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Revert exp reimplementation (causes test failures).
Revert: 2017-12-19 Joseph Myers <joseph@codesourcery.com> * sysdeps/x86_64/fpu/libm-test-ulps: Update. 2017-12-19 Patrick McGehearty <patrick.mcgehearty@oracle.com> * sysdeps/ieee754/dbl-64/e_exp.c: Include <math-svid-compat.h> and <errno.h>. Include "eexp.tbl". (half): New constant. (one): Likewise. (__ieee754_exp): Rewrite. (__slowexp): Remove prototype. * sysdeps/ieee754/dbl-64/eexp.tbl: New file. * sysdeps/ieee754/dbl-64/slowexp.c: Remove file. * sysdeps/i386/fpu/slowexp.c: Likewise. * sysdeps/ia64/fpu/slowexp.c: Likewise. * sysdeps/m68k/m680x0/fpu/slowexp.c: Likewise. * sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Likewise. * sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Likewise. * sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Likewise. * sysdeps/generic/math_private.h (__slowexp): Remove prototype. * sysdeps/ieee754/dbl-64/e_pow.c: Remove mention of slowexp.c in comment. * sysdeps/powerpc/power4/fpu/Makefile [$(subdir) = math] (CPPFLAGS-slowexp.c): Remove variable. * sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines): Remove slowexp-fma, slowexp-fma4 and slowexp-avx. (CFLAGS-slowexp-fma.c): Remove variable. (CFLAGS-slowexp-fma4.c): Likewise. (CFLAGS-slowexp-avx.c): Likewise. * sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Do not define as macro. * sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Likewise. * sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Likewise. * math/Makefile (type-double-routines): Remove slowexp. * manual/probes.texi (slowexp_p6): Remove. (slowexp_p32): Likewise.
This commit is contained in:
Joseph Myers
parent
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ChangeLog
42
ChangeLog
@ -1,3 +1,45 @@
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2017-12-19 Joseph Myers <joseph@codesourcery.com>
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Revert:
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2017-12-19 Joseph Myers <joseph@codesourcery.com>
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* sysdeps/x86_64/fpu/libm-test-ulps: Update.
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2017-12-19 Patrick McGehearty <patrick.mcgehearty@oracle.com>
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* sysdeps/ieee754/dbl-64/e_exp.c: Include <math-svid-compat.h> and
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<errno.h>. Include "eexp.tbl".
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(half): New constant.
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(one): Likewise.
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(__ieee754_exp): Rewrite.
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(__slowexp): Remove prototype.
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* sysdeps/ieee754/dbl-64/eexp.tbl: New file.
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* sysdeps/ieee754/dbl-64/slowexp.c: Remove file.
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* sysdeps/i386/fpu/slowexp.c: Likewise.
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* sysdeps/ia64/fpu/slowexp.c: Likewise.
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* sysdeps/m68k/m680x0/fpu/slowexp.c: Likewise.
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* sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Likewise.
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* sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Likewise.
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* sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Likewise.
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* sysdeps/generic/math_private.h (__slowexp): Remove prototype.
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* sysdeps/ieee754/dbl-64/e_pow.c: Remove mention of slowexp.c in
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comment.
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* sysdeps/powerpc/power4/fpu/Makefile [$(subdir) = math]
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(CPPFLAGS-slowexp.c): Remove variable.
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* sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines):
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Remove slowexp-fma, slowexp-fma4 and slowexp-avx.
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(CFLAGS-slowexp-fma.c): Remove variable.
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(CFLAGS-slowexp-fma4.c): Likewise.
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(CFLAGS-slowexp-avx.c): Likewise.
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* sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Do not
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define as macro.
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* sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Likewise.
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* sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Likewise.
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* math/Makefile (type-double-routines): Remove slowexp.
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* manual/probes.texi (slowexp_p6): Remove.
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(slowexp_p32): Likewise.
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2017-12-19 Adhemerval Zanella <adhemerval.zanella@linaro.org>
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2017-12-19 Adhemerval Zanella <adhemerval.zanella@linaro.org>
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* lib/glob.c (glob): Use a 'char *', not a 'void *', in pointer
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* lib/glob.c (glob): Use a 'char *', not a 'void *', in pointer
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@ -258,6 +258,20 @@ Unless explicitly mentioned otherwise, a precision of 1 implies 24 bits of
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precision in the mantissa of the multiple precision number. Hence, a precision
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precision in the mantissa of the multiple precision number. Hence, a precision
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level of 32 implies 768 bits of precision in the mantissa.
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level of 32 implies 768 bits of precision in the mantissa.
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@deftp Probe slowexp_p6 (double @var{$arg1}, double @var{$arg2})
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This probe is triggered when the @code{exp} function is called with an
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input that results in multiple precision computation with precision
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6. Argument @var{$arg1} is the input value and @var{$arg2} is the
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computed output.
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@end deftp
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@deftp Probe slowexp_p32 (double @var{$arg1}, double @var{$arg2})
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This probe is triggered when the @code{exp} function is called with an
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input that results in multiple precision computation with precision
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32. Argument @var{$arg1} is the input value and @var{$arg2} is the
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computed output.
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@end deftp
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@deftp Probe slowpow_p10 (double @var{$arg1}, double @var{$arg2}, double @var{$arg3}, double @var{$arg4})
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@deftp Probe slowpow_p10 (double @var{$arg1}, double @var{$arg2}, double @var{$arg3}, double @var{$arg4})
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This probe is triggered when the @code{pow} function is called with
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This probe is triggered when the @code{pow} function is called with
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inputs that result in multiple precision computation with precision
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inputs that result in multiple precision computation with precision
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@ -114,7 +114,7 @@ type-ldouble-yes := ldouble
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# double support
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# double support
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type-double-suffix :=
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type-double-suffix :=
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type-double-routines := branred doasin dosincos halfulp mpa mpatan2 \
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type-double-routines := branred doasin dosincos halfulp mpa mpatan2 \
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mpatan mpexp mplog mpsqrt mptan sincos32 \
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mpatan mpexp mplog mpsqrt mptan sincos32 slowexp \
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slowpow sincostab k_rem_pio2
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slowpow sincostab k_rem_pio2
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# float support
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# float support
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@ -262,6 +262,7 @@ extern double __sin32 (double __x, double __res, double __res1);
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extern double __cos32 (double __x, double __res, double __res1);
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extern double __cos32 (double __x, double __res, double __res1);
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extern double __mpsin (double __x, double __dx, bool __range_reduce);
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extern double __mpsin (double __x, double __dx, bool __range_reduce);
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extern double __mpcos (double __x, double __dx, bool __range_reduce);
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extern double __mpcos (double __x, double __dx, bool __range_reduce);
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extern double __slowexp (double __x);
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extern double __slowpow (double __x, double __y, double __z);
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extern double __slowpow (double __x, double __y, double __z);
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extern void __docos (double __x, double __dx, double __v[]);
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extern void __docos (double __x, double __dx, double __v[]);
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1
sysdeps/i386/fpu/slowexp.c
Normal file
1
sysdeps/i386/fpu/slowexp.c
Normal file
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/* Not needed. */
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1
sysdeps/ia64/fpu/slowexp.c
Normal file
1
sysdeps/ia64/fpu/slowexp.c
Normal file
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/* Not needed. */
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@ -1,4 +1,3 @@
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/* EXP function - Compute double precision exponential */
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/*
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/*
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* IBM Accurate Mathematical Library
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* written by International Business Machines Corp.
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@ -24,7 +23,7 @@
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/* exp1 */
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/* exp1 */
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/* */
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/* */
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/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */
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/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */
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/* mpa.c mpexp.x */
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/* mpa.c mpexp.x slowexp.c */
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/* */
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/* */
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/* An ultimate exp routine. Given an IEEE double machine number x */
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/* An ultimate exp routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of e^x */
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/* it computes the correctly rounded (to nearest) value of e^x */
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@ -33,238 +32,207 @@
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/* */
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/* */
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/***************************************************************************/
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/***************************************************************************/
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/* IBM exp(x) replaced by following exp(x) in 2017. IBM exp1(x,xx) remains. */
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/* exp(x)
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Hybrid algorithm of Peter Tang's Table driven method (for large
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arguments) and an accurate table (for small arguments).
