Remove slow paths from exp
Remove the __slowexp code, so exp is no longer correctly rounded. The result is computed to about 70 bits precision so the worst case ulp error is about 0.500007 in nearest rounding mode. * manual/probes.texi: Remove slowexp probes. * math/Makefile: Remove slowexp. * sysdeps/generic/math_private.h (__slowexp): Remove. * sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Remove __slowexp and document error bounds. * sysdeps/i386/fpu/slowexp.c: Remove. * sysdeps/ia64/fpu/slowexp.c: Remove. * sysdeps/ieee754/dbl-64/slowexp.c: Remove. * sysdeps/ieee754/dbl-64/uexp.h (err_0): Remove. * sysdeps/m68k/m680x0/fpu/slowexp.c: Remove. * sysdeps/powerpc/power4/fpu/Makefile (CPPFLAGS-slowexp.c): Remove. * sysdeps/x86_64/fpu/multiarch/Makefile: Remove slowexp-fma. * sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Remove. * sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Remove. * sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Remove. * sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Remove. * sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Remove. * sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Remove.
This commit is contained in:
Szabolcs Nagy
parent
c3d466cba1
commit
de800d8305
21
ChangeLog
21
ChangeLog
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@ -1,3 +1,24 @@
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2018-02-12 Szabolcs Nagy <szabolcs.nagy@arm.com>
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* manual/probes.texi: Remove slowexp probes.
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* math/Makefile: Remove slowexp.
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* sysdeps/generic/math_private.h (__slowexp): Remove.
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* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Remove __slowexp and
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document error bounds.
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* sysdeps/i386/fpu/slowexp.c: Remove.
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* sysdeps/ia64/fpu/slowexp.c: Remove.
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* sysdeps/ieee754/dbl-64/slowexp.c: Remove.
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* sysdeps/ieee754/dbl-64/uexp.h (err_0): Remove.
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* sysdeps/m68k/m680x0/fpu/slowexp.c: Remove.
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* sysdeps/powerpc/power4/fpu/Makefile (CPPFLAGS-slowexp.c): Remove.
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* sysdeps/x86_64/fpu/multiarch/Makefile: Remove slowexp-fma.
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* sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Remove.
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* sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Remove.
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* sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Remove.
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* sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Remove.
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* sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Remove.
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* sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Remove.
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2018-02-12 Wilco Dijkstra <wdijkstr@arm.com>
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[BZ #13932]
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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 slowatan2 (int @var{$arg1}, double @var{$arg2}, double @var{$arg3}, double @var{$arg4})
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This probe is triggered when the @code{atan2} function is called with
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an input that results in multiple precision computation. Argument
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@ -124,7 +124,7 @@ 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 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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sincostab k_rem_pio2
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# float support
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@ -261,7 +261,6 @@ 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 void __docos (double __x, double __dx, double __v[]);
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#ifndef math_opt_barrier
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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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@ -23,10 +23,10 @@
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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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/* it computes an almost correctly rounded (to nearest) value of e^x */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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@ -46,10 +46,6 @@
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# define SECTION
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#endif
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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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@ -93,17 +89,10 @@ __ieee754_exp (double x)
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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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retval = res * binexp.x;
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goto ret;
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}
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else
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{
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retval = __slowexp (x);
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goto ret;
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} /*if error is over bound */
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/* Maximum relative error is 7.8e-22 (70.1 bits).
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Maximum ULP error is 0.500007. */
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retval = res * binexp.x;
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goto ret;
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}
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if (n <= smallint)
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@ -166,38 +155,22 @@ __ieee754_exp (double x)
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if (ex >= -1022)
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{
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binexp.i[HIGH_HALF] = (1023 + ex) << 20;
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if (res == (res + cor * err_0))
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{
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retval = res * binexp.x;
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goto ret;
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}
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else
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{
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retval = __slowexp (x);
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goto check_uflow_ret;
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} /*if error is over bound */
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/* Does not underflow: res >= 1.0, binexp >= 0x1p-1022
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Maximum relative error is 7.8e-22 (70.1 bits).
