[09/17] math: Use exp10m1f from CORE-MATH
Commit Message
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance compared to the generic exp10m1f.
The code was adapted to glibc style and to use the definition of
math_config.h (to handle errno, overflow, and underflow). I mostly
fixed some small issues in corner cases (sNaN handling, -INFINITY,
a specific overflow check).
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 45.4690 49.5845 -9.05%
x86_64v2 46.1604 36.2665 21.43%
x86_64v3 37.8442 31.0359 17.99%
i686 121.367 93.0079 23.37%
aarch64 21.1126 15.0165 28.87%
power10 12.7426 8.4929 33.35%
reciprocal-throughput master patched improvement
x86_64 19.6005 17.4005 11.22%
x86_64v2 19.6008 11.1977 42.87%
x86_64v3 17.5427 10.2898 41.34%
i686 59.4215 60.9675 -2.60%
aarch64 13.9814 7.9173 43.37%
power10 6.7814 6.4258 5.24%
The generic implementation calls __ieee754_exp10f which has an
optimized version, although it is not correctly rounded, which is
the main culprit of the the latency difference for x86_64 and
throughp for i686.
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>
---
SHARED-FILES | 4 +
sysdeps/aarch64/libm-test-ulps | 4 -
sysdeps/arc/fpu/libm-test-ulps | 1 -
sysdeps/arc/nofpu/libm-test-ulps | 1 -
sysdeps/arm/libm-test-ulps | 4 -
sysdeps/hppa/fpu/libm-test-ulps | 4 -
sysdeps/i386/fpu/libm-test-ulps | 4 -
.../i386/i686/fpu/multiarch/libm-test-ulps | 4 -
sysdeps/ieee754/flt-32/s_exp10m1f.c | 225 ++++++++++++++++++
sysdeps/loongarch/lp64/libm-test-ulps | 4 -
sysdeps/m68k/m680x0/fpu/libm-test-ulps | 4 -
sysdeps/mips/mips32/libm-test-ulps | 4 -
sysdeps/mips/mips64/libm-test-ulps | 4 -
sysdeps/powerpc/fpu/libm-test-ulps | 4 -
sysdeps/powerpc/nofpu/libm-test-ulps | 4 -
sysdeps/riscv/nofpu/libm-test-ulps | 1 -
sysdeps/riscv/rvd/libm-test-ulps | 4 -
sysdeps/s390/fpu/libm-test-ulps | 4 -
sysdeps/sparc/fpu/libm-test-ulps | 4 -
sysdeps/x86_64/fpu/libm-test-ulps | 4 -
20 files changed, 229 insertions(+), 63 deletions(-)
create mode 100644 sysdeps/ieee754/flt-32/s_exp10m1f.c
Comments
A few questions but I suspect they're easily answered. LGTM with
reasonable answers. I'll elide the same questions in the other patches
in this series with the assumption that the same answers apply ;-)
Reviewed-by: DJ Delorie <dj@redhat.com>
Adhemerval Zanella <adhemerval.zanella@linaro.org> writes:
> diff --git a/SHARED-FILES b/SHARED-FILES
> +sysdeps/ieee754/flt-32/s_exp10m1f.c
> + (file src/binary32/exp10m1/exp10m1f.c in CORE_MATH)
I notice this file references the CORE MATH project (is it CORE_MATH or
CORE-MATH? The file is inconsistent) but doesn't provide an URL to the
project; such a link would be appreciated in a future patch :-)
> diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
> index 8c333fcd29..00832393f6 100644
> --- a/sysdeps/aarch64/libm-test-ulps
> +++ b/sysdeps/aarch64/libm-test-ulps
> @@ -1083,22 +1083,18 @@ ldouble: 3
>
> Function: "exp10m1":
> double: 4
> -float: 2
> ldouble: 3
Does this mean "we're not testing it any more" or "we expect zero ULPs
and verify that" ? I don't see any ": 0" in any of the ulps files so I
assume the latter.
> Function: "exp10m1_downward":
> double: 3
> -float: 3
> ldouble: 6
>
> Function: "exp10m1_towardzero":
> double: 2
> -float: 3
> ldouble: 6
>
> Function: "exp10m1_upward":
> double: 5
> -float: 3
> ldouble: 6
>
> Function: "exp2":
> diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
> index d1665b9b72..ad4ae4c632 100644
> --- a/sysdeps/arc/fpu/libm-test-ulps
> +++ b/sysdeps/arc/fpu/libm-test-ulps
> @@ -789,7 +789,6 @@ float: 1
>
> Function: "exp10m1":
> double: 4
> -float: 2
>
> Function: "exp10m1_downward":
> double: 3
The other roundings still have ULPs?
> diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
> index e768024eb5..4cecea6919 100644
> --- a/sysdeps/arc/nofpu/libm-test-ulps
> +++ b/sysdeps/arc/nofpu/libm-test-ulps
> @@ -194,7 +194,6 @@ float: 1
>
> Function: "exp10m1":
> double: 3
> -float: 2
>
> Function: "exp2":
> double: 1
Likewise here.
> diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
> diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
> diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
> diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
Ok.
> diff --git a/sysdeps/ieee754/flt-32/s_exp10m1f.c b/sysdeps/ieee754/flt-32/s_exp10m1f.c
> new file mode 100644
> index 0000000000..610f269b01
> --- /dev/null
> +++ b/sysdeps/ieee754/flt-32/s_exp10m1f.c
> @@ -0,0 +1,225 @@
> +/* Implementation of the exp10m1 function for binary32.
> +
> +Copyright (c) 2022-2024 Alexei Sibidanov. Paul Zimmermann.
> +
> +The original version of this file was copied from the CORE-MATH
> +project (file src/binary32/exp10m1/exp10m1f.c, revision d680516).
> +
> +Permission is hereby granted, free of charge, to any person obtaining a copy
> +of this software and associated documentation files (the "Software"), to deal
> +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 <math.h>
> +#include "math_config.h"
> +#include <libm-alias-float.h>
Ok.
> +float
> +__exp10m1f (float x)
> +{
> + const double iln10h = 0x1.a934f09p+1 * 16;
> + const double iln10l = 0x1.e68dc57f2496p-29 * 16;
> + double z = x;
> + uint32_t ux = asuint (x);
> + uint32_t ax = ux & (~0u >> 1);
> + if (__glibc_unlikely (ux > 0xc0f0d2f1u))
> + { /* x < -7.52575 */
> + if (ax > (0xffu << 23))
> + return x + x; /* nan */
> + return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
> + }
Ok.
