[12/15] math: Use cospif from CORE-MATH
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Commit Message
The CORE-MATH implementation is correctly rounded (for any rounding mode)
and shows better performance to the generic cospif.
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 47.4679 38.4157 19.07%
x86_64v2 46.9686 38.3329 18.39%
x86_64v3 43.8929 31.8510 27.43%
aarch64 (Neoverse) 18.8867 13.2089 30.06%
power8 22.9435 7.8023 65.99%
power10 15.4472 7.77505 49.67%
reciprocal-throughput master patched improvement
x86_64 20.9518 11.4991 45.12%
x86_64v2 19.8699 10.5921 46.69%
x86_64v3 19.3475 9.3998 51.42%
aarch64 (Neoverse) 12.5767 6.2158 50.58%
power8 15.0566 3.2654 78.31%
power10 9.2866 3.1147 66.46%
---
SHARED-FILES | 4 +
sysdeps/aarch64/libm-test-ulps | 4 -
sysdeps/arc/fpu/libm-test-ulps | 4 -
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_cospif.c | 136 ++++++++++++++++++
sysdeps/loongarch/lp64/libm-test-ulps | 4 -
sysdeps/mips/mips64/libm-test-ulps | 4 -
sysdeps/or1k/fpu/libm-test-ulps | 4 -
sysdeps/or1k/nofpu/libm-test-ulps | 1 -
sysdeps/powerpc/fpu/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 -
19 files changed, 140 insertions(+), 59 deletions(-)
create mode 100644 sysdeps/ieee754/flt-32/s_cospif.c
Comments
I confirm all binary32 inputs yield correct rounding for all rounding modes on x86-64.
Paul
> From: Adhemerval Zanella <adhemerval.zanella@linaro.org>
> Cc: DJ Delorie <dj@redhat.com>,
> Joseph Myers <josmyers@redhat.com>,
> Paul Zimmermann <Paul.Zimmermann@inria.fr>,
> Alexei Sibidanov <sibid@uvic.ca>
> Date: Fri, 31 Jan 2025 16:17:16 -0300
>
> The CORE-MATH implementation is correctly rounded (for any rounding mode)
> and shows better performance to the generic cospif.
>
> 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 47.4679 38.4157 19.07%
> x86_64v2 46.9686 38.3329 18.39%
> x86_64v3 43.8929 31.8510 27.43%
> aarch64 (Neoverse) 18.8867 13.2089 30.06%
> power8 22.9435 7.8023 65.99%
> power10 15.4472 7.77505 49.67%
>
> reciprocal-throughput master patched improvement
> x86_64 20.9518 11.4991 45.12%
> x86_64v2 19.8699 10.5921 46.69%
> x86_64v3 19.3475 9.3998 51.42%
> aarch64 (Neoverse) 12.5767 6.2158 50.58%
> power8 15.0566 3.2654 78.31%
> power10 9.2866 3.1147 66.46%
> ---
> SHARED-FILES | 4 +
> sysdeps/aarch64/libm-test-ulps | 4 -
> sysdeps/arc/fpu/libm-test-ulps | 4 -
> 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_cospif.c | 136 ++++++++++++++++++
> sysdeps/loongarch/lp64/libm-test-ulps | 4 -
> sysdeps/mips/mips64/libm-test-ulps | 4 -
> sysdeps/or1k/fpu/libm-test-ulps | 4 -
> sysdeps/or1k/nofpu/libm-test-ulps | 1 -
> sysdeps/powerpc/fpu/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 -
> 19 files changed, 140 insertions(+), 59 deletions(-)
> create mode 100644 sysdeps/ieee754/flt-32/s_cospif.c
>
> diff --git a/SHARED-FILES b/SHARED-FILES
> index 5702a2d1c3..3ce38d1542 100644
> --- a/SHARED-FILES
> +++ b/SHARED-FILES
> @@ -350,3 +350,7 @@ sysdeps/ieee754/flt-32/s_atanpif.c:
> (src/binary32/atanpi/atanpif.c in CORE-MATH)
> - the code was adapted to use glibc code style and internal
> functions to handle errno, overflow, and underflow.