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Written by K.C. Ng, November 1988.
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Revised by Patrick McGehearty, Nov 2017 to use j/64 instead of j/32
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Method (large arguments):
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1. Argument Reduction: given the input x, find r and integer k
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and j such that
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x = (k+j/64)*(ln2) + r, |r| <= (1/128)*ln2
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2. exp(x) = 2^k * (2^(j/64) + 2^(j/64)*expm1(r))
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a. expm1(r) is approximated by a polynomial:
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expm1(r) ~ r + t1*r^2 + t2*r^3 + ... + t5*r^6
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Here t1 = 1/2 exactly.
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b. 2^(j/64) is represented to twice double precision
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as TBL[2j]+TBL[2j+1].
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Note: If divide were fast enough, we could use another approximation
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in 2.a:
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expm1(r) ~ (2r)/(2-R), R = r - r^2*(t1 + t2*r^2)
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(for the same t1 and t2 as above)
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Special cases:
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exp(INF) is INF, exp(NaN) is NaN;
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exp(-INF)= 0;
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for finite argument, only exp(0)=1 is exact.
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Accuracy:
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According to an error analysis, the error is always less than
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an ulp (unit in the last place). The largest errors observed
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are less than 0.55 ulp for normal results and less than 0.75 ulp
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for subnormal results.
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Misc. info.
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For IEEE double
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if x > 7.09782712893383973096e+02 then exp(x) overflow
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if x < -7.45133219101941108420e+02 then exp(x) underflow. */
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#include <math.h>
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#include <math.h>
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#include <math-svid-compat.h>
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#include <math_private.h>
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#include <errno.h>
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#include "endian.h"
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#include "endian.h"
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#include "uexp.h"
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#include "uexp.h"
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#include "uexp.tbl"
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#include "mydefs.h"
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#include "mydefs.h"
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#include "MathLib.h"
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#include "MathLib.h"
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#include "uexp.tbl"
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#include <math_private.h>
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#include <fenv.h>
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#include <fenv.h>
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#include <float.h>
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#include <float.h>
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extern double __ieee754_exp (double);
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#ifndef SECTION
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# define SECTION
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#include "eexp.tbl"
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#endif
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static const double
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half = 0.5,
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one = 1.0;
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double __slowexp (double);
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/* An ultimate exp routine. Given an IEEE double machine number x it computes
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the correctly rounded (to nearest) value of e^x. */
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double
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double
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__ieee754_exp (double x_arg)
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SECTION
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__ieee754_exp (double x)
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{
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{
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double z, t;
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double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
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mynumber junk1, junk2, binexp = {{0, 0}};
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int4 i, j, m, n, ex;
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double retval;
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double retval;
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int hx, ix, k, j, m;
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int fe_val;
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union
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{
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int i_part[2];
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double x;
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} xx;
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union
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{
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int y_part[2];
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double y;
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} yy;
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xx.x = x_arg;
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ix = xx.i_part[HIGH_HALF];
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{
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hx = ix & ~0x80000000;
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SET_RESTORE_ROUND (FE_TONEAREST);
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if (hx < 0x3ff0a2b2)
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junk1.x = x;
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{ /* |x| < 3/2 ln 2 */
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m = junk1.i[HIGH_HALF];
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if (hx < 0x3f862e42)
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n = m & hugeint;
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{ /* |x| < 1/64 ln 2 */
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if (hx < 0x3ed00000)
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if (n > smallint && n < bigint)
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{ /* |x| < 2^-18 */
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if (hx < 0x3e300000)
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{
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{
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retval = one + xx.x;
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y = x * log2e.x + three51.x;
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return retval;
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bexp = y - three51.x; /* multiply the result by 2**bexp */
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}
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retval = one + xx.x * (one + half * xx.x);
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junk1.x = y;
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return retval;
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}
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eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */
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/* Use FE_TONEAREST rounding mode for computing yy.y.
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t = x - bexp * ln_two1.x;
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Avoid set/reset of rounding mode if in FE_TONEAREST mode. */
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fe_val = get_rounding_mode ();
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y = t + three33.x;
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if (fe_val == FE_TONEAREST)
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base = y - three33.x; /* t rounded to a multiple of 2**-18 */
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junk2.x = y;
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del = (t - base) - eps; /* x = bexp*ln(2) + base + del */
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eps = del + del * del * (p3.x * del + p2.x);
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binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20;
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i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
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j = (junk2.i[LOW_HALF] & 511) << 1;
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al = coar.x[i] * fine.x[j];
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bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
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+ coar.x[i + 1] * fine.x[j + 1]);
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rem = (bet + bet * eps) + al * eps;
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res = al + rem;
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cor = (al - res) + rem;
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if (res == (res + cor * err_0))
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{
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{
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t = xx.x * xx.x;
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retval = res * binexp.x;
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yy.y = xx.x + (t * (half + xx.x * t2)
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goto ret;
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+ (t * t) * (t3 + xx.x * t4 + t * t5));
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retval = one + yy.y;
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}
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}
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else
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else
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{
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{
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libc_fesetround (FE_TONEAREST);
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retval = __slowexp (x);
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t = xx.x * xx.x;
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goto ret;
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yy.y = xx.x + (t * (half + xx.x * t2)
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} /*if error is over bound */
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+ (t * t) * (t3 + xx.x * t4 + t * t5));
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retval = one + yy.y;
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libc_fesetround (fe_val);
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}
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return retval;
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}
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}
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/* Find the multiple of 2^-6 nearest x. */
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if (n <= smallint)
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k = hx >> 20;
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j = (0x00100000 | (hx & 0x000fffff)) >> (0x40c - k);
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j = (j - 1) & ~1;
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if (ix < 0)
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j += 134;
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/* Use FE_TONEAREST rounding mode for computing yy.y.
