000000000000000000e-01 3ffe1400000000000000000000000000 */
/* cos(x) = 0.dbb25c25b8260c14f6e7bc98ec 991b70c65335198b0ab628bad2 0cc7b229d4dd62183cfa055 */
0x0.dbb25c25b8260c14f6e7bc98ecp0L,
0x0.991b70c65335198b0ab628bad2p-104L,
/* sin(x) = 0.8369b434a372da7eb5c8a71fe3 6ce1e0b2b493f6f5cb2e38bcae c2a556b3678c401940d1c3c */
0x0.8369b434a372da7eb5c8a71fe3p0L,
0x0.6ce1e0b2b493f6f5cb2e38bcaep-104L,
/* x = 5.46875000000000000000000000000000000e-01 3ffe1800000000000000000000000000 */
/* cos(x) = 0.daa9d20860827063fde51c09e8 55e9932e1b17143e7244fd267a 899d41ae1f3bc6a0ec42e27 */
0x0.daa9d20860827063fde51c09e8p0L,
0x0.55e9932e1b17143e7244fd267ap-104L,
/* sin(x) = 0.852010f4f0800521378bd8dd61 4753d080c2e9e0775ffc609947 b9132f5357404f464f06a58 */
0x0.852010f4f0800521378bd8dd61p0L,
0x0.4753d080c2e9e0775ffc609947p-104L,
/* x = 5.54687500000000000000000000000000000e-01 3ffe1c00000000000000000000000000 */
/* cos(x) = 0.d99ddd44e44a43d4d4a3a3ed95 204106fd54d78e8c7684545c0d a0b7c2c72be7a89b7c182ad */
0x0.d99ddd44e44a43d4d4a3a3ed95p0L,
0x0.204106fd54d78e8c7684545c0dp-104L,
/* sin(x) = 0.86d45935ab396cb4e421e822de e54f3562dfcefeaa782184c234 01d231f5ad981a1cc195b18 */
0x0.86d45935ab396cb4e421e822dep0L,
0x0.e54f3562dfcefeaa782184c234p-104L,
/* x = 5.62500000000000000000000000000000000e-01 3ffe2000000000000000000000000000 */
/* cos(x) = 0.d88e820b1526311dd561efbc0c 1a9a5375eb26f65d246c5744b1 3ca26a7e0fd42556da843c8 */
0x0.d88e820b1526311dd561efbc0cp0L,
0x0.1a9a5375eb26f65d246c5744b1p-104L,
/* sin(x) = 0.88868625b4e1dbb23133101330 22527200c143a5cb16637cb7da f8ade82459ff2e98511f40f */
0x0.88868625b4e1dbb23133101330p0L,
0x0.22527200c143a5cb16637cb7dap-104L,
/* x = 5.70312500000000000000000000000000000e-01 3ffe2400000000000000000000000000 */
/* cos(x) = 0.d77bc4985e93a607c9d868b906 bbc6bbe3a04258814acb035846 8b826fc91bd4d814827f65e */
0x0.d77bc4985e93a607c9d868b906p0L,
0x0.bbc6bbe3a04258814acb035846p-104L,
/* sin(x) = 0.8a3690fc5bfc11bf9535e2739a 8512f448a41251514bbed7fc18 d530f9b4650fcbb2861b0aa */
0x0.8a3690fc5bfc11bf9535e2739ap0L,
0x0.8512f448a41251514bbed7fc18p-104L,
/* x = 5.78125000000000000000000000000000000e-01 3ffe2800000000000000000000000000 */
/* cos(x) = 0.d665a937b4ef2b1f6d51bad6d9 88a4419c1d7051faf31a9efa15 1d7631117efac03713f950a */
0x0.d665a937b4ef2b1f6d51bad6d9p0L,
0x0.88a4419c1d7051faf31a9efa15p-104L,
/* sin(x) = 0.8be472f9776d809af2b8817124 3d63d66dfceeeb739cc894e023 fbc165a0e3f26ff729c5d57 */
0x0.8be472f9776d809af2b8817124p0L,
0x0.3d63d66dfceeeb739cc894e023p-104L,
/* x = 5.85937500000000000000000000000000000e-01 3ffe2c00000000000000000000000000 */
/* cos(x) = 0.d54c3441844897fc8f853f0655 f1ba695eba9fbfd7439dbb1171 d862d9d9146ca5136f825ac */
0x0.d54c3441844897fc8f853f0655p0L,
0x0.f1ba695eba9fbfd7439dbb1171p-104L,