> +sysdeps/ieee754/flt-32/s_cospif.c:
> + (src/binary32/cospi/cospif.c in CORE-MATH)
> + - the code was adapted to use glibc code style and internal
> + functions to handle errno, overflow, and underflow.
> diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
> index 10f182a211..a15f3effa0 100644
> --- a/sysdeps/aarch64/libm-test-ulps
> +++ b/sysdeps/aarch64/libm-test-ulps
> @@ -782,7 +782,6 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> ldouble: 2
>
> Function: "cospi_advsimd":
> @@ -791,7 +790,6 @@ float: 1
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: "cospi_sve":
> @@ -800,12 +798,10 @@ float: 1
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: Real part of "cpow":
> diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps
> index 7fb407cecd..f2acbf453e 100644
> --- a/sysdeps/arc/fpu/libm-test-ulps
> +++ b/sysdeps/arc/fpu/libm-test-ulps
> @@ -553,19 +553,15 @@ double: 3
>
> Function: "cospi":
> double: 2
> -float: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
>
> Function: "cospi_upward":
> double: 1
> -float: 2
>
> Function: Real part of "cpow":
> double: 9
> diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps
> index 1859c2bd4f..8716e5d29e 100644
> --- a/sysdeps/arc/nofpu/libm-test-ulps
> +++ b/sysdeps/arc/nofpu/libm-test-ulps
> @@ -134,7 +134,6 @@ double: 2
>
> Function: "cospi":
> double: 2
> -float: 2
>
> Function: Real part of "cpow":
> double: 2
> diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps
> index fa9864adee..647f92944c 100644
> --- a/sysdeps/arm/libm-test-ulps
> +++ b/sysdeps/arm/libm-test-ulps
> @@ -545,19 +545,15 @@ double: 2
>
> Function: "cospi":
> double: 2
> -float: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
>
> Function: "cospi_upward":
> double: 1
> -float: 2
>
> Function: Real part of "cpow":
> double: 2
> diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps
> index a59f61fc4e..88f7701c0e 100644
> --- a/sysdeps/hppa/fpu/libm-test-ulps
> +++ b/sysdeps/hppa/fpu/libm-test-ulps
> @@ -555,19 +555,15 @@ double: 2
>
> Function: "cospi":
> double: 2
> -float: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
>
> Function: "cospi_upward":
> double: 1
> -float: 2
>
> Function: Real part of "cpow":
> double: 2
> diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
> index 8aa52f4600..39066956b0 100644
> --- a/sysdeps/i386/fpu/libm-test-ulps
> +++ b/sysdeps/i386/fpu/libm-test-ulps
> @@ -854,25 +854,21 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> float128: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> float128: 2
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 2
>
> diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
> index 8032636808..a8c4723850 100644
> --- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
> +++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps
> @@ -854,25 +854,21 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> float128: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> float128: 2
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 2
>
> diff --git a/sysdeps/ieee754/flt-32/s_cospif.c b/sysdeps/ieee754/flt-32/s_cospif.c
> new file mode 100644
> index 0000000000..d4c652f8c0
> --- /dev/null
> +++ b/sysdeps/ieee754/flt-32/s_cospif.c
> @@ -0,0 +1,136 @@
> +/* Correctly-rounded cosine of binary32 value for angles in half-revolutions
> +
> +Copyright (c) 2022-2025 Alexei Sibidanov.
> +
> +The original version of this file was copied from the CORE-MATH
> +project (src/binary32/cospi/cospif.c, revision f786e13).