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Avoid set/reset of rounding mode if in FE_TONEAREST mode. */
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fe_val = get_rounding_mode ();
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if (fe_val == FE_TONEAREST)
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|
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{
|
{
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z = xx.x - TBL2[j];
|
retval = 1.0;
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t = z * z;
|
goto ret;
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yy.y = z + (t * (half + (z * t2))
|
}
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+ (t * t) * (t3 + z * t4 + t * t5));
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retval = TBL2[j + 1] + TBL2[j + 1] * yy.y;
|
if (n >= badint)
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|
{
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|
if (n > infint)
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|
{
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|
retval = x + x;
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|
goto ret;
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|
} /* x is NaN */
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|
if (n < infint)
|
||||||
|
{
|
||||||
|
if (x > 0)
|
||||||
|
goto ret_huge;
|
||||||
|
else
|
||||||
|
goto ret_tiny;
|
||||||
|
}
|
||||||
|
/* x is finite, cause either overflow or underflow */
|
||||||
|
if (junk1.i[LOW_HALF] != 0)
|
||||||
|
{
|
||||||
|
retval = x + x;
|
||||||
|
goto ret;
|
||||||
|
} /* x is NaN */
|
||||||
|
retval = (x > 0) ? inf.x : zero; /* |x| = inf; return either inf or 0 */
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
|
||||||
|
y = x * log2e.x + three51.x;
|
||||||
|
bexp = y - three51.x;
|
||||||
|
junk1.x = y;
|
||||||
|
eps = bexp * ln_two2.x;
|
||||||
|
t = x - bexp * ln_two1.x;
|
||||||
|
y = t + three33.x;
|
||||||
|
base = y - three33.x;
|
||||||
|
junk2.x = y;
|
||||||
|
del = (t - base) - eps;
|
||||||
|
eps = del + del * del * (p3.x * del + p2.x);
|
||||||
|
i = ((junk2.i[LOW_HALF] >> 8) & 0xfffffffe) + 356;
|
||||||
|
j = (junk2.i[LOW_HALF] & 511) << 1;
|
||||||
|
al = coar.x[i] * fine.x[j];
|
||||||
|
bet = ((coar.x[i] * fine.x[j + 1] + coar.x[i + 1] * fine.x[j])
|
||||||
|
+ coar.x[i + 1] * fine.x[j + 1]);
|
||||||
|
rem = (bet + bet * eps) + al * eps;
|
||||||
|
res = al + rem;
|
||||||
|
cor = (al - res) + rem;
|
||||||
|
if (m >> 31)
|
||||||
|
{
|
||||||
|
ex = junk1.i[LOW_HALF];
|
||||||
|
if (res < 1.0)
|
||||||
|
{
|
||||||
|
res += res;
|
||||||
|
cor += cor;
|
||||||
|
ex -= 1;
|
||||||
|
}
|
||||||
|
if (ex >= -1022)
|
||||||
|
{
|
||||||
|
binexp.i[HIGH_HALF] = (1023 + ex) << 20;
|
||||||
|
if (res == (res + cor * err_0))
|
||||||
|
{
|
||||||
|
retval = res * binexp.x;
|
||||||
|
goto ret;
|
||||||
}
|
}
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
libc_fesetround (FE_TONEAREST);
|
retval = __slowexp (x);
|
||||||
z = xx.x - TBL2[j];
|
goto check_uflow_ret;
|
||||||
t = z * z;
|
} /*if error is over bound */
|
||||||
yy.y = z + (t * (half + (z * t2))
|
|
||||||
+ (t * t) * (t3 + z * t4 + t * t5));
|
|
||||||
retval = TBL2[j + 1] + TBL2[j + 1] * yy.y;
|
|
||||||
libc_fesetround (fe_val);
|
|
||||||
}
|
}
|
||||||
return retval;
|
ex = -(1022 + ex);
|
||||||
}
|
binexp.i[HIGH_HALF] = (1023 - ex) << 20;
|
||||||
|
res *= binexp.x;
|
||||||
if (hx >= 0x40862e42)
|
cor *= binexp.x;
|
||||||
{ /* x is large, infinite, or nan. */
|
eps = 1.0000000001 + err_0 * binexp.x;
|
||||||
if (hx >= 0x7ff00000)
|
t = 1.0 + res;
|
||||||
|
y = ((1.0 - t) + res) + cor;
|
||||||
|
res = t + y;
|
||||||
|
cor = (t - res) + y;
|
||||||
|
if (res == (res + eps * cor))
|
||||||
{
|
{
|
||||||
if (ix == 0xfff00000 && xx.i_part[LOW_HALF] == 0)
|
binexp.i[HIGH_HALF] = 0x00100000;
|
||||||
return zero; /* exp(-inf) = 0. */
|
retval = (res - 1.0) * binexp.x;
|
||||||
return (xx.x * xx.x); /* exp(nan/inf) is nan or inf. */
|
goto check_uflow_ret;
|
||||||
}
|
|
||||||
if (xx.x > threshold1)
|
|
||||||
{ /* Set overflow error condition. */
|
|
||||||
retval = hhuge * hhuge;
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
if (-xx.x > threshold2)
|
|
||||||
{ /* Set underflow error condition. */
|
|
||||||
double force_underflow = tiny * tiny;
|
|
||||||
math_force_eval (force_underflow);
|
|
||||||
retval = force_underflow;
|
|
||||||
return retval;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
/* Use FE_TONEAREST rounding mode for computing yy.y.
|
|
||||||
Avoid set/reset of rounding mode if already in FE_TONEAREST mode. */
|
|
||||||
fe_val = get_rounding_mode ();
|
|
||||||
if (fe_val == FE_TONEAREST)
|
|
||||||
{
|
|
||||||
t = invln2_64 * xx.x;
|
|
||||||
if (ix < 0)
|
|
||||||
t -= half;
|
|
||||||
else
|
|
||||||
t += half;
|
|
||||||
k = (int) t;
|
|
||||||
j = (k & 0x3f) << 1;
|
|
||||||
m = k >> 6;
|
|
||||||
z = (xx.x - k * ln2_64hi) - k * ln2_64lo;
|
|
||||||
|
|
||||||
/* z is now in primary range. */
|
|
||||||
t = z * z;
|
|
||||||
yy.y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
|
|
||||||
yy.y = TBL[j] + (TBL[j + 1] + TBL[j] * yy.y);
|
|
||||||
}
|
}
|
||||||
else
|
else
|
||||||
{
|
{
|
||||||
libc_fesetround (FE_TONEAREST);
|
retval = __slowexp (x);
|
||||||
t = invln2_64 * xx.x;
|
goto check_uflow_ret;
|
||||||
if (ix < 0)
|
} /* if error is over bound */
|
||||||
t -= half;
|
check_uflow_ret:
|
||||||
else
|
|
||||||
t += half;
|
|
||||||
k = (int) t;
|
|
||||||
j = (k & 0x3f) << 1;
|
|
||||||
m = k >> 6;
|
|
||||||
z = (xx.x - k * ln2_64hi) - k * ln2_64lo;
|
|
||||||
|
|
||||||
/* z is now in primary range. */
|
|
||||||
t = z * z;
|
|
||||||
yy.y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
|
|
||||||
yy.y = TBL[j] + (TBL[j + 1] + TBL[j] * yy.y);
|
|
||||||
libc_fesetround (fe_val);
|
|
||||||
}
|
|
||||||
|
|
||||||
if (m < -1021)
|
|
||||||
{
|
|
||||||
yy.y_part[HIGH_HALF] += (m + 54) << 20;
|
|
||||||
retval = twom54 * yy.y;
|
|
||||||
if (retval < DBL_MIN)
|
if (retval < DBL_MIN)
|
||||||
{
|
{
|
||||||
double force_underflow = tiny * tiny;
|
double force_underflow = tiny * tiny;
|
||||||
math_force_eval (force_underflow);
|
math_force_eval (force_underflow);
|
||||||
}
|
}
|
||||||
return retval;
|
if (retval == 0)
|
||||||
|
goto ret_tiny;
|
||||||
|
goto ret;
|
||||||
}
|
}
|
||||||
yy.y_part[HIGH_HALF] += m << 20;
|
else
|
||||||
return yy.y;
|
{
|
||||||
|
binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20;
|
||||||
|
if (res == (res + cor * err_0))
|
||||||
|
retval = res * binexp.x * t256.x;
|
||||||
|
else
|
||||||
|
retval = __slowexp (x);
|
||||||
|
if (isinf (retval))
|
||||||
|
goto ret_huge;
|
||||||
|
else
|
||||||
|
goto ret;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
ret:
|
||||||
|
return retval;
|
||||||
|
|
||||||
|
ret_huge:
|
||||||
|
return hhuge * hhuge;
|
||||||
|
|
||||||
|
ret_tiny:
|
||||||
|
return tiny * tiny;
|
||||||
}
|
}
|
||||||
#ifndef __ieee754_exp
|
#ifndef __ieee754_exp
|
||||||
strong_alias (__ieee754_exp, __exp_finite)
|
strong_alias (__ieee754_exp, __exp_finite)
|
||||||
#endif
|
#endif
|
||||||
|
|
||||||
#ifndef SECTION
|
|
||||||
# define SECTION
|
|
||||||
#endif
|
|
||||||
|
|
||||||
/* Compute e^(x+xx). The routine also receives bound of error of previous
|
/* Compute e^(x+xx). The routine also receives bound of error of previous
|
||||||
calculation. If after computing exp the error exceeds the allowed bounds,
|
calculation. If after computing exp the error exceeds the allowed bounds,
|
||||||
the routine returns a non-positive number. Otherwise it returns the
|
the routine returns a non-positive number. Otherwise it returns the
|
||||||
|
|||||||
@ -25,7 +25,7 @@
|
|||||||
/* log1 */
|
/* log1 */
|
||||||
/* checkint */
|
/* checkint */
|
||||||
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */
|
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */
|
||||||
/* halfulp.c mpexp.c mplog.c slowpow.c mpa.c */
|
/* halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c */
|
||||||
/* uexp.c upow.c */
|
/* uexp.c upow.c */
|
||||||
/* root.tbl uexp.tbl upow.tbl */
|
/* root.tbl uexp.tbl upow.tbl */
|
||||||
/* An ultimate power routine. Given two IEEE double machine numbers y,x */
|
/* An ultimate power routine. Given two IEEE double machine numbers y,x */
|
||||||
|
|||||||
@ -1,255 +0,0 @@
|
|||||||
/* EXP function tables - for use in computing double precision exponential
|
|
||||||
Copyright (C) 2017 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, see
|
|
||||||
<http://www.gnu.org/licenses/>. */
|
|
||||||
|
|
||||||
|
|
||||||
/*
|
|
||||||
TBL[2*j] is 2**(j/64), rounded to nearest.