/* sin(x) = 0.8d902565817ee7839bce3cd128 060119492cd36d42d82ada30d7 f8bde91324808377ddbf5d4 */
0x0.8d902565817ee7839bce3cd128p0L,
0x0.060119492cd36d42d82ada30d7p-104L,
/* x = 5.93750000000000000000000000000000000e-01 3ffe3000000000000000000000000000 */
/* cos(x) = 0.d42f6a1b9f0168cdf031c2f63c 8d9304d86f8d34cb1d5fccb68c a0f2241427fc18d1fd5bbdf */
0x0.d42f6a1b9f0168cdf031c2f63cp0L,
0x0.8d9304d86f8d34cb1d5fccb68cp-104L,
/* sin(x) = 0.8f39a191b2ba6122a3fa4f41d5 a3ffd421417d46f19a22230a14 f7fcc8fce5c75b4b28b29d1 */
0x0.8f39a191b2ba6122a3fa4f41d5p0L,
0x0.a3ffd421417d46f19a22230a14p-104L,
/* x = 6.01562500000000000000000000000000000e-01 3ffe3400000000000000000000000000 */
/* cos(x) = 0.d30f4f392c357ab0661c5fa8a7 d9b26627846fef214b1d19a223 79ff9eddba087cf410eb097 */
0x0.d30f4f392c357ab0661c5fa8a7p0L,
0x0.d9b26627846fef214b1d19a223p-104L,
/* sin(x) = 0.90e0e0d81ca678796cc92c8ea8 c2815bc72ca78abe571bfa8576 aacc571e096a33237e0e830 */
0x0.90e0e0d81ca678796cc92c8ea8p0L,
0x0.c2815bc72ca78abe571bfa8576p-104L,
/* x = 6.09375000000000000000000000000000000e-01 3ffe3800000000000000000000000000 */
/* cos(x) = 0.d1ebe81a95ee752e48a26bcd32 d6e922d7eb44b8ad2232f69307 95e84b56317269b9dd1dfa6 */
0x0.d1ebe81a95ee752e48a26bcd32p0L,
0x0.d6e922d7eb44b8ad2232f69307p-104L,
/* sin(x) = 0.9285dc9bc45dd9ea3d02457bcc e59c4175aab6ff7929a8d28719 5525fdace200dba032874fb */
0x0.9285dc9bc45dd9ea3d02457bccp0L,
0x0.e59c4175aab6ff7929a8d28719p-104L,
/* x = 6.17187500000000000000000000000000000e-01 3ffe3c00000000000000000000000000 */
/* cos(x) = 0.d0c5394d772228195e25736c03 574707de0af1ca344b13bd3914 bfe27518e9e426f5deff1e1 */
0x0.d0c5394d772228195e25736c03p0L,
0x0.574707de0af1ca344b13bd3914p-104L,
/* sin(x) = 0.94288e48bd0335fc41c4cbd292 0497a8f5d1d8185c99fa0081f9 0c27e2a53ffdd208a0dbe69 */
0x0.94288e48bd0335fc41c4cbd292p0L,
0x0.0497a8f5d1d8185c99fa0081f9p-104L,
/* x = 6.25000000000000000000000000000000000e-01 3ffe4000000000000000000000000000 */
/* cos(x) = 0.cf9b476c897c25c5bfe750dd3f 308eaf7bcc1ed00179a256870f 4200445043dcdb1974b5878 */
0x0.cf9b476c897c25c5bfe750dd3fp0L,
0x0.308eaf7bcc1ed00179a256870fp-104L,
/* sin(x) = 0.95c8ef544210ec0b91c49bd2aa 09e8515fa61a156ebb10f5f8c2 32a6445b61ebf3c2ec268f9 */
0x0.95c8ef544210ec0b91c49bd2aap0L,
0x0.09e8515fa61a156ebb10f5f8c2p-104L,
/* x = 6.32812500000000000000000000000000000e-01 3ffe4400000000000000000000000000 */
/* cos(x) = 0.ce6e171f92f2e27f32225327ec 440ddaefae248413efc0e58cee e1ae369aabe73f88c87ed1a */
0x0.ce6e171f92f2e27f32225327ecp0L,
0x0.440ddaefae248413efc0e58ceep-104L,
/* sin(x) = 0.9766f93cd18413a6aafc1cfc6f c28abb6817bf94ce349901ae3f 48c3215d3eb60acc5f78903 */
0x0.9766f93cd18413a6aafc1cfc6fp0L,
0x0.c28abb6817bf94ce349901ae3fp-104L,
/* x = 6.40625000000000000000000000000000000e-01 3ffe4800000000000000000000000000 */