> +
> +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 <stdint.h>
> +#include <libm-alias-float.h>
> +#include "math_config.h"
> +
> +float
> +__cospif (float x)
> +{
> + static const double sn[] =
> + {
> + 0x1.921fb54442d0fp-37, -0x1.4abbce6102b94p-112, 0x1.4669fa3c58463p-189
> + };
> + static const double cn[] =
> + {
> + -0x1.3bd3cc9be45cfp-74, 0x1.03c1f08088742p-150, -0x1.55d1e5eff55a5p-228
> + };
> + /* S[i] approximates sin(i*pi/2^6) */
> + static const double S[] =
> + {
> + 0x0p+0, 0x1.91f65f10dd814p-5, 0x1.917a6bc29b42cp-4,
> + 0x1.2c8106e8e613ap-3, 0x1.8f8b83c69a60bp-3, 0x1.f19f97b215f1bp-3,
> + 0x1.294062ed59f06p-2, 0x1.58f9a75ab1fddp-2, 0x1.87de2a6aea963p-2,
> + 0x1.b5d1009e15ccp-2, 0x1.e2b5d3806f63bp-2, 0x1.073879922ffeep-1,
> + 0x1.1c73b39ae68c8p-1, 0x1.30ff7fce17035p-1, 0x1.44cf325091dd6p-1,
> + 0x1.57d69348cecap-1, 0x1.6a09e667f3bcdp-1, 0x1.7b5df226aafafp-1,
> + 0x1.8bc806b151741p-1, 0x1.9b3e047f38741p-1, 0x1.a9b66290ea1a3p-1,
> + 0x1.b728345196e3ep-1, 0x1.c38b2f180bdb1p-1, 0x1.ced7af43cc773p-1,
> + 0x1.d906bcf328d46p-1, 0x1.e212104f686e5p-1, 0x1.e9f4156c62ddap-1,
> + 0x1.f0a7efb9230d7p-1, 0x1.f6297cff75cbp-1, 0x1.fa7557f08a517p-1,
> + 0x1.fd88da3d12526p-1, 0x1.ff621e3796d7ep-1, 0x1p+0,
> + 0x1.ff621e3796d7ep-1, 0x1.fd88da3d12526p-1, 0x1.fa7557f08a517p-1,
> + 0x1.f6297cff75cbp-1, 0x1.f0a7efb9230d7p-1, 0x1.e9f4156c62ddap-1,
> + 0x1.e212104f686e5p-1, 0x1.d906bcf328d46p-1, 0x1.ced7af43cc773p-1,
> + 0x1.c38b2f180bdb1p-1, 0x1.b728345196e3ep-1, 0x1.a9b66290ea1a3p-1,
> + 0x1.9b3e047f38741p-1, 0x1.8bc806b151741p-1, 0x1.7b5df226aafafp-1,
> + 0x1.6a09e667f3bcdp-1, 0x1.57d69348cecap-1, 0x1.44cf325091dd6p-1,
> + 0x1.30ff7fce17035p-1, 0x1.1c73b39ae68c8p-1, 0x1.073879922ffeep-1,
> + 0x1.e2b5d3806f63bp-2, 0x1.b5d1009e15ccp-2, 0x1.87de2a6aea963p-2,
> + 0x1.58f9a75ab1fddp-2, 0x1.294062ed59f06p-2, 0x1.f19f97b215f1bp-3,
> + 0x1.8f8b83c69a60bp-3, 0x1.2c8106e8e613ap-3, 0x1.917a6bc29b42cp-4,
> + 0x1.91f65f10dd814p-5, 0x0p+0, -0x1.91f65f10dd814p-5,
> + -0x1.917a6bc29b42cp-4, -0x1.2c8106e8e613ap-3, -0x1.8f8b83c69a60bp-3,
> + -0x1.f19f97b215f1bp-3, -0x1.294062ed59f06p-2, -0x1.58f9a75ab1fddp-2,
> + -0x1.87de2a6aea963p-2, -0x1.b5d1009e15ccp-2, -0x1.e2b5d3806f63bp-2,
> + -0x1.073879922ffeep-1, -0x1.1c73b39ae68c8p-1, -0x1.30ff7fce17035p-1,
> + -0x1.44cf325091dd6p-1, -0x1.57d69348cecap-1, -0x1.6a09e667f3bcdp-1,
> + -0x1.7b5df226aafafp-1, -0x1.8bc806b151741p-1, -0x1.9b3e047f38741p-1,
> + -0x1.a9b66290ea1a3p-1, -0x1.b728345196e3ep-1, -0x1.c38b2f180bdb1p-1,
> + -0x1.ced7af43cc773p-1, -0x1.d906bcf328d46p-1, -0x1.e212104f686e5p-1,
> + -0x1.e9f4156c62ddap-1, -0x1.f0a7efb9230d7p-1, -0x1.f6297cff75cbp-1,
> + -0x1.fa7557f08a517p-1, -0x1.fd88da3d12526p-1, -0x1.ff621e3796d7ep-1,
> + -0x1p+0, -0x1.ff621e3796d7ep-1, -0x1.fd88da3d12526p-1,
> + -0x1.fa7557f08a517p-1, -0x1.f6297cff75cbp-1, -0x1.f0a7efb9230d7p-1,
> + -0x1.e9f4156c62ddap-1, -0x1.e212104f686e5p-1, -0x1.d906bcf328d46p-1,