> + else if (__glibc_unlikely (ax > 0x421a209au))
> + { /* x > 38.5318 */
> + if (ax >= asuint (INFINITY))
> + return x + x; /* +Inf or NaN */
> + return __math_oflowf (0);
> + }
Ok.
> + else if (__glibc_unlikely (ax < 0x3d89c604u))
> + { /* |x| < 0.1549/log(10) */
> + double z2 = z * z, r;
> + if (__glibc_unlikely (ax < 0x3d1622fbu))
> + { /* |x| < 8.44e-2/log(10) */
> + if (__glibc_unlikely (ax < 0x3c8b76a3u))
> + { /* |x| < 3.92e-2/log(10) */
> + if (__glibc_unlikely (ax < 0x3bcced04u))
> + { /* |x| < 1.44e-2/log(10) */
> + if (__glibc_unlikely (ax < 0x3acf33ebu))
> + { /* |x| < 3.64e-3/log(10 */
> + if (__glibc_unlikely (ax < 0x395a966bu))
> + { /* |x| < 4.8e-4/log(10 */
> + if (__glibc_unlikely (ax < 0x36fe4a4bu))
> + { /* |x| < 1.745e-5/log(10) */
> + if (__glibc_unlikely (ax < 0x32407f39u))
> + { /* |x| < 2.58e-8/log(10) */
> + if (__glibc_unlikely (ax < 0x245e5bd9u))
> + { /* |x| < 4.82164e-17 */
> + r = 0x1.26bb1bbb55516p+1;
> + }
> + else
> + {
> + if (__glibc_unlikely (ux == 0x2c994b7bu))
> + return 0x1.60f974p-37f - 0x1p-90f;
> + r = 0x1.26bb1bbb55516p+1
> + + z * 0x1.53524c73cea69p+1;
> + }
> + }
> + else
> + {
> + if (__glibc_unlikely (ux == 0xb6fa215bu))
> + return -0x1.1ff87ep-16 + 0x1p-68;
> + r = 0x1.26bb1bbb55516p+1
> + + z * (0x1.53524c73ea62fp+1
> + + z * 0x1.0470591de2c75p+1);
> + }
> + }
> + else
> + {
> + static const double cp[] =
> + {
> + 0x1.26bb1bbb55515p+1, 0x1.53524c73cea69p+1,
> + 0x1.0470595038cc2p+1, 0x1.2bd7609fe1561p+0
> + };
> + r = (cp[0] + z * cp[1])
> + + z2 * (cp[2] + z * cp[3]);
> + }
> + }
> + else
> + {
> + static const double cp[] =
> + {
> + 0x1.26bb1bbb55516p+1, 0x1.53524c73ce6dbp+1,
> + 0x1.0470591de3024p+1, 0x1.2bd76b79060e6p+0,
> + 0x1.1429ffd3a963dp-1
> + };
> + r = (cp[0] + z * cp[1])
> + + z2 * (cp[2] + z * (cp[3] + z * cp[4]));
> + }
> + }
> + else
> + {
> + static const double cp[] =
> + {
> + 0x1.26bb1bbb55516p+1, 0x1.53524c73cea67p+1,
> + 0x1.0470591dc2953p+1, 0x1.2bd760a004d64p+0,
> + 0x1.142a85da6f072p-1, 0x1.a7ed70725b00ep-3
> + };
> + r = (cp[0] + z * cp[1]) + z2
> + * ((cp[2] + z * cp[3])
> + + z2 * (cp[4] + z * cp[5]));
> + }
> + }
> + else
> + {
> + static const double cp[] =
> + {
> + 0x1.26bb1bbb55516p+1, 0x1.53524c73ceadep+1,
> + 0x1.0470591de2bb4p+1, 0x1.2bd76099a9d33p+0,
> + 0x1.1429ffd829b0bp-1, 0x1.a7f2a6a0f7dc8p-3,
> + 0x1.16e4dfbce0f56p-4
> + };
> + r = (cp[0] + z * cp[1])
> + + z2 * ((cp[2] + z * cp[3])
> + + z2 * (cp[4] + z * (cp[5] + z * cp[6])));
> + }
> + }
> + else
> + {
> + static const double cp[] =
> + {
> + 0x1.26bb1bbb55515p+1, 0x1.53524c73cea6ap+1,
> + 0x1.0470591de476p+1, 0x1.2bd7609fd4ee2p+0,
> + 0x1.1429ff70a9b48p-1, 0x1.a7ed71259ba5bp-3,
> + 0x1.16f3004fb3ac1p-4, 0x1.4116b0388aa9fp-6
> + };
> + r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
> + + (z2 * z2) * ((cp[4] + z * cp[5]) + z2 * (cp[6]
> + + z * cp[7]));
> + }
> + }
> + else
> + {
> + static const double cp[] =
> + {
> + 0x1.26bb1bbb55515p+1, 0x1.53524c73cea42p+1, 0x1.0470591de2d1dp+1,
> + 0x1.2bd760a010a53p+0, 0x1.1429ffd16170cp-1, 0x1.a7ed6b2a0d97fp-3,
> + 0x1.16e4e37fa51e4p-4, 0x1.4147fe4c1676fp-6, 0x1.4897c4b3e329ap-8
> + };
> + r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
> + + (z2 * z2) * ((cp[4] + z * cp[5])
> + + z2 * (cp[6] + z * (cp[7] + z * cp[8])));
> + }
> + r *= z;
> + return r;
> + }
I'm not a fan of having 99% of the code be in a hugely nested "else"
clause, but I assume the upstream code is the same way. Better would be
to keep each block of code near its conditional by inverting the
conditionals, assuming performance isn't affected by it.
Not a blocker though, just hard to understand.