/* cos(x) = 0.cd3dad1b5328a2e459f993f4f5 108819faccbc4eeba9604e81c7 adad51cc8a2561631a06826 */
0x0.cd3dad1b5328a2e459f993f4f5p0L,
0x0.108819faccbc4eeba9604e81c7p-104L,
/* sin(x) = 0.9902a58a45e27bed68412b426b 675ed503f54d14c8172e0d373f 42cadf04daf67319a7f94be */
0x0.9902a58a45e27bed68412b426bp0L,
0x0.675ed503f54d14c8172e0d373fp-104L,
/* x = 6.48437500000000000000000000000000000e-01 3ffe4c00000000000000000000000000 */
/* cos(x) = 0.cc0a0e21709883a3ff00911e11 a07ee3bd7ea2b04e081be99be0 264791170761ae64b8b744a */
0x0.cc0a0e21709883a3ff00911e11p0L,
0x0.a07ee3bd7ea2b04e081be99be0p-104L,
/* sin(x) = 0.9a9bedcdf01b38d993f3d78207 81de292033ead73b89e28f3931 3dbe3a6e463f845b5fa8490 */
0x0.9a9bedcdf01b38d993f3d78207p0L,
0x0.81de292033ead73b89e28f3931p-104L,
/* x = 6.56250000000000000000000000000000000e-01 3ffe5000000000000000000000000000 */
/* cos(x) = 0.cad33f00658fe5e8204bbc0f3a 66a0e6a773f87987a780b243d7 be83b3db1448ca0e0e62787 */
0x0.cad33f00658fe5e8204bbc0f3ap0L,
0x0.66a0e6a773f87987a780b243d7p-104L,
/* sin(x) = 0.9c32cba2b14156ef05256c4f85 7991ca6a547cd7ceb1ac8a8e62 a282bd7b9183648a462bd04 */
0x0.9c32cba2b14156ef05256c4f85p0L,
0x0.7991ca6a547cd7ceb1ac8a8e62p-104L,
/* x = 6.64062500000000000000000000000000000e-01 3ffe5400000000000000000000000000 */
/* cos(x) = 0.c99944936cf48c8911ff93fe64 b3ddb7981e414bdaf6aae12035 77de44878c62bc3bc9cf7b9 */
0x0.c99944936cf48c8911ff93fe64p0L,
0x0.b3ddb7981e414bdaf6aae12035p-104L,
/* sin(x) = 0.9dc738ad14204e689ac582d0f8 5826590feece34886cfefe2e08 cf2bb8488d55424dc9d3525 */
0x0.9dc738ad14204e689ac582d0f8p0L,
0x0.5826590feece34886cfefe2e08p-104L,
/* x = 6.71875000000000000000000000000000000e-01 3ffe5800000000000000000000000000 */
/* cos(x) = 0.c85c23c26ed7b6f014ef546c47 929682122876bfbf157de0aff3 c4247d820c746e32cd4174f */
0x0.c85c23c26ed7b6f014ef546c47p0L,
0x0.929682122876bfbf157de0aff3p-104L,
/* sin(x) = 0.9f592e9b66a9cf906a3c7aa3c1 0199849040c45ec3f0a7475973 11038101780c5f266059dbf */
0x0.9f592e9b66a9cf906a3c7aa3c1p0L,
0x0.0199849040c45ec3f0a7475973p-104L,
/* x = 6.79687500000000000000000000000000000e-01 3ffe5c00000000000000000000000000 */
/* cos(x) = 0.c71be181ecd6875ce2da5615a0 3cca207d9adcb9dfb0a1d6c40a 4f0056437f1a59ccddd06ee */
0x0.c71be181ecd6875ce2da5615a0p0L,
0x0.3cca207d9adcb9dfb0a1d6c40ap-104L,
/* sin(x) = 0.a0e8a725d33c828c11fa50fd9e 9a15ffecfad43f3e534358076b 9b0f6865694842b1e8c67dc */
0x0.a0e8a725d33c828c11fa50fd9ep0L,
0x0.9a15ffecfad43f3e534358076bp-104L,
/* x = 6.87500000000000000000000000000000000e-01 3ffe6000000000000000000000000000 */
/* cos(x) = 0.c5d882d2ee48030c7c07d28e98 1e34804f82ed4cf93655d23653 89b716de6ad44676a1cc5da */
0x0.c5d882d2ee48030c7c07d28e98p0L,
0x0.1e34804f82ed4cf93655d23653p-104L,
/* sin(x) = 0.a2759c0e79c35582527c32b55f 5405c182c66160cb1d9eb7bb0b 7cdf4ad66f317bda4332914 */
