libclc/generic/lib/math/clc_remainder.cl

   1 /*
   2  * Copyright (c) 2014 Advanced Micro Devices, Inc.
   3  *
   4  * Permission is hereby granted, free of charge, to any person obtaining a copy
   5  * of this software and associated documentation files (the "Software"), to deal
   6  * in the Software without restriction, including without limitation the rights
   7  * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   8  * copies of the Software, and to permit persons to whom the Software is
   9  * furnished to do so, subject to the following conditions:
  10  *
  11  * The above copyright notice and this permission notice shall be included in
  12  * all copies or substantial portions of the Software.
  13  *
  14  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  15  * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  16  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  17  * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  18  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  19  * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  20  * THE SOFTWARE.
  21  */
  22
  23 #include <clc/clc.h>
  24 #include <clc/clcmacro.h>
  25 #include <clc/math/clc_floor.h>
  26 #include <clc/math/clc_trunc.h>
  27 #include <clc/shared/clc_max.h>
  28
  29 #include <math/clc_remainder.h>
  30 #include "config.h"
  31 #include "math.h"
  32
  33 _CLC_DEF _CLC_OVERLOAD float __clc_remainder(float x, float y)
  34 {
  35     int ux = as_int(x);
  36     int ax = ux & EXSIGNBIT_SP32;
  37     float xa = as_float(ax);
  38     int sx = ux ^ ax;
  39     int ex = ax >> EXPSHIFTBITS_SP32;
  40
  41     int uy = as_int(y);
  42     int ay = uy & EXSIGNBIT_SP32;
  43     float ya = as_float(ay);
  44     int ey = ay >> EXPSHIFTBITS_SP32;
  45
  46     float xr = as_float(0x3f800000 | (ax & 0x007fffff));
  47     float yr = as_float(0x3f800000 | (ay & 0x007fffff));
  48     int c;
  49     int k = ex - ey;
  50
  51     uint q = 0;
  52
  53     while (k > 0) {
  54         c = xr >= yr;
  55         q = (q << 1) | c;
  56         xr -= c ? yr : 0.0f;
  57         xr += xr;
  58         --k;
  59     }
  60
  61     c = xr > yr;
  62     q = (q << 1) | c;
  63     xr -= c ? yr : 0.0f;
  64
  65     int lt = ex < ey;
  66
  67     q = lt ? 0 : q;
  68     xr = lt ? xa : xr;
  69     yr = lt ? ya : yr;
  70
  71     c = (yr < 2.0f * xr) | ((yr == 2.0f * xr) & ((q & 0x1) == 0x1));
  72     xr -= c ? yr : 0.0f;
  73     q += c;
  74
  75     float s = as_float(ey << EXPSHIFTBITS_SP32);
  76     xr *= lt ? 1.0f : s;
  77
  78     c = ax == ay;
  79     xr = c ? 0.0f : xr;
  80
  81     xr = as_float(sx ^ as_int(xr));
  82
  83     c = ax > PINFBITPATT_SP32 | ay > PINFBITPATT_SP32 | ax == PINFBITPATT_SP32 | ay == 0;
  84     xr = c ? as_float(QNANBITPATT_SP32) : xr;
  85
  86     return xr;
  87
  88 }
  89 _CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_remainder, float, float);
  90
  91 #ifdef cl_khr_fp64
  92 _CLC_DEF _CLC_OVERLOAD double __clc_remainder(double x, double y)
  93 {
  94     ulong ux = as_ulong(x);
  95     ulong ax = ux & ~SIGNBIT_DP64;
  96     ulong xsgn = ux ^ ax;
  97     double dx = as_double(ax);
  98     int xexp = convert_int(ax >> EXPSHIFTBITS_DP64);
  99     int xexp1 = 11 - (int) clz(ax & MANTBITS_DP64);
 100     xexp1 = xexp < 1 ? xexp1 : xexp;
 101
 102     ulong uy = as_ulong(y);
 103     ulong ay = uy & ~SIGNBIT_DP64;
 104     double dy = as_double(ay);
 105     int yexp = convert_int(ay >> EXPSHIFTBITS_DP64);
 106     int yexp1 = 11 - (int) clz(ay & MANTBITS_DP64);
 107     yexp1 = yexp < 1 ? yexp1 : yexp;
 108
 109     int qsgn = ((ux ^ uy) & SIGNBIT_DP64) == 0UL ? 1 : -1;
 110
 111     // First assume |x| > |y|
 112
 113     // Set ntimes to the number of times we need to do a
 114     // partial remainder. If the exponent of x is an exact multiple
 115     // of 53 larger than the exponent of y, and the mantissa of x is
 116     // less than the mantissa of y, ntimes will be one too large
 117     // but it doesn't matter - it just means that we'll go round
 118     // the loop below one extra time.