> + else
> + {
> + /* -7.52575 < x < -0.1549/log(10) or 0.1549/log(10) < x < 38.5318 */
> + static const double tb[] =
> + {
> + 0x1p+0, 0x1.0b5586cf9890fp+0, 0x1.172b83c7d517bp+0,
> + 0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0, 0x1.3dea64c123422p+0,
> + 0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0, 0x1.6a09e667f3bcdp+0,
> + 0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0, 0x1.9c49182a3f09p+0,
> + 0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0, 0x1.d5818dcfba487p+0,
> + 0x1.ea4afa2a490dap+0
> + };
> + static const double c[] =
> + {
> + 0x1.62e42fefa398bp-5, 0x1.ebfbdff84555ap-11, 0x1.c6b08d4ad86d3p-17,
> + 0x1.3b2ad1b1716a2p-23, 0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
> + };
> +
> + if (__glibc_unlikely ((ux << 11) == 0))
> + {
> + uint32_t k = (ux >> 21) - 0x1fc;
> + if (k <= 0xb)
> + {
> + if (k == 0)
> + return 10.0f - 1.0f;
> + if (k == 4)
> + return 100.0f - 1.0f;
> + if (k == 6)
> + return 1000.0f - 1.0f;
> + if (k == 8)
> + return 10000.0f - 1.0f;
> + if (k == 9)
> + return 100000.0f - 1.0f;
> + if (k == 10)
> + return 1000000.0f - 1.0f;
> + if (k == 11)
> + return 10000000.0f - 1.0f;
> + }
> + }
Ok.
> + double a = iln10h * z;
> + double ia = floor (a);
> + double h = (a - ia) + iln10l * z;
> + int64_t i = ia;
> + int64_t j = i & 0xf;
> + int64_t e = i - j;
> + e >>= 4;
> + double s = tb[j];
> + s *= asdouble ((e + 0x3ffull) << 52);
> + double h2 = h * h;
> + double c0 = c[0] + h * c[1];
> + double c2 = c[2] + h * c[3];
> + double c4 = c[4] + h * c[5];
> + c0 += h2 * (c2 + h2 * c4);
> + double w = s * h;
> + return (s - 1.0) + w * c0;
> + }
> +}
> +libm_alias_float (__exp10m1, exp10m1)
Ok.
> diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
> diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
> diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps
> diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
> diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
> diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps
> diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
Ok.
> index 4adad138b0..2271e1ee6c 100644
> --- a/sysdeps/riscv/nofpu/libm-test-ulps
> +++ b/sysdeps/riscv/nofpu/libm-test-ulps
> @@ -974,7 +974,6 @@ ldouble: 3
>
> Function: "exp10m1":
> double: 2
> -float: 1
> ldouble: 1
>
> Function: "exp2":
The others are missing?
> diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
> diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
> diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
> diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
Ok.
On 29/10/24 18:09, DJ Delorie wrote:
>
> A few questions but I suspect they're easily answered. LGTM with
> reasonable answers. I'll elide the same questions in the other patches
> in this series with the assumption that the same answers apply ;-)
>
> Reviewed-by: DJ Delorie <dj@redhat.com>
>
> Adhemerval Zanella <adhemerval.zanella@linaro.org> writes:
>> diff --git a/SHARED-FILES b/SHARED-FILES
>> +sysdeps/ieee754/flt-32/s_exp10m1f.c
>> + (file src/binary32/exp10m1/exp10m1f.c in CORE_MATH)
>
> I notice this file references the CORE MATH project (is it CORE_MATH or
> CORE-MATH? The file is inconsistent) but doesn't provide an URL to the
> project; such a link would be appreciated in a future patch :-)
It is CORE-MATH, I will fix it. And I will send patch to add a proper
link to the project.
>
>> diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
>> index 8c333fcd29..00832393f6 100644
>> --- a/sysdeps/aarch64/libm-test-ulps
>> +++ b/sysdeps/aarch64/libm-test-ulps
>> @@ -1083,22 +1083,18 @@ ldouble: 3
>>
>> Function: "exp10m1":
>> double: 4
>> -float: 2
>> ldouble: 3
>
> Does this mean "we're not testing it any more" or "we expect zero ULPs
> and verify that" ? I don't see any ": 0" in any of the ulps files so I
> assume the latter.
The former, we are expecting a correctly rounded implementation for the
inputs we test.
>
>> Function: "exp10m1_downward":
>> double: 3
>> -float: 3
>> ldouble: 6
>>
>> Function: "exp10m1_towardzero":
>> double: 2
>> -float: 3
>> ldouble: 6
>>
>> Function: "exp10m1_upward":
>> double: 5
>> -float: 3
>> ldouble: 6
>>
>> Function: "exp2":
>> diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
>> index d1665b9b72..ad4ae4c632 100644
>> --- a/sysdeps/arc/fpu/libm-test-ulps
>> +++ b/sysdeps/arc/fpu/libm-test-ulps
>> @@ -789,7 +789,6 @@ float: 1
>>
>> Function: "exp10m1":
>> double: 4
>> -float: 2
>>
>> Function: "exp10m1_downward":
>> double: 3
>
> The other roundings still have ULPs?
I should, since arc uses the generic implementation. I missed these entries,
thank for spotting it.
>
>> diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
>> index e768024eb5..4cecea6919 100644
>> --- a/sysdeps/arc/nofpu/libm-test-ulps
>> +++ b/sysdeps/arc/nofpu/libm-test-ulps
>> @@ -194,7 +194,6 @@ float: 1
>>
>> Function: "exp10m1":
>> double: 3
>> -float: 2
>>
>> Function: "exp2":
>> double: 1
>
> Likewise here.
This is different because usually for soft-fp and for some hard-fp as well,
only one rounding mode is support. For such cases, there is no symbol_rounding
entries.
>
>> diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
>> diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
>> diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
>> diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
>
> Ok.
>
>> diff --git a/sysdeps/ieee754/flt-32/s_exp10m1f.c b/sysdeps/ieee754/flt-32/s_exp10m1f.c
>> new file mode 100644
>> index 0000000000..610f269b01
>> --- /dev/null
>> +++ b/sysdeps/ieee754/flt-32/s_exp10m1f.c
>> @@ -0,0 +1,225 @@
>> +/* Implementation of the exp10m1 function for binary32.
>> +
>> +Copyright (c) 2022-2024 Alexei Sibidanov. Paul Zimmermann.
>> +
>> +The original version of this file was copied from the CORE-MATH
>> +project (file src/binary32/exp10m1/exp10m1f.c, revision d680516).