> + -0x1.ced7af43cc773p-1, -0x1.c38b2f180bdb1p-1, -0x1.b728345196e3ep-1,
> + -0x1.a9b66290ea1a3p-1, -0x1.9b3e047f38741p-1, -0x1.8bc806b151741p-1,
> + -0x1.7b5df226aafafp-1, -0x1.6a09e667f3bcdp-1, -0x1.57d69348cecap-1,
> + -0x1.44cf325091dd6p-1, -0x1.30ff7fce17035p-1, -0x1.1c73b39ae68c8p-1,
> + -0x1.073879922ffeep-1, -0x1.e2b5d3806f63bp-2, -0x1.b5d1009e15ccp-2,
> + -0x1.87de2a6aea963p-2, -0x1.58f9a75ab1fddp-2, -0x1.294062ed59f06p-2,
> + -0x1.f19f97b215f1bp-3, -0x1.8f8b83c69a60bp-3, -0x1.2c8106e8e613ap-3,
> + -0x1.917a6bc29b42cp-4, -0x1.91f65f10dd814p-5
> + };
> +
> + uint32_t ix = asuint (x);
> + int32_t e = (ix >> 23) & 0xff;
> + if (__glibc_unlikely (e == 0xff))
> + {
> + if (!(ix << 9))
> + return __math_invalidf (x);
> + return x + x; /* nan */
> + }
> + int32_t m = (ix & ~0u >> 9) | 1 << 23;
> + int32_t s = 143 - e;
> + int32_t p = e - 112;
> + if (__glibc_unlikely (p < 0)) /* |x| < 2^-15 */
> + {
> + uint32_t ax = ix & (~0u>>1);
> + /* Warning: -0x1.3bd3ccp+2f * x underflows for |x| < 0x1.9f03p-129 */
> + if (ax >= 0x19f030u)
> + return fmaf (-0x1.3bd3ccp+2f * x, x, 1.0f);
> + else /* |x| < 0x1.9f03p-129 */
> + return fmaf (-x, x, 1.0f);
> + }
> + if (__glibc_unlikely (p > 31))
> + {
> + if (__glibc_unlikely (p > 63))
> + return 1.0f;
> + int32_t iq = m << (p - 32);
> + return S[(iq + 32) & 127];
> + }
> + int32_t k = m << p;
> + if (__glibc_unlikely (k == 0))
> + {
> + int32_t iq = m >> (32 - p);
> + return S[(iq + 32) & 127];
> + }
> + double z = k;
> + double z2 = z * z;
> + double fs = sn[0] + z2 * (sn[1] + z2 * sn[2]);
> + double fc = cn[0] + z2 * (cn[1] + z2 * cn[2]);
> + uint32_t iq = m >> s;
> + iq = (iq + 1) >> 1;
> + uint32_t is = iq & 127, ic = (iq + 32) & 127;
> + double ts = S[ic], tc = S[is];
> + double r = ts + (ts * z2) * fc - (tc * z) * fs;
> + return r;
> +}
> +libm_alias_float (__cospi, cospi)
> diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps
> index 0cac55cbe4..fe84c60913 100644
> --- a/sysdeps/loongarch/lp64/libm-test-ulps
> +++ b/sysdeps/loongarch/lp64/libm-test-ulps
> @@ -701,22 +701,18 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: Real part of "cpow":
> diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps
> index 1b5bcff11e..ddc78d0239 100644
> --- a/sysdeps/mips/mips64/libm-test-ulps
> +++ b/sysdeps/mips/mips64/libm-test-ulps
> @@ -701,22 +701,18 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: Real part of "cpow":
> diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps
> index a608e3c949..884b4cc361 100644
> --- a/sysdeps/or1k/fpu/libm-test-ulps
> +++ b/sysdeps/or1k/fpu/libm-test-ulps
> @@ -545,19 +545,15 @@ double: 2
>
> Function: "cospi":
> double: 2
> -float: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
>
> Function: "cospi_upward":
> double: 1
> -float: 2
>
> Function: Real part of "cpow":
> double: 2
> diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps
