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author | Adhemerval Zanella Netto <adhemerval.zanella@linaro.org> | 2023-03-20 13:01:16 -0300 |
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committer | Adhemerval Zanella <adhemerval.zanella@linaro.org> | 2023-04-03 16:36:24 -0300 |
commit | 34b9f8bc170810c44184ad57ecf1800587e752a6 (patch) | |
tree | 9be9f9e44652729248cfef192eafa4227d670752 /sysdeps/ieee754 | |
parent | 5c11701c518276fcf12ff7d8f27e3c7102e97542 (diff) | |
download | glibc-34b9f8bc170810c44184ad57ecf1800587e752a6.zip glibc-34b9f8bc170810c44184ad57ecf1800587e752a6.tar.gz glibc-34b9f8bc170810c44184ad57ecf1800587e752a6.tar.bz2 |
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 <kirill.okhotnikov@gmail.com>
[1] https://sourceware.org/pipermail/libc-alpha/2020-November/119794.html
Reviewed-by: Wilco Dijkstra <Wilco.Dijkstra@arm.com>
Diffstat (limited to 'sysdeps/ieee754')
-rw-r--r-- | sysdeps/ieee754/dbl-64/e_fmod.c | 243 | ||||
-rw-r--r-- | sysdeps/ieee754/dbl-64/math_config.h | 61 |
2 files changed, 208 insertions, 96 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_fmod.c b/sysdeps/ieee754/dbl-64/e_fmod.c index 60b8bbb..e661ca1 100644 --- a/sysdeps/ieee754/dbl-64/e_fmod.c +++ b/sysdeps/ieee754/dbl-64/e_fmod.c @@ -1,105 +1,156 @@ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * __ieee754_fmod(x,y) - * Return x mod y in exact arithmetic - * Method: shift and subtract - */ +/* Floating-point remainder function. + Copyright (C) 2023 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ -#include <math.h> -#include <math_private.h> -#include <stdint.h> #include <libm-alias-finite.h> +#include <math.h> +#include "math_config.h" + +/* 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) + + or -static const double one = 1.0, Zero[] = {0.0, -0.0,}; + while (ex > ey) + { + mx *= 2; + --ex; + mx %= my; + } + + With the mathematical equivalence of: + + r == x % y == (x % (N * y)) % y + + And with mx/my being mantissa of double floating point number (which uses + less bits than the storage type), on each step the argument reduction can + be improved by 11 (which is the size of uint64_t minus MANTISSA_WIDTH plus + the signal bit): + + mx * 2^ex == 2^11 * mx * 2^(ex - 11) + + or + + while (ex > ey) + { + mx << 11; + ex -= 11; + mx %= my; + } */ double __ieee754_fmod (double x, double y) { - int32_t n,ix,iy; - int64_t hx,hy,hz,sx,i; - - EXTRACT_WORDS64(hx,x); - EXTRACT_WORDS64(hy,y); - sx = hx&UINT64_C(0x8000000000000000); /* sign of x */ - hx ^=sx; /* |x| */ - hy &= UINT64_C(0x7fffffffffffffff); /* |y| */ - - /* purge off exception values */ - if(__builtin_expect(hy==0 - || hx >= UINT64_C(0x7ff0000000000000) - || hy > UINT64_C(0x7ff0000000000000), 0)) - /* y=0,or x not finite or y is NaN */ - return (x*y)/(x*y); - if(__builtin_expect(hx<=hy, 0)) { - if(hx<hy) return x; /* |x|<|y| return x */ - return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/ - } - - /* determine ix = ilogb(x) */ - if(__builtin_expect(hx<UINT64_C(0x0010000000000000), 