>> +
>> +Permission is hereby granted, free of charge, to any person obtaining a copy
>> +of this software and associated documentation files (the "Software"), to deal
>> +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 <math.h>
>> +#include "math_config.h"
>> +#include <libm-alias-float.h>
>
> Ok.
>
>> +float
>> +__exp10m1f (float x)
>> +{
>> + const double iln10h = 0x1.a934f09p+1 * 16;
>> + const double iln10l = 0x1.e68dc57f2496p-29 * 16;
>> + double z = x;
>> + uint32_t ux = asuint (x);
>> + uint32_t ax = ux & (~0u >> 1);
>> + if (__glibc_unlikely (ux > 0xc0f0d2f1u))
>> + { /* x < -7.52575 */
>> + if (ax > (0xffu << 23))
>> + return x + x; /* nan */
>> + return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
>> + }
>
> Ok.
>
>> + else if (__glibc_unlikely (ax > 0x421a209au))
>> + { /* x > 38.5318 */
>> + if (ax >= asuint (INFINITY))
>> + return x + x; /* +Inf or NaN */
>> + return __math_oflowf (0);
>> + }
>
> Ok.
>
>> + else if (__glibc_unlikely (ax < 0x3d89c604u))
>> + { /* |x| < 0.1549/log(10) */
>> + double z2 = z * z, r;
>> + if (__glibc_unlikely (ax < 0x3d1622fbu))
>> + { /* |x| < 8.44e-2/log(10) */
>> + if (__glibc_unlikely (ax < 0x3c8b76a3u))
>> + { /* |x| < 3.92e-2/log(10) */
>> + if (__glibc_unlikely (ax < 0x3bcced04u))
>> + { /* |x| < 1.44e-2/log(10) */
>> + if (__glibc_unlikely (ax < 0x3acf33ebu))
>> + { /* |x| < 3.64e-3/log(10 */
>> + if (__glibc_unlikely (ax < 0x395a966bu))
>> + { /* |x| < 4.8e-4/log(10 */
>> + if (__glibc_unlikely (ax < 0x36fe4a4bu))
>> + { /* |x| < 1.745e-5/log(10) */
>> + if (__glibc_unlikely (ax < 0x32407f39u))
>> + { /* |x| < 2.58e-8/log(10) */
>> + if (__glibc_unlikely (ax < 0x245e5bd9u))
>> + { /* |x| < 4.82164e-17 */
>> + r = 0x1.26bb1bbb55516p+1;
>> + }
>> + else
>> + {
>> + if (__glibc_unlikely (ux == 0x2c994b7bu))
>> + return 0x1.60f974p-37f - 0x1p-90f;
>> + r = 0x1.26bb1bbb55516p+1
>> + + z * 0x1.53524c73cea69p+1;
>> + }
>> + }
>> + else
>> + {
>> + if (__glibc_unlikely (ux == 0xb6fa215bu))
>> + return -0x1.1ff87ep-16 + 0x1p-68;
>> + r = 0x1.26bb1bbb55516p+1
>> + + z * (0x1.53524c73ea62fp+1
>> + + z * 0x1.0470591de2c75p+1);
>> + }
>> + }
>> + else
>> + {
>> + static const double cp[] =
>> + {
>> + 0x1.26bb1bbb55515p+1, 0x1.53524c73cea69p+1,
>> + 0x1.0470595038cc2p+1, 0x1.2bd7609fe1561p+0
>> + };
>> + r = (cp[0] + z * cp[1])
>> + + z2 * (cp[2] + z * cp[3]);
>> + }
>> + }
>> + else
>> + {
>> + static const double cp[] =
>> + {
>> + 0x1.26bb1bbb55516p+1, 0x1.53524c73ce6dbp+1,
>> + 0x1.0470591de3024p+1, 0x1.2bd76b79060e6p+0,
>> + 0x1.1429ffd3a963dp-1
>> + };
>> + r = (cp[0] + z * cp[1])
>> + + z2 * (cp[2] + z * (cp[3] + z * cp[4]));
>> + }
>> + }
>> + else
>> + {
>> + static const double cp[] =
>> + {
>> + 0x1.26bb1bbb55516p+1, 0x1.53524c73cea67p+1,
>> + 0x1.0470591dc2953p+1, 0x1.2bd760a004d64p+0,
>> + 0x1.142a85da6f072p-1, 0x1.a7ed70725b00ep-3
>> + };
>> + r = (cp[0] + z * cp[1]) + z2
>> + * ((cp[2] + z * cp[3])
>> + + z2 * (cp[4] + z * cp[5]));
>> + }
>> + }
>> + else
>> + {
>> + static const double cp[] =
>> + {
>> + 0x1.26bb1bbb55516p+1, 0x1.53524c73ceadep+1,
>> + 0x1.0470591de2bb4p+1, 0x1.2bd76099a9d33p+0,
>> + 0x1.1429ffd829b0bp-1, 0x1.a7f2a6a0f7dc8p-3,
>> + 0x1.16e4dfbce0f56p-4
>> + };
>> + r = (cp[0] + z * cp[1])
>> + + z2 * ((cp[2] + z * cp[3])
>> + + z2 * (cp[4] + z * (cp[5] + z * cp[6])));
>> + }
>> + }
>> + else
>> + {
>> + static const double cp[] =
>> + {
>> + 0x1.26bb1bbb55515p+1, 0x1.53524c73cea6ap+1,
>> + 0x1.0470591de476p+1, 0x1.2bd7609fd4ee2p+0,
>> + 0x1.1429ff70a9b48p-1, 0x1.a7ed71259ba5bp-3,
>> + 0x1.16f3004fb3ac1p-4, 0x1.4116b0388aa9fp-6
>> + };
>> + r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
>> + + (z2 * z2) * ((cp[4] + z * cp[5]) + z2 * (cp[6]
>> + + z * cp[7]));
>> + }
>> + }
>> + else
>> + {
>> + static const double cp[] =
>> + {
>> + 0x1.26bb1bbb55515p+1, 0x1.53524c73cea42p+1, 0x1.0470591de2d1dp+1,
>> + 0x1.2bd760a010a53p+0, 0x1.1429ffd16170cp-1, 0x1.a7ed6b2a0d97fp-3,
>> + 0x1.16e4e37fa51e4p-4, 0x1.4147fe4c1676fp-6, 0x1.4897c4b3e329ap-8
>> + };
>> + r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
>> + + (z2 * z2) * ((cp[4] + z * cp[5])
>> + + z2 * (cp[6] + z * (cp[7] + z * cp[8])));
>> + }
>> + r *= z;
>> + return r;
>> + }
>
> I'm not a fan of having 99% of the code be in a hugely nested "else"
> clause, but I assume the upstream code is the same way. Better would be
> to keep each block of code near its conditional by inverting the
> conditionals, assuming performance isn't affected by it.
