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Optimize accurate 64-bit routines for FMA4 on x86-64
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ChangeLog
57
ChangeLog
@ -1,5 +1,62 @@
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2011-10-24 Ulrich Drepper <drepper@gmail.com>
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* config.make.in: Add have-mfma4 entry.
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* configure.in: Substitute libc_cv_cc_fma4.
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* math/Makefile (dbl-only-routines): Add sincostab.
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* sysdeps/ieee754/dbl-64/dosincos.c: Don't include sincos.tbl.
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Use __sincostab not sincos.
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* sysdeps/ieee754/dbl-64/e_asin.c: Don't define aliases when function
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name is a macro.
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* sysdeps/ieee754/dbl-64/e_exp.c: Likewise.
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* sysdeps/ieee754/dbl-64/e_log.c: Likewise.
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* sysdeps/ieee754/dbl-64/e_pow.c: Likewise.
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* sysdeps/ieee754/dbl-64/e_atan2.c: Likewise. Define singArctan2
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using __copysign.
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* sysdeps/ieee754/dbl-64/mpa.c: Don't export __acr. Don't define
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__cr and __cpymn. Define __cpy unless NO___CPY is defined. Define
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norm, denorm, and __mp_dbl unless NO___MP_DBL is defined.
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* sysdeps/ieee754/dbl-64/mpa.h: Don't declare __acr, __cr, __cpymn,
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and __inv.
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* sysdeps/ieee754/dbl-64/mpsqrt.c: Make fastiroot static.
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* sysdeps/ieee754/dbl-64/s_atan.c: Define __signArctan using
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__copysign.
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* sysdeps/ieee754/dbl-64/s_sin.c: Use __sincostab not sincos. Don't
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define aliases when function name is a macro.
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* sysdeps/ieee754/dbl-64/sincostab.c: Renamed from
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sysdeps/ieee754/dbl-64/sincos.tbl.
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* sysdeps/x86_64/fpu/multiarch/Makefile: Add entries to build
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fma4-enabled routines.
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* sysdeps/x86_64/fpu/multiarch/brandred-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/doasin-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/dosincos-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_asin-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_asin.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_atan2-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_atan2.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_exp.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_log-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_log.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/e_pow.c: New file.
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* sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/mpa-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/mpatan-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/mpatan2-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/mpexp-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/mplog-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/mpsqrt-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/mptan-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/s_atan-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/s_atan.c: New file.
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* sysdeps/x86_64/fpu/multiarch/s_sin-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/s_sin.c: New file.
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* sysdeps/x86_64/fpu/multiarch/s_tan-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/s_tan.c: New file.
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* sysdeps/x86_64/fpu/multiarch/sincos32-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: New file.
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* sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c: New file.
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* sysdeps/ieee754/dbl-64/doasin.c: Adjust for DLA_FMA -> DLA_FMS
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rename.
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* sysdeps/ieee754/dbl-64/dosincos.c: Likewise.
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@ -59,6 +59,7 @@ have-cpp-asm-debuginfo = @libc_cv_cpp_asm_debuginfo@
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enable-check-abi = @enable_check_abi@
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have-forced-unwind = @libc_cv_forced_unwind@
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have-fpie = @libc_cv_fpie@
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have-mfma4 = @libc_cv_cc_fma4@
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gnu89-inline-CFLAGS = @gnu89_inline@
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have-ssp = @libc_cv_ssp@
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have-selinux = @have_selinux@
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2
configure
vendored
2
configure
vendored
@ -623,6 +623,7 @@ elf
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ldd_rewrite_script
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use_ldconfig
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libc_cv_as_i686
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libc_cv_cc_fma4
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libc_cv_cc_novzeroupper
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libc_cv_cc_avx
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libc_cv_cc_sse4
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@ -7944,6 +7945,7 @@ fi
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if test $elf = yes; then
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$as_echo "#define HAVE_ELF 1" >>confdefs.h
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@ -2339,6 +2339,7 @@ AC_SUBST(libc_cv_cpp_asm_debuginfo)
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AC_SUBST(libc_cv_cc_sse4)
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AC_SUBST(libc_cv_cc_avx)
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AC_SUBST(libc_cv_cc_novzeroupper)
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AC_SUBST(libc_cv_cc_fma4)
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AC_SUBST(libc_cv_as_i686)
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AC_SUBST(use_ldconfig)
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@ -66,7 +66,7 @@ include ../Makeconfig
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dbl-only-routines := branred doasin dosincos halfulp mpa mpatan2 \
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mpatan mpexp mplog mpsqrt mptan sincos32 slowexp \
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slowpow
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slowpow sincostab
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libm-routines = $(strip $(libm-support) $(libm-calls) \
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$(patsubst %_rf,%f_r,$(libm-calls:=f)) \
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$(long-m-$(long-double-fcts))) \
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@ -35,11 +35,16 @@
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#include "endian.h"
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#include "mydefs.h"
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#include "sincos.tbl"
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#include <dla.h>
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#include "dosincos.h"
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#include "math_private.h"
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extern const union
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{
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int4 i[880];
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double x[440];
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} __sincostab attribute_hidden;
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/***********************************************************************/
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/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
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/* as Double-Length number and store it at array v .It computes it by */
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@ -66,10 +71,10 @@ void __dubsin(double x, double dx, double v[]) {
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dd=(x-d)+dx;
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/* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
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MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
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sn=sincos.x[k]; /* */
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ssn=sincos.x[k+1]; /* sin(Xi) and cos(Xi) */
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cs=sincos.x[k+2]; /* */
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ccs=sincos.x[k+3]; /* */
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sn=__sincostab.x[k]; /* */
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ssn=__sincostab.x[k+1]; /* sin(Xi) and cos(Xi) */
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cs=__sincostab.x[k+2]; /* */