> index 56986f0be0..aec66e0fa3 100644
> --- a/sysdeps/or1k/nofpu/libm-test-ulps
> +++ b/sysdeps/or1k/nofpu/libm-test-ulps
> @@ -509,7 +509,6 @@ double: 2
>
> Function: "cospi":
> double: 2
> -float: 2
>
> Function: Real part of "cpow":
> double: 2
> diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps
> index 630111e6c4..bdf0c98dc7 100644
> --- a/sysdeps/powerpc/fpu/libm-test-ulps
> +++ b/sysdeps/powerpc/fpu/libm-test-ulps
> @@ -858,25 +858,21 @@ ldouble: 2
>
> Function: "cospi":
> double: 2
> -float: 2
> float128: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 4
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> float128: 2
> ldouble: 6
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 6
>
> diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps
> index 087dcd79fc..08af2495f3 100644
> --- a/sysdeps/riscv/nofpu/libm-test-ulps
> +++ b/sysdeps/riscv/nofpu/libm-test-ulps
> @@ -650,7 +650,6 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> ldouble: 2
>
> Function: Real part of "cpow":
> diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps
> index efd83affa4..6644e38ebc 100644
> --- a/sysdeps/riscv/rvd/libm-test-ulps
> +++ b/sysdeps/riscv/rvd/libm-test-ulps
> @@ -709,22 +709,18 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: Real part of "cpow":
> diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps
> index 709debb205..6318760eb5 100644
> --- a/sysdeps/s390/fpu/libm-test-ulps
> +++ b/sysdeps/s390/fpu/libm-test-ulps
> @@ -701,22 +701,18 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: Real part of "cpow":
> diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps
> index becf5da3d6..2c319f8ae2 100644
> --- a/sysdeps/sparc/fpu/libm-test-ulps
> +++ b/sysdeps/sparc/fpu/libm-test-ulps
> @@ -701,22 +701,18 @@ ldouble: 3
>
> Function: "cospi":
> double: 2
> -float: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> ldouble: 2
>
> Function: Real part of "cpow":
> diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
> index 8c5d4fd471..e2cf3e04b6 100644
> --- a/sysdeps/x86_64/fpu/libm-test-ulps
> +++ b/sysdeps/x86_64/fpu/libm-test-ulps
> @@ -1050,25 +1050,21 @@ float: 2
>
> Function: "cospi":
> double: 2
> -float: 2
> float128: 2
> ldouble: 2
>
> Function: "cospi_downward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 2
>
> Function: "cospi_towardzero":
> double: 1
> -float: 1
> float128: 2
> ldouble: 2
>
> Function: "cospi_upward":
> double: 1
> -float: 2
> float128: 2
> ldouble: 2
>
> --
> 2.43.0
>
>
@@ -350,3 +350,7 @@ sysdeps/ieee754/flt-32/s_atanpif.c:
(src/binary32/atanpi/atanpif.c in CORE-MATH)
- the code was adapted to use glibc code style and internal
functions to handle errno, overflow, and underflow.
+sysdeps/ieee754/flt-32/s_cospif.c:
+ (src/binary32/cospi/cospif.c in CORE-MATH)
+ - the code was adapted to use glibc code style and internal
+ functions to handle errno, overflow, and underflow.
