Improve __ieee754_exp() performance by greater than 5x on sparc/x86.
These changes will be active for all platforms that don't provide
their own exp() routines. They will also be active for ieee754
versions of ccos, ccosh, cosh, csin, csinh, sinh, exp10, gamma, and
erf.
Typical performance gains is typically around 5x when measured on
Sparc s7 for common values between exp(1) and exp(40).
Using the glibc perf tests on sparc,
sparc (nsec) x86 (nsec)
old new old new
max 17629 395 5173 144
min 399 54 15 13
mean 5317 200 1349 23
The extreme max times for the old (ieee754) exp are due to the
multiprecision computation in the old algorithm when the true value is
very near 0.5 ulp away from an value representable in double
precision. The new algorithm does not take special measures for those
cases. The current glibc exp perf tests overrepresent those values.
Informal testing suggests approximately one in 200 cases might
invoke the high cost computation. The performance advantage of the new
algorithm for other values is still large but not as large as indicated
by the chart above.
Glibc correctness tests for exp() and expf() were run. Within the
test suite 3 input values were found to cause 1 bit differences (ulp)
when "FE_TONEAREST" rounding mode is set. No differences in exp() were
seen for the tested values for the other rounding modes.
Typical example:
exp(-0x1.760cd2p+0) (-1.46113312244415283203125)
new code: 2.31973271630014299393707e-01 0x1.db14cd799387ap-3
old code: 2.31973271630014271638132e-01 0x1.db14cd7993879p-3
exp = 2.31973271630014285508337 (high precision)
Old delta: off by 0.49 ulp
New delta: off by 0.51 ulp
In addition, because ieee754_exp() is used by other routines, cexp()
showed test results with very small imaginary input values where the
imaginary portion of the result was off by 3 ulp when in upward
rounding mode, but not in the other rounding modes. For x86, tgamma
showed a few values where the ulp increased to 6 (max ulp for tgamma
is 5). Sparc tgamma did not show these failures. I presume the tgamma
differences are due to compiler optimization differences within the
gamma function.The gamma function is known to be difficult to compute
accurately.
* 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:
Patrick McGehearty
Joseph Myers
parent
3bb1ef58b9
commit
6fd0a3c6a8
34
ChangeLog
34
ChangeLog
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@ -1,3 +1,37 @@
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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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James Clarke <jrtc27@jrtc27.com>
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@ -258,20 +258,6 @@ 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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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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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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@ -114,7 +114,7 @@ type-ldouble-yes := ldouble
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# double support
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type-double-suffix :=
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type-double-routines := branred doasin dosincos halfulp mpa mpatan2 \
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mpatan mpexp mplog mpsqrt mptan sincos32 slowexp \
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mpatan mpexp mplog mpsqrt mptan sincos32 \
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slowpow sincostab k_rem_pio2
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# float support
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@ -262,7 +262,6 @@ 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 __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 __slowexp (double __x);
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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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@ -1 +0,0 @@
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/* Not needed. */
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@ -1 +0,0 @@
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/* Not needed. */
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@ -1,3 +1,4 @@
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/* EXP function - Compute double precision exponential */
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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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@ -23,7 +24,7 @@
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/* exp1 */
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/* */
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/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */
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/* mpa.c mpexp.x slowexp.c */
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/* mpa.c mpexp.x */
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/* */
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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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@ -32,207 +33,238 @@
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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-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 "uexp.h"