0x0.a2759c0e79c35582527c32b55fp0L,
0x0.5405c182c66160cb1d9eb7bb0bp-104L,
/* x = 6.95312500000000000000000000000000000e-01 3ffe6400000000000000000000000000 */
/* cos(x) = 0.c4920cc2ec38fb891b38827db0 8884fc66371ac4c2052ca8885b 981bbcfd3bb7b093ee31515 */
0x0.c4920cc2ec38fb891b38827db0p0L,
0x0.8884fc66371ac4c2052ca8885bp-104L,
/* sin(x) = 0.a400072188acf49cd6b173825e 038346f105e1301afe642bcc36 4cea455e21e506e3e927ed8 */
0x0.a400072188acf49cd6b173825ep0L,
0x0.038346f105e1301afe642bcc36p-104L,
/* x = 7.03125000000000000000000000000000000e-01 3ffe6800000000000000000000000000 */
/* cos(x) = 0.c348846bbd3631338ffe2bfe9d d1381a35b4e9c0c51b4c13fe37 6bad1bf5caacc4542be0aa9 */
0x0.c348846bbd3631338ffe2bfe9dp0L,
0x0.d1381a35b4e9c0c51b4c13fe37p-104L,
/* sin(x) = 0.a587e23555bb08086d02b9c662 cdd29316c3e9bd08d93793634a 21b1810cce73bdb97a99b9e */
0x0.a587e23555bb08086d02b9c662p0L,
0x0.cdd29316c3e9bd08d93793634ap-104L,
/* x = 7.10937500000000000000000000000000000e-01 3ffe6c00000000000000000000000000 */
/* cos(x) = 0.c1fbeef380e4ffdd5a613ec872 2f643ffe814ec2343e53adb549 627224fdc9f2a7b77d3d69f */
0x0.c1fbeef380e4ffdd5a613ec872p0L,
0x0.2f643ffe814ec2343e53adb549p-104L,
/* sin(x) = 0.a70d272a76a8d4b6da0ec90712 bb748b96dabf88c3079246f3db 7eea6e58ead4ed0e2843303 */
0x0.a70d272a76a8d4b6da0ec90712p0L,
0x0.bb748b96dabf88c3079246f3dbp-104L,
/* x = 7.18750000000000000000000000000000000e-01 3ffe7000000000000000000000000000 */
/* cos(x) = 0.c0ac518c8b6ae710ba37a3eeb9 0cb15aebcb8bed4356fb507a48 a6e97de9aa6d9660116b436 */
0x0.c0ac518c8b6ae710ba37a3eeb9p0L,
0x0.0cb15aebcb8bed4356fb507a48p-104L,
/* sin(x) = 0.a88fcfebd9a8dd47e2f3c76ef9 e2439920f7e7fbe735f8bcc985 491ec6f12a2d4214f8cfa99 */
0x0.a88fcfebd9a8dd47e2f3c76ef9p0L,
0x0.e2439920f7e7fbe735f8bcc985p-104L,
/* x = 7.26562500000000000000000000000000000e-01 3ffe7400000000000000000000000000 */
/* cos(x) = 0.bf59b17550a440687596929656 7cf3e3b4e483061877c02811c6 cae85fad5a6c3da58f49292 */
0x0.bf59b17550a440687596929656p0L,
0x0.7cf3e3b4e483061877c02811c6p-104L,
/* sin(x) = 0.aa0fd66eddb921232c28520d39 11b8a03193b47f187f1471ac21 6fbcd5bb81029294d3a73f1 */
0x0.aa0fd66eddb921232c28520d39p0L,
0x0.11b8a03193b47f187f1471ac21p-104L,
/* x = 7.34375000000000000000000000000000000e-01 3ffe7800000000000000000000000000 */
/* cos(x) = 0.be0413f84f2a771c614946a88c bf4da1d75a5560243de8f2283f efa0ea4a48468a52d51d8b3 */
0x0.be0413f84f2a771c614946a88cp0L,
0x0.bf4da1d75a5560243de8f2283fp-104L,
/* sin(x) = 0.ab8d34b36acd987210ed343ec6 5d7e3adc2e7109fce43d55c8d5 7dfdf55b9e01d2cc1f1b9ec */
0x0.ab8d34b36acd987210ed343ec6p0L,
0x0.5d7e3adc2e7109fce43d55c8d5p-104L,
/* x = 7.42187500000000000000000000000000000e-01 3ffe7c00000000000000000000000000 */
/* cos(x) = 0.bcab7e6bfb2a14a9b122c574a3 76bec98ab14808c64a4e731b34 047e217611013ac99c0f25d */
