math: Use expm1f from CORE-MATH

The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic expm1f.

The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow).

Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1,
gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1):

Latency                      master        patched   improvement
x86_64                      96.7402        36.4026        62.37%
x86_64v2                    97.5391        33.4625        65.69%
x86_64v3                    82.1778        30.8668        62.44%
i686                         120.58        94.8302        21.35%
aarch64                     32.3558        12.8881        60.17%
power10                     23.5087        9.8574         58.07%
powerpc                     23.4776        9.06325        61.40%

reciprocal-throughput        master        patched   improvement
x86_64                      27.8224        15.9255        42.76%
x86_64v2                    27.8364        9.6438         65.36%
x86_64v3                    20.3227        9.6146         52.69%
i686                        63.5629        59.4718         6.44%
aarch64                     17.4838        7.1082         59.34%
power10                     12.4644        8.7829         29.54%
powerpc                     14.2152        5.94765        58.16%

Signed-off-by: Alexei Sibidanov <sibid@uvic.ca>
Signed-off-by: Paul Zimmermann <Paul.Zimmermann@inria.fr>
Signed-off-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: DJ Delorie <dj@redhat.com>
This commit is contained in:
Adhemerval Zanella 2024-10-25 15:21:49 -03:00
parent 5c22fd25c1
commit bbd578b38d
29 changed files with 123 additions and 320 deletions

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@ -248,3 +248,7 @@ sysdeps/ieee754/flt-32/s_exp2m1f.c
(file src/binary32/exp2m1/exp2m1f.c in CORE-MATH) (file src/binary32/exp2m1/exp2m1f.c in CORE-MATH)
- The code was adapted to use glibc code style and internal - The code was adapted to use glibc code style and internal
functions to handle errno, overflow, and underflow. functions to handle errno, overflow, and underflow.
sysdeps/ieee754/flt-32/s_expm1f.c
(file src/binary32/expm1/expm1f.c in CORE-MATH)
- The code was adapted to use glibc code style and internal
functions to handle errno, overflow, and underflow.

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@ -801,6 +801,7 @@ float: 1
ldouble: 1 ldouble: 1
Function: Imaginary part of "csin": Function: Imaginary part of "csin":
float: 1
ldouble: 1 ldouble: 1
Function: Real part of "csin_downward": Function: Real part of "csin_downward":
@ -1163,7 +1164,6 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_advsimd": Function: "expm1_advsimd":
@ -1172,7 +1172,6 @@ float: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_sve": Function: "expm1_sve":
@ -1181,12 +1180,10 @@ float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

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@ -1034,22 +1034,18 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

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@ -839,19 +839,15 @@ float: 2
Function: "expm1": Function: "expm1":
double: 2 double: 2
float: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 2 double: 2
float: 2
Function: "gamma": Function: "gamma":
double: 7 double: 7

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@ -203,7 +203,6 @@ double: 2
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

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@ -574,6 +574,9 @@ Function: Real part of "csin":
double: 1 double: 1
float: 1 float: 1
Function: Imaginary part of "csin":
float: 1
Function: Real part of "csin_downward": Function: Real part of "csin_downward":
double: 3 double: 3
float: 3 float: 3
@ -831,19 +834,15 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

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@ -799,19 +799,15 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

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@ -797,19 +797,15 @@ double: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

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@ -850,20 +850,16 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 1 ldouble: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

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@ -1234,19 +1234,16 @@ ldouble: 3
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
float128: 2 float128: 2
ldouble: 4 ldouble: 4
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 1
float128: 4 float128: 4
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
float128: 3 float128: 3
ldouble: 4 ldouble: 4