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#include "uexp.tbl"
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#include "mydefs.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 <float.h>
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#ifndef SECTION
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# define SECTION
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#endif
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extern double __ieee754_exp (double);
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#include "eexp.tbl"
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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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SECTION
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__ieee754_exp (double x)
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__ieee754_exp (double x_arg)
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{
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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 z, t;
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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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SET_RESTORE_ROUND (FE_TONEAREST);
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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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junk1.x = x;
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m = junk1.i[HIGH_HALF];
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n = m & hugeint;
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ix = xx.i_part[HIGH_HALF];
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hx = ix & ~0x80000000;
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if (n > smallint && n < bigint)
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{
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y = x * log2e.x + three51.x;
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bexp = y - three51.x; /* multiply the result by 2**bexp */
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if (hx < 0x3ff0a2b2)
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{ /* |x| < 3/2 ln 2 */
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if (hx < 0x3f862e42)
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{ /* |x| < 1/64 ln 2 */
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if (hx < 0x3ed00000)
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{ /* |x| < 2^-18 */
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if (hx < 0x3e300000)
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{
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retval = one + xx.x;
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return retval;
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}
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retval = one + xx.x * (one + half * xx.x);
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return retval;
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}
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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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t = xx.x * xx.x;
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yy.y = xx.x + (t * (half + xx.x * t2)
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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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else
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{
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libc_fesetround (FE_TONEAREST);
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t = xx.x * xx.x;
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yy.y = xx.x + (t * (half + xx.x * t2)
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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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junk1.x = y;
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/* Find the multiple of 2^-6 nearest x. */
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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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z = xx.x - TBL2[j];
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t = z * z;
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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;
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}
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else
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{
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libc_fesetround (FE_TONEAREST);
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z = xx.x - TBL2[j];
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t = z * z;
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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;
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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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eps = bexp * ln_two2.x; /* x = bexp*ln(2) + t - eps */
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t = x - bexp * ln_two1.x;
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if (hx >= 0x40862e42)