0x0.bcab7e6bfb2a14a9b122c574a3p0L,
0x0.76bec98ab14808c64a4e731b34p-104L,
/* sin(x) = 0.ad07e4c409d08c4fa3a9057bb0 ac24b8636e74e76f51e09bd6b2 319707cbd9f5e254643897a */
0x0.ad07e4c409d08c4fa3a9057bb0p0L,
0x0.ac24b8636e74e76f51e09bd6b2p-104L,
/* x = 7.50000000000000000000000000000000000e-01 3ffe8000000000000000000000000000 */
/* cos(x) = 0.bb4ff632a908f73ec151839cb9 d993b4e0bfb8f20e7e44e6e4ae e845e35575c3106dbe6fd06 */
0x0.bb4ff632a908f73ec151839cb9p0L,
0x0.d993b4e0bfb8f20e7e44e6e4aep-104L,
/* sin(x) = 0.ae7fe0b5fc786b2d966e1d6af1 40a488476747c2646425fc7533 f532cd044cb10a971a49a6a */
0x0.ae7fe0b5fc786b2d966e1d6af1p0L,
0x0.40a488476747c2646425fc7533p-104L,
/* x = 7.57812500000000000000000000000000000e-01 3ffe8400000000000000000000000000 */
/* cos(x) = 0.b9f180ba77dd0751628e135a95 08299012230f14becacdd14c3f 8862d122de5b56d55b53360 */
0x0.b9f180ba77dd0751628e135a95p0L,
0x0.08299012230f14becacdd14c3fp-104L,
/* sin(x) = 0.aff522a954f2ba16d9defdc416 e33f5e9a5dfd5a6c228e0abc4d 521327ff6e2517a7b3851dd */
0x0.aff522a954f2ba16d9defdc416p0L,
0x0.e33f5e9a5dfd5a6c228e0abc4dp-104L,
/* x = 7.65625000000000000000000000000000000e-01 3ffe8800000000000000000000000000 */
/* cos(x) = 0.b890237d3bb3c284b614a05390 16bfa1053730bbdf940fa895e1 85f8e58884d3dda15e63371 */
0x0.b890237d3bb3c284b614a05390p0L,
0x0.16bfa1053730bbdf940fa895e1p-104L,
/* sin(x) = 0.b167a4c90d63c4244cf5493b7c c23bd3c3c1225e078baa0c53d6 d400b926281f537a1a260e6 */
0x0.b167a4c90d63c4244cf5493b7cp0L,
0x0.c23bd3c3c1225e078baa0c53d6p-104L,
/* x = 7.73437500000000000000000000000000000e-01 3ffe8c00000000000000000000000000 */
/* cos(x) = 0.b72be40067aaf2c050dbdb7a14 c3d7d4f203f6b3f0224a4afe55 d6ec8e92b508fd5c5984b3b */
0x0.b72be40067aaf2c050dbdb7a14p0L,
0x0.c3d7d4f203f6b3f0224a4afe55p-104L,
/* sin(x) = 0.b2d7614b1f3aaa24df2d6e20a7 7e1ca3e6d838c03e29c1bcb026 e6733324815fadc9eb89674 */
0x0.b2d7614b1f3aaa24df2d6e20a7p0L,
0x0.7e1ca3e6d838c03e29c1bcb026p-104L,
/* x = 7.81250000000000000000000000000000000e-01 3ffe9000000000000000000000000000 */
/* cos(x) = 0.b5c4c7d4f7dae915ac786ccf4b 1a498d3e73b6e5e74fe7519d9c 53ee6d6b90e881bddfc33e1 */
0x0.b5c4c7d4f7dae915ac786ccf4bp0L,
0x0.1a498d3e73b6e5e74fe7519d9cp-104L,
/* sin(x) = 0.b44452709a5975290591376543 4a59d111f0433eb2b133f7d103 207e2aeb4aae111ddc385b3 */
0x0.b44452709a5975290591376543p0L,
0x0.4a59d111f0433eb2b133f7d103p-104L,
/* x = 7.89062500000000000000000000000000000e-01 3ffe9400000000000000000000000000 */
/* cos(x) = 0.b45ad4975b1294cadca4cf40ec 8f22a68cd14b175835239a37e6 3acb85e8e9505215df18140 */
0x0.b45ad4975b1294cadca4cf40ecp0L,
0x0.8f22a68cd14b175835239a37e6p-104L,
/* sin(x) = 0.b5ae7285bc10cf515753847e8f 8b7a30e0a580d929d770103509 880680f7b8b0e8ad23b65d8 */
0x0.b5ae7285bc10cf515753847e8fp0L,
0x0.8b7a30e0a580d929d770103509p-104L
};

