From 34b9f8bc170810c44184ad57ecf1800587e752a6 Mon Sep 17 00:00:00 2001 From: Adhemerval Zanella Netto Date: Mon, 20 Mar 2023 13:01:16 -0300 Subject: math: Improve fmod This uses a new algorithm similar to already proposed earlier [1]. With x = mx * 2^ex and y = my * 2^ey (mx, my, ex, ey being integers), the simplest implementation is: mx * 2^ex == 2 * mx * 2^(ex - 1) while (ex > ey) { mx *= 2; --ex; mx %= my; } With mx/my being mantissa of double floating pointer, on each step the argument reduction can be improved 11 (which is sizeo of uint64_t minus MANTISSA_WIDTH plus the signal bit): while (ex > ey) { mx << 11; ex -= 11; mx %= my; } */ The implementation uses builtin clz and ctz, along with shifts to convert hx/hy back to doubles. Different than the original patch, this path assume modulo/divide operation is slow, so use multiplication with invert values. I see the following performance improvements using fmod benchtests (result only show the 'mean' result): Architecture | Input | master | patch -----------------|-----------------|----------|-------- x86_64 (Ryzen 9) | subnormals | 19.1584 | 12.5049 x86_64 (Ryzen 9) | normal | 1016.51 | 296.939 x86_64 (Ryzen 9) | close-exponents | 18.4428 | 16.0244 aarch64 (N1) | subnormal | 11.153 | 6.81778 aarch64 (N1) | normal | 528.649 | 155.62 aarch64 (N1) | close-exponents | 11.4517 | 8.21306 I also see similar improvements on arm-linux-gnueabihf when running on the N1 aarch64 chips, where it a lot of soft-fp implementation (for modulo, clz, ctz, and multiplication): Architecture | Input | master | patch -----------------|-----------------|----------|-------- armhf (N1) | subnormal | 15.908 | 15.1083 armhf (N1) | normal | 837.525 | 244.833 armhf (N1) | close-exponents | 16.2111 | 21.8182 Instead of using the math_private.h definitions, I used the math_config.h instead which is used on newer math implementations. Co-authored-by: kirill [1] https://sourceware.org/pipermail/libc-alpha/2020-November/119794.html Reviewed-by: Wilco Dijkstra --- math/libm-test-fmod.inc | 14 ++++++++++++++ 1 file changed, 14 insertions(+) (limited to 'math') diff --git a/math/libm-test-fmod.inc b/math/libm-test-fmod.inc index 39fd02f..8841c13 100644 --- a/math/libm-test-fmod.inc +++ b/math/libm-test-fmod.inc @@ -152,6 +152,16 @@ static const struct test_ff_f_data fmod_test_data[] = TEST_ff_f (fmod, 6.5, -2.25L, 2.0L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, -6.5, -2.25L, -2.0L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x1.e848p+18, 0x1.6p+3, 0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x1.e848p+18, -0x1.6p+3, 0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.e848p+18, 0x1.6p+3, -0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.e848p+18, -0x1.6p+3, -0x1.8p+2, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + + TEST_ff_f (fmod, 0x1.4p+2, 0x1p+0, 0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x1.4p+2, -0x1p+0, 0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.4p+2, 0x1p+0, -0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x1.4p+2, -0x1p+0, -0x0p+0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, max_value, max_value, 0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, max_value, -max_value, 0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, max_value, min_value, 0, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), @@ -216,6 +226,10 @@ static const struct test_ff_f_data fmod_test_data[] = TEST_ff_f (fmod, -0x1p1023L, -0x3p-1073L, -0x1p-1073L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, -0x1p1023L, 0x3p-1022L, -0x1p-1021L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), TEST_ff_f (fmod, -0x1p1023L, -0x3p-1022L, -0x1p-1021L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x0.cded0a47373e9p-1022, 0x0.3212f5b8c8c16p-1022, 0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, 0x0.cded0a47373e9p-1022, -0x0.3212f5b8c8c16p-1022, 0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x0.cded0a47373e9p-1022, 0x0.3212f5b8c8c16p-1022, -0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), + TEST_ff_f (fmod, -0x0.cded0a47373e9p-1022, -0x0.3212f5b8c8c16p-1022, -0x0.05a1336414391p-1022, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), #endif #if MIN_EXP <= -16381 TEST_ff_f (fmod, 0x1p16383L, 0x3p-16445L, 0x1p-16445L, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED), -- cgit v1.1