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{ /* x is large, infinite, or nan. */
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if (hx >= 0x7ff00000)
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{
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if (ix == 0xfff00000 && xx.i_part[LOW_HALF] == 0)
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return zero; /* exp(-inf) = 0. */
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return (xx.x * xx.x); /* exp(nan/inf) is nan or inf. */
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}
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if (xx.x > threshold1)
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{ /* Set overflow error condition. */
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retval = hhuge * hhuge;
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return retval;
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}
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if (-xx.x > threshold2)
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{ /* Set underflow error condition. */
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double force_underflow = tiny * tiny;
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math_force_eval (force_underflow);
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retval = force_underflow;
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return retval;
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}
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}
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y = t + three33.x;
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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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/* Use FE_TONEAREST rounding mode for computing yy.y.
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Avoid set/reset of rounding mode if already 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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t = invln2_64 * xx.x;
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if (ix < 0)
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t -= half;
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else
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t += half;
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k = (int) t;
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j = (k & 0x3f) << 1;
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m = k >> 6;
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z = (xx.x - k * ln2_64hi) - k * ln2_64lo;
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binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 1023) << 20;
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/* z is now in primary range. */
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t = z * z;
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yy.y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
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yy.y = TBL[j] + (TBL[j + 1] + TBL[j] * yy.y);
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}
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else
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{
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libc_fesetround (FE_TONEAREST);
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t = invln2_64 * xx.x;
|
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if (ix < 0)
|
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t -= half;
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else
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t += half;
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k = (int) t;
|
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j = (k & 0x3f) << 1;
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m = k >> 6;
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z = (xx.x - k * ln2_64hi) - k * ln2_64lo;
|
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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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/* z is now in primary range. */
|
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t = z * z;
|
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yy.y = z + (t * (half + z * t2) + (t * t) * (t3 + z * t4 + t * t5));
|
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yy.y = TBL[j] + (TBL[j + 1] + TBL[j] * yy.y);
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libc_fesetround (fe_val);
|
||||
}
|
||||
|
||||
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 (res == (res + cor * err_0))
|
||||
{
|
||||
retval = res * binexp.x;
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
retval = __slowexp (x);
|
||||
goto ret;
|
||||
} /*if error is over bound */
|
||||
}
|
||||
|
||||
if (n <= smallint)
|
||||
{
|
||||
retval = 1.0;
|
||||
goto ret;
|
||||
}
|
||||
|
||||
if (n >= badint)
|
||||
{
|
||||
if (n > infint)
|
||||
{
|
||||
retval = x + x;
|
||||
goto ret;
|
||||
} /* x is NaN */
|
||||
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
|
||||
{
|
||||
retval = __slowexp (x);
|
||||
goto check_uflow_ret;
|
||||
} /*if error is over bound */
|
||||
}
|
||||
ex = -(1022 + ex);
|
||||
binexp.i[HIGH_HALF] = (1023 - ex) << 20;
|
||||
res *= binexp.x;
|
||||
cor *= binexp.x;
|
||||