6
sysdeps/ieee754/ldbl-128ibm/w_expl.c Normal file
View File

@ -0,0 +1,6 @@
/* Looks like we can use ieee854 w_expl.c as is for IBM extended format. */
#include <math_ldbl_opt.h>
#undef weak_alias
#define weak_alias(n,a)
#include <sysdeps/ieee754/ldbl-128/w_expl.c>
long_double_symbol (libm, __expl, expl);

4
sysdeps/powerpc/Implies
View File

@ -1,2 +1,4 @@
ieee754/flt-32
# On PowerPC we use the IBM extended long double format.
ieee754/ldbl-128ibm
ieee754/dbl-64
ieee754/flt-32

9
sysdeps/powerpc/fpu/bits/mathdef.h
View File

@ -1,4 +1,5 @@
/* Copyright (C) 1997,1998,1999,2000,2003,2004 Free Software Foundation, Inc.
/* Copyright (C) 1997,1998,1999,2000,2003,2004,2006
Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@ -61,9 +62,3 @@ typedef double double_t;
# define FP_ILOGBNAN (2147483647)
#endif /* ISO C99 */
#ifndef __NO_LONG_DOUBLE_MATH
/* Signal that we do not really have a `long double'. The disables the
declaration of all the `long double' function variants. */
# define __NO_LONG_DOUBLE_MATH 1
#endif

596
sysdeps/powerpc/fpu/libm-test-ulps
View File

File diff suppressed because it is too large Load Diff

3
sysdeps/powerpc/fpu/s_isnan.c
View File

@ -1,5 +1,5 @@
/* Return 1 if argument is a NaN, else 0.
Copyright (C) 1997, 2000, 2002 Free Software Foundation, Inc.
Copyright (C) 1997, 2000, 2002, 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@ -23,6 +23,7 @@
#define __GI___isnanf __GI___Xisnanf
#include "math.h"
#include <math_ldbl_opt.h>
#include <fenv_libc.h>
#undef __isnanf

1
sysdeps/powerpc/powerpc32/Implies
View File

@ -1,2 +1 @@
wordsize-32
powerpc/soft-fp

4
sysdeps/powerpc/powerpc32/fpu/s_ceil.S
View File

@ -18,6 +18,7 @@
02110-1301 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
.section .rodata.cst4,"aM",@progbits,4
.align 2
@ -77,3 +78,6 @@ weak_alias (__ceil, ceil)
weak_alias (__ceil, ceill)
strong_alias (__ceil, __ceill)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0)
compat_symbol (libm, __ceil, ceill, GLIBC_2_0)
#endif

9
sysdeps/powerpc/powerpc32/fpu/s_copysign.S
View File

@ -21,6 +21,7 @@
when it's coded in C. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
ENTRY(__copysign)
/* double [f1] copysign (double [f1] x, double [f2] y);
@ -32,6 +33,7 @@ ENTRY(__copysign)
lwz r3,8(r1)
cmpwi r3,0
addi r1,r1,16
cfi_adjust_cfa_offset (-16)
blt L(0)
fabs fp1,fp1
blr
@ -49,3 +51,10 @@ strong_alias(__copysign,__copysignf)
weak_alias (__copysign,copysignl)
strong_alias(__copysign,__copysignl)
#endif
#ifdef IS_IN_libm
# if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0)
compat_symbol (libm, __copysign, copysignl, GLIBC_2_0)
# endif
#elif LONG_DOUBLE_COMPAT(libc, GLIBC_2_0)
compat_symbol (libc, __copysign, copysignl, GLIBC_2_0)
#endif

