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math: Use coshf from CORE-MATH
The CORE-MATH implementation is correctly rounded (for any rounding mode), although it should worse performance than current one. The current implementation performance comes mainly from the internal usage of the optimize expf implementation, and shows a maximum ULPs of 2 for FE_TONEAREST and 3 for other rounding modes. 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 40.6995 49.0737 -20.58% x86_64v2 40.5841 44.3604 -9.30% x86_64v3 39.3879 39.7502 -0.92% i686 112.3380 129.8570 -15.59% aarch64 (Neoverse) 18.6914 17.0946 8.54% power10 11.1343 9.3245 16.25% reciprocal-throughput master patched improvement x86_64 18.6471 24.1077 -29.28% x86_64v2 17.7501 20.2946 -14.34% x86_64v3 17.8262 17.1877 3.58% i686 64.1454 86.5645 -34.95% aarch64 (Neoverse) 9.77226 12.2314 -25.16% power10 4.0200 5.3316 -32.63% 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
parent
7cfd8b5698
commit
9583836785
@ -322,3 +322,7 @@ sysdeps/ieee754/flt-32/e_atanhf.c:
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(src/binary32/atanh/atanhf.c in CORE-MATH)
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- The code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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sysdeps/ieee754/flt-32/e_coshf.c:
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(src/binary32/cosh/coshf.c in CORE-MATH)
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- the code was adapted to use glibc code style and internal
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functions to handle errno, overflow, and underflow.
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@ -774,7 +774,6 @@ ldouble: 2
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Function: "cosh":
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double: 2
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float: 2
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ldouble: 2
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Function: "cosh_advsimd":
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@ -783,7 +782,6 @@ float: 2
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Function: "cosh_downward":
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double: 3
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float: 1
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ldouble: 3
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Function: "cosh_sve":
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@ -792,12 +790,10 @@ float: 2
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Function: "cosh_towardzero":
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double: 3
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float: 1
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ldouble: 3
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Function: "cosh_upward":
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double: 2
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float: 2
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ldouble: 3
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Function: "cospi":
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@ -621,22 +621,18 @@ ldouble: 2
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Function: "cosh":
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double: 2
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float: 2
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ldouble: 2
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Function: "cosh_downward":
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double: 3
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float: 1
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ldouble: 3
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Function: "cosh_towardzero":
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double: 3
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float: 1
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ldouble: 3
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Function: "cosh_upward":
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double: 2
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float: 2
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ldouble: 3
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Function: Real part of "cpow":
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@ -493,19 +493,15 @@ float: 2
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Function: "cosh":
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double: 3
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float: 3
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Function: "cosh_downward":
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double: 3
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float: 1
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Function: "cosh_towardzero":
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double: 3
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float: 1
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Function: "cosh_upward":
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double: 3
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float: 2
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Function: Real part of "cpow":
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double: 9
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@ -123,7 +123,6 @@ float: 1
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Function: "cosh":
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double: 2
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float: 2
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Function: Real part of "cpow":
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double: 2
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@ -84,8 +84,6 @@ float: 1
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Function: "atan":
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double: 1
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Function: "atan2":
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Function: "atan2_downward":
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double: 1
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@ -553,19 +551,15 @@ float: 2
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Function: "cosh":
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double: 2
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float: 2
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Function: "cosh_downward":
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double: 3
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float: 1
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Function: "cosh_towardzero":
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double: 3
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float: 1
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Function: "cosh_upward":
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double: 2
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float: 2
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Function: "cospi":
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double: 1
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@ -750,7 +744,7 @@ float: 2
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Function: Real part of "ctanh_downward":
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double: 4
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float: 2
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float: 3
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Function: Imaginary part of "ctanh_downward":
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double: 6
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@ -485,19 +485,15 @@ float: 1
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Function: "cosh":
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double: 2