eps = 1.0000000001 + err_0 * binexp.x;
|
||||
t = 1.0 + res;
|
||||
y = ((1.0 - t) + res) + cor;
|
||||
res = t + y;
|
||||
cor = (t - res) + y;
|
||||
if (res == (res + eps * cor))
|
||||
{
|
||||
binexp.i[HIGH_HALF] = 0x00100000;
|
||||
retval = (res - 1.0) * binexp.x;
|
||||
goto check_uflow_ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
retval = __slowexp (x);
|
||||
goto check_uflow_ret;
|
||||
} /* if error is over bound */
|
||||
check_uflow_ret:
|
||||
if (retval < DBL_MIN)
|
||||
{
|
||||
double force_underflow = tiny * tiny;
|
||||
math_force_eval (force_underflow);
|
||||
}
|
||||
if (retval == 0)
|
||||
goto ret_tiny;
|
||||
goto ret;
|
||||
}
|
||||
else
|
||||
{
|
||||
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;
|
||||
if (m < -1021)
|
||||
{
|
||||
yy.y_part[HIGH_HALF] += (m + 54) << 20;
|
||||
retval = twom54 * yy.y;
|
||||
if (retval < DBL_MIN)
|
||||
{
|
||||
double force_underflow = tiny * tiny;
|
||||
math_force_eval (force_underflow);
|
||||
}
|
||||
return retval;
|
||||
}
|
||||
yy.y_part[HIGH_HALF] += m << 20;
|
||||
return yy.y;
|
||||
}
|
||||
#ifndef __ieee754_exp
|
||||
strong_alias (__ieee754_exp, __exp_finite)
|
||||
#endif
|
||||
|
||||
#ifndef SECTION
|
||||
# define SECTION
|
||||
#endif
|
||||
|
||||
/* Compute e^(x+xx). The routine also receives bound of error of previous
|
||||
calculation. If after computing exp the error exceeds the allowed bounds,
|
||||
the routine returns a non-positive number. Otherwise it returns the
|
||||
|
|
|
|||
|
|
@ -25,7 +25,7 @@
|
|||
/* log1 */
|
||||
/* checkint */
|
||||
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */
|
||||
/* halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c */
|
||||
/* halfulp.c mpexp.c mplog.c slowpow.c mpa.c */
|
||||
/* uexp.c upow.c */
|
||||
/* root.tbl uexp.tbl upow.tbl */
|
||||
/* An ultimate power routine. Given two IEEE double machine numbers y,x */
|
||||
|
|
|
|||
255
sysdeps/ieee754/dbl-64/eexp.tbl
Normal file
255
sysdeps/ieee754/dbl-64/eexp.tbl
Normal file
|
|
@ -0,0 +1,255 @@
|
|||
/* 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 */
|
||||
|
|
@ -1,86 +0,0 @@
|
|||
/*
|
||||
* 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 +0,0 @@
|
|||
/* Not needed. */
|
||||
|
|
@ -3,5 +3,4 @@
|
|||
ifeq ($(subdir),math)
|
||||
CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
|
||||
CPPFLAGS-slowpow.c += -DUSE_LONG_DOUBLE_FOR_MP=1
|
||||
CPPFLAGS-slowexp.c += -DUSE_LONG_DOUBLE_FOR_MP=1
|
||||
endif
|
||||
|
|
|
|||
|
|
@ -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 \
|
||||
e_asin-fma e_atan2-fma s_sin-fma s_tan-fma \
|
||||
mplog-fma mpa-fma slowexp-fma slowpow-fma \
|
||||
mplog-fma mpa-fma slowpow-fma \
|
||||
sincos32-fma doasin-fma dosincos-fma \
|
||||
halfulp-fma mpexp-fma \
|
||||
mpatan2-fma mpatan-fma mpsqrt-fma mptan-fma
|
||||
|
|
@ -32,7 +32,6 @@ CFLAGS-mpsqrt-fma.c = -mfma -mavx2
|
|||
CFLAGS-mptan-fma.c = -mfma -mavx2
|
||||
CFLAGS-s_atan-fma.c = -mfma -mavx2
|
||||
CFLAGS-sincos32-fma.c = -mfma -mavx2
|
||||
CFLAGS-slowexp-fma.c = -mfma -mavx2
|
||||
CFLAGS-slowpow-fma.c = -mfma -mavx2
|
||||
CFLAGS-s_sin-fma.c = -mfma -mavx2
|
||||
CFLAGS-s_tan-fma.c = -mfma -mavx2
|
||||
|
|
@ -52,7 +51,7 @@ CFLAGS-s_cosf-fma.c = -mfma -mavx2
|
|||
|
||||
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 \
|
||||
mplog-fma4 mpa-fma4 slowpow-fma4 \
|
||||
sincos32-fma4 doasin-fma4 dosincos-fma4 \
|
||||
halfulp-fma4 mpexp-fma4 \
|
||||
mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
|
||||
|
|
@ -74,14 +73,13 @@ 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
|
||||
CFLAGS-s_sin-fma4.c = -mfma4
|
||||
CFLAGS-s_tan-fma4.c = -mfma4
|
||||
|
||||
libm-sysdep_routines += e_exp-avx e_log-avx s_atan-avx \
|
||||
e_atan2-avx s_sin-avx s_tan-avx \
|
||||
mplog-avx mpa-avx slowexp-avx \
|
||||
mplog-avx mpa-avx \
|
||||
mpexp-avx
|
||||
|
||||
CFLAGS-e_atan2-avx.c = -msse2avx -DSSE2AVX
|
||||
|
|
@ -92,7 +90,6 @@ CFLAGS-mpexp-avx.c = -msse2avx -DSSE2AVX
|
|||
CFLAGS-mplog-avx.c = -msse2avx -DSSE2AVX
|
||||
CFLAGS-s_atan-avx.c = -msse2avx -DSSE2AVX
|
||||
CFLAGS-s_sin-avx.c = -msse2avx -DSSE2AVX
|
||||
CFLAGS-slowexp-avx.c = -msse2avx -DSSE2AVX
|
||||
CFLAGS-s_tan-avx.c = -msse2avx -DSSE2AVX
|
||||
endif
|
||||
|
||||
|
|
|
|||
|
|
@ -1,6 +1,5 @@
|
|||
#define __ieee754_exp __ieee754_exp_avx
|
||||
#define __exp1 __exp1_avx
|
||||
#define __slowexp __slowexp_avx
|
||||
#define SECTION __attribute__ ((section (".text.avx")))
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
||||
|
|
|
|||
|
|
@ -1,6 +1,5 @@
|
|||
#define __ieee754_exp __ieee754_exp_fma
|
||||
#define __exp1 __exp1_fma
|
||||
#define __slowexp __slowexp_fma
|
||||
#define SECTION __attribute__ ((section (".text.fma")))
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
||||
|
|
|
|||
|
|
@ -1,6 +1,5 @@
|
|||
#define __ieee754_exp __ieee754_exp_fma4
|
||||
#define __exp1 __exp1_fma4
|
||||
#define __slowexp __slowexp_fma4
|
||||
#define SECTION __attribute__ ((section (".text.fma4")))
|
||||
|
||||
#include <sysdeps/ieee754/dbl-64/e_exp.c>
|
||||
|
|
|
|||
|
|
@ -1,9 +0,0 @@
|
|||
#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>
|
||||
|
|
@ -1,9 +0,0 @@
|
|||
#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>
|
||||
|
|
@ -1,9 +0,0 @@
|
|||
#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 a new issue