0)) { - /* subnormal x */ - for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; - } else ix = (hx>>52)-1023; - - /* determine iy = ilogb(y) */ - if(__builtin_expect(hy<UINT64_C(0x0010000000000000), 0)) { /* subnormal y */ - for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; - } else iy = (hy>>52)-1023; - - /* set up hx, hy and align y to x */ - if(__builtin_expect(ix >= -1022, 1)) - hx = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hx); - else { /* subnormal x, shift x to normal */ - n = -1022-ix; - hx<<=n; - } - if(__builtin_expect(iy >= -1022, 1)) - hy = UINT64_C(0x0010000000000000)|(UINT64_C(0x000fffffffffffff)&hy); - else { /* subnormal y, shift y to normal */ - n = -1022-iy; - hy<<=n; - } - - /* fix point fmod */ - n = ix - iy; - while(n--) { - hz=hx-hy; - if(hz<0){hx = hx+hx;} - else { - if(hz==0) /* return sign(x)*0 */ - return Zero[(uint64_t)sx>>63]; - hx = hz+hz; - } - } - hz=hx-hy; - if(hz>=0) {hx=hz;} - - /* convert back to floating value and restore the sign */ - if(hx==0) /* return sign(x)*0 */ - return Zero[(uint64_t)sx>>63]; - while(hx<UINT64_C(0x0010000000000000)) { /* normalize x */ - hx = hx+hx; - iy -= 1; - } - if(__builtin_expect(iy>= -1022, 1)) { /* normalize output */ - hx = ((hx-UINT64_C(0x0010000000000000))|((uint64_t)(iy+1023)<<52)); - INSERT_WORDS64(x,hx|sx); - } else { /* subnormal output */ - n = -1022 - iy; - hx>>=n; - INSERT_WORDS64(x,hx|sx); - x *= one; /* create necessary signal */ - } - return x; /* exact output */ + uint64_t hx = asuint64 (x); + uint64_t hy = asuint64 (y); + + uint64_t sx = hx & SIGN_MASK; + /* Get |x| and |y|. */ + hx ^= sx; + hy &= ~SIGN_MASK; + + /* Special cases: + - If x or y is a Nan, NaN is returned. + - If x is an inifinity, a NaN is returned. + - If y is zero, Nan is returned. + - If x is +0/-0, and y is not zero, +0/-0 is returned. */ + if (__glibc_unlikely (hy == 0 || hx >= EXPONENT_MASK || hy > EXPONENT_MASK)) + return (x * y) / (x * y); + + if (__glibc_unlikely (hx <= hy)) + { + if (hx < hy) + return x; + return asdouble (sx); + } + + int ex = hx >> MANTISSA_WIDTH; + int ey = hy >> MANTISSA_WIDTH; + + /* Common case where exponents are close: ey >= -907 and |x/y| < 2^52, */ + if (__glibc_likely (ey > MANTISSA_WIDTH && ex - ey <= EXPONENT_WIDTH)) + { + uint64_t mx = (hx & MANTISSA_MASK) | (MANTISSA_MASK + 1); + uint64_t my = (hy & MANTISSA_MASK) | (MANTISSA_MASK + 1); + + uint64_t d = (ex == ey) ? (mx - my) : (mx << (ex - ey)) % my; + return make_double (d, ey - 1, sx); + } + + /* Special case, both x and y are subnormal. */ + if (__glibc_unlikely (ex == 0 && ey == 0)) + return asdouble (sx | hx % hy); + + /* Convert |x| and |y| to 'mx + 2^ex' and 'my + 2^ey'. Assume that hx is + not subnormal by conditions above. */ + uint64_t mx = get_mantissa (hx) | (MANTISSA_MASK + 1); + ex--; + uint64_t my = get_mantissa (hy) | (MANTISSA_MASK + 1); + + int lead_zeros_my = EXPONENT_WIDTH; + if (__glibc_likely (ey > 0)) + ey--; + else + { + my = hy; + lead_zeros_my = clz_uint64 (my); + } + + /* Assume hy != 0 */ + int tail_zeros_my = ctz_uint64 (my); + int sides_zeroes = lead_zeros_my + tail_zeros_my; + int exp_diff = ex - ey; + + int right_shift = exp_diff < tail_zeros_my ? exp_diff : tail_zeros_my; + my >>= right_shift; + exp_diff -= right_shift; + ey += right_shift; + + int left_shift = exp_diff < EXPONENT_WIDTH ? exp_diff : EXPONENT_WIDTH; + mx <<= left_shift; + exp_diff -= left_shift; + + mx %= my; + + if (__glibc_unlikely (mx == 0)) + return asdouble (sx); + + if (exp_diff == 0) + return make_double (mx, ey, sx); + + /* Assume modulo/divide operation is slow, so use multiplication with invert + values. */ + uint64_t inv_hy = UINT64_MAX / my; + while (exp_diff > sides_zeroes) { + exp_diff -= sides_zeroes; + uint64_t hd = (mx * inv_hy) >> (BIT_WIDTH - sides_zeroes); + mx <<= sides_zeroes; + mx -= hd * my; + while (__glibc_unlikely (mx > my)) + mx -= my; + } + uint64_t hd = (mx * inv_hy) >> (BIT_WIDTH - exp_diff); + mx <<= exp_diff; + mx -= hd * my; + while (__glibc_unlikely (mx > my)) + mx -= my; + + return make_double (mx, ey, sx); } libm_alias_finite (__ieee754_fmod, __fmod) diff --git a/sysdeps/ieee754/dbl-64/math_config.h b/sysdeps/ieee754/dbl-64/math_config.h index 3cbaeed..2049cea 100644 --- a/sysdeps/ieee754/dbl-64/math_config.h +++ b/sysdeps/ieee754/dbl-64/math_config.h @@ -43,6 +43,24 @@ # define TOINT_INTRINSICS 0 #endif +static inline int +clz_uint64 (uint64_t x) +{ + if (sizeof (uint64_t) == sizeof (unsigned long)) + return __builtin_clzl (x); + else + return __builtin_clzll (x); +} + +static inline int +ctz_uint64 (uint64_t x) +{ + if (sizeof (uint64_t) == sizeof (unsigned long)) + return __builtin_ctzl (x); + else + return __builtin_ctzll (x); +} + #if TOINT_INTRINSICS /* Round x to nearest int in all rounding modes, ties have to be rounded consistently with converttoint so the results match. If the result @@ -88,6 +106,49 @@ issignaling_inline (double x) return 2 * (ix ^ 0x0008000000000000) > 2 * 0x7ff8000000000000ULL; } +#define BIT_WIDTH 64 +#define MANTISSA_WIDTH 52 +#define EXPONENT_WIDTH 11 +#define MANTISSA_MASK UINT64_C(0x000fffffffffffff) +#define EXPONENT_MASK UINT64_C(0x7ff0000000000000) +#define EXP_MANT_MASK UINT64_C(0x7fffffffffffffff) +#define QUIET_NAN_MASK UINT64_C(0x0008000000000000) +#define SIGN_MASK UINT64_C(0x8000000000000000) + +static inline bool +is_nan (uint64_t x) +{ + return (x & EXP_MANT_MASK) > EXPONENT_MASK; +} + +static inline uint64_t +get_mantissa (uint64_t x) +{ + return x & MANTISSA_MASK; +} + +/* Convert integer number X, unbiased exponent EP, and sign S to double: + + result = X * 2^(EP+1 - exponent_bias) + + NB: zero is not supported. */ +static inline double +make_double (uint64_t x, int64_t ep, uint64_t s) +{ + int lz = clz_uint64 (x) - EXPONENT_WIDTH; + x <<= lz; + ep -= lz; + + if (__glibc_unlikely (ep < 0 || x == 0)) + { + x >>= -ep; + ep = 0; + } + + return asdouble (s + x + (ep << MANTISSA_WIDTH)); +} + + #define NOINLINE __attribute__ ((noinline)) /* Error handling tail calls for special cases, with a sign argument. |