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float: 2
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Function: "cosh_downward":
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double: 3
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float: 1
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Function: "cosh_towardzero":
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double: 3
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float: 1
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Function: "cosh_upward":
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double: 2
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float: 2
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Function: Real part of "cpow":
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double: 2
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@ -483,19 +483,15 @@ float: 2
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Function: "cosh":
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double: 2
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float: 2
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Function: "cosh_downward":
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double: 1
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float: 1
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Function: "cosh_towardzero":
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double: 1
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float: 1
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Function: "cosh_upward":
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double: 1
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float: 2
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Function: Real part of "cpow":
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double: 2
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@ -563,19 +563,15 @@ float: 2
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Function: "cosh":
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double: 2
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float: 2
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Function: "cosh_downward":
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double: 3
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float: 1
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Function: "cosh_towardzero":
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double: 3
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float: 1
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Function: "cosh_upward":
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double: 2
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float: 2
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Function: "cospi":
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double: 1
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@ -850,25 +850,21 @@ ldouble: 2
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Function: "cosh":
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double: 1
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float: 2
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float128: 2
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ldouble: 3
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Function: "cosh_downward":
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double: 3
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float: 1
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float128: 3
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ldouble: 3
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Function: "cosh_towardzero":
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double: 3
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float: 1
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float128: 3
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ldouble: 3
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Function: "cosh_upward":
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double: 4
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float: 2
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float128: 3
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ldouble: 3
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@ -850,25 +850,21 @@ ldouble: 2
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Function: "cosh":
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double: 1
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float: 2
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float128: 2
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ldouble: 3
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Function: "cosh_downward":
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double: 3
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float: 1
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float128: 3
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ldouble: 3
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Function: "cosh_towardzero":
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double: 3
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float: 1
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float128: 3
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ldouble: 3
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Function: "cosh_upward":
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double: 4
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float: 2
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float128: 3
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ldouble: 3
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@ -130,9 +130,9 @@ __ieee754_atan2f (float y, float x)
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if (yinf & xinf)
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{
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if (ux >> 31)
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return 0x1.2d97c7f3321d2p+1 * sgn[uy >> 31];
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return 0x1.2d97c7f3321d2p+1 * sgn[uy >> 31]; /* +/-3pi/4 */
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else
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return 0x1.921fb54442d18p-1 * sgn[uy >> 31];
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return 0x1.921fb54442d18p-1 * sgn[uy >> 31]; /* +/-pi/4 */
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}
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if (xinf)
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{
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@ -146,7 +146,7 @@ __ieee754_atan2f (float y, float x)
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}
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if (__glibc_unlikely (ay == 0))
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{
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if (__glibc_unlikely (!(ay | ax)))
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if (__glibc_unlikely (!ax))
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{
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uint32_t i = (uy >> 31) * 4 + (ux >> 31) * 2;
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if (ux >> 31)
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@ -1,63 +1,117 @@
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/* e_coshf.c -- float version of e_cosh.c.
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*/
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/* Correctly-rounded hyperbolic cosine function for binary32 value.
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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Copyright (c) 2022-2024 Alexei Sibidanov.
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The original version of this file was copied from the CORE-MATH
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project (file src/binary32/cosh/coshf.c, revision 5c58ea1).