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ccs=__sincostab.x[k+3]; /* */
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MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* Taylor */
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ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* series */
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@ -118,10 +123,10 @@ void __dubcos(double x, double dx, double v[]) {
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d=x+dx;
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dd=(x-d)+dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
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MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
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sn=sincos.x[k]; /* */
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ssn=sincos.x[k+1]; /* sin(Xi) and cos(Xi) */
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cs=sincos.x[k+2]; /* */
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ccs=sincos.x[k+3]; /* */
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sn=__sincostab.x[k]; /* */
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ssn=__sincostab.x[k+1]; /* sin(Xi) and cos(Xi) */
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cs=__sincostab.x[k+2]; /* */
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ccs=__sincostab.x[k+3]; /* */
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MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
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MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
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@ -324,7 +324,9 @@ double __ieee754_asin(double x){
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return u.x/v.x; /* NaN */
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}
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}
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#ifndef __ieee754_asin
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strong_alias (__ieee754_asin, __asin_finite)
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#endif
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/*******************************************************************/
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/* */
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@ -636,4 +638,6 @@ double __ieee754_acos(double x)
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return u.x/v.x;
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}
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}
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#ifndef __ieee754_acos
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strong_alias (__ieee754_acos, __acos_finite)
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#endif
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@ -51,7 +51,11 @@
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/* round to nearest mode of IEEE 754 standard. */
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/************************************************************************/
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static double atan2Mp(double ,double ,const int[]);
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static double signArctan2(double ,double);
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/* Fix the sign and return after stage 1 or stage 2 */
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static double signArctan2(double y,double z)
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{
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return __copysign(z, y);
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}
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static double normalized(double ,double,double ,double);
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void __mpatan2(mp_no *,mp_no *,mp_no *,int);
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@ -375,7 +379,9 @@ double __ieee754_atan2(double y,double x) {
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}
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}
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}
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#ifndef __ieee754_atan2
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strong_alias (__ieee754_atan2, __atan2_finite)
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#endif
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/* Treat the Denormalized case */
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static double normalized(double ax,double ay,double y, double z)
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@ -386,11 +392,6 @@ static double normalized(double ax,double ay,double y, double z)
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__dbl_mp(ue.d,&mpt1,p); __mul(&mpz,&mpt1,&mperr,p);
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__sub(&mpz,&mperr,&mpz2,p); __mp_dbl(&mpz2,&z,p);
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return signArctan2(y,z);
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}
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/* Fix the sign and return after stage 1 or stage 2 */
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static double signArctan2(double y,double z)
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{
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return ((y<ZERO) ? -z : z);
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}
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/* Stage 3: Perform a multi-Precision computation */
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static double atan2Mp(double x,double y,const int pr[])
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@ -145,7 +145,9 @@ double __ieee754_exp(double x) {
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else return __slowexp(x);
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}
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}
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#ifndef __ieee754_exp
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strong_alias (__ieee754_exp, __exp_finite)
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#endif
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/************************************************************************/
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/* Compute e^(x+xx)(Double-Length number) .The routine also receive */
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@ -207,4 +207,6 @@ double __ieee754_log(double x) {
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}
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return y1;
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}
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#ifndef __ieee754_log
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strong_alias (__ieee754_log, __log_finite)
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#endif
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@ -153,7 +153,9 @@ double __ieee754_pow(double x, double y) {
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if (y<0) return (x<1.0)?INF.x:0;
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return 0; /* unreachable, to make the compiler happy */
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}
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#ifndef __ieee754_pow
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strong_alias (__ieee754_pow, __pow_finite)
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#endif
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/**************************************************************************/
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/* Computing x^y using more accurate but more slow log routine */
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@ -1,8 +1,7 @@
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/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001 Free Software Foundation
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* Copyright (C) 2001, 2011 Free Software Foundation
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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@ -64,7 +63,7 @@ static int mcr(const mp_no *x, const mp_no *y, int p) {
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/* acr() compares the absolute values of two multiple precision numbers */
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int __acr(const mp_no *x, const mp_no *y, int p) {
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static int __acr(const mp_no *x, const mp_no *y, int p) {
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int i;
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if (X[0] == ZERO) {
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@ -82,8 +81,9 @@ int __acr(const mp_no *x, const mp_no *y, int p) {
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}
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#if 0
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/* cr90 compares the values of two multiple precision numbers */
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int __cr(const mp_no *x, const mp_no *y, int p) {
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static int __cr(const mp_no *x, const mp_no *y, int p) {
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int i;
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if (X[0] > Y[0]) i= 1;
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@ -93,26 +93,26 @@ int __cr(const mp_no *x, const mp_no *y, int p) {
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return i;
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}
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#endif
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#ifndef NO___CPY
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/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
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void __cpy(const mp_no *x, mp_no *y, int p) {
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int i;