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@ -1,112 +0,0 @@
/* ix87 specific implementation of exp(x)-1.
Copyright (C) 1996-2024 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
<https://www.gnu.org/licenses/>. */
/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
#include <sysdep.h>
#include <machine/asm.h>
#include <i386-math-asm.h>
#include <libm-alias-float.h>
.section .rodata
.align ALIGNARG(4)
.type minus1,@object
minus1: .double -1.0
ASM_SIZE_DIRECTIVE(minus1)
.type one,@object
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
.type l2e,@object
l2e: .quad 0xb8aa3b295c17f0bc /* 1.442695040888963407359924681002 */
.short 0x3fff
ASM_SIZE_DIRECTIVE(l2e)
DEFINE_FLT_MIN
#ifdef PIC
#define MO(op) op##@GOTOFF(%edx)
#else
#define MO(op) op
#endif
.text
ENTRY(__expm1f)
movzwl 4+2(%esp), %eax
xorb $0x80, %ah // invert sign bit (now 1 is "positive")
cmpl $0xc2b1, %eax // is num >= 88.5?
jae HIDDEN_JUMPTARGET (__expf)
flds 4(%esp) // x
fxam // Is NaN, +-Inf or +-0?
xorb $0x80, %ah
cmpl $0xc190, %eax // is num <= -18.0?
fstsw %ax
movb $0x45, %ch
jb 4f
// Below -18.0 (may be -NaN or -Inf).
andb %ah, %ch
#ifdef PIC
LOAD_PIC_REG (dx)
#endif
cmpb $0x01, %ch
je 5f // If -NaN, jump.
jmp 2f // -large, possibly -Inf.
4: // In range -18.0 to 88.5 (may be +-0 but not NaN or +-Inf).
andb %ah, %ch
cmpb $0x40, %ch
je 3f // If +-0, jump.
#ifdef PIC
LOAD_PIC_REG (dx)
#endif
5: fldt MO(l2e) // log2(e) : x
fmulp // log2(e)*x
fld %st // log2(e)*x : log2(e)*x
// Set round-to-nearest temporarily.
subl $8, %esp
cfi_adjust_cfa_offset (8)
fstcw 4(%esp)
movl $0xf3ff, %ecx
andl 4(%esp), %ecx
movl %ecx, (%esp)
fldcw (%esp)
frndint // int(log2(e)*x) : log2(e)*x
fldcw 4(%esp)
addl $8, %esp
cfi_adjust_cfa_offset (-8)
fsubr %st, %st(1) // int(log2(e)*x) : fract(log2(e)*x)
fxch // fract(log2(e)*x) : int(log2(e)*x)
f2xm1 // 2^fract(log2(e)*x)-1 : int(log2(e)*x)
fscale // 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
fxch // int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fldl MO(one) // 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fscale // 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fsubrl MO(one) // 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fstp %st(1) // 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
fsubrp %st, %st(1) // 2^(log2(e)*x)
FLT_CHECK_FORCE_UFLOW
ret
2: fstp %st
fldl MO(minus1) // Set result to -1.0.
3: ret
END(__expm1f)
libm_alias_float (__expm1, expm1)

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@ -1237,19 +1237,16 @@ ldouble: 3
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
float128: 2 float128: 2
ldouble: 4 ldouble: 4
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 1
float128: 4 float128: 4
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
float128: 3 float128: 3
ldouble: 4 ldouble: 4

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@ -3,7 +3,7 @@
Copyright (c) 2022-2024 Alexei Sibidanov. Copyright (c) 2022-2024 Alexei Sibidanov.
The original version of this file was copied from the CORE-MATH The original version of this file was copied from the CORE-MATH
project (file src/binary32/exp2m1/exp2m1f.c, revision bc385c2). project (file src/binary32/exp2m1/exp2m1f.c, revision baf5f6b).
Permission is hereby granted, free of charge, to any person obtaining a copy Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal of this software and associated documentation files (the "Software"), to deal

