src/util/half_float.c

   1 /*
   2  * Mesa 3-D graphics library
   3  *
   4  * Copyright (C) 1999-2007  Brian Paul   All Rights Reserved.
   5  * Copyright 2015 Philip Taylor <philip@zaynar.co.uk>
   6  * Copyright 2018 Advanced Micro Devices, Inc.
   7  *
   8  * Permission is hereby granted, free of charge, to any person obtaining a
   9  * copy of this software and associated documentation files (the "Software"),
  10  * to deal in the Software without restriction, including without limitation
  11  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
  12  * and/or sell copies of the Software, and to permit persons to whom the
  13  * Software is furnished to do so, subject to the following conditions:
  14  *
  15  * The above copyright notice and this permission notice shall be included
  16  * in all copies or substantial portions of the Software.
  17  *
  18  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  19  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  20  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
  21  * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
  22  * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
  23  * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
  24  * OTHER DEALINGS IN THE SOFTWARE.
  25  */
  26
  27 #include <math.h>
  28 #include <assert.h>
  29 #include "half_float.h"
  30 #include "util/u_half.h"
  31 #include "rounding.h"
  32 #include "macros.h"
  33
  34 typedef union { float f; int32_t i; uint32_t u; } fi_type;
  35
  36 /**
  37  * Convert a 4-byte float to a 2-byte half float.
  38  *
  39  * Not all float32 values can be represented exactly as a float16 value. We
  40  * round such intermediate float32 values to the nearest float16. When the
  41  * float32 lies exactly between to float16 values, we round to the one with
  42  * an even mantissa.
  43  *
  44  * This rounding behavior has several benefits:
  45  *   - It has no sign bias.
  46  *
  47  *   - It reproduces the behavior of real hardware: opcode F32TO16 in Intel's
  48  *     GPU ISA.
  49  *
  50  *   - By reproducing the behavior of the GPU (at least on Intel hardware),
  51  *     compile-time evaluation of constant packHalf2x16 GLSL expressions will
  52  *     result in the same value as if the expression were executed on the GPU.
  53  */
  54 uint16_t
  55 _mesa_float_to_half(float val)
  56 {
  57    const fi_type fi = {val};
  58    const int flt_m = fi.i & 0x7fffff;
  59    const int flt_e = (fi.i >> 23) & 0xff;
  60    const int flt_s = (fi.i >> 31) & 0x1;
  61    int s, e, m = 0;
  62    uint16_t result;
  63
  64    /* sign bit */
  65    s = flt_s;
  66
  67    /* handle special cases */
  68    if ((flt_e == 0) && (flt_m == 0)) {
  69       /* zero */
  70       /* m = 0; - already set */
  71       e = 0;
  72    }
  73    else if ((flt_e == 0) && (flt_m != 0)) {
  74       /* denorm -- denorm float maps to 0 half */
  75       /* m = 0; - already set */
  76       e = 0;
  77    }
  78    else if ((flt_e == 0xff) && (flt_m == 0)) {
  79       /* infinity */
  80       /* m = 0; - already set */
  81       e = 31;
  82    }
  83    else if ((flt_e == 0xff) && (flt_m != 0)) {
  84       /* NaN */
  85       m = 1;
  86       e = 31;
  87    }
  88    else {
  89       /* regular number */
  90       const int new_exp = flt_e - 127;
  91       if (new_exp < -14) {
  92          /* The float32 lies in the range (0.0, min_normal16) and is rounded
  93           * to a nearby float16 value. The result will be either zero, subnormal,
  94           * or normal.
  95           */
  96          e = 0;
  97          m = _mesa_lroundevenf((1 << 24) * fabsf(fi.f));
  98       }
  99       else if (new_exp > 15) {
 100          /* map this value to infinity */
 101          /* m = 0; - already set */
 102          e = 31;
 103       }
 104       else {
 105          /* The float32 lies in the range
 106           *   [min_normal16, max_normal16 + max_step16)
 107           * and is rounded to a nearby float16 value. The result will be
 108           * either normal or infinite.