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EY = EX;
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for (i=0; i <= p; i++) Y[i] = X[i];
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return;
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for (int i=0; i <= p; i++) Y[i] = X[i];
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}
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#endif
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#if 0
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/* Copy a multiple precision number x of precision m into a */
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/* multiple precision number y of precision n. In case n>m, */
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/* the digits of y beyond the m'th are set to zero. In case */
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/* n<m, the digits of x beyond the n'th are ignored. */
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/* x=y is permissible. */
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void __cpymn(const mp_no *x, int m, mp_no *y, int n) {
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static void __cpymn(const mp_no *x, int m, mp_no *y, int n) {
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int i,k;
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@ -122,7 +122,10 @@ void __cpymn(const mp_no *x, int m, mp_no *y, int n) {
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return;
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}
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#endif
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#ifndef NO___MP_DBL
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/* Convert a multiple precision number *x into a double precision */
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/* number *y, normalized case (|x| >= 2**(-1022))) */
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static void norm(const mp_no *x, double *y, int p)
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@ -141,7 +144,7 @@ static void norm(const mp_no *x, double *y, int p)
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}
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else {
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for (a=ONE, z[1]=X[1]; z[1] < TWO23; )
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{a *= TWO; z[1] *= TWO; }
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{a *= TWO; z[1] *= TWO; }
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for (i=2; i<5; i++) {
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z[i] = X[i]*a;
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@ -157,10 +160,10 @@ static void norm(const mp_no *x, double *y, int p)
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if (v == TWO18) {
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if (z[4] == ZERO) {
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for (i=5; i <= p; i++) {
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if (X[i] == ZERO) continue;
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else {z[3] += ONE; break; }
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}
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for (i=5; i <= p; i++) {
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if (X[i] == ZERO) continue;
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else {z[3] += ONE; break; }
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}
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}
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else z[3] += ONE;
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}
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@ -242,6 +245,7 @@ void __mp_dbl(const mp_no *x, double *y, int p) {
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else if (EX==-42 && X[1]>=TWO10) norm(x,y,p);
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else denorm(x,y,p);
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}
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#endif
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/* dbl_mp() converts a double precision number x into a multiple precision */
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@ -336,11 +340,11 @@ static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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else {
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i=p; j=p+1-j; k=p;
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if (Y[j] > ZERO) {
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Z[k+1] = RADIX - Y[j--];
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Z[k] = MONE; }
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Z[k+1] = RADIX - Y[j--];
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Z[k] = MONE; }
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else {
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Z[k+1] = ZERO;
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Z[k] = ZERO; j--;}
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Z[k+1] = ZERO;
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Z[k] = ZERO; j--;}
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}
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}
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@ -431,11 +435,11 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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int i, i1, i2, j, k, k2;
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double u;
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/* Is z=0? */
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/* Is z=0? */
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if (X[0]*Y[0]==ZERO)
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{ Z[0]=ZERO; return; }
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/* Multiply, add and carry */
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/* Multiply, add and carry */
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k2 = (p<3) ? p+p : p+3;
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Z[k2]=ZERO;
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for (k=k2; k>1; ) {
|
||||
@ -449,7 +453,7 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
Z[--k] = u*RADIXI;
|
||||
}
|
||||
|
||||
/* Is there a carry beyond the most significant digit? */
|
||||
/* Is there a carry beyond the most significant digit? */
|
||||
if (Z[1] == ZERO) {
|
||||
for (i=1; i<=p; i++) Z[i]=Z[i+1];
|
||||
EZ = EX + EY - 1; }
|
||||
@ -466,7 +470,7 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
/* 2.001*r**(1-p) for p>3. */
|
||||
/* *x=0 is not permissible. *x is left unchanged. */
|
||||
|
||||
void __inv(const mp_no *x, mp_no *y, int p) {
|
||||
static void __inv(const mp_no *x, mp_no *y, int p) {
|
||||
int i;
|
||||
#if 0
|
||||
int l;
|
||||
@ -474,11 +478,11 @@ void __inv(const mp_no *x, mp_no *y, int p) {
|
||||
double t;
|
||||
mp_no z,w;
|
||||
static const int np1[] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,
|
||||
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4};
|
||||
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4};
|
||||
const mp_no mptwo = {1,{1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
|
||||
|
||||
__cpy(x,&z,p); z.e=0; __mp_dbl(&z,&t,p);
|
||||
t=ONE/t; __dbl_mp(t,y,p); EY -= EX;
|
||||
|
@ -1,8 +1,7 @@
|
||||
|
||||
/*
|
||||
* IBM Accurate Mathematical Library
|
||||
* Written by International Business Machines Corp.
|
||||
* Copyright (C) 2001 Free Software Foundation, Inc.
|
||||
* Copyright (C) 2001, 2011 Free Software Foundation, Inc.
|
||||
*
|
||||
* 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
|
||||
@ -45,14 +44,14 @@ typedef struct {/* This structure holds the details of a multi-precision */
|
||||
int e; /* floating point number, x: d[0] holds its sign (-1,0 or 1) */
|
||||
double d[40]; /* e holds its exponent (...,-2,-1,0,1,2,...) and */
|
||||
} mp_no; /* d[1]...d[p] hold its mantissa digits. The value of x is, */
|
||||
/* x = d[1]*r**(e-1) + d[2]*r**(e-2) + ... + d[p]*r**(e-p). */
|
||||
/* Here r = 2**24, 0 <= d[i] < r and 1 <= p <= 32. */
|
||||
/* p is a global variable. A multi-precision number is */
|
||||
/* always normalized. Namely, d[1] > 0. An exception is */
|
||||
/* a zero which is characterized by d[0] = 0. The terms */
|
||||
/* d[p+1], d[p+2], ... of a none zero number have no */
|
||||
/* significance and so are the terms e, d[1],d[2],... */
|
||||
/* of a zero. */
|
||||
/* x = d[1]*r**(e-1) + d[2]*r**(e-2) + ... + d[p]*r**(e-p). */
|
||||
/* Here r = 2**24, 0 <= d[i] < r and 1 <= p <= 32. */
|
||||
/* p is a global variable. A multi-precision number is */
|
||||
/* always normalized. Namely, d[1] > 0. An exception is */
|
||||
/* a zero which is characterized by d[0] = 0. The terms */
|
||||
/* d[p+1], d[p+2], ... of a none zero number have no */
|
||||
/* significance and so are the terms e, d[1],d[2],... */
|
||||
/* of a zero. */
|
||||
|
||||
typedef union { int i[2]; double d; } number;
|
||||
|
||||
@ -65,16 +64,16 @@ typedef union { int i[2]; double d; } number;
|
||||
|
||||
#define ABS(x) ((x) < 0 ? -(x) : (x))
|
||||
|
||||
int __acr(const mp_no *, const mp_no *, int);
|
||||
int __cr(const mp_no *, const mp_no *, int);
|
||||
// int __acr(const mp_no *, const mp_no *, int);
|
||||
// int __cr(const mp_no *, const mp_no *, int);
|
||||
void __cpy(const mp_no *, mp_no *, int);
|
||||
void __cpymn(const mp_no *, int, mp_no *, int);
|
||||
// void __cpymn(const mp_no *, int, mp_no *, int);
|
||||
void __mp_dbl(const mp_no *, double *, int);
|
||||
void __dbl_mp(double, mp_no *, int);
|
||||
void __add(const mp_no *, const mp_no *, mp_no *, int);
|
||||
void __sub(const mp_no *, const mp_no *, mp_no *, int);
|
||||
void __mul(const mp_no *, const mp_no *, mp_no *, int);
|
||||
void __inv(const mp_no *, mp_no *, int);
|
||||
// void __inv(const mp_no *, mp_no *, int);
|
||||
void __dvd(const mp_no *, const mp_no *, mp_no *, int);
|
||||
|
||||
extern void __mpatan (mp_no *, mp_no *, int);
|
||||
|
@ -1,8 +1,7 @@
|
||||
|
||||
/*
|
||||
* IBM Accurate Mathematical Library
|
||||
* written by International Business Machines Corp.