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Maximum ULP error is 0.500007. */
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retval = res * binexp.x;
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goto ret;
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}
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ex = -(1022 + ex);
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binexp.i[HIGH_HALF] = (1023 - ex) << 20;
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res *= binexp.x;
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cor *= binexp.x;
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eps = 1.0000000001 + err_0 * binexp.x;
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t = 1.0 + res;
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y = ((1.0 - t) + res) + cor;
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res = t + y;
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cor = (t - res) + y;
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if (res == (res + eps * cor))
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{
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binexp.i[HIGH_HALF] = 0x00100000;
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retval = (res - 1.0) * binexp.x;
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goto check_uflow_ret;
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}
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else
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{
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retval = __slowexp (x);
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goto check_uflow_ret;
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} /* if error is over bound */
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check_uflow_ret:
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/* Maximum ULP error is 0.5000035. */
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binexp.i[HIGH_HALF] = 0x00100000;
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retval = (res - 1.0) * binexp.x;
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if (retval < DBL_MIN)
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{
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double force_underflow = tiny * tiny;
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@ -210,10 +183,9 @@ __ieee754_exp (double x)
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else
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{
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binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20;
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if (res == (res + cor * err_0))
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retval = res * binexp.x * t256.x;
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else
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retval = __slowexp (x);
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/* Maximum relative error is 7.8e-22 (70.1 bits).
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Maximum ULP error is 0.500007. */
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retval = res * binexp.x * t256.x;
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if (isinf (retval))
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goto ret_huge;
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else
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@ -1,86 +0,0 @@
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/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2018 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/**************************************************************************/
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/* MODULE_NAME:slowexp.c */
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/* */
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/* FUNCTION:slowexp */
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/* */
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/* FILES NEEDED:mpa.h */
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/* mpa.c mpexp.c */
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/* */
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/*Converting from double precision to Multi-precision and calculating */
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/* e^x */
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/**************************************************************************/
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#include <math_private.h>
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#include <stap-probe.h>
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#ifndef USE_LONG_DOUBLE_FOR_MP
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# include "mpa.h"
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void __mpexp (mp_no *x, mp_no *y, int p);
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#endif
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#ifndef SECTION
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# define SECTION
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#endif
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/*Converting from double precision to Multi-precision and calculating e^x */
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double
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SECTION
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__slowexp (double x)
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{
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#ifndef USE_LONG_DOUBLE_FOR_MP
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double w, z, res, eps = 3.0e-26;
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int p;
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mp_no mpx, mpy, mpz, mpw, mpeps, mpcor;
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/* Use the multiple precision __MPEXP function to compute the exponential
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First at 144 bits and if it is not accurate enough, at 768 bits. */
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p = 6;
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__dbl_mp (x, &mpx, p);
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__mpexp (&mpx, &mpy, p);
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__dbl_mp (eps, &mpeps, p);
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__mul (&mpeps, &mpy, &mpcor, p);
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__add (&mpy, &mpcor, &mpw, p);
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__sub (&mpy, &mpcor, &mpz, p);
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__mp_dbl (&mpw, &w, p);
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__mp_dbl (&mpz, &z, p);
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if (w == z)
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{
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/* Track how often we get to the slow exp code plus
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its input/output values. */
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LIBC_PROBE (slowexp_p6, 2, &x, &w);
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return w;
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}
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else
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{
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p = 32;
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__dbl_mp (x, &mpx, p);
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__mpexp (&mpx, &mpy, p);
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__mp_dbl (&mpy, &res, p);
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/* Track how often we get to the uber-slow exp code plus
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its input/output values. */
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LIBC_PROBE (slowexp_p32, 2, &x, &res);
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return res;
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}
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#else