50
sysdeps/powerpc/powerpc32/fpu/s_copysignl.S Normal file
View File

@ -0,0 +1,50 @@
/* Copy a sign bit between floating-point values.
IBM extended format long double version.
Copyright (C) 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
ENTRY(__copysignl)
/* long double [f1,f2] copysign (long double [f1,f2] x, long double [f3,f4] y);
copysign(x,y) returns a value with the magnitude of x and
with the sign bit of y. */
stwu r1,-16(r1)
cfi_adjust_cfa_offset (16)
stfd fp3,8(r1)
fmr fp0,fp1
fabs fp1,fp1
fcmpu cr7,fp0,fp1
lwz r3,8(r1)
cmpwi cr6,r3,0
addi r1,r1,16
cfi_adjust_cfa_offset (-16)
beq cr7,L(0)
fneg fp2,fp2
L(0): bgelr cr6
fneg fp1,fp1
fneg fp2,fp2
blr
END (__copysignl)
#ifdef IS_IN_libm
long_double_symbol (libm, __copysignl, copysignl)
#else
long_double_symbol (libc, __copysignl, copysignl)
#endif

5
sysdeps/powerpc/powerpc32/fpu/s_fabs.S Normal file
View File

@ -0,0 +1,5 @@
#include <math_ldbl_opt.h>
#include <sysdeps/powerpc/fpu/s_fabs.S>
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0)
compat_symbol (libm, __fabs, fabsl, GLIBC_2_0)
#endif

36
sysdeps/powerpc/powerpc32/fpu/s_fabsl.S Normal file
View File

@ -0,0 +1,36 @@
/* Copy a sign bit between floating-point values.
IBM extended format long double version.
Copyright (C) 2004, 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
ENTRY(__fabsl)
/* long double [f1,f2] fabs (long double [f1,f2] x);
fabs(x,y) returns a value with the magnitude of x and
with the sign bit of y. */
fmr fp0,fp1
fabs fp1,fp1
fcmpu cr1,fp0,fp1
beqlr cr1
fneg fp2,fp2
blr
END (__fabsl)
long_double_symbol (libm, __fabsl, fabsl)

5
sysdeps/powerpc/powerpc32/fpu/s_fdim.c Normal file
View File

@ -0,0 +1,5 @@
#include <math_ldbl_opt.h>
#include <sysdeps/powerpc/fpu/s_fdim.c>
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __fdim, fdiml, GLIBC_2_1);
#endif

4
sysdeps/powerpc/powerpc32/fpu/s_floor.S
View File

@ -18,6 +18,7 @@
02110-1301 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
.section .rodata.cst4,"aM",@progbits,4
.align 2
@ -77,3 +78,6 @@ weak_alias (__floor, floor)
weak_alias (__floor, floorl)
strong_alias (__floor, __floorl)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0)
compat_symbol (libm, __floor, floorl, GLIBC_2_0)
#endif

5
sysdeps/powerpc/powerpc32/fpu/s_fmax.S Normal file
View File

@ -0,0 +1,5 @@
#include <math_ldbl_opt.h>
#include <sysdeps/powerpc/fpu/s_fmax.S>
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __fmax, fmaxl, GLIBC_2_1)
#endif

5
sysdeps/powerpc/powerpc32/fpu/s_fmin.S Normal file
View File

@ -0,0 +1,5 @@
#include <math_ldbl_opt.h>
#include <sysdeps/powerpc/fpu/s_fmin.S>
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __fmin, fminl, GLIBC_2_1)
#endif

7
sysdeps/powerpc/powerpc32/fpu/s_isnan.c Normal file
View File

@ -0,0 +1,7 @@
#include <sysdeps/powerpc/fpu/s_isnan.c>
#ifndef IS_IN_libm
# if LONG_DOUBLE_COMPAT(libc, GLIBC_2_0)
compat_symbol (libc, __isnan, __isnanl, GLIBC_2_0);
compat_symbol (libc, isnan, isnanl, GLIBC_2_0);
# endif
#endif

8
sysdeps/powerpc/powerpc32/fpu/s_llrint.c
View File

@ -1,5 +1,5 @@
/* Round a double value to a long long in the current rounding mode.
Copyright (C) 1997 Free Software Foundation, Inc.
Copyright (C) 1997, 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@ -17,7 +17,8 @@
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include "math.h"
#include <math.h>
#include <math_ldbl_opt.h>
long long int
__llrint (double x)
@ -29,3 +30,6 @@ weak_alias (__llrint, llrint)
strong_alias (__llrint, __llrintl)
weak_alias (__llrint, llrintl)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __llrint, llrintl, GLIBC_2_1);
#endif