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@ -1,132 +1,124 @@
/* s_expm1f.c -- float version of s_expm1.c. /* Correctly-rounded natural exponent function biased by 1 for binary32 value.
*/
/* Copyright (c) 2022-2024 Alexei Sibidanov.
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. This file is part of the CORE-MATH project
* project (file src/binary32/expm1/expm1f.c, revision bc385c2).
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this Permission is hereby granted, free of charge, to any person obtaining a copy
* software is freely granted, provided that this notice of this software and associated documentation files (the "Software"), to deal
* is preserved. in the Software without restriction, including without limitation the rights
* ==================================================== to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
*/ copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#include <errno.h>
#include <float.h>
#include <math.h> #include <math.h>
#include <math-barriers.h>
#include <math_private.h>
#include <math-underflow.h> #include <math-underflow.h>
#include <libm-alias-float.h> #include <libm-alias-float.h>
#include "math_config.h"
static const float huge = 1.0e+30;
static const float tiny = 1.0e-30;
static const float
one = 1.0,
o_threshold = 8.8721679688e+01,/* 0x42b17180 */
ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
/* scaled coefficients related to expm1 */
Q1 = -3.3333335072e-02, /* 0xbd088889 */
Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
Q3 = -7.9365076090e-05, /* 0xb8a670cd */
Q4 = 4.0082177293e-06, /* 0x36867e54 */
Q5 = -2.0109921195e-07; /* 0xb457edbb */
float float
__expm1f(float x) __expm1f (float x)
{ {
float y,hi,lo,c,t,e,hxs,hfx,r1; static const double c[] =
int32_t k,xsb; {
uint32_t hx; 1, 0x1.62e42fef4c4e7p-6, 0x1.ebfd1b232f475p-13, 0x1.c6b19384ecd93p-20
};
GET_FLOAT_WORD(hx,x); static const double ch[] =
xsb = hx&0x80000000; /* sign bit of x */ {
if(xsb==0) y=x; else y= -x; /* y = |x| */ 0x1.62e42fefa39efp-6, 0x1.ebfbdff82c58fp-13, 0x1.c6b08d702e0edp-20,
hx &= 0x7fffffff; /* high word of |x| */ 0x1.3b2ab6fb92e5ep-27, 0x1.5d886e6d54203p-35, 0x1.430976b8ce6efp-43
};
/* filter out huge and non-finite argument */ static const double td[] =
if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ {
if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 0x1p+0, 0x1.059b0d3158574p+0, 0x1.0b5586cf9890fp+0,
if(hx>0x7f800000) 0x1.11301d0125b51p+0, 0x1.172b83c7d517bp+0, 0x1.1d4873168b9aap+0,
return x+x; /* NaN */ 0x1.2387a6e756238p+0, 0x1.29e9df51fdee1p+0, 0x1.306fe0a31b715p+0,
if(hx==0x7f800000) 0x1.371a7373aa9cbp+0, 0x1.3dea64c123422p+0, 0x1.44e086061892dp+0,
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 0x1.4bfdad5362a27p+0, 0x1.5342b569d4f82p+0, 0x1.5ab07dd485429p+0,
if(x > o_threshold) { 0x1.6247eb03a5585p+0, 0x1.6a09e667f3bcdp+0, 0x1.71f75e8ec5f74p+0,
__set_errno (ERANGE); 0x1.7a11473eb0187p+0, 0x1.82589994cce13p+0, 0x1.8ace5422aa0dbp+0,
return huge*huge; /* overflow */ 0x1.93737b0cdc5e5p+0, 0x1.9c49182a3f09p+0, 0x1.a5503b23e255dp+0,
0x1.ae89f995ad3adp+0, 0x1.b7f76f2fb5e47p+0, 0x1.c199bdd85529cp+0,
0x1.cb720dcef9069p+0, 0x1.d5818dcfba487p+0, 0x1.dfc97337b9b5fp+0,
0x1.ea4afa2a490dap+0, 0x1.f50765b6e454p+0
};
const double iln2 = 0x1.71547652b82fep+5;
const double big = 0x1.8p52;
double z = x;
uint32_t ux = asuint (x);
uint32_t ax = ux << 1;
if (__glibc_likely (ax < 0x7c400000u))
{ /* |x| < 0.15625 */
if (__glibc_unlikely (ax < 0x676a09e8u))
{ /* |x| < 0x1.6a09e8p-24 */
if (__glibc_unlikely (ax == 0x0u))
return x; /* x = +-0 */
return fmaf (fabsf (x), 0x1p-25f, x);
} }
static const double b[] =
{
0x1.fffffffffffc2p-2, 0x1.55555555555fep-3, 0x1.555555559767fp-5,
0x1.1111111098dc1p-7, 0x1.6c16bca988aa9p-10, 0x1.a01a07658483fp-13,
0x1.a05b04d2c3503p-16, 0x1.71de3a960b5e3p-19
};
double z2 = z * z, z4 = z2 * z2;
double r = z + z2
* ((b[0] + z * b[1]) + z2 * (b[2] + z * b[3])
+ z4 * ((b[4] + z * b[5]) + z2 * (b[6] + z * b[7])));
return r;
} }
if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ if (__glibc_unlikely (ax >= 0x8562e430u))
math_force_eval(x+tiny);/* raise inexact */ { /* |x| > 88.72 */
return tiny-one; /* return -1 */ if (ax > (0xffu << 24))
return x + x; /* nan */
if (__glibc_unlikely (ux >> 31))
{ /* x < 0 */
if (ax == (0xffu << 24))
return -1.0f;
return -1.0f + 0x1p-26f;
} }
if (ax == (0xffu << 24))
return INFINITY;
return __math_oflowf (0);
} }
double a = iln2 * z;
/* argument reduction */ double ia = roundeven (a);
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ double h = a - ia;
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ double h2 = h * h;
if(xsb==0) uint64_t u = asuint64 (ia + big);
{hi = x - ln2_hi; lo = ln2_lo; k = 1;} double c2 = c[2] + h * c[3], c0 = c[0] + h * c[1];
else const uint64_t *tdl = (uint64_t *) ((void *) td);
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;} double sv = asdouble (tdl[u & 0x1f] + ((u >> 5) << 52));
} else { double r = (c0 + h2 * c2) * sv - 1.0;
k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); float ub = r, lb = r - sv * 0x1.3b3p-33;
t = k; if (__glibc_unlikely (ub != lb))
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ {
lo = t*ln2_lo; if (__glibc_unlikely (ux > 0xc18aa123u)) /* x < -17.32 */
return -1.0f + 0x1p-26f;
const double iln2h = 0x1.7154765p+5;
const double iln2l = 0x1.5c17f0bbbe88p-26;
double s = sv;
h = (iln2h * z - ia) + iln2l * z;
h2 = h * h;
double w = s * h;
r = (s - 1) + w
* ((ch[0] + h * ch[1])
+ h2 * ((ch[2] + h * ch[3]) + h2 * (ch[4] + h * ch[5])));
ub = r;
} }
x = hi - lo; return ub;
c = (hi-x)-lo;
}
else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
math_check_force_underflow (x);
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = (float)0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = (float)3.0-r1*hfx;
e = hxs*((r1-t)/((float)6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return (float)0.5*(x-e)-(float)0.5;
if(k==1) {
if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
else return one+(float)2.0*(x-e);
}
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
int32_t i;
y = one-(e-x);
GET_FLOAT_WORD(i,y);
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
return y-one;
}
t = one;
if(k<23) {
int32_t i;
SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
y = t-(e-x);
GET_FLOAT_WORD(i,y);
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
} else {
int32_t i;
SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
y = x-(e+t);
y += one;
GET_FLOAT_WORD(i,y);
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
}
}
return y;
} }
libm_alias_float (__expm1, expm1) libm_alias_float (__expm1, expm1)