|
||||
* Copyright (C) 2001 Free Software Foundation
|
||||
* Copyright (C) 2001, 2011 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
|
||||
@ -41,7 +40,7 @@
|
||||
/* p as integer. Routine computes sqrt(*x) and stores result in *y */
|
||||
/****************************************************************************/
|
||||
|
||||
double fastiroot(double);
|
||||
static double fastiroot(double);
|
||||
|
||||
void __mpsqrt(mp_no *x, mp_no *y, int p) {
|
||||
#include "mpsqrt.h"
|
||||
@ -50,11 +49,11 @@ void __mpsqrt(mp_no *x, mp_no *y, int p) {
|
||||
double dx,dy;
|
||||
mp_no
|
||||
mphalf = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
|
||||
mp3halfs = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
|
||||
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
|
||||
mp_no mpxn,mpz,mpu,mpt1,mpt2;
|
||||
|
||||
/* Prepare multi-precision 1/2 and 3/2 */
|
||||
@ -82,7 +81,7 @@ void __mpsqrt(mp_no *x, mp_no *y, int p) {
|
||||
/* Compute a double precision approximation for 1/sqrt(x) */
|
||||
/* with the relative error bounded by 2**-51. */
|
||||
/***********************************************************/
|
||||
double fastiroot(double x) {
|
||||
static double fastiroot(double x) {
|
||||
union {int i[2]; double d;} p,q;
|
||||
double y,z, t;
|
||||
int n;
|
||||
|
@ -46,7 +46,13 @@
|
||||
|
||||
void __mpatan(mp_no *,mp_no *,int); /* see definition in mpatan.c */
|
||||
static double atanMp(double,const int[]);
|
||||
double __signArctan(double,double);
|
||||
|
||||
/* Fix the sign of y and return */
|
||||
static double __signArctan(double x,double y){
|
||||
return __copysign(y, x);
|
||||
}
|
||||
|
||||
|
||||
/* An ultimate atan() routine. Given an IEEE double machine number x, */
|
||||
/* routine computes the correctly rounded (to nearest) value of atan(x). */
|
||||
double atan(double x) {
|
||||
@ -203,14 +209,6 @@ double atan(double x) {
|
||||
|
||||
}
|
||||
|
||||
|
||||
/* Fix the sign of y and return */
|
||||
double __signArctan(double x,double y){
|
||||
|
||||
if (x<ZERO) return -y;
|
||||
else return y;
|
||||
}
|
||||
|
||||
/* Final stages. Compute atan(x) by multiple precision arithmetic */
|
||||
static double atanMp(double x,const int pr[]){
|
||||
mp_no mpx,mpy,mpy2,mperr,mpt1,mpy1;
|
||||
|
@ -1,7 +1,7 @@
|
||||
/*
|
||||
* IBM Accurate Mathematical Library
|
||||
* written by International Business Machines Corp.
|
||||
* Copyright (C) 2001, 2009 Free Software Foundation
|
||||
* Copyright (C) 2001, 2009, 2011 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
|
||||
@ -53,15 +53,20 @@
|
||||
#include "mydefs.h"
|
||||
#include "usncs.h"
|
||||
#include "MathLib.h"
|
||||
#include "sincos.tbl"
|
||||
#include "math_private.h"
|
||||
|
||||
extern const union
|
||||
{
|
||||
int4 i[880];
|
||||
double x[440];
|
||||
} __sincostab attribute_hidden;
|
||||
|
||||
static const double
|
||||
sn3 = -1.66666666666664880952546298448555E-01,
|
||||
sn5 = 8.33333214285722277379541354343671E-03,
|
||||
cs2 = 4.99999999999999999999950396842453E-01,
|
||||
cs4 = -4.16666666666664434524222570944589E-02,
|
||||
cs6 = 1.38888874007937613028114285595617E-03;
|
||||
sn3 = -1.66666666666664880952546298448555E-01,
|
||||
sn5 = 8.33333214285722277379541354343671E-03,
|
||||
cs2 = 4.99999999999999999999950396842453E-01,
|
||||
cs4 = -4.16666666666664434524222570944589E-02,
|
||||
cs6 = 1.38888874007937613028114285595617E-03;
|
||||
|
||||
void __dubsin(double x, double dx, double w[]);
|
||||
void __docos(double x, double dx, double w[]);
|
||||
@ -120,10 +125,10 @@ double __sin(double x){
|
||||
s = y + y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=(m>0)?sincos.x[k]:-sincos.x[k];
|
||||
ssn=(m>0)?sincos.x[k+1]:-sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=(m>0)?__sincostab.x[k]:-__sincostab.x[k];
|
||||
ssn=(m>0)?__sincostab.x[k+1]:-__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ssn+s*ccs-sn*c)+cs*s;
|
||||
res=sn+cor;
|
||||
cor=(sn-res)+cor;
|
||||
@ -146,10 +151,10 @@ double __sin(double x){
|
||||
s = y + y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ccs-s*ssn-cs*c)-sn*s;
|
||||
res=cs+cor;
|
||||
cor=(cs-res)+cor;
|
||||
@ -174,7 +179,7 @@ double __sin(double x){
|
||||
xx = a*a;
|
||||
if (n) {a=-a;da=-da;}
|
||||
if (xx < 0.01588) {
|
||||
/*Taylor series */
|
||||
/*Taylor series */
|
||||
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
|
||||
res = a+t;
|
||||
cor = (a-res)+t;
|
||||
@ -192,10 +197,10 @@ double __sin(double x){
|
||||
s = y + (db+y*xx*(sn3 +xx*sn5));
|
||||
c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ssn+s*ccs-sn*c)+cs*s;
|
||||
res=sn+cor;
|
||||
cor=(sn-res)+cor;
|
||||
@ -212,10 +217,10 @@ double __sin(double x){
|
||||
y=a-(u.x-big.x)+da;
|
||||
xx=y*y;
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
s = y + y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
cor=(ccs-s*ssn-cs*c)-sn*s;
|
||||
@ -253,7 +258,7 @@ double __sin(double x){
|
||||
xx = a*a;
|
||||
if (n) {a=-a;da=-da;}
|
||||
if (xx < 0.01588) {
|
||||
/* Taylor series */
|
||||
/* Taylor series */
|
||||
t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da;
|
||||
res = a+t;
|
||||
cor = (a-res)+t;
|
||||
@ -269,10 +274,10 @@ double __sin(double x){
|
||||
s = y + (db+y*xx*(sn3 +xx*sn5));
|
||||
c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ssn+s*ccs-sn*c)+cs*s;
|
||||
res=sn+cor;
|
||||
cor=(sn-res)+cor;
|
||||
@ -289,10 +294,10 @@ double __sin(double x){
|
||||
y=a-(u.x-big.x)+da;
|
||||
xx=y*y;
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