6
sysdeps/powerpc/powerpc32/fpu/s_lrint.S
View File

@ -1,5 +1,5 @@
/* Round double to long int. PowerPC32 version.
Copyright (C) 2004 Free Software Foundation, Inc.
Copyright (C) 2004, 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@ -18,6 +18,7 @@
02111-1307 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
/* long int[r3] __lrint (double x[fp1]) */
ENTRY (__lrint)
@ -39,3 +40,6 @@ weak_alias (__lrint, lrintf)
strong_alias (__lrint, __lrintl)
weak_alias (__lrint, lrintl)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __lrint, lrintl, GLIBC_2_1)
#endif

4
sysdeps/powerpc/powerpc32/fpu/s_lround.S
View File

@ -18,6 +18,7 @@
02110-1301 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
.section .rodata.cst8,"aM",@progbits,8
.align 2
@ -93,3 +94,6 @@ weak_alias (__lround, lroundf)
weak_alias (__lround, lroundl)
strong_alias (__lround, __lroundl)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __lround, lroundl, GLIBC_2_1)
#endif

4
sysdeps/powerpc/powerpc32/fpu/s_rint.S
View File

@ -21,6 +21,7 @@
when it's coded in C. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
.section .rodata.cst4,"aM",@progbits,4
.align 2
@ -73,3 +74,6 @@ weak_alias (__rint, rint)
weak_alias (__rint, rintl)
strong_alias (__rint, __rintl)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0)
compat_symbol (libm, __rint, rintl, GLIBC_2_0)
#endif

4
sysdeps/powerpc/powerpc32/fpu/s_round.S
View File

@ -18,6 +18,7 @@
02110-1301 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
.section .rodata.cst8,"aM",@progbits,8
.align 2
@ -97,3 +98,6 @@ weak_alias (__round, round)
weak_alias (__round, roundl)
strong_alias (__round, __roundl)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __round, roundl, GLIBC_2_1)
#endif

6
sysdeps/powerpc/powerpc32/fpu/s_trunc.S
View File

@ -18,6 +18,7 @@
02110-1301 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
.section .rodata.cst4,"aM",@progbits,4
.align 2
@ -65,7 +66,7 @@ ENTRY (__trunc)
fsub fp1,fp1,fp13 /* x-= TWO52; */
fabs fp1,fp1 /* if (x == 0.0) */
/* x = 0.0; */
mtfsf 0x01,fp11 /* restore previous truncing mode. */
mtfsf 0x01,fp11 /* restore previous rounding mode. */
blr
.L4:
bge- cr6,.L9 /* if (x < 0.0) */
@ -84,3 +85,6 @@ weak_alias (__trunc, trunc)
weak_alias (__trunc, truncl)
strong_alias (__trunc, __truncl)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_1)
compat_symbol (libm, __trunc, truncl, GLIBC_2_1)
#endif

2
sysdeps/powerpc/powerpc32/fpu/s_truncf.S
View File

@ -65,7 +65,7 @@ ENTRY (__truncf)
fsubs fp1,fp1,fp13 /* x-= TWO23; */
fabs fp1,fp1 /* if (x == 0.0) */
/* x = 0.0; */
mtfsf 0x01,fp11 /* restore previous truncing mode. */
mtfsf 0x01,fp11 /* restore previous rounding mode. */
blr
.L4:
bge- cr6,.L9 /* if (x < 0.0) */

6
sysdeps/powerpc/powerpc64/fpu/s_ceil.S
View File

@ -1,5 +1,5 @@
/* ceil function. PowerPC64 version.
Copyright (C) 2004 Free Software Foundation, Inc.
Copyright (C) 2004, 2006 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@ -18,6 +18,7 @@
02111-1307 USA. */
#include <sysdep.h>
#include <math_ldbl_opt.h>
.section ".toc","aw"
.LC0: /* 2**52 */
@ -58,3 +59,6 @@ weak_alias (__ceil, ceil)
weak_alias (__ceil, ceill)
strong_alias (__ceil, __ceill)
#endif
#if LONG_DOUBLE_COMPAT(libm, GLIBC_2_0)
compat_symbol (libm, __ceil, ceill, GLIBC_2_0)
#endif

Some files were not shown because too many files have changed in this diff Show More