sysdeps/ieee754/flt-32/e_fmodf.c

   1 /* Floating-point remainder function.
   2    Copyright (C) 2023 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4
   5    The GNU C Library is free software; you can redistribute it and/or
   6    modify it under the terms of the GNU Lesser General Public
   7    License as published by the Free Software Foundation; either
   8    version 2.1 of the License, or (at your option) any later version.
   9
  10    The GNU C Library is distributed in the hope that it will be useful,
  11    but WITHOUT ANY WARRANTY; without even the implied warranty of
  12    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13    Lesser General Public License for more details.
  14
  15    You should have received a copy of the GNU Lesser General Public
  16    License along with the GNU C Library; if not, see
  17    <https://www.gnu.org/licenses/>.  */
  18
  19 #include <libm-alias-finite.h>
  20 #include <libm-alias-float.h>
  21 #include <math-svid-compat.h>
  22 #include <math.h>
  23 #include "math_config.h"
  24
  25 /* With x = mx * 2^ex and y = my * 2^ey (mx, my, ex, ey being integers), the
  26    simplest implementation is:
  27
  28    mx * 2^ex == 2 * mx * 2^(ex - 1)
  29
  30    or
  31
  32    while (ex > ey)
  33      {
  34        mx *= 2;
  35        --ex;
  36        mx %= my;
  37      }
  38
  39    With the mathematical equivalence of:
  40
  41    r == x % y == (x % (N * y)) % y
  42
  43    And with mx/my being mantissa of double floating point number (which uses
  44    less bits than the storage type), on each step the argument reduction can
  45    be improved by 8 (which is the size of uint32_t minus MANTISSA_WIDTH plus
  46    the signal bit):
  47
  48    mx * 2^ex == 2^8 * mx * 2^(ex - 8)
  49
  50    or
  51
  52    while (ex > ey)
  53      {
  54        mx << 8;
  55        ex -= 8;
  56        mx %= my;
  57      }  */
  58
  59 float
  60 __fmodf (float x, float y)
  61 {
  62   uint32_t hx = asuint (x);
  63   uint32_t hy = asuint (y);
  64
  65   uint32_t sx = hx & SIGN_MASK;
  66   /* Get |x| and |y|.  */
  67   hx ^= sx;
  68   hy &= ~SIGN_MASK;
  69
  70   /* Special cases:
  71      - If x or y is a Nan, NaN is returned.
  72      - If x is an inifinity, a NaN is returned.
  73      - If y is zero, Nan is returned.
  74      - If x is +0/-0, and y is not zero, +0/-0 is returned.  */
  75   if (__glibc_unlikely (hy == 0
  76                         || hx >= EXPONENT_MASK || hy > EXPONENT_MASK))
  77     {
  78       if (is_nan (hx) || is_nan (hy))
  79         return (x * y) / (x * y);
  80       return __math_edomf ((x * y) / (x * y));
  81     }
  82
  83   if (__glibc_unlikely (hx <= hy))
  84     {
  85       if (hx < hy)
  86         return x;
  87       return asfloat (sx);
  88     }
  89
  90   int ex = hx >> MANTISSA_WIDTH;
  91   int ey = hy >> MANTISSA_WIDTH;
  92
  93   /* Common case where exponents are close: ey >= -103 and |x/y| < 2^8,  */
  94   if (__glibc_likely (ey > MANTISSA_WIDTH && ex - ey <= EXPONENT_WIDTH))
  95     {
  96       uint64_t mx = (hx & MANTISSA_MASK) | (MANTISSA_MASK + 1);
  97       uint64_t my = (hy & MANTISSA_MASK) | (MANTISSA_MASK + 1);
  98
  99       uint32_t d = (ex == ey) ? (mx - my) : (mx << (ex - ey)) % my;
 100       return make_float (d, ey - 1, sx);
 101     }
 102
 103   /* Special case, both x and y are subnormal.  */
 104   if (__glibc_unlikely (ex == 0 && ey == 0))
 105     return asfloat (sx | hx % hy);
 106
 107   /* Convert |x| and |y| to 'mx + 2^ex' and 'my + 2^ey'.  Assume that hx is
 108      not subnormal by conditions above.  */
 109   uint32_t mx = get_mantissa (hx) | (MANTISSA_MASK + 1);
 110   ex--;
 111
 112   uint32_t my = get_mantissa (hy) | (MANTISSA_MASK + 1);
 113   int lead_zeros_my = EXPONENT_WIDTH;
 114   if (__glibc_likely (ey > 0))
 115     ey--;
 116   else
 117     {
 118       my = hy;
 119       lead_zeros_my = __builtin_clz (my);
 120     }
 121
 122   int tail_zeros_my = __builtin_ctz (my);
 123   int sides_zeroes = lead_zeros_my + tail_zeros_my;
 124   int exp_diff = ex - ey;
 125
 126   int right_shift = exp_diff < tail_zeros_my ? exp_diff : tail_zeros_my;
 127   my >>= right_shift;
 128   exp_diff -= right_shift;
 129   ey += right_shift;
 130
 131   int left_shift = exp_diff < EXPONENT_WIDTH ? exp_diff : EXPONENT_WIDTH;
 132   mx <<= left_shift;
 133   exp_diff -= left_shift;
 134
 135   mx %= my;
 136
 137   if (__glibc_unlikely (mx == 0))
 138     return asfloat (sx);
 139
 140   if (exp_diff == 0)
 141     return make_float (mx, ey, sx);
 142
 143   /* Assume modulo/divide operation is slow, so use multiplication with invert
 144      values.  */
 145   uint32_t inv_hy = UINT32_MAX / my;
 146   while (exp_diff > sides_zeroes) {
 147     exp_diff -= sides_zeroes;
 148     uint32_t hd = (mx * inv_hy) >> (BIT_WIDTH - sides_zeroes);
 149     mx <<= sides_zeroes;
 150     mx -= hd * my;
 151     while (__glibc_unlikely (mx > my))
 152       mx -= my;
 153   }
 154   uint32_t hd = (mx * inv_hy) >> (BIT_WIDTH - exp_diff);
 155   mx <<= exp_diff;
 156   mx -= hd * my;
 157   while (__glibc_unlikely (mx > my))
 158     mx -= my;
 159
 160   return make_float (mx, ey, sx);
 161 }
 162 strong_alias (__fmodf, __ieee754_fmodf)
 163 #if LIBM_SVID_COMPAT
 164 versioned_symbol (libm, __fmodf, fmodf, GLIBC_2_38);
 165 libm_alias_float_other (__fmod, fmod)
 166 #else
 167 libm_alias_float (__fmod, fmod)
 168 #endif
 169 libm_alias_finite (__ieee754_fmodf, __fmodf)