@@ -782,7 +782,6 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
ldouble: 2
Function: "cospi_advsimd":
@@ -791,7 +790,6 @@ float: 1
Function: "cospi_downward":
double: 1
-float: 2
ldouble: 2
Function: "cospi_sve":
@@ -800,12 +798,10 @@ float: 1
Function: "cospi_towardzero":
double: 1
-float: 1
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
ldouble: 2
Function: Real part of "cpow":
@@ -553,19 +553,15 @@ double: 3
Function: "cospi":
double: 2
-float: 2
Function: "cospi_downward":
double: 1
-float: 2
Function: "cospi_towardzero":
double: 1
-float: 1
Function: "cospi_upward":
double: 1
-float: 2
Function: Real part of "cpow":
double: 9
@@ -134,7 +134,6 @@ double: 2
Function: "cospi":
double: 2
-float: 2
Function: Real part of "cpow":
double: 2
@@ -545,19 +545,15 @@ double: 2
Function: "cospi":
double: 2
-float: 2
Function: "cospi_downward":
double: 1
-float: 2
Function: "cospi_towardzero":
double: 1
-float: 1
Function: "cospi_upward":
double: 1
-float: 2
Function: Real part of "cpow":
double: 2
@@ -555,19 +555,15 @@ double: 2
Function: "cospi":
double: 2
-float: 2
Function: "cospi_downward":
double: 1
-float: 2
Function: "cospi_towardzero":
double: 1
-float: 1
Function: "cospi_upward":
double: 1
-float: 2
Function: Real part of "cpow":
double: 2
@@ -854,25 +854,21 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
float128: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
float128: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
float128: 2
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
float128: 2
ldouble: 2
@@ -854,25 +854,21 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
float128: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
float128: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
float128: 2
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
float128: 2
ldouble: 2
new file mode 100644
@@ -0,0 +1,136 @@
+/* Correctly-rounded cosine of binary32 value for angles in half-revolutions
+
+Copyright (c) 2022-2025 Alexei Sibidanov.
+
+The original version of this file was copied from the CORE-MATH
+project (src/binary32/cospi/cospif.c, revision f786e13).
+
+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 <stdint.h>
+#include <libm-alias-float.h>
+#include "math_config.h"
+
+float
+__cospif (float x)
+{
+ static const double sn[] =
+ {
+ 0x1.921fb54442d0fp-37, -0x1.4abbce6102b94p-112, 0x1.4669fa3c58463p-189
+ };
+ static const double cn[] =
+ {
+ -0x1.3bd3cc9be45cfp-74, 0x1.03c1f08088742p-150, -0x1.55d1e5eff55a5p-228
+ };
+ /* S[i] approximates sin(i*pi/2^6) */
+ static const double S[] =
+ {
+ 0x0p+0, 0x1.91f65f10dd814p-5, 0x1.917a6bc29b42cp-4,
+ 0x1.2c8106e8e613ap-3, 0x1.8f8b83c69a60bp-3, 0x1.f19f97b215f1bp-3,
+ 0x1.294062ed59f06p-2, 0x1.58f9a75ab1fddp-2, 0x1.87de2a6aea963p-2,