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return (double) __ieee754_expl((long double)x);
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#endif
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}
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@ -29,8 +29,7 @@
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#include "mydefs.h"
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const static double zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300,
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err_0 = 1.000014;
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const static double zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300;
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const static int4 bigint = 0x40862002,
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badint = 0x40876000,smallint = 0x3C8fffff;
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const static int4 hugeint = 0x7FFFFFFF, infint = 0x7ff00000;
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@ -1 +0,0 @@
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/* Not needed. */
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@ -2,5 +2,4 @@
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ifeq ($(subdir),math)
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CFLAGS-mpa.c += --param max-unroll-times=4 -funroll-loops -fpeel-loops
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CPPFLAGS-slowexp.c += -DUSE_LONG_DOUBLE_FOR_MP=1
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endif
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@ -10,7 +10,7 @@ libm-sysdep_routines += s_ceil-sse4_1 s_ceilf-sse4_1 s_floor-sse4_1 \
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libm-sysdep_routines += e_exp-fma e_log-fma e_pow-fma s_atan-fma \
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e_asin-fma e_atan2-fma s_sin-fma s_tan-fma \
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mplog-fma mpa-fma slowexp-fma \
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mplog-fma mpa-fma \
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sincos32-fma doasin-fma dosincos-fma \
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mpexp-fma \
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mpatan2-fma mpatan-fma mpsqrt-fma mptan-fma
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@ -31,7 +31,6 @@ CFLAGS-mpsqrt-fma.c = -mfma -mavx2
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CFLAGS-mptan-fma.c = -mfma -mavx2
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CFLAGS-s_atan-fma.c = -mfma -mavx2
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CFLAGS-sincos32-fma.c = -mfma -mavx2
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CFLAGS-slowexp-fma.c = -mfma -mavx2
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CFLAGS-s_sin-fma.c = -mfma -mavx2
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CFLAGS-s_tan-fma.c = -mfma -mavx2
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@ -51,7 +50,7 @@ CFLAGS-s_sincosf-fma.c = -mfma -mavx2
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libm-sysdep_routines += e_exp-fma4 e_log-fma4 e_pow-fma4 s_atan-fma4 \
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e_asin-fma4 e_atan2-fma4 s_sin-fma4 s_tan-fma4 \
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mplog-fma4 mpa-fma4 slowexp-fma4 \
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mplog-fma4 mpa-fma4 \
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sincos32-fma4 doasin-fma4 dosincos-fma4 \
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mpexp-fma4 \
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mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
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@ -72,13 +71,12 @@ CFLAGS-mpsqrt-fma4.c = -mfma4
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CFLAGS-mptan-fma4.c = -mfma4
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CFLAGS-s_atan-fma4.c = -mfma4
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CFLAGS-sincos32-fma4.c = -mfma4
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CFLAGS-slowexp-fma4.c = -mfma4
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CFLAGS-s_sin-fma4.c = -mfma4
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CFLAGS-s_tan-fma4.c = -mfma4
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libm-sysdep_routines += e_exp-avx e_log-avx s_atan-avx \
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e_atan2-avx s_sin-avx s_tan-avx \
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mplog-avx mpa-avx slowexp-avx \
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mplog-avx mpa-avx \
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mpexp-avx
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CFLAGS-e_atan2-avx.c = -msse2avx -DSSE2AVX
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@ -89,7 +87,6 @@ CFLAGS-mpexp-avx.c = -msse2avx -DSSE2AVX
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CFLAGS-mplog-avx.c = -msse2avx -DSSE2AVX
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CFLAGS-s_atan-avx.c = -msse2avx -DSSE2AVX
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CFLAGS-s_sin-avx.c = -msse2avx -DSSE2AVX
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CFLAGS-slowexp-avx.c = -msse2avx -DSSE2AVX
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CFLAGS-s_tan-avx.c = -msse2avx -DSSE2AVX
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endif
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@ -1,6 +1,5 @@
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#define __ieee754_exp __ieee754_exp_avx
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#define __exp1 __exp1_avx
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#define __slowexp __slowexp_avx
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#define SECTION __attribute__ ((section (".text.avx")))
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#include <sysdeps/ieee754/dbl-64/e_exp.c>
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|
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@ -1,6 +1,5 @@
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#define __ieee754_exp __ieee754_exp_fma
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#define __exp1 __exp1_fma
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#define __slowexp __slowexp_fma
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#define SECTION __attribute__ ((section (".text.fma")))
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#include <sysdeps/ieee754/dbl-64/e_exp.c>
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|
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@ -1,6 +1,5 @@
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#define __ieee754_exp __ieee754_exp_fma4
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#define __exp1 __exp1_fma4
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#define __slowexp __slowexp_fma4
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#define SECTION __attribute__ ((section (".text.fma4")))
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#include <sysdeps/ieee754/dbl-64/e_exp.c>
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|
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@ -1,9 +0,0 @@
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#define __slowexp __slowexp_avx
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#define __add __add_avx
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#define __dbl_mp __dbl_mp_avx
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#define __mpexp __mpexp_avx
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#define __mul __mul_avx
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#define __sub __sub_avx
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#define SECTION __attribute__ ((section (".text.avx")))
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#include <sysdeps/ieee754/dbl-64/slowexp.c>
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@ -1,9 +0,0 @@
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#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>
|
||||
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Reference in a new issue