|
|
||||||
TBL[2*j+1] is 2**(j/64) - TBL[2*j], rounded to nearest.
|
|
||||||
These values are used to approximate exp(x) using the formula
|
|
||||||
given in the comments for e_exp.c. */
|
|
||||||
|
|
||||||
static const double TBL[128] = {
|
|
||||||
0x1.0000000000000p+0, 0x0.0000000000000p+0,
|
|
||||||
0x1.02c9a3e778061p+0, -0x1.19083535b085dp-56,
|
|
||||||
0x1.059b0d3158574p+0, 0x1.d73e2a475b465p-55,
|
|
||||||
0x1.0874518759bc8p+0, 0x1.186be4bb284ffp-57,
|
|
||||||
0x1.0b5586cf9890fp+0, 0x1.8a62e4adc610bp-54,
|
|
||||||
0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c57b52p-59,
|
|
||||||
0x1.11301d0125b51p+0, -0x1.6c51039449b3ap-54,
|
|
||||||
0x1.1429aaea92de0p+0, -0x1.32fbf9af1369ep-54,
|
|
||||||
0x1.172b83c7d517bp+0, -0x1.19041b9d78a76p-55,
|
|
||||||
0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4968e4p-55,
|
|
||||||
0x1.1d4873168b9aap+0, 0x1.e016e00a2643cp-54,
|
|
||||||
0x1.2063b88628cd6p+0, 0x1.dc775814a8495p-55,
|
|
||||||
0x1.2387a6e756238p+0, 0x1.9b07eb6c70573p-54,
|
|
||||||
0x1.26b4565e27cddp+0, 0x1.2bd339940e9d9p-55,
|
|
||||||
0x1.29e9df51fdee1p+0, 0x1.612e8afad1255p-55,
|
|
||||||
0x1.2d285a6e4030bp+0, 0x1.0024754db41d5p-54,
|
|
||||||
0x1.306fe0a31b715p+0, 0x1.6f46ad23182e4p-55,
|
|
||||||
0x1.33c08b26416ffp+0, 0x1.32721843659a6p-54,
|
|
||||||
0x1.371a7373aa9cbp+0, -0x1.63aeabf42eae2p-54,
|
|
||||||
0x1.3a7db34e59ff7p+0, -0x1.5e436d661f5e3p-56,
|
|
||||||
0x1.3dea64c123422p+0, 0x1.ada0911f09ebcp-55,
|
|
||||||
0x1.4160a21f72e2ap+0, -0x1.ef3691c309278p-58,
|
|
||||||
0x1.44e086061892dp+0, 0x1.89b7a04ef80d0p-59,
|
|
||||||
0x1.486a2b5c13cd0p+0, 0x1.3c1a3b69062f0p-56,
|
|
||||||
0x1.4bfdad5362a27p+0, 0x1.d4397afec42e2p-56,
|
|
||||||
0x1.4f9b2769d2ca7p+0, -0x1.4b309d25957e3p-54,
|
|
||||||
0x1.5342b569d4f82p+0, -0x1.07abe1db13cadp-55,
|
|
||||||
0x1.56f4736b527dap+0, 0x1.9bb2c011d93adp-54,
|
|
||||||
0x1.5ab07dd485429p+0, 0x1.6324c054647adp-54,
|
|
||||||
0x1.5e76f15ad2148p+0, 0x1.ba6f93080e65ep-54,
|
|
||||||
0x1.6247eb03a5585p+0, -0x1.383c17e40b497p-54,
|
|
||||||
0x1.6623882552225p+0, -0x1.bb60987591c34p-54,
|
|
||||||
0x1.6a09e667f3bcdp+0, -0x1.bdd3413b26456p-54,
|
|
||||||
0x1.6dfb23c651a2fp+0, -0x1.bbe3a683c88abp-57,
|
|
||||||
0x1.71f75e8ec5f74p+0, -0x1.16e4786887a99p-55,
|
|
||||||
0x1.75feb564267c9p+0, -0x1.0245957316dd3p-54,
|
|
||||||
0x1.7a11473eb0187p+0, -0x1.41577ee04992fp-55,
|
|
||||||
0x1.7e2f336cf4e62p+0, 0x1.05d02ba15797ep-56,
|
|
||||||
0x1.82589994cce13p+0, -0x1.d4c1dd41532d8p-54,
|
|
||||||
0x1.868d99b4492edp+0, -0x1.fc6f89bd4f6bap-54,
|
|
||||||
0x1.8ace5422aa0dbp+0, 0x1.6e9f156864b27p-54,
|
|
||||||
0x1.8f1ae99157736p+0, 0x1.5cc13a2e3976cp-55,
|
|
||||||
0x1.93737b0cdc5e5p+0, -0x1.75fc781b57ebcp-57,
|
|
||||||
0x1.97d829fde4e50p+0, -0x1.d185b7c1b85d1p-54,
|
|
||||||
0x1.9c49182a3f090p+0, 0x1.c7c46b071f2bep-56,
|
|
||||||
0x1.a0c667b5de565p+0, -0x1.359495d1cd533p-54,
|
|
||||||
0x1.a5503b23e255dp+0, -0x1.d2f6edb8d41e1p-54,
|
|
||||||
0x1.a9e6b5579fdbfp+0, 0x1.0fac90ef7fd31p-54,
|
|
||||||
0x1.ae89f995ad3adp+0, 0x1.7a1cd345dcc81p-54,
|
|
||||||
0x1.b33a2b84f15fbp+0, -0x1.2805e3084d708p-57,
|
|
||||||
0x1.b7f76f2fb5e47p+0, -0x1.5584f7e54ac3bp-56,
|
|
||||||
0x1.bcc1e904bc1d2p+0, 0x1.23dd07a2d9e84p-55,
|
|
||||||
0x1.c199bdd85529cp+0, 0x1.11065895048ddp-55,
|
|
||||||
0x1.c67f12e57d14bp+0, 0x1.2884dff483cadp-54,
|
|
||||||
0x1.cb720dcef9069p+0, 0x1.503cbd1e949dbp-56,
|
|
||||||
0x1.d072d4a07897cp+0, -0x1.cbc3743797a9cp-54,
|
|
||||||
0x1.d5818dcfba487p+0, 0x1.2ed02d75b3707p-55,
|
|
||||||
0x1.da9e603db3285p+0, 0x1.c2300696db532p-54,
|
|
||||||
0x1.dfc97337b9b5fp+0, -0x1.1a5cd4f184b5cp-54,
|
|
||||||
0x1.e502ee78b3ff6p+0, 0x1.39e8980a9cc8fp-55,
|
|
||||||
0x1.ea4afa2a490dap+0, -0x1.e9c23179c2893p-54,
|
|
||||||
0x1.efa1bee615a27p+0, 0x1.dc7f486a4b6b0p-54,
|
|
||||||
0x1.f50765b6e4540p+0, 0x1.9d3e12dd8a18bp-54,
|
|
||||||
0x1.fa7c1819e90d8p+0, 0x1.74853f3a5931ep-55};
|
|
||||||
|
|
||||||
/* For i = 0, ..., 66,
|
|
||||||
TBL2[2*i] is a double precision number near (i+1)*2^-6, and
|
|
||||||
TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
|
|
||||||
than 2^-60.