>
> Not a blocker though, just hard to understand.
Me neither, but in this case I did not change the original code (just
use glibc code style). I will check with Paul if a code restructuring
would be worth.
>
>> + else
>> + {
>> + /* -7.52575 < x < -0.1549/log(10) or 0.1549/log(10) < x < 38.5318 */
>> + static const double tb[] =
>> + {
>> + 0x1p+0, 0x1.0b5586cf9890fp+0, 0x1.172b83c7d517bp+0,
>> + 0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0, 0x1.3dea64c123422p+0,
>> + 0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0, 0x1.6a09e667f3bcdp+0,
>> + 0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0, 0x1.9c49182a3f09p+0,
>> + 0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0, 0x1.d5818dcfba487p+0,
>> + 0x1.ea4afa2a490dap+0
>> + };
>> + static const double c[] =
>> + {
>> + 0x1.62e42fefa398bp-5, 0x1.ebfbdff84555ap-11, 0x1.c6b08d4ad86d3p-17,
>> + 0x1.3b2ad1b1716a2p-23, 0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
>> + };
>> +
>> + if (__glibc_unlikely ((ux << 11) == 0))
>> + {
>> + uint32_t k = (ux >> 21) - 0x1fc;
>> + if (k <= 0xb)
>> + {
>> + if (k == 0)
>> + return 10.0f - 1.0f;
>> + if (k == 4)
>> + return 100.0f - 1.0f;
>> + if (k == 6)
>> + return 1000.0f - 1.0f;
>> + if (k == 8)
>> + return 10000.0f - 1.0f;
>> + if (k == 9)
>> + return 100000.0f - 1.0f;
>> + if (k == 10)
>> + return 1000000.0f - 1.0f;
>> + if (k == 11)
>> + return 10000000.0f - 1.0f;
>> + }
>> + }
>
> Ok.
>
>> + double a = iln10h * z;
>> + double ia = floor (a);
>> + double h = (a - ia) + iln10l * z;
>> + int64_t i = ia;
>> + int64_t j = i & 0xf;
>> + int64_t e = i - j;
>> + e >>= 4;
>> + double s = tb[j];
>> + s *= asdouble ((e + 0x3ffull) << 52);
>> + double h2 = h * h;
>> + double c0 = c[0] + h * c[1];
>> + double c2 = c[2] + h * c[3];
>> + double c4 = c[4] + h * c[5];
>> + c0 += h2 * (c2 + h2 * c4);
>> + double w = s * h;
>> + return (s - 1.0) + w * c0;
>> + }
>> +}
>> +libm_alias_float (__exp10m1, exp10m1)
>
> Ok.
>
>> diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
>> diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps
>> diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps
>> diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
>> diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
>> diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps
>> diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
>
> Ok.
>
>> index 4adad138b0..2271e1ee6c 100644
>> --- a/sysdeps/riscv/nofpu/libm-test-ulps
>> +++ b/sysdeps/riscv/nofpu/libm-test-ulps
>> @@ -974,7 +974,6 @@ ldouble: 3
>>
>> Function: "exp10m1":
>> double: 2
>> -float: 1
>> ldouble: 1
>>
>> Function: "exp2":
>
> The others are missing?
Same case for arc-nofpu, riscv softfp only has support for one rounding.
>
>> diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
>> diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
>> diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
>> diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
>
> Ok.
>
Hi,
> >> Function: "exp10m1":
> >> double: 4
> >> -float: 2
> >> ldouble: 3
> >
> > Does this mean "we're not testing it any more" or "we expect zero ULPs
> > and verify that" ? I don't see any ": 0" in any of the ulps files so I
> > assume the latter.
>
> The former, we are expecting a correctly rounded implementation for the
> inputs we test.
I guess Adhemerval meant the latter: the CORE-MATH code should be correctly
rounded for all inputs (and all rounding modes).
Paul
On 04/11/24 07:37, Paul Zimmermann wrote:
> Hi,
>
>>>> Function: "exp10m1":
>>>> double: 4
>>>> -float: 2
>>>> ldouble: 3
>>>
>>> Does this mean "we're not testing it any more" or "we expect zero ULPs
>>> and verify that" ? I don't see any ": 0" in any of the ulps files so I
>>> assume the latter.
>>
>> The former, we are expecting a correctly rounded implementation for the
>> inputs we test.
>
> I guess Adhemerval meant the latter: the CORE-MATH code should be correctly
> rounded for all inputs (and all rounding modes).
>
> Paul
Yes, the latter. An non-existent entry for the type means a correctly rounded
implementation.
* Adhemerval Zanella:
> The CORE-MATH implementation is correctly rounded (for any rounding mode)
> and shows better performance compared to the generic exp10m1f.
When compiled with GCC 11, it's not correctly rounded on x86-64 (both
current AMD and Intel CPUs, with and without FMA):
Failure: Test: exp10m1_towardzero (-0x1.1p+4)
Result:
is: -1.00000000e+00 -0x1.000000p+0
should be: -9.99999940e-01 -0x1.fffffep-1
difference: 5.96046447e-08 0x1.000000p-24
ulp : 1.0000
max.ulp : 0.0000
I don't see this with GCC 14.
Any suggestions how to debug this further?
Thanks,
Florian
Hi Florian,
there was a missing 'f' suffix:
--- a/sysdeps/ieee754/flt-32/s_exp10m1f.c
+++ b/sysdeps/ieee754/flt-32/s_exp10m1f.c
@@ -40,7 +40,7 @@ __exp10m1f (float x)
{ /* x < -7.52575 */
if (ax > (0xffu << 23))
return x + x; /* nan */
- return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
+ return (ux == 0xff800000) ? -0x1p+0f : -0x1p+0f + 0x1p-26f;
}
else if (__glibc_unlikely (ax > 0x421a209au))
{ /* x > 38.5318 */
The same patch should be applied to exp2m1f.