s = y + y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
cor=(ccs-s*ssn-cs*c)-sn*s;
|
||||
@ -364,10 +369,10 @@ double __cos(double x)
|
||||
s = y + y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ccs-s*ssn-cs*c)-sn*s;
|
||||
res=cs+cor;
|
||||
cor=(cs-res)+cor;
|
||||
@ -396,10 +401,10 @@ double __cos(double x)
|
||||
s = y + (db+y*xx*(sn3 +xx*sn5));
|
||||
c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ssn+s*ccs-sn*c)+cs*s;
|
||||
res=sn+cor;
|
||||
cor=(sn-res)+cor;
|
||||
@ -442,10 +447,10 @@ double __cos(double x)
|
||||
s = y + (db+y*xx*(sn3 +xx*sn5));
|
||||
c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ssn+s*ccs-sn*c)+cs*s;
|
||||
res=sn+cor;
|
||||
cor=(sn-res)+cor;
|
||||
@ -461,10 +466,10 @@ double __cos(double x)
|
||||
y=a-(u.x-big.x)+da;
|
||||
xx=y*y;
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
s = y + y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
cor=(ccs-s*ssn-cs*c)-sn*s;
|
||||
@ -473,7 +478,7 @@ double __cos(double x)
|
||||
cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps;
|
||||
return (res==res+cor)? ((n)?-res:res) : csloww2(a,da,x,n);
|
||||
|
||||
break;
|
||||
break;
|
||||
|
||||
}
|
||||
|
||||
@ -517,10 +522,10 @@ double __cos(double x)
|
||||
s = y + (db+y*xx*(sn3 +xx*sn5));
|
||||
c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
cor=(ssn+s*ccs-sn*c)+cs*s;
|
||||
res=sn+cor;
|
||||
cor=(sn-res)+cor;
|
||||
@ -536,10 +541,10 @@ double __cos(double x)
|
||||
y=a-(u.x-big.x)+da;
|
||||
xx=y*y;
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
s = y + y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
cor=(ccs-s*ssn-cs*c)-sn*s;
|
||||
@ -611,7 +616,7 @@ static const double th2_36 = 206158430208.0; /* 1.5*2**37 */
|
||||
}
|
||||
}
|
||||
/*******************************************************************************/
|
||||
/* Routine compute sin(x) for 0.25<|x|< 0.855469 by sincos.tbl and Taylor */
|
||||
/* Routine compute sin(x) for 0.25<|x|< 0.855469 by __sincostab.tbl and Taylor */
|
||||
/* and if result still doesn't accurate enough by mpsin or dubsin */
|
||||
/*******************************************************************************/
|
||||
|
||||
@ -627,10 +632,10 @@ static double slow1(double x) {
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k]; /* Data */
|
||||
ssn=sincos.x[k+1]; /* from */
|
||||
cs=sincos.x[k+2]; /* tables */
|
||||
ccs=sincos.x[k+3]; /* sincos.tbl */
|
||||
sn=__sincostab.x[k]; /* Data */
|
||||
ssn=__sincostab.x[k+1]; /* from */
|
||||
cs=__sincostab.x[k+2]; /* tables */
|
||||
ccs=__sincostab.x[k+3]; /* __sincostab.tbl */
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = y - y1;
|
||||
c1 = (cs+t22)-t22;
|
||||
@ -648,7 +653,7 @@ static double slow1(double x) {
|
||||
}
|
||||
}
|
||||
/**************************************************************************/
|
||||
/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by sincos.tbl */
|
||||
/* Routine compute sin(x) for 0.855469 <|x|<2.426265 by __sincostab.tbl */
|
||||
/* and if result still doesn't accurate enough by mpsin or dubsin */
|
||||
/**************************************************************************/
|
||||
static double slow2(double x) {
|
||||
@ -672,10 +677,10 @@ static double slow2(double x) {
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = y*del+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = (y - y1)+del;
|
||||
e1 = (sn+t22)-t22;
|
||||
@ -763,10 +768,10 @@ static double sloww1(double x, double dx, double orig) {
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = (y - y1)+dx;
|
||||
c1 = (cs+t22)-t22;
|
||||
@ -805,10 +810,10 @@ static double sloww2(double x, double dx, double orig, int n) {
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = (y - y1)+dx;
|
||||
@ -882,10 +887,10 @@ mynumber u;
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = (y - y1)+dx;
|
||||
c1 = (cs+t22)-t22;
|
||||
@ -925,10 +930,10 @@ mynumber u;
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = (y - y1)+dx;
|
||||
@ -966,10 +971,10 @@ static double cslow2(double x) {
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = y - y1;
|
||||
e1 = (sn+t22)-t22;
|
||||
@ -1059,10 +1064,10 @@ static double csloww1(double x, double dx, double orig) {
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = (y - y1)+dx;
|
||||
c1 = (cs+t22)-t22;
|
||||
@ -1103,10 +1108,10 @@ static double csloww2(double x, double dx, double orig, int n) {
|
||||
s = y*xx*(sn3 +xx*sn5);
|
||||
c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6));
|
||||
k=u.i[LOW_HALF]<<2;
|
||||
sn=sincos.x[k];
|
||||
ssn=sincos.x[k+1];
|
||||
cs=sincos.x[k+2];
|
||||
ccs=sincos.x[k+3];
|
||||
sn=__sincostab.x[k];
|
||||
ssn=__sincostab.x[k+1];
|
||||
cs=__sincostab.x[k+2];
|
||||
ccs=__sincostab.x[k+3];
|
||||
|
||||
y1 = (y+t22)-t22;
|
||||
y2 = (y - y1)+dx;
|
||||
@ -1127,12 +1132,17 @@ static double csloww2(double x, double dx, double orig, int n) {
|
||||
}
|
||||
}
|
||||
|
||||
#ifndef __cos
|
||||
weak_alias (__cos, cos)
|
||||
weak_alias (__sin, sin)
|
||||
|
||||
#ifdef NO_LONG_DOUBLE
|
||||
strong_alias (__sin, __sinl)
|
||||
weak_alias (__sin, sinl)
|
||||
# ifdef NO_LONG_DOUBLE
|
||||
strong_alias (__cos, __cosl)
|
||||
weak_alias (__cos, cosl)
|
||||
# endif
|
||||
#endif
|
||||
#ifndef __sin
|
||||
weak_alias (__sin, sin)
|
||||
# ifdef NO_LONG_DOUBLE
|
||||
strong_alias (__sin, __sinl)
|
||||
weak_alias (__sin, sinl)
|
||||
# endif
|
||||
#endif
|
||||
|
@ -1,7 +1,7 @@
|
||||
/*
|
||||
* IBM Accurate Mathematical Library
|
||||
* Written by International Business Machines Corp.
