Rob Clark | 183db3a | 2015-10-10 13:26:03 -0400 | [diff] [blame^] | 1 | /* |
| 2 | * Mesa 3-D graphics library |
| 3 | * |
| 4 | * Copyright (C) 1999-2007 Brian Paul All Rights Reserved. |
| 5 | * |
| 6 | * Permission is hereby granted, free of charge, to any person obtaining a |
| 7 | * copy of this software and associated documentation files (the "Software"), |
| 8 | * to deal in the Software without restriction, including without limitation |
| 9 | * the rights to use, copy, modify, merge, publish, distribute, sublicense, |
| 10 | * and/or sell copies of the Software, and to permit persons to whom the |
| 11 | * Software is furnished to do so, subject to the following conditions: |
| 12 | * |
| 13 | * The above copyright notice and this permission notice shall be included |
| 14 | * in all copies or substantial portions of the Software. |
| 15 | * |
| 16 | * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS |
| 17 | * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| 18 | * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
| 19 | * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR |
| 20 | * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, |
| 21 | * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR |
| 22 | * OTHER DEALINGS IN THE SOFTWARE. |
| 23 | */ |
| 24 | |
| 25 | #include <math.h> |
| 26 | #include <assert.h> |
| 27 | #include "half_float.h" |
| 28 | #include "rounding.h" |
| 29 | |
| 30 | typedef union { float f; int32_t i; uint32_t u; } fi_type; |
| 31 | |
| 32 | /** |
| 33 | * Convert a 4-byte float to a 2-byte half float. |
| 34 | * |
| 35 | * Not all float32 values can be represented exactly as a float16 value. We |
| 36 | * round such intermediate float32 values to the nearest float16. When the |
| 37 | * float32 lies exactly between to float16 values, we round to the one with |
| 38 | * an even mantissa. |
| 39 | * |
| 40 | * This rounding behavior has several benefits: |
| 41 | * - It has no sign bias. |
| 42 | * |
| 43 | * - It reproduces the behavior of real hardware: opcode F32TO16 in Intel's |
| 44 | * GPU ISA. |
| 45 | * |
| 46 | * - By reproducing the behavior of the GPU (at least on Intel hardware), |
| 47 | * compile-time evaluation of constant packHalf2x16 GLSL expressions will |
| 48 | * result in the same value as if the expression were executed on the GPU. |
| 49 | */ |
| 50 | uint16_t |
| 51 | _mesa_float_to_half(float val) |
| 52 | { |
| 53 | const fi_type fi = {val}; |
| 54 | const int flt_m = fi.i & 0x7fffff; |
| 55 | const int flt_e = (fi.i >> 23) & 0xff; |
| 56 | const int flt_s = (fi.i >> 31) & 0x1; |
| 57 | int s, e, m = 0; |
| 58 | uint16_t result; |
| 59 | |
| 60 | /* sign bit */ |
| 61 | s = flt_s; |
| 62 | |
| 63 | /* handle special cases */ |
| 64 | if ((flt_e == 0) && (flt_m == 0)) { |
| 65 | /* zero */ |
| 66 | /* m = 0; - already set */ |
| 67 | e = 0; |
| 68 | } |
| 69 | else if ((flt_e == 0) && (flt_m != 0)) { |
| 70 | /* denorm -- denorm float maps to 0 half */ |
| 71 | /* m = 0; - already set */ |
| 72 | e = 0; |
| 73 | } |
| 74 | else if ((flt_e == 0xff) && (flt_m == 0)) { |