 119     int ntimes = __clc_max(0, (xexp1 - yexp1) / 53);
 120     double w =  ldexp(dy, ntimes * 53);
 121     w = ntimes == 0 ? dy : w;
 122     double scale = ntimes == 0 ? 1.0 : 0x1.0p-53;
 123
 124     // Each time round the loop we compute a partial remainder.
 125     // This is done by subtracting a large multiple of w
 126     // from x each time, where w is a scaled up version of y.
 127     // The subtraction must be performed exactly in quad
 128     // precision, though the result at each stage can
 129     // fit exactly in a double precision number.
 130     int i;
 131     double t, v, p, pp;
 132
 133     for (i = 0; i < ntimes; i++) {
 134         // Compute integral multiplier
 135         t = __clc_trunc(dx / w);
 136
 137         // Compute w * t in quad precision
 138         p = w * t;
 139         pp = fma(w, t, -p);
 140
 141         // Subtract w * t from dx
 142         v = dx - p;
 143         dx = v + (((dx - v) - p) - pp);
 144
 145         // If t was one too large, dx will be negative. Add back one w.
 146         dx += dx < 0.0 ? w : 0.0;
 147
 148         // Scale w down by 2^(-53) for the next iteration
 149         w *= scale;
 150     }
 151
 152     // One more time
 153     // Variable todd says whether the integer t is odd or not
 154     t = __clc_floor(dx / w);
 155     long lt = (long)t;
 156     int todd = lt & 1;
 157
 158     p = w * t;
 159     pp = fma(w, t, -p);
 160     v = dx - p;
 161     dx = v + (((dx - v) - p) - pp);
 162     i = dx < 0.0;
 163     todd ^= i;
 164     dx += i ? w : 0.0;
 165
 166     // At this point, dx lies in the range [0,dy)
 167
 168     // For the fmod function, we're done apart from setting the correct sign.
 169     //
 170     // For the remainder function, we need to adjust dx
 171     // so that it lies in the range (-y/2, y/2] by carefully
 172     // subtracting w (== dy == y) if necessary. The rigmarole
 173     // with todd is to get the correct sign of the result
 174     // when x/y lies exactly half way between two integers,
 175     // when we need to choose the even integer.
 176
 177     int al = (2.0*dx > w) | (todd & (2.0*dx == w));
 178     double dxl = dx - (al ? w : 0.0);
 179
 180     int ag = (dx > 0.5*w) | (todd & (dx == 0.5*w));
 181     double dxg = dx - (ag ? w : 0.0);
 182
 183     dx = dy < 0x1.0p+1022 ? dxl : dxg;
 184
 185     double ret = as_double(xsgn ^ as_ulong(dx));
 186     dx = as_double(ax);
 187
 188     // Now handle |x| == |y|
 189     int c = dx == dy;
 190     t = as_double(xsgn);
 191     ret = c ? t : ret;
 192
 193     // Next, handle |x| < |y|
 194     c = dx < dy;
 195     ret = c ? x : ret;
 196
 197     c &= (yexp < 1023 & 2.0*dx > dy) | (dx > 0.5*dy);
 198     // we could use a conversion here instead since qsgn = +-1
 199     p = qsgn == 1 ? -1.0 : 1.0;
 200     t = fma(y, p, x);
 201     ret = c ? t : ret;
 202
 203     // We don't need anything special for |x| == 0
 204
 205     // |y| is 0
 206     c = dy == 0.0;
 207     ret = c ? as_double(QNANBITPATT_DP64) : ret;
 208
 209     // y is +-Inf, NaN
 210     c = yexp > BIASEDEMAX_DP64;
 211     t = y == y ? x : y;
 212     ret = c ? t : ret;
 213
 214     // x is +=Inf, NaN
 215     c = xexp > BIASEDEMAX_DP64;
 216     ret = c ? as_double(QNANBITPATT_DP64) : ret;
 217
 218     return ret;
 219 }
 220 _CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_remainder, double, double);
 221 #endif