2 * Mesa 3-D graphics library
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.
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:
15 * The above copyright notice and this permission notice shall be included
16 * in all copies or substantial portions of the Software.
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.
29 #include "half_float.h"
32 typedef union { float f
; int32_t i
; uint32_t u
; } fi_type
;
35 * Convert a 4-byte float to a 2-byte half float.
37 * Not all float32 values can be represented exactly as a float16 value. We
38 * round such intermediate float32 values to the nearest float16. When the
39 * float32 lies exactly between to float16 values, we round to the one with
42 * This rounding behavior has several benefits:
43 * - It has no sign bias.
45 * - It reproduces the behavior of real hardware: opcode F32TO16 in Intel's
48 * - By reproducing the behavior of the GPU (at least on Intel hardware),
49 * compile-time evaluation of constant packHalf2x16 GLSL expressions will
50 * result in the same value as if the expression were executed on the GPU.
53 _mesa_float_to_half(float val
)
55 const fi_type fi
= {val
};
56 const int flt_m
= fi
.i
& 0x7fffff;
57 const int flt_e
= (fi
.i
>> 23) & 0xff;
58 const int flt_s
= (fi
.i
>> 31) & 0x1;
65 /* handle special cases */
66 if ((flt_e
== 0) && (flt_m
== 0)) {
68 /* m = 0; - already set */
71 else if ((flt_e
== 0) && (flt_m
!= 0)) {
72 /* denorm -- denorm float maps to 0 half */
73 /* m = 0; - already set */
76 else if ((flt_e
== 0xff) && (flt_m
== 0)) {
78 /* m = 0; - already set */
81 else if ((flt_e
== 0xff) && (flt_m
!= 0)) {
88 const int new_exp
= flt_e
- 127;
90 /* The float32 lies in the range (0.0, min_normal16) and is rounded
91 * to a nearby float16 value. The result will be either zero, subnormal,
95 m
= _mesa_lroundevenf((1 << 24) * fabsf(fi
.f
));
97 else if (new_exp
> 15) {
98 /* map this value to infinity */
99 /* m = 0; - already set */
103 /* The float32 lies in the range
104 * [min_normal16, max_normal16 + max_step16)
105 * and is rounded to a nearby float16 value. The result will be
106 * either normal or infinite.
109 m
= _mesa_lroundevenf(flt_m
/ (float) (1 << 13));
113 assert(0 <= m
&& m
<= 1024);
115 /* The float32 was rounded upwards into the range of the next exponent,
116 * so bump the exponent. This correctly handles the case where f32
117 * should be rounded up to float16 infinity.
123 result
= (s
<< 15) | (e
<< 10) | m
;
129 * Convert a 2-byte half float to a 4-byte float.
130 * Based on code from:
131 * http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html
134 _mesa_half_to_float(uint16_t val
)
136 /* XXX could also use a 64K-entry lookup table */
137 const int m
= val
& 0x3ff;
138 const int e
= (val
>> 10) & 0x1f;
139 const int s
= (val
>> 15) & 0x1;
140 int flt_m
, flt_e
, flt_s
;
147 /* handle special cases */
148 if ((e
== 0) && (m
== 0)) {
153 else if ((e
== 0) && (m
!= 0)) {
154 /* denorm -- denorm half will fit in non-denorm single */
155 const float half_denorm
= 1.0f
/ 16384.0f
; /* 2^-14 */
156 float mantissa
= ((float) (m
)) / 1024.0f
;
157 float sign
= s
? -1.0f
: 1.0f
;
158 return sign
* mantissa
* half_denorm
;
160 else if ((e
== 31) && (m
== 0)) {
165 else if ((e
== 31) && (m
!= 0)) {
176 fi
.i
= (flt_s
<< 31) | (flt_e
<< 23) | flt_m
;
182 * Convert 0.0 to 0x00, 1.0 to 0xff.
183 * Values outside the range [0.0, 1.0] will give undefined results.
185 uint8_t _mesa_half_to_unorm8(uint16_t val
)
187 const int m
= val
& 0x3ff;
188 const int e
= (val
>> 10) & 0x1f;
189 const int s
= (val
>> 15) & 0x1;
191 /* v = round_to_nearest(1.mmmmmmmmmm * 2^(e-15) * 255)
192 * = round_to_nearest((1.mmmmmmmmmm * 255) * 2^(e-15))
193 * = round_to_nearest((1mmmmmmmmmm * 255) * 2^(e-25))
194 * = round_to_zero((1mmmmmmmmmm * 255) * 2^(e-25) + 0.5)
195 * = round_to_zero(((1mmmmmmmmmm * 255) * 2^(e-24) + 1) / 2)
197 * This happens to give the correct answer for zero/subnormals too
199 assert(s
== 0 && val
<= FP16_ONE
); /* check 0 <= this <= 1 */
200 /* (implies e <= 15, which means the bit-shifts below are safe) */
202 uint32_t v
= ((1 << 10) | m
) * 255;
203 v
= ((v
>> (24 - e
)) + 1) >> 1;
208 * Takes a uint16_t, divides by 65536, converts the infinite-precision
209 * result to fp16 with round-to-zero. Used by the ASTC decoder.
211 uint16_t _mesa_uint16_div_64k_to_half(uint16_t v
)
213 /* Zero or subnormal. Set the mantissa to (v << 8) and return. */
217 /* Count the leading 0s in the uint16_t */
218 int n
= __builtin_clz(v
) - (sizeof(unsigned int) - sizeof(uint16_t)) * 8;
220 /* Shift the mantissa up so bit 16 is the hidden 1 bit,
221 * mask it off, then shift back down to 10 bits
223 int m
= ( ((uint32_t)v
<< (n
+ 1)) & 0xffff ) >> 6;
225 /* (0{n} 1 X{15-n}) * 2^-16
226 * = 1.X * 2^(15-n-16)
227 * = 1.X * 2^(14-n - 15)
228 * which is the FP16 form with e = 14 - n
232 assert(e
>= 1 && e
<= 30);
233 assert(m
>= 0 && m
< 0x400);
235 return (e
<< 10) | m
;