|
|
||||||
|
|
||||||
For i = 67, ..., 133,
|
|
||||||
TBL2[2*i] is a double precision number near -(i+1)*2^-6, and
|
|
||||||
TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
|
|
||||||
than 2^-60. */
|
|
||||||
|
|
||||||
static const double TBL2[268] = {
|
|
||||||
0x1.ffffffffffc82p-7, 0x1.04080ab55de32p+0,
|
|
||||||
0x1.fffffffffffdbp-6, 0x1.08205601127ecp+0,
|
|
||||||
0x1.80000000000a0p-5, 0x1.0c49236829e91p+0,
|
|
||||||
0x1.fffffffffff79p-5, 0x1.1082b577d34e9p+0,
|
|
||||||
0x1.3fffffffffffcp-4, 0x1.14cd4fc989cd6p+0,
|
|
||||||
0x1.8000000000060p-4, 0x1.192937074e0d4p+0,
|
|
||||||
0x1.c000000000061p-4, 0x1.1d96b0eff0e80p+0,
|
|
||||||
0x1.fffffffffffd6p-4, 0x1.2216045b6f5cap+0,
|
|
||||||
0x1.1ffffffffff58p-3, 0x1.26a7793f6014cp+0,
|
|
||||||
0x1.3ffffffffff75p-3, 0x1.2b4b58b372c65p+0,
|
|
||||||
0x1.5ffffffffff00p-3, 0x1.3001ecf601ad1p+0,
|
|
||||||
0x1.8000000000020p-3, 0x1.34cb8170b583ap+0,
|
|
||||||
0x1.9ffffffffa629p-3, 0x1.39a862bd3b344p+0,
|
|
||||||
0x1.c00000000000fp-3, 0x1.3e98deaa11dcep+0,
|
|
||||||
0x1.e00000000007fp-3, 0x1.439d443f5f16dp+0,
|
|
||||||
0x1.0000000000072p-2, 0x1.48b5e3c3e81abp+0,
|
|
||||||
0x1.0fffffffffecap-2, 0x1.4de30ec211dfbp+0,
|
|
||||||
0x1.1ffffffffff8fp-2, 0x1.5325180cfacd2p+0,
|
|
||||||
0x1.300000000003bp-2, 0x1.587c53c5a7b04p+0,
|
|
||||||
0x1.4000000000034p-2, 0x1.5de9176046007p+0,
|
|
||||||
0x1.4ffffffffff89p-2, 0x1.636bb9a98322fp+0,
|
|
||||||
0x1.5ffffffffffe7p-2, 0x1.690492cbf942ap+0,
|
|
||||||
0x1.6ffffffffff78p-2, 0x1.6eb3fc55b1e45p+0,
|
|
||||||
0x1.7ffffffffff65p-2, 0x1.747a513dbef32p+0,
|
|
||||||
0x1.8ffffffffffd5p-2, 0x1.7a57ede9ea22ep+0,
|
|
||||||
0x1.9ffffffffff6ep-2, 0x1.804d30347b50fp+0,
|
|
||||||
0x1.affffffffffc3p-2, 0x1.865a7772164aep+0,
|
|
||||||
0x1.c000000000053p-2, 0x1.8c802477b0030p+0,
|
|
||||||
0x1.d00000000004dp-2, 0x1.92be99a09bf1ep+0,
|
|
||||||
0x1.e000000000096p-2, 0x1.99163ad4b1e08p+0,
|
|
||||||
0x1.efffffffffefap-2, 0x1.9f876d8e8c4fcp+0,
|
|
||||||
0x1.fffffffffffd0p-2, 0x1.a61298e1e0688p+0,
|
|
||||||
0x1.0800000000002p-1, 0x1.acb82581eee56p+0,
|
|
||||||
0x1.100000000001fp-1, 0x1.b3787dc80f979p+0,
|
|
||||||
0x1.17ffffffffff8p-1, 0x1.ba540dba56e4fp+0,
|
|
||||||
0x1.1fffffffffffap-1, 0x1.c14b431256441p+0,
|
|
||||||
0x1.27fffffffffc4p-1, 0x1.c85e8d43f7c9bp+0,
|
|
||||||
0x1.2fffffffffffdp-1, 0x1.cf8e5d84758a6p+0,
|
|
||||||
0x1.380000000001fp-1, 0x1.d6db26d16cd84p+0,
|
|
||||||
0x1.3ffffffffffd8p-1, 0x1.de455df80e39bp+0,
|
|
||||||
0x1.4800000000052p-1, 0x1.e5cd799c6a59cp+0,
|
|
||||||
0x1.4ffffffffffc8p-1, 0x1.ed73f240dc10cp+0,
|
|
||||||
0x1.5800000000013p-1, 0x1.f539424d90f71p+0,
|
|
||||||
0x1.5ffffffffffbcp-1, 0x1.fd1de6182f885p+0,
|
|
||||||
0x1.680000000002dp-1, 0x1.02912df5ce741p+1,
|
|
||||||
0x1.7000000000040p-1, 0x1.06a39207f0a2ap+1,
|
|
||||||
0x1.780000000004fp-1, 0x1.0ac660691652ap+1,
|
|
||||||
0x1.7ffffffffff6fp-1, 0x1.0ef9db467dcabp+1,
|
|
||||||
0x1.87fffffffffe5p-1, 0x1.133e45d82e943p+1,
|
|
||||||
0x1.9000000000035p-1, 0x1.1793e4652cc6dp+1,
|
|
||||||
0x1.97fffffffffb3p-1, 0x1.1bfafc47bda48p+1,
|
|
||||||
0x1.a000000000000p-1, 0x1.2073d3f1bd518p+1,
|
|
||||||
0x1.a80000000004ap-1, 0x1.24feb2f105ce2p+1,
|
|
||||||
0x1.affffffffffedp-1, 0x1.299be1f3e7f11p+1,
|
|
||||||
0x1.b7ffffffffffbp-1, 0x1.2e4baacdb6611p+1,
|
|
||||||
0x1.c00000000001dp-1, 0x1.330e587b62b39p+1,
|
|
||||||
0x1.c800000000079p-1, 0x1.37e437282d538p+1,
|
|
||||||
0x1.cffffffffff51p-1, 0x1.3ccd943268248p+1,
|
|
||||||
0x1.d7fffffffff74p-1, 0x1.41cabe304cadcp+1,
|
|
||||||
0x1.e000000000011p-1, 0x1.46dc04f4e5343p+1,
|
|
||||||
0x1.e80000000001ep-1, 0x1.4c01b9950a124p+1,
|
|
||||||
0x1.effffffffff9ep-1, 0x1.513c2e6c73196p+1,
|
|
||||||
0x1.f7fffffffffedp-1, 0x1.568bb722dd586p+1,
|
|
||||||
0x1.0000000000034p+0, 0x1.5bf0a8b1457b0p+1,
|
|
||||||
0x1.03fffffffffe2p+0, 0x1.616b5967376dfp+1,
|
|
||||||
0x1.07fffffffff4bp+0, 0x1.66fc20f0337a9p+1,
|
|
||||||
0x1.0bffffffffffdp+0, 0x1.6ca35859290f5p+1,
|
|
||||||
-0x1.fffffffffffe4p-7, 0x1.f80feabfeefa5p-1,
|
|
||||||
-0x1.ffffffffffb0bp-6, 0x1.f03f56a88b5fep-1,
|
|
||||||
-0x1.7ffffffffffa7p-5, 0x1.e88dc6afecfc5p-1,
|
|
||||||
-0x1.ffffffffffea8p-5, 0x1.e0fabfbc702b8p-1,
|
|
||||||
-0x1.3ffffffffffb3p-4, 0x1.d985c89d041acp-1,
|
|
||||||
-0x1.7ffffffffffe3p-4, 0x1.d22e6a0197c06p-1,
|
|
||||||
-0x1.bffffffffff9ap-4, 0x1.caf42e73a4c89p-1,
|
|
||||||
-0x1.fffffffffff98p-4, 0x1.c3d6a24ed822dp-1,
|
|
||||||
-0x1.1ffffffffffe9p-3, 0x1.bcd553b9d7b67p-1,
|
|
||||||
-0x1.3ffffffffffe0p-3, 0x1.b5efd29f24c2dp-1,
|
|
||||||
-0x1.5fffffffff553p-3, 0x1.af25b0a61a9f4p-1,
|
|
||||||
-0x1.7ffffffffff8bp-3, 0x1.a876812c08794p-1,
|
|
||||||