 109           */
 110          e = new_exp + 15;
 111          m = _mesa_lroundevenf(flt_m / (float) (1 << 13));
 112       }
 113    }
 114
 115    assert(0 <= m && m <= 1024);
 116    if (m == 1024) {
 117       /* The float32 was rounded upwards into the range of the next exponent,
 118        * so bump the exponent. This correctly handles the case where f32
 119        * should be rounded up to float16 infinity.
 120        */
 121       ++e;
 122       m = 0;
 123    }
 124
 125    result = (s << 15) | (e << 10) | m;
 126    return result;
 127 }
 128
 129
 130 /**
 131  * Convert a 2-byte half float to a 4-byte float.
 132  * Based on code from:
 133  * http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html
 134  */
 135 float
 136 _mesa_half_to_float(uint16_t val)
 137 {
 138    return util_half_to_float(val);
 139 }
 140
 141 /**
 142   * Convert 0.0 to 0x00, 1.0 to 0xff.
 143   * Values outside the range [0.0, 1.0] will give undefined results.
 144   */
 145 uint8_t _mesa_half_to_unorm8(uint16_t val)
 146 {
 147    const int m = val & 0x3ff;
 148    const int e = (val >> 10) & 0x1f;
 149    ASSERTED const int s = (val >> 15) & 0x1;
 150
 151    /* v = round_to_nearest(1.mmmmmmmmmm * 2^(e-15) * 255)
 152     *   = round_to_nearest((1.mmmmmmmmmm * 255) * 2^(e-15))
 153     *   = round_to_nearest((1mmmmmmmmmm * 255) * 2^(e-25))
 154     *   = round_to_zero((1mmmmmmmmmm * 255) * 2^(e-25) + 0.5)
 155     *   = round_to_zero(((1mmmmmmmmmm * 255) * 2^(e-24) + 1) / 2)
 156     *
 157     * This happens to give the correct answer for zero/subnormals too
 158     */
 159    assert(s == 0 && val <= FP16_ONE); /* check 0 <= this <= 1 */
 160    /* (implies e <= 15, which means the bit-shifts below are safe) */
 161
 162    uint32_t v = ((1 << 10) | m) * 255;
 163    v = ((v >> (24 - e)) + 1) >> 1;
 164    return v;
 165 }
 166
 167 /**
 168   * Takes a uint16_t, divides by 65536, converts the infinite-precision
 169   * result to fp16 with round-to-zero. Used by the ASTC decoder.
 170   */
 171 uint16_t _mesa_uint16_div_64k_to_half(uint16_t v)
 172 {
 173    /* Zero or subnormal. Set the mantissa to (v << 8) and return. */
 174    if (v < 4)
 175       return v << 8;
 176
 177    /* Count the leading 0s in the uint16_t */
 178 #ifdef HAVE___BUILTIN_CLZ
 179    int n = __builtin_clz(v) - 16;
 180 #else
 181    int n = 16;
 182    for (int i = 15; i >= 0; i--) {
 183       if (v & (1 << i)) {
 184          n = 15 - i;
 185          break;
 186       }
 187    }
 188 #endif
 189
 190    /* Shift the mantissa up so bit 16 is the hidden 1 bit,
 191     * mask it off, then shift back down to 10 bits
 192     */
 193    int m = ( ((uint32_t)v << (n + 1)) & 0xffff ) >> 6;
 194
 195    /*  (0{n} 1 X{15-n}) * 2^-16
 196     * = 1.X * 2^(15-n-16)
 197     * = 1.X * 2^(14-n - 15)
 198     * which is the FP16 form with e = 14 - n
 199     */
 200    int e = 14 - n;
 201
 202    assert(e >= 1 && e <= 30);
 203    assert(m >= 0 && m < 0x400);
 204
 205    return (e << 10) | m;
 206 }