|
||||
* Copyright (C) 2001, 2007 Free Software Foundation, Inc.
|
||||
* Copyright (C) 2001, 2007, 2011 Free Software Foundation, Inc.
|
||||
*
|
||||
* 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
|
||||
@ -18,13 +18,16 @@
|
||||
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
|
||||
*/
|
||||
|
||||
#include <mydefs.h>
|
||||
#include <endian.h>
|
||||
|
||||
/****************************************************************/
|
||||
/* TABLES FOR THE usin() and ucos() FUNCTION */
|
||||
/****************************************************************/
|
||||
|
||||
|
||||
#ifdef BIG_ENDI
|
||||
static const union {int4 i[880]; double x[440];}sincos = { .i = {
|
||||
const union {int4 i[880]; double x[440];}__sincostab = { .i = {
|
||||
/**/ 0x00000000, 0x00000000,
|
||||
/**/ 0x00000000, 0x00000000,
|
||||
/**/ 0x3FF00000, 0x00000000,
|
||||
@ -467,7 +470,7 @@ static const union {int4 i[880]; double x[440];}sincos = { .i = {
|
||||
/**/ 0x3C747A10, 0x8073C259 } };
|
||||
#else
|
||||
#ifdef LITTLE_ENDI
|
||||
static const union {int4 i[880]; double x[440];} sincos = { .i = {
|
||||
const union {int4 i[880]; double x[440];} __sincostab = { .i = {
|
||||
/**/ 0x00000000, 0x00000000,
|
||||
/**/ 0x00000000, 0x00000000,
|
||||
/**/ 0x00000000, 0x3FF00000,
|
@ -1,4 +1,36 @@
|
||||
ifeq ($(subdir),math)
|
||||
libm-sysdep_routines += s_floor-c s_ceil-c s_floorf-c s_ceilf-c \
|
||||
s_rint-c s_rintf-c s_nearbyint-c s_nearbyintf-c
|
||||
|
||||
ifeq ($(have-mfma4),yes)
|
||||
libm-sysdep_routines += e_exp-fma4 e_log-fma4 e_pow-fma4 s_atan-fma4 \
|
||||
e_asin-fma4 e_atan2-fma4 s_sin-fma4 s_tan-fma4 \
|
||||
mplog-fma4 mpa-fma4 slowexp-fma4 slowpow-fma4 \
|
||||
sincos32-fma4 doasin-fma4 dosincos-fma4 \
|
||||
brandred-fma4 halfulp-fma4 mpexp-fma4 \
|
||||
mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
|
||||
|
||||
CFLAGS-brandred-fma4.c = -mfma4
|
||||
CFLAGS-doasin-fma4.c = -mfma4
|
||||
CFLAGS-dosincos-fma4.c = -mfma4
|
||||
CFLAGS-e_asin-fma4.c = -mfma4
|
||||
CFLAGS-e_atan2-fma4.c = -mfma4
|
||||
CFLAGS-e_exp-fma4.c = -mfma4
|
||||
CFLAGS-e_log-fma4.c = -mfma4
|
||||
CFLAGS-e_pow-fma4.c = -mfma4
|
||||
CFLAGS-halfulp-fma4.c = -mfma4
|
||||
CFLAGS-mpa-fma4.c = -mfma4
|
||||
CFLAGS-mpatan-fma4.c = -mfma4
|
||||
CFLAGS-mpatan2-fma4.c = -mfma4
|
||||
CFLAGS-mpexp-fma4.c = -mfma4
|
||||
CFLAGS-mplog-fma4.c = -mfma4
|
||||
CFLAGS-mpsqrt-fma4.c = -mfma4
|
||||
CFLAGS-mptan-fma4.c = -mfma4
|
||||
CFLAGS-s_atan-fma4.c = -mfma4
|
||||
CFLAGS-sincos32-fma4.c = -mfma4
|
||||
CFLAGS-slowexp-fma4.c = -mfma4
|
||||
CFLAGS-slowpow-fma4.c = -mfma4
|
||||
CLFAGS-s_sin-fma4.c = -mfma4
|
||||
CLFAGS-s_tan-fma4.c = -mfma4
|
||||
endif
|
||||
endif
|
||||
|
3
sysdeps/x86_64/fpu/multiarch/brandred-fma4.c
Normal file
3
sysdeps/x86_64/fpu/multiarch/brandred-fma4.c
Normal file
@ -0,0 +1,3 @@
|
||||
#define __branred __branred_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/branred.c>
|
3
sysdeps/x86_64/fpu/multiarch/doasin-fma4.c
Normal file
3
sysdeps/x86_64/fpu/multiarch/doasin-fma4.c
Normal file
@ -0,0 +1,3 @@
|
||||
#define __doasin __doasin_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/doasin.c>
|
5
sysdeps/x86_64/fpu/multiarch/dosincos-fma4.c
Normal file
5
sysdeps/x86_64/fpu/multiarch/dosincos-fma4.c
Normal file
@ -0,0 +1,5 @@
|
||||
#define __docos __docos_fma4
|
||||
#define __dubcos __dubcos_fma4
|
||||
#define __dubsin __dubsin_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/dosincos.c>
|
10
sysdeps/x86_64/fpu/multiarch/e_asin-fma4.c
Normal file
10
sysdeps/x86_64/fpu/multiarch/e_asin-fma4.c
Normal file
@ -0,0 +1,10 @@
|
||||
#define __ieee754_acos __ieee754_acos_fma4
|
||||
#define __ieee754_asin __ieee754_asin_fma4
|
||||
#define __cos32 __cos32_fma4
|
||||
#define __doasin __doasin_fma4
|
||||
#define __docos __docos_fma4
|
||||
#define __dubcos __dubcos_fma4
|
||||
#define __dubsin __dubsin_fma4
|
||||
#define __sin32 __sin32_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_asin.c>
|
23
sysdeps/x86_64/fpu/multiarch/e_asin.c
Normal file
23
sysdeps/x86_64/fpu/multiarch/e_asin.c
Normal file
@ -0,0 +1,23 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math_private.h>
|
||||
|
||||
extern double __ieee754_acos_sse2 (double);
|
||||
extern double __ieee754_acos_fma4 (double);
|
||||
extern double __ieee754_asin_sse2 (double);
|
||||
extern double __ieee754_asin_fma4 (double);
|
||||
|
||||
libm_ifunc (__ieee754_acos,
|
||||
HAS_FMA4 ? __ieee754_acos_fma4 : __ieee754_acos_sse2);
|
||||
strong_alias (__ieee754_acos, __acos_finite)
|
||||
|
||||
libm_ifunc (__ieee754_asin,
|
||||
HAS_FMA4 ? __ieee754_asin_fma4 : __ieee754_asin_sse2);
|
||||
strong_alias (__ieee754_asin, __asin_finite)
|
||||
|
||||
# define __ieee754_acos __ieee754_acos_sse2
|
||||
# define __ieee754_asin __ieee754_asin_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_asin.c>
|
9
sysdeps/x86_64/fpu/multiarch/e_atan2-fma4.c
Normal file
9
sysdeps/x86_64/fpu/multiarch/e_atan2-fma4.c
Normal file
@ -0,0 +1,9 @@
|
||||