-0x1.9fffffffffe51p-3, 0x1.a1e1d93d68828p-1,
|
|
||||||
-0x1.bffffffffff6ep-3, 0x1.9b674f8f2f3f5p-1,
|
|
||||||
-0x1.dffffffffff7fp-3, 0x1.95067c7837a0cp-1,
|
|
||||||
-0x1.fffffffffff7ap-3, 0x1.8ebef9eac8225p-1,
|
|
||||||
-0x1.0fffffffffffep-2, 0x1.8890636e31f55p-1,
|
|
||||||
-0x1.1ffffffffff41p-2, 0x1.827a56188975ep-1,
|
|
||||||
-0x1.2ffffffffffbap-2, 0x1.7c7c708877656p-1,
|
|
||||||
-0x1.3fffffffffff8p-2, 0x1.769652df22f81p-1,
|
|
||||||
-0x1.4ffffffffff90p-2, 0x1.70c79eba33c2fp-1,
|
|
||||||
-0x1.5ffffffffffdbp-2, 0x1.6b0ff72deb8aap-1,
|
|
||||||
-0x1.6ffffffffff9ap-2, 0x1.656f00bf5798ep-1,
|
|
||||||
-0x1.7ffffffffff9fp-2, 0x1.5fe4615e98eb0p-1,
|
|
||||||
-0x1.8ffffffffffeep-2, 0x1.5a6fc061433cep-1,
|
|
||||||
-0x1.9fffffffffc4ap-2, 0x1.5510c67cd26cdp-1,
|
|
||||||
-0x1.affffffffff30p-2, 0x1.4fc71dc13566bp-1,
|
|
||||||
-0x1.bfffffffffff0p-2, 0x1.4a9271936fd0ep-1,
|
|
||||||
-0x1.cfffffffffff3p-2, 0x1.45726ea84fb8cp-1,
|
|
||||||
-0x1.dfffffffffff3p-2, 0x1.4066c2ff3912bp-1,
|
|
||||||
-0x1.effffffffff80p-2, 0x1.3b6f1ddd05ab9p-1,
|
|
||||||
-0x1.fffffffffffdfp-2, 0x1.368b2fc6f9614p-1,
|
|
||||||
-0x1.0800000000000p-1, 0x1.31baaa7dca843p-1,
|
|
||||||
-0x1.0ffffffffffa4p-1, 0x1.2cfd40f8bdce4p-1,
|
|
||||||
-0x1.17fffffffff0ap-1, 0x1.2852a760d5ce7p-1,
|
|
||||||
-0x1.2000000000000p-1, 0x1.23ba930c1568bp-1,
|
|
||||||
-0x1.27fffffffffbbp-1, 0x1.1f34ba78d568dp-1,
|
|
||||||
-0x1.2fffffffffe32p-1, 0x1.1ac0d5492c1dbp-1,
|
|
||||||
-0x1.37ffffffff042p-1, 0x1.165e9c3e67ef2p-1,
|
|
||||||
-0x1.3ffffffffff77p-1, 0x1.120dc93499431p-1,
|
|
||||||
-0x1.47fffffffff6bp-1, 0x1.0dce171e34ecep-1,
|
|
||||||
-0x1.4fffffffffff1p-1, 0x1.099f41ffbe588p-1,
|
|
||||||
-0x1.57ffffffffe02p-1, 0x1.058106eb8a7aep-1,
|
|
||||||
-0x1.5ffffffffffe5p-1, 0x1.017323fd9002ep-1,
|
|
||||||
-0x1.67fffffffffb0p-1, 0x1.faeab0ae9386cp-2,
|
|
||||||
-0x1.6ffffffffffb2p-1, 0x1.f30ec837503d7p-2,
|
|
||||||
-0x1.77fffffffff7fp-1, 0x1.eb5210d627133p-2,
|
|
||||||
-0x1.7ffffffffffe8p-1, 0x1.e3b40ebefcd95p-2,
|
|
||||||
-0x1.87fffffffffc8p-1, 0x1.dc3448110dae2p-2,
|
|
||||||
-0x1.8fffffffffb30p-1, 0x1.d4d244cf4ef06p-2,
|
|
||||||
-0x1.97fffffffffefp-1, 0x1.cd8d8ed8ee395p-2,
|
|
||||||
-0x1.9ffffffffffa7p-1, 0x1.c665b1e1f1e5cp-2,
|
|
||||||
-0x1.a7fffffffffdcp-1, 0x1.bf5a3b6bf18d6p-2,
|
|
||||||
-0x1.affffffffff95p-1, 0x1.b86ababeef93bp-2,
|
|
||||||
-0x1.b7fffffffffcbp-1, 0x1.b196c0e24d256p-2,
|
|
||||||
-0x1.bffffffffff32p-1, 0x1.aadde095dadf7p-2,
|
|
||||||
-0x1.c7fffffffff6ap-1, 0x1.a43fae4b047c9p-2,
|
|
||||||
-0x1.cffffffffffb6p-1, 0x1.9dbbc01e182a4p-2,
|
|
||||||
-0x1.d7fffffffffcap-1, 0x1.9751adcfa81ecp-2,
|
|
||||||
-0x1.dffffffffffcdp-1, 0x1.910110be0699ep-2,
|
|
||||||
-0x1.e7ffffffffffbp-1, 0x1.8ac983dedbc69p-2,
|
|
||||||
-0x1.effffffffff88p-1, 0x1.84aaa3b8d51a9p-2,
|
|
||||||
-0x1.f7fffffffffbbp-1, 0x1.7ea40e5d6d92ep-2,
|
|
||||||
-0x1.fffffffffffdbp-1, 0x1.78b56362cef53p-2,
|
|
||||||
-0x1.03fffffffff00p+0, 0x1.72de43ddcb1f2p-2,
|
|
||||||
-0x1.07ffffffffe6fp+0, 0x1.6d1e525bed085p-2,
|
|
||||||
-0x1.0bfffffffffd6p+0, 0x1.677532dda1c57p-2};
|
|
||||||
|
|
||||||
static const double
|
|
||||||
/* invln2_64 = 64/ln2 - used to scale x to primary range. */
|
|
||||||
invln2_64 = 0x1.71547652b82fep+6,
|
|
||||||
/* ln2_64hi = high 32 bits of log(2.)/64. */
|
|
||||||
ln2_64hi = 0x1.62e42fee00000p-7,
|
|
||||||
/* ln2_64lo = remainder bits for log(2.)/64 - ln2_64hi. */
|
|
||||||
ln2_64lo = 0x1.a39ef35793c76p-39,
|
|
||||||
/* t2-t5 terms used for polynomial computation. */
|
|
||||||
t2 = 0x1.5555555555555p-3, /* 1.6666666666666665741e-1 */
|
|
||||||
t3 = 0x1.5555555555555p-5, /* 4.1666666666666664354e-2 */
|
|
||||||
t4 = 0x1.1111111111111p-7, /* 8.3333333333333332177e-3 */
|
|
||||||
t5 = 0x1.6c16c16c16c17p-10, /* 1.3888888888888719040e-3 */
|
|
||||||
/* Maximum value for x to not overflow. */
|
|
||||||
threshold1 = 0x1.62e42fefa39efp+9, /* 7.09782712893383973096e+02 */
|
|
||||||
/* Maximum value for -x to not underflow to zero in FE_TONEAREST mode. */
|
|
||||||
threshold2 = 0x1.74910d52d3051p+9, /* 7.45133219101941108420e+02 */
|
|
||||||
/* Scaling factor used when result near zero. */
|
|
||||||
twom54 = 0x1.0000000000000p-54; /* 5.55111512312578270212e-17 */
|
|
||||||
86
sysdeps/ieee754/dbl-64/slowexp.c
Normal file
86
sysdeps/ieee754/dbl-64/slowexp.c
Normal file
@ -0,0 +1,86 @@
|
|||||||
|
/*
|
||||||
|
* IBM Accurate Mathematical Library
|
||||||
|
* written by International Business Machines Corp.
|
||||||
|
* Copyright (C) 2001-2017 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
|
||||||
|
* 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, see <http://www.gnu.org/licenses/>.