Paul
> From: Florian Weimer <fweimer@redhat.com>
> Cc: libc-alpha@sourceware.org, Paul Zimmermann <Paul.Zimmermann@inria.fr>,
> Alexei Sibidanov <sibid@uvic.ca>
> Date: Wed, 06 Nov 2024 11:29:04 +0100
>
> * Adhemerval Zanella:
>
> > The CORE-MATH implementation is correctly rounded (for any rounding mode)
> > and shows better performance compared to the generic exp10m1f.
>
> When compiled with GCC 11, it's not correctly rounded on x86-64 (both
> current AMD and Intel CPUs, with and without FMA):
>
> Failure: Test: exp10m1_towardzero (-0x1.1p+4)
> Result:
> is: -1.00000000e+00 -0x1.000000p+0
> should be: -9.99999940e-01 -0x1.fffffep-1
> difference: 5.96046447e-08 0x1.000000p-24
> ulp : 1.0000
> max.ulp : 0.0000
>
> I don't see this with GCC 14.
>
> Any suggestions how to debug this further?
>
> Thanks,
> Florian
>
Thanks, I was about to debug this further since I haven't seen this
with gcc 12, gcc 13 or gcc 14.
I will handle this, thanks again Paul.
On 06/11/24 08:07, Paul Zimmermann wrote:
> Hi Florian,
>
> there was a missing 'f' suffix:
>
> --- a/sysdeps/ieee754/flt-32/s_exp10m1f.c
> +++ b/sysdeps/ieee754/flt-32/s_exp10m1f.c
> @@ -40,7 +40,7 @@ __exp10m1f (float x)
> { /* x < -7.52575 */
> if (ax > (0xffu << 23))
> return x + x; /* nan */
> - return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
> + return (ux == 0xff800000) ? -0x1p+0f : -0x1p+0f + 0x1p-26f;
> }
> else if (__glibc_unlikely (ax > 0x421a209au))
> { /* x > 38.5318 */
>
> The same patch should be applied to exp2m1f.
>
> Paul
>
>> From: Florian Weimer <fweimer@redhat.com>
>> Cc: libc-alpha@sourceware.org, Paul Zimmermann <Paul.Zimmermann@inria.fr>,
>> Alexei Sibidanov <sibid@uvic.ca>
>> Date: Wed, 06 Nov 2024 11:29:04 +0100
>>
>> * Adhemerval Zanella:
>>
>>> The CORE-MATH implementation is correctly rounded (for any rounding mode)
>>> and shows better performance compared to the generic exp10m1f.
>>
>> When compiled with GCC 11, it's not correctly rounded on x86-64 (both
>> current AMD and Intel CPUs, with and without FMA):
>>
>> Failure: Test: exp10m1_towardzero (-0x1.1p+4)
>> Result:
>> is: -1.00000000e+00 -0x1.000000p+0
>> should be: -9.99999940e-01 -0x1.fffffep-1
>> difference: 5.96046447e-08 0x1.000000p-24
>> ulp : 1.0000
>> max.ulp : 0.0000
>>
>> I don't see this with GCC 14.
>>
>> Any suggestions how to debug this further?
>>
>> Thanks,
>> Florian
>>
@@ -231,3 +231,7 @@ sysdeps/ieee754/flt-32/e_gammaf_r.c
- replace 0x1p127f * 0x1p127f by math_narrow_eval (x * 0x1p127f)
- replace 0x1p-127f * sgn[k&1] by math_narrow_eval (0x1p-127f * sgn[k&1])
- add libm_alias_finite (__ieee754_gammaf_r, __gammaf_r) at the end
+sysdeps/ieee754/flt-32/s_exp10m1f.c
+ (file src/binary32/exp10m1/exp10m1f.c in CORE_MATH)
+ - The code was adapted to use glibc code style and internal
+ functions to handle errno, overflow, and underflow.
@@ -1083,22 +1083,18 @@ ldouble: 3
Function: "exp10m1":
double: 4
-float: 2
ldouble: 3
Function: "exp10m1_downward":
double: 3
-float: 3
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 3
ldouble: 6
Function: "exp10m1_upward":
double: 5
-float: 3
ldouble: 6
Function: "exp2":
@@ -789,7 +789,6 @@ float: 1
Function: "exp10m1":
double: 4
-float: 2
Function: "exp10m1_downward":
double: 3
@@ -194,7 +194,6 @@ float: 1
Function: "exp10m1":
double: 3
-float: 2
Function: "exp2":
double: 1
@@ -779,19 +779,15 @@ float: 1
Function: "exp10m1":
double: 3
-float: 2
Function: "exp10m1_downward":
double: 3
-float: 3
Function: "exp10m1_towardzero":
double: 2
-float: 3
Function: "exp10m1_upward":
double: 4
-float: 4
Function: "exp2":
double: 1
@@ -798,19 +798,15 @@ float: 1
Function: "exp10m1":
double: 4
-float: 2
Function: "exp10m1_downward":
double: 3
-float: 3
Function: "exp10m1_towardzero":
double: 2
-float: 3
Function: "exp10m1_upward":
double: 5
-float: 4
Function: "exp2":
double: 1
@@ -1155,25 +1155,21 @@ ldouble: 2
Function: "exp10m1":
double: 3
-float: 1
float128: 3
ldouble: 4
Function: "exp10m1_downward":
double: 3
-float: 3
float128: 6
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 2
float128: 6
ldouble: 5
Function: "exp10m1_upward":
double: 5
-float: 3
float128: 6
ldouble: 6
@@ -1158,25 +1158,21 @@ ldouble: 2
Function: "exp10m1":
double: 3
-float: 1
float128: 3
ldouble: 4
Function: "exp10m1_downward":
double: 3
-float: 3
float128: 6
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 2
float128: 6
ldouble: 5
Function: "exp10m1_upward":
double: 5
-float: 3
float128: 6
ldouble: 6
new file mode 100644
@@ -0,0 +1,225 @@
+/* Implementation of the exp10m1 function for binary32.
+
+Copyright (c) 2022-2024 Alexei Sibidanov. Paul Zimmermann.
+
+The original version of this file was copied from the CORE-MATH
+project (file src/binary32/exp10m1/exp10m1f.c, revision d680516).