#define __ieee754_atan2 __ieee754_atan2_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __dvd __dvd_fma4
|
||||
#define __mpatan2 __mpatan2_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_atan2.c>
|
16
sysdeps/x86_64/fpu/multiarch/e_atan2.c
Normal file
16
sysdeps/x86_64/fpu/multiarch/e_atan2.c
Normal file
@ -0,0 +1,16 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math_private.h>
|
||||
|
||||
extern double __ieee754_atan2_sse2 (double, double);
|
||||
extern double __ieee754_atan2_fma4 (double, double);
|
||||
|
||||
libm_ifunc (__ieee754_atan2,
|
||||
HAS_FMA4 ? __ieee754_atan2_fma4 : __ieee754_atan2_sse2);
|
||||
strong_alias (__ieee754_atan2, __atan2_finite)
|
||||
|
||||
# define __ieee754_atan2 __ieee754_atan2_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_atan2.c>
|
5
sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
Normal file
5
sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c
Normal file
@ -0,0 +1,5 @@
|
||||
#define __ieee754_exp __ieee754_exp_fma4
|
||||
#define __exp1 __exp1_fma4
|
||||
#define __slowexp __slowexp_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
15
sysdeps/x86_64/fpu/multiarch/e_exp.c
Normal file
15
sysdeps/x86_64/fpu/multiarch/e_exp.c
Normal file
@ -0,0 +1,15 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math_private.h>
|
||||
|
||||
extern double __ieee754_exp_sse2 (double);
|
||||
extern double __ieee754_exp_fma4 (double);
|
||||
|
||||
libm_ifunc (__ieee754_exp, HAS_FMA4 ? __ieee754_exp_fma4 : __ieee754_exp_sse2);
|
||||
strong_alias (__ieee754_exp, __exp_finite)
|
||||
|
||||
# define __ieee754_exp __ieee754_exp_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
7
sysdeps/x86_64/fpu/multiarch/e_log-fma4.c
Normal file
7
sysdeps/x86_64/fpu/multiarch/e_log-fma4.c
Normal file
@ -0,0 +1,7 @@
|
||||
#define __ieee754_log __ieee754_log_fma4
|
||||
#define __mplog __mplog_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_log.c>
|
15
sysdeps/x86_64/fpu/multiarch/e_log.c
Normal file
15
sysdeps/x86_64/fpu/multiarch/e_log.c
Normal file
@ -0,0 +1,15 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math_private.h>
|
||||
|
||||
extern double __ieee754_log_sse2 (double);
|
||||
extern double __ieee754_log_fma4 (double);
|
||||
|
||||
libm_ifunc (__ieee754_log, HAS_FMA4 ? __ieee754_log_fma4 : __ieee754_log_sse2);
|
||||
strong_alias (__ieee754_log, __log_finite)
|
||||
|
||||
# define __ieee754_log __ieee754_log_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_log.c>
|
5
sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c
Normal file
5
sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c
Normal file
@ -0,0 +1,5 @@
|
||||
#define __ieee754_pow __ieee754_pow_fma4
|
||||
#define __exp1 __exp1_fma4
|
||||
#define __slowpow __slowpow_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_pow.c>
|
15
sysdeps/x86_64/fpu/multiarch/e_pow.c
Normal file
15
sysdeps/x86_64/fpu/multiarch/e_pow.c
Normal file
@ -0,0 +1,15 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math_private.h>
|
||||
|
||||
extern double __ieee754_pow_sse2 (double, double);
|
||||
extern double __ieee754_pow_fma4 (double, double);
|
||||
|
||||
libm_ifunc (__ieee754_pow, HAS_FMA4 ? __ieee754_pow_fma4 : __ieee754_pow_sse2);
|
||||
strong_alias (__ieee754_pow, __pow_finite)
|
||||
|
||||
# define __ieee754_pow __ieee754_pow_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_pow.c>
|
3
sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c
Normal file
3
sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c
Normal file
@ -0,0 +1,3 @@
|
||||
#define __halfulp __halfulp_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/halfulp.c>
|
10
sysdeps/x86_64/fpu/multiarch/mpa-fma4.c
Normal file
10
sysdeps/x86_64/fpu/multiarch/mpa-fma4.c
Normal file
@ -0,0 +1,10 @@
|
||||
#define __add __add_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __dvd __dvd_fma4
|
||||
|
||||
#define NO___CPY 1
|
||||
#define NO___MP_DBL 1
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/mpa.c>
|
8
sysdeps/x86_64/fpu/multiarch/mpatan-fma4.c
Normal file
8
sysdeps/x86_64/fpu/multiarch/mpatan-fma4.c
Normal file
@ -0,0 +1,8 @@
|
||||
#define __mpatan __mpatan_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dvd __dvd_fma4
|
||||
#define __mpsqrt __mpsqrt_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/mpatan.c>
|
8
sysdeps/x86_64/fpu/multiarch/mpatan2-fma4.c
Normal file
8
sysdeps/x86_64/fpu/multiarch/mpatan2-fma4.c
Normal file
@ -0,0 +1,8 @@
|
||||
#define __mpatan2 __mpatan2_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dvd __dvd_fma4
|
||||
#define __mpatan __mpatan_fma4
|
||||
#define __mpsqrt __mpsqrt_fma4
|
||||
#define __mul __mul_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/mpatan2.c>
|
7
sysdeps/x86_64/fpu/multiarch/mpexp-fma4.c
Normal file
7
sysdeps/x86_64/fpu/multiarch/mpexp-fma4.c
Normal file
@ -0,0 +1,7 @@
|
||||
#define __mpexp __mpexp_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __dvd __dvd_fma4
|
||||
#define __mul __mul_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/mpexp.c>