|
||||||
|
*/
|
||||||
|
/**************************************************************************/
|
||||||
|
/* MODULE_NAME:slowexp.c */
|
||||||
|
/* */
|
||||||
|
/* FUNCTION:slowexp */
|
||||||
|
/* */
|
||||||
|
/* FILES NEEDED:mpa.h */
|
||||||
|
/* mpa.c mpexp.c */
|
||||||
|
/* */
|
||||||
|
/*Converting from double precision to Multi-precision and calculating */
|
||||||
|
/* e^x */
|
||||||
|
/**************************************************************************/
|
||||||
|
#include <math_private.h>
|
||||||
|
|
||||||
|
#include <stap-probe.h>
|
||||||
|
|
||||||
|
#ifndef USE_LONG_DOUBLE_FOR_MP
|
||||||
|
# include "mpa.h"
|
||||||
|
void __mpexp (mp_no *x, mp_no *y, int p);
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#ifndef SECTION
|
||||||
|
# define SECTION
|
||||||
|
#endif
|
||||||
|
|
||||||
|
/*Converting from double precision to Multi-precision and calculating e^x */
|
||||||
|
double
|
||||||
|
SECTION
|
||||||
|
__slowexp (double x)
|
||||||
|
{
|
||||||
|
#ifndef USE_LONG_DOUBLE_FOR_MP
|
||||||
|
double w, z, res, eps = 3.0e-26;
|
||||||
|
int p;
|
||||||
|
mp_no mpx, mpy, mpz, mpw, mpeps, mpcor;
|
||||||
|
|
||||||
|
/* Use the multiple precision __MPEXP function to compute the exponential
|
||||||
|
First at 144 bits and if it is not accurate enough, at 768 bits. */
|
||||||
|
p = 6;
|
||||||
|
__dbl_mp (x, &mpx, p);
|
||||||
|
__mpexp (&mpx, &mpy, p);
|
||||||
|
__dbl_mp (eps, &mpeps, p);
|
||||||
|
__mul (&mpeps, &mpy, &mpcor, p);
|
||||||
|
__add (&mpy, &mpcor, &mpw, p);
|
||||||
|
__sub (&mpy, &mpcor, &mpz, p);
|
||||||
|
__mp_dbl (&mpw, &w, p);
|
||||||
|
__mp_dbl (&mpz, &z, p);
|
||||||
|
if (w == z)
|
||||||
|
{
|
||||||
|
/* Track how often we get to the slow exp code plus
|
||||||
|
its input/output values. */
|
||||||
|
LIBC_PROBE (slowexp_p6, 2, &x, &w);
|
||||||
|
return w;
|
||||||
|
}
|
||||||
|
else
|
||||||
|
{
|
||||||
|
p = 32;
|
||||||
|
__dbl_mp (x, &mpx, p);
|
||||||
|
__mpexp (&mpx, &mpy, p);
|
||||||
|
__mp_dbl (&mpy, &res, p);
|
||||||
|
|
||||||
|
/* Track how often we get to the uber-slow exp code plus
|
||||||
|
its input/output values. */
|
||||||
|
LIBC_PROBE (slowexp_p32, 2, &x, &res);
|
||||||
|
return res;
|
||||||
|
}
|
||||||
|
#else
|
||||||
|
return (double) __ieee754_expl((long double)x);
|
||||||
|
#endif
|
||||||
|
}
|
||||||
1
sysdeps/m68k/m680x0/fpu/slowexp.c
Normal file
1
sysdeps/m68k/m680x0/fpu/slowexp.c
Normal file
@ -0,0 +1 @@
|
|||||||
|
/* Not needed. */
|
||||||
@ -3,4 +3,5 @@
|
|||||||
ifeq ($(subdir),math)
|
ifeq ($(subdir),math)
|
||||||
CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
|
CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
|
||||||
CPPFLAGS-slowpow.c += -DUSE_LONG_DOUBLE_FOR_MP=1
|
CPPFLAGS-slowpow.c += -DUSE_LONG_DOUBLE_FOR_MP=1
|
||||||
|
CPPFLAGS-slowexp.c += -DUSE_LONG_DOUBLE_FOR_MP=1
|
||||||
endif
|
endif
|
||||||
|
|||||||
@ -1094,10 +1094,10 @@ ildouble: 2
|
|||||||
ldouble: 2
|
ldouble: 2
|
||||||
|
|
||||||
Function: Imaginary part of "cexp_upward":
|
Function: Imaginary part of "cexp_upward":
|
||||||
double: 3
|
double: 1
|
||||||
float: 2
|
float: 2
|
||||||
float128: 3
|
float128: 3
|
||||||
idouble: 3
|
idouble: 1
|
||||||
ifloat: 2
|
ifloat: 2
|
||||||
ifloat128: 3
|
ifloat128: 3
|
||||||
ildouble: 3
|
ildouble: 3
|
||||||
@ -1902,9 +1902,7 @@ ildouble: 5
|
|||||||
ldouble: 5
|
ldouble: 5
|
||||||
|
|
||||||
Function: "exp":
|
Function: "exp":
|
||||||
double: 1
|
|
||||||
float128: 1
|
float128: 1
|
||||||
idouble: 1
|
|
||||||
ifloat128: 1
|
ifloat128: 1
|
||||||
ildouble: 1
|
ildouble: 1
|
||||||
ldouble: 1
|
ldouble: 1
|
||||||
@ -2756,30 +2754,30 @@ ildouble: 5
|
|||||||
ldouble: 5
|
ldouble: 5
|
||||||
|
|
||||||
Function: "tgamma_downward":
|
Function: "tgamma_downward":
|
||||||
double: 6
|
double: 5
|
||||||
float: 5
|
float: 5
|
||||||
float128: 5
|
float128: 5
|
||||||
idouble: 6
|
idouble: 5
|
||||||
ifloat: 5
|
ifloat: 5
|
||||||
ifloat128: 5
|
ifloat128: 5
|
||||||
ildouble: 5
|
ildouble: 5
|
||||||
ldouble: 5
|
ldouble: 5
|
||||||
|
|
||||||
Function: "tgamma_towardzero":
|
Function: "tgamma_towardzero":
|
||||||
double: 7
|
double: 5
|
||||||
float: 5
|
float: 5
|
||||||
float128: 5
|
float128: 5
|
||||||
idouble: 7
|
idouble: 5
|
||||||
ifloat: 5
|
ifloat: 5
|
||||||
ifloat128: 5
|
ifloat128: 5
|
||||||
ildouble: 5
|
ildouble: 5
|
||||||
ldouble: 5
|
ldouble: 5
|
||||||
|
|
||||||
Function: "tgamma_upward":
|
Function: "tgamma_upward":
|
||||||
double: 6
|
double: 5
|
||||||
float: 5
|
float: 5
|
||||||
float128: 4
|
float128: 4
|
||||||
idouble: 6
|
idouble: 5
|
||||||
ifloat: 5
|
ifloat: 5
|
||||||
ifloat128: 4
|
ifloat128: 4
|
||||||
ildouble: 5
|
ildouble: 5
|
||||||
|
|||||||
@ -10,7 +10,7 @@ libm-sysdep_routines += s_ceil-sse4_1 s_ceilf-sse4_1 s_floor-sse4_1 \
|
|||||||
|
|
||||||
libm-sysdep_routines += e_exp-fma e_log-fma e_pow-fma s_atan-fma \
|
libm-sysdep_routines += e_exp-fma e_log-fma e_pow-fma s_atan-fma \
|
||||||
e_asin-fma e_atan2-fma s_sin-fma s_tan-fma \
|
e_asin-fma e_atan2-fma s_sin-fma s_tan-fma \
|
||||||
mplog-fma mpa-fma slowpow-fma \
|
mplog-fma mpa-fma slowexp-fma slowpow-fma \
|
||||||
sincos32-fma doasin-fma dosincos-fma \
|
sincos32-fma doasin-fma dosincos-fma \
|
||||||
halfulp-fma mpexp-fma \
|
halfulp-fma mpexp-fma \
|
||||||
mpatan2-fma mpatan-fma mpsqrt-fma mptan-fma
|
mpatan2-fma mpatan-fma mpsqrt-fma mptan-fma
|
||||||