| 75 | /* infinity */ |
| 76 | /* m = 0; - already set */ |
| 77 | e = 31; |
| 78 | } |
| 79 | else if ((flt_e == 0xff) && (flt_m != 0)) { |
| 80 | /* NaN */ |
| 81 | m = 1; |
| 82 | e = 31; |
| 83 | } |
| 84 | else { |
| 85 | /* regular number */ |
| 86 | const int new_exp = flt_e - 127; |
| 87 | if (new_exp < -14) { |
| 88 | /* The float32 lies in the range (0.0, min_normal16) and is rounded |
| 89 | * to a nearby float16 value. The result will be either zero, subnormal, |
| 90 | * or normal. |
| 91 | */ |
| 92 | e = 0; |
| 93 | m = _mesa_lroundevenf((1 << 24) * fabsf(fi.f)); |
| 94 | } |
| 95 | else if (new_exp > 15) { |
| 96 | /* map this value to infinity */ |
| 97 | /* m = 0; - already set */ |
| 98 | e = 31; |
| 99 | } |
| 100 | else { |
| 101 | /* The float32 lies in the range |
| 102 | * [min_normal16, max_normal16 + max_step16) |
| 103 | * and is rounded to a nearby float16 value. The result will be |
| 104 | * either normal or infinite. |
| 105 | */ |
| 106 | e = new_exp + 15; |
| 107 | m = _mesa_lroundevenf(flt_m / (float) (1 << 13)); |
| 108 | } |
| 109 | } |
| 110 | |
| 111 | assert(0 <= m && m <= 1024); |
| 112 | if (m == 1024) { |
| 113 | /* The float32 was rounded upwards into the range of the next exponent, |
| 114 | * so bump the exponent. This correctly handles the case where f32 |
| 115 | * should be rounded up to float16 infinity. |
| 116 | */ |
| 117 | ++e; |
| 118 | m = 0; |
| 119 | } |
| 120 | |
| 121 | result = (s << 15) | (e << 10) | m; |
| 122 | return result; |
| 123 | } |
| 124 | |
| 125 | |
| 126 | /** |
| 127 | * Convert a 2-byte half float to a 4-byte float. |
| 128 | * Based on code from: |
| 129 | * http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html |
| 130 | */ |
| 131 | float |
| 132 | _mesa_half_to_float(uint16_t val) |
| 133 | { |
| 134 | /* XXX could also use a 64K-entry lookup table */ |
| 135 | const int m = val & 0x3ff; |
| 136 | const int e = (val >> 10) & 0x1f; |
| 137 | const int s = (val >> 15) & 0x1; |
| 138 | int flt_m, flt_e, flt_s; |
| 139 | fi_type fi; |
| 140 | float result; |
| 141 | |
| 142 | /* sign bit */ |
| 143 | flt_s = s; |
| 144 | |
| 145 | /* handle special cases */ |
| 146 | if ((e == 0) && (m == 0)) { |
| 147 | /* zero */ |
| 148 | flt_m = 0; |
| 149 | flt_e = 0; |
| 150 | } |
| 151 | else if ((e == 0) && (m != 0)) { |
| 152 | /* denorm -- denorm half will fit in non-denorm single */ |
| 153 | const float half_denorm = 1.0f / 16384.0f; /* 2^-14 */ |
| 154 | float mantissa = ((float) (m)) / 1024.0f; |
| 155 | float sign = s ? -1.0f : 1.0f; |
| 156 | return sign * mantissa * half_denorm; |
| 157 | } |
| 158 | else if ((e == 31) && (m == 0)) { |
| 159 | /* infinity */ |
| 160 | flt_e = 0xff; |
| 161 | flt_m = 0; |
| 162 | } |
| 163 | else if ((e == 31) && (m != 0)) { |
| 164 | /* NaN */ |
| 165 | flt_e = 0xff; |
| 166 | flt_m = 1; |
| 167 | } |
| 168 | else { |
| 169 | /* regular */ |
| 170 | flt_e = e + 112; |
| 171 | flt_m = m << 13; |
| 172 | } |
| 173 | |
| 174 | fi.i = (flt_s << 31) | (flt_e << 23) | flt_m; |
| 175 | result = fi.f; |
| 176 | return result; |
| 177 | } |