+ 0x1.b5d1009e15ccp-2, 0x1.e2b5d3806f63bp-2, 0x1.073879922ffeep-1,
+ 0x1.1c73b39ae68c8p-1, 0x1.30ff7fce17035p-1, 0x1.44cf325091dd6p-1,
+ 0x1.57d69348cecap-1, 0x1.6a09e667f3bcdp-1, 0x1.7b5df226aafafp-1,
+ 0x1.8bc806b151741p-1, 0x1.9b3e047f38741p-1, 0x1.a9b66290ea1a3p-1,
+ 0x1.b728345196e3ep-1, 0x1.c38b2f180bdb1p-1, 0x1.ced7af43cc773p-1,
+ 0x1.d906bcf328d46p-1, 0x1.e212104f686e5p-1, 0x1.e9f4156c62ddap-1,
+ 0x1.f0a7efb9230d7p-1, 0x1.f6297cff75cbp-1, 0x1.fa7557f08a517p-1,
+ 0x1.fd88da3d12526p-1, 0x1.ff621e3796d7ep-1, 0x1p+0,
+ 0x1.ff621e3796d7ep-1, 0x1.fd88da3d12526p-1, 0x1.fa7557f08a517p-1,
+ 0x1.f6297cff75cbp-1, 0x1.f0a7efb9230d7p-1, 0x1.e9f4156c62ddap-1,
+ 0x1.e212104f686e5p-1, 0x1.d906bcf328d46p-1, 0x1.ced7af43cc773p-1,
+ 0x1.c38b2f180bdb1p-1, 0x1.b728345196e3ep-1, 0x1.a9b66290ea1a3p-1,
+ 0x1.9b3e047f38741p-1, 0x1.8bc806b151741p-1, 0x1.7b5df226aafafp-1,
+ 0x1.6a09e667f3bcdp-1, 0x1.57d69348cecap-1, 0x1.44cf325091dd6p-1,
+ 0x1.30ff7fce17035p-1, 0x1.1c73b39ae68c8p-1, 0x1.073879922ffeep-1,
+ 0x1.e2b5d3806f63bp-2, 0x1.b5d1009e15ccp-2, 0x1.87de2a6aea963p-2,
+ 0x1.58f9a75ab1fddp-2, 0x1.294062ed59f06p-2, 0x1.f19f97b215f1bp-3,
+ 0x1.8f8b83c69a60bp-3, 0x1.2c8106e8e613ap-3, 0x1.917a6bc29b42cp-4,
+ 0x1.91f65f10dd814p-5, 0x0p+0, -0x1.91f65f10dd814p-5,
+ -0x1.917a6bc29b42cp-4, -0x1.2c8106e8e613ap-3, -0x1.8f8b83c69a60bp-3,
+ -0x1.f19f97b215f1bp-3, -0x1.294062ed59f06p-2, -0x1.58f9a75ab1fddp-2,
+ -0x1.87de2a6aea963p-2, -0x1.b5d1009e15ccp-2, -0x1.e2b5d3806f63bp-2,
+ -0x1.073879922ffeep-1, -0x1.1c73b39ae68c8p-1, -0x1.30ff7fce17035p-1,
+ -0x1.44cf325091dd6p-1, -0x1.57d69348cecap-1, -0x1.6a09e667f3bcdp-1,
+ -0x1.7b5df226aafafp-1, -0x1.8bc806b151741p-1, -0x1.9b3e047f38741p-1,
+ -0x1.a9b66290ea1a3p-1, -0x1.b728345196e3ep-1, -0x1.c38b2f180bdb1p-1,
+ -0x1.ced7af43cc773p-1, -0x1.d906bcf328d46p-1, -0x1.e212104f686e5p-1,
+ -0x1.e9f4156c62ddap-1, -0x1.f0a7efb9230d7p-1, -0x1.f6297cff75cbp-1,
+ -0x1.fa7557f08a517p-1, -0x1.fd88da3d12526p-1, -0x1.ff621e3796d7ep-1,
+ -0x1p+0, -0x1.ff621e3796d7ep-1, -0x1.fd88da3d12526p-1,
+ -0x1.fa7557f08a517p-1, -0x1.f6297cff75cbp-1, -0x1.f0a7efb9230d7p-1,
+ -0x1.e9f4156c62ddap-1, -0x1.e212104f686e5p-1, -0x1.d906bcf328d46p-1,
+ -0x1.ced7af43cc773p-1, -0x1.c38b2f180bdb1p-1, -0x1.b728345196e3ep-1,
+ -0x1.a9b66290ea1a3p-1, -0x1.9b3e047f38741p-1, -0x1.8bc806b151741p-1,
+ -0x1.7b5df226aafafp-1, -0x1.6a09e667f3bcdp-1, -0x1.57d69348cecap-1,
+ -0x1.44cf325091dd6p-1, -0x1.30ff7fce17035p-1, -0x1.1c73b39ae68c8p-1,
+ -0x1.073879922ffeep-1, -0x1.e2b5d3806f63bp-2, -0x1.b5d1009e15ccp-2,
+ -0x1.87de2a6aea963p-2, -0x1.58f9a75ab1fddp-2, -0x1.294062ed59f06p-2,
+ -0x1.f19f97b215f1bp-3, -0x1.8f8b83c69a60bp-3, -0x1.2c8106e8e613ap-3,
+ -0x1.917a6bc29b42cp-4, -0x1.91f65f10dd814p-5
+ };
+
+ uint32_t ix = asuint (x);
+ int32_t e = (ix >> 23) & 0xff;
+ if (__glibc_unlikely (e == 0xff))
+ {