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+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 <math.h>
+#include "math_config.h"
+#include <libm-alias-float.h>
+
+float
+__exp10m1f (float x)
+{
+ const double iln10h = 0x1.a934f09p+1 * 16;
+ const double iln10l = 0x1.e68dc57f2496p-29 * 16;
+ double z = x;
+ uint32_t ux = asuint (x);
+ uint32_t ax = ux & (~0u >> 1);
+ if (__glibc_unlikely (ux > 0xc0f0d2f1u))
+ { /* x < -7.52575 */
+ if (ax > (0xffu << 23))
+ return x + x; /* nan */
+ return (ux == 0xff800000) ? -0x1p+0 : -0x1p+0 + 0x1p-26f;
+ }
+ else if (__glibc_unlikely (ax > 0x421a209au))
+ { /* x > 38.5318 */
+ if (ax >= asuint (INFINITY))
+ return x + x; /* +Inf or NaN */
+ return __math_oflowf (0);
+ }
+ else if (__glibc_unlikely (ax < 0x3d89c604u))
+ { /* |x| < 0.1549/log(10) */
+ double z2 = z * z, r;
+ if (__glibc_unlikely (ax < 0x3d1622fbu))
+ { /* |x| < 8.44e-2/log(10) */
+ if (__glibc_unlikely (ax < 0x3c8b76a3u))
+ { /* |x| < 3.92e-2/log(10) */
+ if (__glibc_unlikely (ax < 0x3bcced04u))
+ { /* |x| < 1.44e-2/log(10) */
+ if (__glibc_unlikely (ax < 0x3acf33ebu))
+ { /* |x| < 3.64e-3/log(10 */
+ if (__glibc_unlikely (ax < 0x395a966bu))
+ { /* |x| < 4.8e-4/log(10 */
+ if (__glibc_unlikely (ax < 0x36fe4a4bu))
+ { /* |x| < 1.745e-5/log(10) */
+ if (__glibc_unlikely (ax < 0x32407f39u))
+ { /* |x| < 2.58e-8/log(10) */
+ if (__glibc_unlikely (ax < 0x245e5bd9u))
+ { /* |x| < 4.82164e-17 */
+ r = 0x1.26bb1bbb55516p+1;
+ }
+ else
+ {
+ if (__glibc_unlikely (ux == 0x2c994b7bu))
+ return 0x1.60f974p-37f - 0x1p-90f;
+ r = 0x1.26bb1bbb55516p+1
+ + z * 0x1.53524c73cea69p+1;
+ }
+ }
+ else
+ {
+ if (__glibc_unlikely (ux == 0xb6fa215bu))
+ return -0x1.1ff87ep-16 + 0x1p-68;
+ r = 0x1.26bb1bbb55516p+1
+ + z * (0x1.53524c73ea62fp+1
+ + z * 0x1.0470591de2c75p+1);
+ }
+ }
+ else
+ {
+ static const double cp[] =
+ {
+ 0x1.26bb1bbb55515p+1, 0x1.53524c73cea69p+1,
+ 0x1.0470595038cc2p+1, 0x1.2bd7609fe1561p+0
+ };
+ r = (cp[0] + z * cp[1])
+ + z2 * (cp[2] + z * cp[3]);
+ }
+ }
+ else
+ {
+ static const double cp[] =
+ {
+ 0x1.26bb1bbb55516p+1, 0x1.53524c73ce6dbp+1,
+ 0x1.0470591de3024p+1, 0x1.2bd76b79060e6p+0,
+ 0x1.1429ffd3a963dp-1
+ };
+ r = (cp[0] + z * cp[1])
+ + z2 * (cp[2] + z * (cp[3] + z * cp[4]));
+ }
+ }
+ else
+ {
+ static const double cp[] =
+ {
+ 0x1.26bb1bbb55516p+1, 0x1.53524c73cea67p+1,
+ 0x1.0470591dc2953p+1, 0x1.2bd760a004d64p+0,
+ 0x1.142a85da6f072p-1, 0x1.a7ed70725b00ep-3
+ };
+ r = (cp[0] + z * cp[1]) + z2
+ * ((cp[2] + z * cp[3])
+ + z2 * (cp[4] + z * cp[5]));
+ }
+ }
+ else
+ {
+ static const double cp[] =
+ {
+ 0x1.26bb1bbb55516p+1, 0x1.53524c73ceadep+1,
+ 0x1.0470591de2bb4p+1, 0x1.2bd76099a9d33p+0,
+ 0x1.1429ffd829b0bp-1, 0x1.a7f2a6a0f7dc8p-3,
+ 0x1.16e4dfbce0f56p-4
+ };
+ r = (cp[0] + z * cp[1])
+ + z2 * ((cp[2] + z * cp[3])
+ + z2 * (cp[4] + z * (cp[5] + z * cp[6])));
+ }
+ }
+ else
+ {
+ static const double cp[] =
+ {
+ 0x1.26bb1bbb55515p+1, 0x1.53524c73cea6ap+1,
+ 0x1.0470591de476p+1, 0x1.2bd7609fd4ee2p+0,
+ 0x1.1429ff70a9b48p-1, 0x1.a7ed71259ba5bp-3,
+ 0x1.16f3004fb3ac1p-4, 0x1.4116b0388aa9fp-6
+ };
+ r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
+ + (z2 * z2) * ((cp[4] + z * cp[5]) + z2 * (cp[6]
+ + z * cp[7]));
+ }
+ }
+ else
+ {
+ static const double cp[] =
+ {
+ 0x1.26bb1bbb55515p+1, 0x1.53524c73cea42p+1, 0x1.0470591de2d1dp+1,
+ 0x1.2bd760a010a53p+0, 0x1.1429ffd16170cp-1, 0x1.a7ed6b2a0d97fp-3,
+ 0x1.16e4e37fa51e4p-4, 0x1.4147fe4c1676fp-6, 0x1.4897c4b3e329ap-8
+ };
+ r = ((cp[0] + z * cp[1]) + z2 * (cp[2] + z * cp[3]))
+ + (z2 * z2) * ((cp[4] + z * cp[5])
+ + z2 * (cp[6] + z * (cp[7] + z * cp[8])));
+ }
+ r *= z;
+ return r;
+ }
+ else
+ {
+ /* -7.52575 < x < -0.1549/log(10) or 0.1549/log(10) < x < 38.5318 */
+ static const double tb[] =
+ {
+ 0x1p+0, 0x1.0b5586cf9890fp+0, 0x1.172b83c7d517bp+0,
+ 0x1.2387a6e756238p+0, 0x1.306fe0a31b715p+0, 0x1.3dea64c123422p+0,
+ 0x1.4bfdad5362a27p+0, 0x1.5ab07dd485429p+0, 0x1.6a09e667f3bcdp+0,
+ 0x1.7a11473eb0187p+0, 0x1.8ace5422aa0dap+0, 0x1.9c49182a3f09p+0,