@ -32,6 +32,7 @@ CFLAGS-mpsqrt-fma.c = -mfma -mavx2
|
|||||||
CFLAGS-mptan-fma.c = -mfma -mavx2
|
CFLAGS-mptan-fma.c = -mfma -mavx2
|
||||||
CFLAGS-s_atan-fma.c = -mfma -mavx2
|
CFLAGS-s_atan-fma.c = -mfma -mavx2
|
||||||
CFLAGS-sincos32-fma.c = -mfma -mavx2
|
CFLAGS-sincos32-fma.c = -mfma -mavx2
|
||||||
|
CFLAGS-slowexp-fma.c = -mfma -mavx2
|
||||||
CFLAGS-slowpow-fma.c = -mfma -mavx2
|
CFLAGS-slowpow-fma.c = -mfma -mavx2
|
||||||
CFLAGS-s_sin-fma.c = -mfma -mavx2
|
CFLAGS-s_sin-fma.c = -mfma -mavx2
|
||||||
CFLAGS-s_tan-fma.c = -mfma -mavx2
|
CFLAGS-s_tan-fma.c = -mfma -mavx2
|
||||||
@ -51,7 +52,7 @@ CFLAGS-s_cosf-fma.c = -mfma -mavx2
|
|||||||
|
|
||||||
libm-sysdep_routines += e_exp-fma4 e_log-fma4 e_pow-fma4 s_atan-fma4 \
|
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 \
|
e_asin-fma4 e_atan2-fma4 s_sin-fma4 s_tan-fma4 \
|
||||||
mplog-fma4 mpa-fma4 slowpow-fma4 \
|
mplog-fma4 mpa-fma4 slowexp-fma4 slowpow-fma4 \
|
||||||
sincos32-fma4 doasin-fma4 dosincos-fma4 \
|
sincos32-fma4 doasin-fma4 dosincos-fma4 \
|
||||||
halfulp-fma4 mpexp-fma4 \
|
halfulp-fma4 mpexp-fma4 \
|
||||||
mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
|
mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
|
||||||
@ -73,13 +74,14 @@ CFLAGS-mpsqrt-fma4.c = -mfma4
|
|||||||
CFLAGS-mptan-fma4.c = -mfma4
|
CFLAGS-mptan-fma4.c = -mfma4
|
||||||
CFLAGS-s_atan-fma4.c = -mfma4
|
CFLAGS-s_atan-fma4.c = -mfma4
|
||||||
CFLAGS-sincos32-fma4.c = -mfma4
|
CFLAGS-sincos32-fma4.c = -mfma4
|
||||||
|
CFLAGS-slowexp-fma4.c = -mfma4
|
||||||
CFLAGS-slowpow-fma4.c = -mfma4
|
CFLAGS-slowpow-fma4.c = -mfma4
|
||||||
CFLAGS-s_sin-fma4.c = -mfma4
|
CFLAGS-s_sin-fma4.c = -mfma4
|
||||||
CFLAGS-s_tan-fma4.c = -mfma4
|
CFLAGS-s_tan-fma4.c = -mfma4
|
||||||
|
|
||||||
libm-sysdep_routines += e_exp-avx e_log-avx s_atan-avx \
|
libm-sysdep_routines += e_exp-avx e_log-avx s_atan-avx \
|
||||||
e_atan2-avx s_sin-avx s_tan-avx \
|
e_atan2-avx s_sin-avx s_tan-avx \
|
||||||
mplog-avx mpa-avx \
|
mplog-avx mpa-avx slowexp-avx \
|
||||||
mpexp-avx
|
mpexp-avx
|
||||||
|
|
||||||
CFLAGS-e_atan2-avx.c = -msse2avx -DSSE2AVX
|
CFLAGS-e_atan2-avx.c = -msse2avx -DSSE2AVX
|
||||||
@ -90,6 +92,7 @@ CFLAGS-mpexp-avx.c = -msse2avx -DSSE2AVX
|
|||||||
CFLAGS-mplog-avx.c = -msse2avx -DSSE2AVX
|
CFLAGS-mplog-avx.c = -msse2avx -DSSE2AVX
|
||||||
CFLAGS-s_atan-avx.c = -msse2avx -DSSE2AVX
|
CFLAGS-s_atan-avx.c = -msse2avx -DSSE2AVX
|
||||||
CFLAGS-s_sin-avx.c = -msse2avx -DSSE2AVX
|
CFLAGS-s_sin-avx.c = -msse2avx -DSSE2AVX
|
||||||
|
CFLAGS-slowexp-avx.c = -msse2avx -DSSE2AVX
|
||||||
CFLAGS-s_tan-avx.c = -msse2avx -DSSE2AVX
|
CFLAGS-s_tan-avx.c = -msse2avx -DSSE2AVX
|
||||||
endif
|
endif
|
||||||
|
|
||||||
|
|||||||
@ -1,5 +1,6 @@
|
|||||||
#define __ieee754_exp __ieee754_exp_avx
|
#define __ieee754_exp __ieee754_exp_avx
|
||||||
#define __exp1 __exp1_avx
|
#define __exp1 __exp1_avx
|
||||||
|
#define __slowexp __slowexp_avx
|
||||||
#define SECTION __attribute__ ((section (".text.avx")))
|
#define SECTION __attribute__ ((section (".text.avx")))
|
||||||
|
|
||||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
||||||
|
|||||||
@ -1,5 +1,6 @@
|
|||||||
#define __ieee754_exp __ieee754_exp_fma
|
#define __ieee754_exp __ieee754_exp_fma
|
||||||
#define __exp1 __exp1_fma
|
#define __exp1 __exp1_fma
|
||||||
|
#define __slowexp __slowexp_fma
|
||||||
#define SECTION __attribute__ ((section (".text.fma")))
|
#define SECTION __attribute__ ((section (".text.fma")))
|
||||||
|
|
||||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
||||||
|
|||||||
@ -1,5 +1,6 @@
|
|||||||
#define __ieee754_exp __ieee754_exp_fma4
|
#define __ieee754_exp __ieee754_exp_fma4
|
||||||
#define __exp1 __exp1_fma4
|
#define __exp1 __exp1_fma4
|
||||||
|
#define __slowexp __slowexp_fma4
|
||||||
#define SECTION __attribute__ ((section (".text.fma4")))
|
#define SECTION __attribute__ ((section (".text.fma4")))
|
||||||
|
|
||||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
||||||
|
|||||||
9
sysdeps/x86_64/fpu/multiarch/slowexp-avx.c
Normal file
9
sysdeps/x86_64/fpu/multiarch/slowexp-avx.c
Normal file
@ -0,0 +1,9 @@
|
|||||||
|
#define __slowexp __slowexp_avx
|
||||||
|
#define __add __add_avx
|
||||||
|
#define __dbl_mp __dbl_mp_avx
|
||||||
|
#define __mpexp __mpexp_avx
|
||||||
|
#define __mul __mul_avx
|
||||||
|
#define __sub __sub_avx
|
||||||
|
#define SECTION __attribute__ ((section (".text.avx")))
|
||||||
|
|
||||||
|
#include <sysdeps/ieee754/dbl-64/slowexp.c>
|
||||||
9
sysdeps/x86_64/fpu/multiarch/slowexp-fma.c
Normal file
9
sysdeps/x86_64/fpu/multiarch/slowexp-fma.c
Normal file
@ -0,0 +1,9 @@
|
|||||||
|
#define __slowexp __slowexp_fma
|
||||||
|
#define __add __add_fma
|
||||||
|
#define __dbl_mp __dbl_mp_fma
|
||||||
|
#define __mpexp __mpexp_fma
|
||||||
|
#define __mul __mul_fma
|
||||||
|
#define __sub __sub_fma
|
||||||
|
#define SECTION __attribute__ ((section (".text.fma")))
|
||||||
|
|
||||||
|
#include <sysdeps/ieee754/dbl-64/slowexp.c>
|
||||||
9
sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
Normal file
9
sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c
Normal file
@ -0,0 +1,9 @@
|
|||||||
|
#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
|
||||||
|
#define SECTION __attribute__ ((section (".text.fma4")))
|
||||||
|
|
||||||
|
#include <sysdeps/ieee754/dbl-64/slowexp.c>
|
||||||
Loading…
Reference in New Issue
Block a user