+ if (!(ix << 9))
+ return __math_invalidf (x);
+ return x + x; /* nan */
+ }
+ int32_t m = (ix & ~0u >> 9) | 1 << 23;
+ int32_t s = 143 - e;
+ int32_t p = e - 112;
+ if (__glibc_unlikely (p < 0)) /* |x| < 2^-15 */
+ {
+ uint32_t ax = ix & (~0u>>1);
+ /* Warning: -0x1.3bd3ccp+2f * x underflows for |x| < 0x1.9f03p-129 */
+ if (ax >= 0x19f030u)
+ return fmaf (-0x1.3bd3ccp+2f * x, x, 1.0f);
+ else /* |x| < 0x1.9f03p-129 */
+ return fmaf (-x, x, 1.0f);
+ }
+ if (__glibc_unlikely (p > 31))
+ {
+ if (__glibc_unlikely (p > 63))
+ return 1.0f;
+ int32_t iq = m << (p - 32);
+ return S[(iq + 32) & 127];
+ }
+ int32_t k = m << p;
+ if (__glibc_unlikely (k == 0))
+ {
+ int32_t iq = m >> (32 - p);
+ return S[(iq + 32) & 127];
+ }
+ double z = k;
+ double z2 = z * z;
+ double fs = sn[0] + z2 * (sn[1] + z2 * sn[2]);
+ double fc = cn[0] + z2 * (cn[1] + z2 * cn[2]);
+ uint32_t iq = m >> s;
+ iq = (iq + 1) >> 1;
+ uint32_t is = iq & 127, ic = (iq + 32) & 127;
+ double ts = S[ic], tc = S[is];
+ double r = ts + (ts * z2) * fc - (tc * z) * fs;
+ return r;
+}
+libm_alias_float (__cospi, cospi)
@@ -701,22 +701,18 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
ldouble: 2
Function: Real part of "cpow":
@@ -701,22 +701,18 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
ldouble: 2
Function: Real part of "cpow":
@@ -545,19 +545,15 @@ double: 2
Function: "cospi":
double: 2
-float: 2
Function: "cospi_downward":
double: 1
-float: 2
Function: "cospi_towardzero":
double: 1
-float: 1
Function: "cospi_upward":
double: 1
-float: 2
Function: Real part of "cpow":
double: 2
@@ -509,7 +509,6 @@ double: 2
Function: "cospi":
double: 2
-float: 2
Function: Real part of "cpow":
double: 2
@@ -858,25 +858,21 @@ ldouble: 2
Function: "cospi":
double: 2
-float: 2
float128: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
float128: 2
ldouble: 4
Function: "cospi_towardzero":
double: 1
-float: 1
float128: 2
ldouble: 6
Function: "cospi_upward":
double: 1
-float: 2
float128: 2
ldouble: 6
@@ -650,7 +650,6 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
ldouble: 2
Function: Real part of "cpow":
@@ -709,22 +709,18 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
ldouble: 2
Function: Real part of "cpow":
@@ -701,22 +701,18 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
ldouble: 2
Function: Real part of "cpow":
@@ -701,22 +701,18 @@ ldouble: 3
Function: "cospi":
double: 2
-float: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
ldouble: 2
Function: Real part of "cpow":
@@ -1050,25 +1050,21 @@ float: 2
Function: "cospi":
double: 2
-float: 2
float128: 2
ldouble: 2
Function: "cospi_downward":
double: 1
-float: 2
float128: 2
ldouble: 2
Function: "cospi_towardzero":
double: 1
-float: 1
float128: 2
ldouble: 2
Function: "cospi_upward":
double: 1
-float: 2
float128: 2
ldouble: 2