+ 0x1.ae89f995ad3adp+0, 0x1.c199bdd85529cp+0, 0x1.d5818dcfba487p+0,
+ 0x1.ea4afa2a490dap+0
+ };
+ static const double c[] =
+ {
+ 0x1.62e42fefa398bp-5, 0x1.ebfbdff84555ap-11, 0x1.c6b08d4ad86d3p-17,
+ 0x1.3b2ad1b1716a2p-23, 0x1.5d7472718ce9dp-30, 0x1.4a1d7f457ac56p-37
+ };
+
+ if (__glibc_unlikely ((ux << 11) == 0))
+ {
+ uint32_t k = (ux >> 21) - 0x1fc;
+ if (k <= 0xb)
+ {
+ if (k == 0)
+ return 10.0f - 1.0f;
+ if (k == 4)
+ return 100.0f - 1.0f;
+ if (k == 6)
+ return 1000.0f - 1.0f;
+ if (k == 8)
+ return 10000.0f - 1.0f;
+ if (k == 9)
+ return 100000.0f - 1.0f;
+ if (k == 10)
+ return 1000000.0f - 1.0f;
+ if (k == 11)
+ return 10000000.0f - 1.0f;
+ }
+ }
+ double a = iln10h * z;
+ double ia = floor (a);
+ double h = (a - ia) + iln10l * z;
+ int64_t i = ia;
+ int64_t j = i & 0xf;
+ int64_t e = i - j;
+ e >>= 4;
+ double s = tb[j];
+ s *= asdouble ((e + 0x3ffull) << 52);
+ double h2 = h * h;
+ double c0 = c[0] + h * c[1];
+ double c2 = c[2] + h * c[3];
+ double c4 = c[4] + h * c[5];
+ c0 += h2 * (c2 + h2 * c4);
+ double w = s * h;
+ return (s - 1.0) + w * c0;
+ }
+}
+libm_alias_float (__exp10m1, exp10m1)
@@ -977,22 +977,18 @@ ldouble: 3
Function: "exp10m1":
double: 4
-float: 2
ldouble: 3
Function: "exp10m1_downward":
double: 3
-float: 3
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 3
ldouble: 6
Function: "exp10m1_upward":
double: 5
-float: 3
ldouble: 6
Function: "exp2":
@@ -882,19 +882,15 @@ ldouble: 3
Function: "exp10m1":
double: 1
-float: 1
Function: "exp10m1_downward":
double: 1
-float: 1
Function: "exp10m1_towardzero":
double: 1
-float: 1
Function: "exp10m1_upward":
double: 3
-float: 1
Function: "exp2":
double: 1
@@ -779,19 +779,15 @@ float: 1
Function: "exp10m1":
double: 3
-float: 2
Function: "exp10m1_downward":
double: 3
-float: 3
Function: "exp10m1_towardzero":
double: 2
-float: 3
Function: "exp10m1_upward":
double: 4
-float: 4
Function: "exp2":
double: 1
@@ -978,22 +978,18 @@ ldouble: 3
Function: "exp10m1":
double: 3
-float: 2
ldouble: 3
Function: "exp10m1_downward":
double: 3
-float: 3
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 3
ldouble: 6
Function: "exp10m1_upward":
double: 4
-float: 4
ldouble: 6
Function: "exp2":
@@ -1186,25 +1186,21 @@ ldouble: 4
Function: "exp10m1":
double: 4
-float: 2
float128: 3
ldouble: 4
Function: "exp10m1_downward":
double: 3
-float: 3
float128: 6
ldouble: 9
Function: "exp10m1_towardzero":
double: 2
-float: 3
float128: 6
ldouble: 9
Function: "exp10m1_upward":
double: 5
-float: 3
float128: 6
ldouble: 8
@@ -987,22 +987,18 @@ ldouble: 4
Function: "exp10m1":
double: 3
-float: 2
ldouble: 3
Function: "exp10m1_downward":
double: 3
-float: 3
ldouble: 9
Function: "exp10m1_towardzero":
double: 2
-float: 3
ldouble: 9
Function: "exp10m1_upward":
double: 4
-float: 4
ldouble: 10
Function: "exp2":
@@ -974,7 +974,6 @@ ldouble: 3
Function: "exp10m1":
double: 2
-float: 1
ldouble: 1
Function: "exp2":
@@ -977,22 +977,18 @@ ldouble: 3
Function: "exp10m1":
double: 4
-float: 2
ldouble: 3
Function: "exp10m1_downward":
double: 3
-float: 3
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 3
ldouble: 6
Function: "exp10m1_upward":
double: 5
-float: 3
ldouble: 6
Function: "exp2":
@@ -978,22 +978,18 @@ ldouble: 3
Function: "exp10m1":
double: 4
-float: 2
ldouble: 3
Function: "exp10m1_downward":
double: 3
-float: 3
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 3
ldouble: 6
Function: "exp10m1_upward":
double: 5
-float: 3
ldouble: 6
Function: "exp2":
@@ -978,22 +978,18 @@ ldouble: 3
Function: "exp10m1":
double: 3
-float: 2
ldouble: 3
Function: "exp10m1_downward":
double: 3
-float: 3
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 3
ldouble: 6
Function: "exp10m1_upward":
double: 4
-float: 4
ldouble: 6
Function: "exp2":
@@ -1431,25 +1431,21 @@ float: 1
Function: "exp10m1":
double: 4
-float: 2
float128: 3
ldouble: 4
Function: "exp10m1_downward":
double: 3
-float: 3
float128: 6
ldouble: 6
Function: "exp10m1_towardzero":
double: 2
-float: 3
float128: 6
ldouble: 5
Function: "exp10m1_upward":
double: 5
-float: 4
float128: 6
ldouble: 6