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#include <stdint.h>
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#include <math.h>
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#include <math-narrow-eval.h>
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#include <math_private.h>
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#include <libm-alias-finite.h>
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static const float huge = 1.0e30;
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static const float one = 1.0, half=0.5;
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#include "math_config.h"
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float
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__ieee754_coshf (float x)
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{
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float t,w;
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int32_t ix;
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GET_FLOAT_WORD(ix,x);
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ix &= 0x7fffffff;
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/* |x| in [0,22] */
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if (ix < 0x41b00000) {
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/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
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if(ix<0x3eb17218) {
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if (ix<0x24000000) return one; /* cosh(tiny) = 1 */
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t = __expm1f(fabsf(x));
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w = one+t;
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return one+(t*t)/(w+w);
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}
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/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
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t = __ieee754_expf(fabsf(x));
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return half*t+half/t;
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static const double c[] =
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{
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1, 0x1.62e42fef4c4e7p-6, 0x1.ebfd1b232f475p-13, 0x1.c6b19384ecd93p-20
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};
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static const double ch[] =
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{
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1, 0x1.62e42fefa39efp-6, 0x1.ebfbdff82c58fp-13,
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0x1.c6b08d702e0edp-20, 0x1.3b2ab6fb92e5ep-27, 0x1.5d886e6d54203p-35,
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0x1.430976b8ce6efp-43
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};
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static const uint64_t tb[] =
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{
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0x3fe0000000000000, 0x3fe059b0d3158574, 0x3fe0b5586cf9890f,
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0x3fe11301d0125b51, 0x3fe172b83c7d517b, 0x3fe1d4873168b9aa,
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0x3fe2387a6e756238, 0x3fe29e9df51fdee1, 0x3fe306fe0a31b715,
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0x3fe371a7373aa9cb, 0x3fe3dea64c123422, 0x3fe44e086061892d,
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0x3fe4bfdad5362a27, 0x3fe5342b569d4f82, 0x3fe5ab07dd485429,
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0x3fe6247eb03a5585, 0x3fe6a09e667f3bcd, 0x3fe71f75e8ec5f74,
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0x3fe7a11473eb0187, 0x3fe82589994cce13, 0x3fe8ace5422aa0db,
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0x3fe93737b0cdc5e5, 0x3fe9c49182a3f090, 0x3fea5503b23e255d,
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0x3feae89f995ad3ad, 0x3feb7f76f2fb5e47, 0x3fec199bdd85529c,
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0x3fecb720dcef9069, 0x3fed5818dcfba487, 0x3fedfc97337b9b5f,
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0x3feea4afa2a490da, 0x3fef50765b6e4540
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};
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const double iln2 = 0x1.71547652b82fep+5;
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double z = x;
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uint32_t ax = asuint (x) << 1;
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if (__glibc_unlikely (ax > 0x8565a9f8u))
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{ /* |x| >~ 89.4 */
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if (ax >= 0xff000000u)
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{
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if (ax << 8)
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return x + x; /* nan */
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return INFINITY; /* +-inf */
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}
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/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
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if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x));
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/* |x| in [log(maxdouble), overflowthresold] */
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if (ix<=0x42b2d4fc) {
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w = __ieee754_expf(half*fabsf(x));
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t = half*w;
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return t*w;
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return __math_oflowf (0);
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}
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if (__glibc_unlikely (ax < 0x7c000000u))
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{ /* |x| < 0.125 */
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if (__glibc_unlikely (ax < 0x74000000u))
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{ /* |x| < 0x1p-11 */
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if (__glibc_unlikely (ax < 0x66000000u)) /* |x| < 0x1p-24 */
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return fmaf (fabsf (x), 0x1p-25, 1.0f);
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return (0.5f * x) * x + 1.0f;
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}
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/* x is INF or NaN */
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if(ix>=0x7f800000) return x*x;
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/* |x| > overflowthresold, cosh(x) overflow */
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return math_narrow_eval (huge*huge);
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static const double cp[] =
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{
