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/* 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 <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
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 8 (which is the size of uint32_t minus MANTISSA_WIDTH plus
the signal bit):
mx * 2^ex == 2^8 * mx * 2^(ex - 8)
or
while (ex > ey)
{
mx << 8;
ex -= 8;
mx %= my;
} */
float
__ieee754_fmodf (float x, float y)
{
uint32_t hx = asuint (x);
uint32_t hy = asuint (y);
uint32_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 asfloat (sx);
}
int ex = hx >> MANTISSA_WIDTH;
int ey = hy >> MANTISSA_WIDTH;
/* Common case where exponents are close: ey >= -103 and |x/y| < 2^8, */
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);
uint32_t d = (ex == ey) ? (mx - my) : (mx << (ex - ey)) % my;
return make_float (d, ey - 1, sx);
}
/* Special case, both x and y are subnormal. */
if (__glibc_unlikely (ex == 0 && ey == 0))
return asfloat (sx | hx % hy);
/* Convert |x| and |y| to 'mx + 2^ex' and 'my + 2^ey'. Assume that hx is
not subnormal by conditions above. */
uint32_t mx = get_mantissa (hx) | (MANTISSA_MASK + 1);
ex--;
uint32_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 = __builtin_clz (my);
}
int tail_zeros_my = __builtin_ctz (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 asfloat (sx);
if (exp_diff == 0)
return make_float (mx, ey, sx);
/* Assume modulo/divide operation is slow, so use multiplication with invert
values. */
uint32_t inv_hy = UINT32_MAX / my;
while (exp_diff > sides_zeroes) {
exp_diff -= sides_zeroes;
uint32_t hd = (mx * inv_hy) >> (BIT_WIDTH - sides_zeroes);
mx <<= sides_zeroes;
mx -= hd * my;
while (__glibc_unlikely (mx > my))
mx -= my;
}
uint32_t hd = (mx * inv_hy) >> (BIT_WIDTH - exp_diff);
mx <<= exp_diff;
mx -= hd * my;
while (__glibc_unlikely (mx > my))
mx -= my;
return make_float (mx, ey, sx);
}
libm_alias_finite (__ieee754_fmodf, __fmodf)
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