|
7
sysdeps/x86_64/fpu/multiarch/mplog-fma4.c
Normal file
7
sysdeps/x86_64/fpu/multiarch/mplog-fma4.c
Normal file
@ -0,0 +1,7 @@
|
||||
#define __mplog __mplog_fma4
|
||||
#define __add __add_fma4
|
||||
#define __mpexp __mpexp_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/mplog.c>
|
6
sysdeps/x86_64/fpu/multiarch/mpsqrt-fma4.c
Normal file
6
sysdeps/x86_64/fpu/multiarch/mpsqrt-fma4.c
Normal file
@ -0,0 +1,6 @@
|
||||
#define __mpsqrt __mpsqrt_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/mpsqrt.c>
|
6
sysdeps/x86_64/fpu/multiarch/mptan-fma4.c
Normal file
6
sysdeps/x86_64/fpu/multiarch/mptan-fma4.c
Normal file
@ -0,0 +1,6 @@
|
||||
#define __mptan __mptan_fma4
|
||||
#define __c32 __c32_fma4
|
||||
#define __dvd __dvd_fma4
|
||||
#define __mpranred __mpranred_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/mptan.c>
|
8
sysdeps/x86_64/fpu/multiarch/s_atan-fma4.c
Normal file
8
sysdeps/x86_64/fpu/multiarch/s_atan-fma4.c
Normal file
@ -0,0 +1,8 @@
|
||||
#define atan __atan_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __mpatan __mpatan_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/s_atan.c>
|
14
sysdeps/x86_64/fpu/multiarch/s_atan.c
Normal file
14
sysdeps/x86_64/fpu/multiarch/s_atan.c
Normal file
@ -0,0 +1,14 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math.h>
|
||||
|
||||
extern double __atan_sse2 (double);
|
||||
extern double __atan_fma4 (double);
|
||||
|
||||
libm_ifunc (atan, HAS_FMA4 ? __atan_fma4 : __atan_sse2);
|
||||
|
||||
# define atan __atan_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/s_atan.c>
|
11
sysdeps/x86_64/fpu/multiarch/s_sin-fma4.c
Normal file
11
sysdeps/x86_64/fpu/multiarch/s_sin-fma4.c
Normal file
@ -0,0 +1,11 @@
|
||||
#define __cos __cos_fma4
|
||||
#define __sin __sin_fma4
|
||||
#define __branred __branred_fma4
|
||||
#define __docos __docos_fma4
|
||||
#define __dubsin __dubsin_fma4
|
||||
#define __mpcos __mpcos_fma4
|
||||
#define __mpcos1 __mpcos1_fma4
|
||||
#define __mpsin __mpsin_fma4
|
||||
#define __mpsin1 __mpsin1_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/s_sin.c>
|
22
sysdeps/x86_64/fpu/multiarch/s_sin.c
Normal file
22
sysdeps/x86_64/fpu/multiarch/s_sin.c
Normal file
@ -0,0 +1,22 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math.h>
|
||||
# undef NAN
|
||||
|
||||
extern double __cos_sse2 (double);
|
||||
extern double __cos_fma4 (double);
|
||||
extern double __sin_sse2 (double);
|
||||
extern double __sin_fma4 (double);
|
||||
|
||||
libm_ifunc (__cos, HAS_FMA4 ? __cos_fma4 : __cos_sse2);
|
||||
weak_alias (__cos, cos)
|
||||
|
||||
libm_ifunc (__sin, HAS_FMA4 ? __sin_fma4 : __sin_sse2);
|
||||
weak_alias (__sin, sin)
|
||||
|
||||
# define __cos __cos_sse2
|
||||
# define __sin __sin_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/s_sin.c>
|
9
sysdeps/x86_64/fpu/multiarch/s_tan-fma4.c
Normal file
9
sysdeps/x86_64/fpu/multiarch/s_tan-fma4.c
Normal file
@ -0,0 +1,9 @@
|
||||
#define tan __tan_fma4
|
||||
#define __branred __branred_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __mpranred __mpranred_fma4
|
||||
#define __mptan __mptan_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/s_tan.c>
|
14
sysdeps/x86_64/fpu/multiarch/s_tan.c
Normal file
14
sysdeps/x86_64/fpu/multiarch/s_tan.c
Normal file
@ -0,0 +1,14 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math.h>
|
||||
|
||||
extern double __tan_sse2 (double);
|
||||
extern double __tan_fma4 (double);
|
||||
|
||||
libm_ifunc (tan, HAS_FMA4 ? __tan_fma4 : __tan_sse2);
|
||||
|
||||
# define tan __tan_sse2
|
||||
#endif
|
||||
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/s_tan.c>
|
14
sysdeps/x86_64/fpu/multiarch/sincos32-fma4.c
Normal file
14
sysdeps/x86_64/fpu/multiarch/sincos32-fma4.c
Normal file
@ -0,0 +1,14 @@
|
||||
#define __cos32 __cos32_fma4
|
||||
#define __sin32 __sin32_fma4
|
||||
#define __c32 __c32_fma4
|
||||
#define __mpsin __mpsin_fma4
|
||||
#define __mpsin1 __mpsin1_fma4
|
||||
#define __mpcos __mpcos_fma4
|
||||
#define __mpcos1 __mpcos1_fma4
|
||||
#define __mpranred __mpranred_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/sincos32.c>
|
8
sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
Normal file
8
sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
Normal file
@ -0,0 +1,8 @@
|
||||
#define __slowexp __slowexp_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __mpexp __mpexp_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/slowexp.c>
|
10
sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c
Normal file
10
sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c
Normal file
@ -0,0 +1,10 @@
|
||||
#define __slowpow __slowpow_fma4
|
||||
#define __add __add_fma4
|
||||
#define __dbl_mp __dbl_mp_fma4
|
||||
#define __mpexp __mpexp_fma4
|
||||
#define __mplog __mplog_fma4
|
||||
#define __mul __mul_fma4
|
||||
#define __sub __sub_fma4
|
||||
#define __halfulp __halfulp_fma4
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/slowpow.c>
|
Loading…
Reference in New Issue
Block a user