Remove slow paths from pow

System Internals / glibc - Wilco Dijkstra [arm.com] - 12 February 2018 10:47 EST

Remove the slow paths from pow. Like several other double precision math functions, pow is exactly rounded. This is not required from math functions and causes major overheads as it requires multiple fallbacks using higher precision arithmetic if a result is close to 0.5ULP. Ridiculous slowdowns of up to 100000x have been reported when the highest precision path triggers.

All GLIBC math tests pass on AArch64 and x64 (with ULP of pow set to 1). The worst case error is ~0.506ULP. A simple test over a few hundred million
values shows pow is 10% faster on average. This fixes BZ #13932.

[BZ #13932]
- sysdeps/ieee754/dbl-64/uexp.h (err_1): Remove.
- benchtests/pow-inputs: Update comment for slow path cases.
- manual/probes.texi (slowpow_p10): Delete removed probe. (slowpow_p10): Likewise.
- math/Makefile: Remove halfulp.c and slowpow.c.
- sysdeps/aarch64/libm-test-ulps: Set ULP of pow to 1.
- sysdeps/generic/math_private.h (__exp1): Remove error argument. (__halfulp): Remove. (__slowpow): Remove.
- sysdeps/i386/fpu/halfulp.c: Delete file.
- sysdeps/i386/fpu/slowpow.c: Likewise.
- sysdeps/ia64/fpu/halfulp.c: Likewise.
- sysdeps/ia64/fpu/slowpow.c: Likewise.
- sysdeps/ieee754/dbl-64/e_exp.c (__exp1): Remove error argument, improve comments and add error analysis.
- sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Add error analysis. (power1): Remove function: (log1): Remove error argument, add error analysis. (my_log2): Remove function.
- sysdeps/ieee754/dbl-64/halfulp.c: Delete file.
- sysdeps/ieee754/dbl-64/slowpow.c: Likewise.
- sysdeps/m68k/m680x0/fpu/halfulp.c: Likewise.
- sysdeps/m68k/m680x0/fpu/slowpow.c: Likewise.
- sysdeps/powerpc/power4/fpu/Makefile: Remove CPPFLAGS-slowpow.c.
- sysdeps/x86_64/fpu/libm-test-ulps: Set ULP of pow to 1.
- sysdeps/x86_64/fpu/multiarch/Makefile: Remove slowpow-fma.c, slowpow-fma4.c, halfulp-fma.c, halfulp-fma4.c.
- sysdeps/x86_64/fpu/multiarch/e_pow-fma.c (__slowpow): Remove define.
- sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c (__slowpow): Likewise.
- sysdeps/x86_64/fpu/multiarch/halfulp-fma.c: Delete file.
- sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c: Likewise.
- sysdeps/x86_64/fpu/multiarch/slowpow-fma.c: Likewise.
- sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c: Likewise.

c3d466cba1 Remove slow paths from pow
ChangeLog | 37 ++++++
benchtests/pow-inputs | 6 +-
manual/probes.texi | 16 ---
math/Makefile | 4 +-
sysdeps/aarch64/libm-test-ulps | 2 +
sysdeps/generic/math_private.h | 4 +-
sysdeps/i386/fpu/halfulp.c | 1 -
sysdeps/i386/fpu/slowpow.c | 1 -
sysdeps/ia64/fpu/halfulp.c | 1 -
sysdeps/ia64/fpu/slowpow.c | 1 -
sysdeps/ieee754/dbl-64/e_exp.c | 42 +++----
sysdeps/ieee754/dbl-64/e_pow.c | 172 ++++------------------------
sysdeps/ieee754/dbl-64/halfulp.c | 152 ------------------------
sysdeps/ieee754/dbl-64/slowpow.c | 125 --------------------
sysdeps/ieee754/dbl-64/uexp.h | 2 +-
sysdeps/m68k/m680x0/fpu/halfulp.c | 1 -
sysdeps/m68k/m680x0/fpu/slowpow.c | 1 -
sysdeps/powerpc/power4/fpu/Makefile | 1 -
sysdeps/x86_64/fpu/libm-test-ulps | 2 +
sysdeps/x86_64/fpu/multiarch/Makefile | 12 +-
sysdeps/x86_64/fpu/multiarch/e_pow-fma.c | 1 -
sysdeps/x86_64/fpu/multiarch/e_pow-fma4.c | 1 -
sysdeps/x86_64/fpu/multiarch/halfulp-fma.c | 4 -
sysdeps/x86_64/fpu/multiarch/halfulp-fma4.c | 4 -
sysdeps/x86_64/fpu/multiarch/slowpow-fma.c | 11 --
sysdeps/x86_64/fpu/multiarch/slowpow-fma4.c | 11 --
26 files changed, 90 insertions(+), 525 deletions(-)

Upstream: sourceware.org


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