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0x1.fffffffffffe3p-2, 0x1.55555555723cfp-5,
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0x1.6c16bee4a5986p-10, 0x1.a0483fc0328f7p-16
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};
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double z2 = z * z;
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double z4 = z2 * z2;
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return 1.0 + z2 * ((cp[0] + z2 * cp[1]) + z4 * (cp[2] + z2 * (cp[3])));
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}
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double a = iln2 * z;
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double ia = roundeven_finite (a);
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double h = a - ia;
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double h2 = h * h;
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int64_t jp = asuint64 (ia + 0x1.8p52);
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int64_t jm = -jp;
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double sp = asdouble (tb[jp & 31] + ((jp >> 5) << 52));
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double sm = asdouble (tb[jm & 31] + ((jm >> 5) << 52));
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double te = c[0] + h2 * c[2];
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double to = (c[1] + h2 * c[3]);
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double rp = sp * (te + h * to);
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double rm = sm * (te - h * to);
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double r = rp + rm;
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float ub = r;
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double lb = r - 1.45e-10 * r;
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if (__glibc_unlikely (ub != lb))
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{
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const double iln2h = 0x1.7154765p+5;
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const double iln2l = 0x1.5c17f0bbbe88p-26;
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h = (iln2h * z - ia) + iln2l * z;
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h2 = h * h;
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te = ch[0] + h2 * ch[2] + (h2 * h2) * (ch[4] + h2 * ch[6]);
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to = ch[1] + h2 * (ch[3] + h2 * ch[5]);
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r = sp * (te + h * to) + sm * (te - h * to);
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ub = r;
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}
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return ub;
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}
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libm_alias_finite (__ieee754_coshf, __coshf)
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@ -621,22 +621,18 @@ ldouble: 2
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Function: "cosh":
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double: 2
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float: 2
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ldouble: 2
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Function: "cosh_downward":
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double: 3
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float: 1
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ldouble: 3
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Function: "cosh_towardzero":
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double: 3
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float: 1
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ldouble: 3
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Function: "cosh_upward":
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double: 2
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float: 2
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ldouble: 3
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Function: Real part of "cpow":
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@ -118,7 +118,6 @@ float: 1
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|
||||
Function: "cosh":
|
||||
double: 1
|
||||
float: 1
|
||||
|
||||
Function: Real part of "cpow":
|
||||
double: 2
|
||||
|
||||
@ -489,19 +489,15 @@ float: 2
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: Real part of "cpow":
|
||||
double: 2
|
||||
|
||||
@ -621,22 +621,18 @@ ldouble: 2
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: Real part of "cpow":
|
||||
|
||||
@ -489,19 +489,15 @@ float: 1
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: Real part of "cpow":
|
||||
double: 2
|
||||
|
||||
@ -505,19 +505,15 @@ float: 1
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 2
|
||||
float: 1
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 2
|
||||
float: 1
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "cospi":
|
||||
double: 1
|
||||
|
||||
@ -854,25 +854,21 @@ ldouble: 5
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
float128: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 6
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
float128: 3
|
||||
ldouble: 2
|
||||
|
||||
|
||||
@ -625,22 +625,18 @@ ldouble: 5
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 6
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 6
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: Real part of "cpow":
|
||||
|
||||
@ -618,22 +618,18 @@ ldouble: 2
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ldouble: 2
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 1
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: Real part of "cpow":
|
||||
|
||||
@ -621,22 +621,18 @@ ldouble: 2
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: Real part of "cpow":
|
||||
|
||||
@ -621,22 +621,18 @@ ldouble: 2
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "cospi":
|
||||
|
||||
@ -241,11 +241,9 @@ float: 1
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
|
||||
Function: Real part of "cpow":
|
||||
double: 2
|
||||
|
||||
@ -621,22 +621,18 @@ ldouble: 2
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "cospi":
|
||||
|
||||
@ -1026,25 +1026,21 @@ float: 1
|
||||
|
||||
Function: "cosh":
|
||||
double: 2
|
||||
float: 2
|
||||
float128: 2
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_downward":
|
||||
double: 3
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_towardzero":
|
||||
double: 3
|
||||
float: 1
|
||||
float128: 3
|
||||
ldouble: 3
|
||||
|
||||
Function: "cosh_upward":
|
||||
double: 2
|
||||
float: 2
|
||||
float128: 3
|
||||
ldouble: 3
|
||||
|
||||
@ -1342,7 +1338,7 @@ ldouble: 2
|
||||
|
||||
Function: Real part of "ctanh_downward":
|
||||
double: 4
|
||||
float: 2
|
||||
float: 3
|
||||
float128: 5
|
||||
ldouble: 4
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user