View File

@ -1038,22 +1038,18 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

View File

@ -191,7 +191,6 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

View File

@ -831,19 +831,15 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

View File

@ -1042,22 +1042,18 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

View File

@ -197,7 +197,6 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

View File

@ -804,19 +804,15 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

View File

@ -802,19 +802,15 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
Function: "gamma": Function: "gamma":
double: 4 double: 4

View File

@ -870,6 +870,7 @@ float128: 1
ldouble: 2 ldouble: 2
Function: Imaginary part of "csin": Function: Imaginary part of "csin":
float: 1
float128: 1 float128: 1
ldouble: 1 ldouble: 1
@ -1262,25 +1263,21 @@ ldouble: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
float128: 2 float128: 2
ldouble: 1 ldouble: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
float128: 2 float128: 2
ldouble: 7 ldouble: 7
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
float128: 4 float128: 4
ldouble: 6 ldouble: 6
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
float128: 3 float128: 3
ldouble: 6 ldouble: 6

View File

@ -1054,22 +1054,18 @@ ldouble: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 1 ldouble: 1
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 5 ldouble: 5
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 5 ldouble: 5
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 6 ldouble: 6
Function: "fma": Function: "fma":

View File

@ -1011,22 +1011,18 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

View File

@ -1038,22 +1038,18 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

View File

@ -1039,22 +1039,18 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

View File

@ -394,11 +394,9 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
Function: "fma_towardzero": Function: "fma_towardzero":
double: 1 double: 1

View File

@ -1042,22 +1042,18 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
ldouble: 2 ldouble: 2
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
ldouble: 3 ldouble: 3
Function: "gamma": Function: "gamma":

View File

@ -1062,6 +1062,7 @@ float128: 1
ldouble: 1 ldouble: 1
Function: Imaginary part of "csin": Function: Imaginary part of "csin":
float: 1
float128: 1 float128: 1
Function: Real part of "csin_downward": Function: Real part of "csin_downward":
@ -1550,25 +1551,21 @@ float: 1
Function: "expm1": Function: "expm1":
double: 1 double: 1
float: 1
float128: 2 float128: 2
ldouble: 3 ldouble: 3
Function: "expm1_downward": Function: "expm1_downward":
double: 1 double: 1
float: 1
float128: 2 float128: 2
ldouble: 4 ldouble: 4
Function: "expm1_towardzero": Function: "expm1_towardzero":
double: 1 double: 1
float: 2
float128: 4 float128: 4
ldouble: 4 ldouble: 4
Function: "expm1_upward": Function: "expm1_upward":
double: 1 double: 1
float: 1
float128: 3 float128: 3
ldouble: 4 ldouble: 4