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/*
* Mesa 3-D graphics library
*
* Copyright (C) 1999-2007 Brian Paul All Rights Reserved.
* Copyright 2015 Philip Taylor <philip@zaynar.co.uk>
* Copyright 2018 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
* OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/
#include <math.h>
#include <assert.h>
#include "half_float.h"
#include "util/u_half.h"
#include "rounding.h"
#include "macros.h"
typedef union { float f; int32_t i; uint32_t u; } fi_type;
/**
* Convert a 4-byte float to a 2-byte half float.
*
* Not all float32 values can be represented exactly as a float16 value. We
* round such intermediate float32 values to the nearest float16. When the
* float32 lies exactly between to float16 values, we round to the one with
* an even mantissa.
*
* This rounding behavior has several benefits:
* - It has no sign bias.
*
* - It reproduces the behavior of real hardware: opcode F32TO16 in Intel's
* GPU ISA.
*
* - By reproducing the behavior of the GPU (at least on Intel hardware),
* compile-time evaluation of constant packHalf2x16 GLSL expressions will
* result in the same value as if the expression were executed on the GPU.
*/
uint16_t
_mesa_float_to_half(float val)
{
const fi_type fi = {val};
const int flt_m = fi.i & 0x7fffff;
const int flt_e = (fi.i >> 23) & 0xff;
const int flt_s = (fi.i >> 31) & 0x1;
int s, e, m = 0;
uint16_t result;
/* sign bit */
s = flt_s;
/* handle special cases */
if ((flt_e == 0) && (flt_m == 0)) {
/* zero */
/* m = 0; - already set */
e = 0;
}
else if ((flt_e == 0) && (flt_m != 0)) {
/* denorm -- denorm float maps to 0 half */
/* m = 0; - already set */
e = 0;
}
else if ((flt_e == 0xff) && (flt_m == 0)) {
/* infinity */
/* m = 0; - already set */
e = 31;
}
else if ((flt_e == 0xff) && (flt_m != 0)) {
/* NaN */
m = 1;
e = 31;
}
else {
/* regular number */
const int new_exp = flt_e - 127;
if (new_exp < -14) {
/* The float32 lies in the range (0.0, min_normal16) and is rounded
* to a nearby float16 value. The result will be either zero, subnormal,
* or normal.
*/
e = 0;
m = _mesa_lroundevenf((1 << 24) * fabsf(fi.f));
}
else if (new_exp > 15) {
/* map this value to infinity */
/* m = 0; - already set */
e = 31;
}
else {
/* The float32 lies in the range
* [min_normal16, max_normal16 + max_step16)
* and is rounded to a nearby float16 value. The result will be
* either normal or infinite.
*/
e = new_exp + 15;
m = _mesa_lroundevenf(flt_m / (float) (1 << 13));
}
}
assert(0 <= m && m <= 1024);
if (m == 1024) {
/* The float32 was rounded upwards into the range of the next exponent,
* so bump the exponent. This correctly handles the case where f32
* should be rounded up to float16 infinity.
*/
++e;
m = 0;
}
result = (s << 15) | (e << 10) | m;
return result;
}
/**
* Convert a 2-byte half float to a 4-byte float.
* Based on code from:
* http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html
*/
float
_mesa_half_to_float(uint16_t val)
{
return util_half_to_float(val);
}
/**
* Convert 0.0 to 0x00, 1.0 to 0xff.
* Values outside the range [0.0, 1.0] will give undefined results.
*/
uint8_t _mesa_half_to_unorm8(uint16_t val)
{
const int m = val & 0x3ff;
const int e = (val >> 10) & 0x1f;
ASSERTED const int s = (val >> 15) & 0x1;
/* v = round_to_nearest(1.mmmmmmmmmm * 2^(e-15) * 255)
* = round_to_nearest((1.mmmmmmmmmm * 255) * 2^(e-15))
* = round_to_nearest((1mmmmmmmmmm * 255) * 2^(e-25))
* = round_to_zero((1mmmmmmmmmm * 255) * 2^(e-25) + 0.5)
* = round_to_zero(((1mmmmmmmmmm * 255) * 2^(e-24) + 1) / 2)
*
* This happens to give the correct answer for zero/subnormals too
*/
assert(s == 0 && val <= FP16_ONE); /* check 0 <= this <= 1 */
/* (implies e <= 15, which means the bit-shifts below are safe) */
uint32_t v = ((1 << 10) | m) * 255;
v = ((v >> (24 - e)) + 1) >> 1;
return v;
}
/**
* Takes a uint16_t, divides by 65536, converts the infinite-precision
* result to fp16 with round-to-zero. Used by the ASTC decoder.
*/
uint16_t _mesa_uint16_div_64k_to_half(uint16_t v)
{
/* Zero or subnormal. Set the mantissa to (v << 8) and return. */
if (v < 4)
return v << 8;
/* Count the leading 0s in the uint16_t */
#ifdef HAVE___BUILTIN_CLZ
int n = __builtin_clz(v) - 16;
#else
int n = 16;
for (int i = 15; i >= 0; i--) {
if (v & (1 << i)) {
n = 15 - i;
break;
}
}
#endif
/* Shift the mantissa up so bit 16 is the hidden 1 bit,
* mask it off, then shift back down to 10 bits
*/
int m = ( ((uint32_t)v << (n + 1)) & 0xffff ) >> 6;
/* (0{n} 1 X{15-n}) * 2^-16
* = 1.X * 2^(15-n-16)
* = 1.X * 2^(14-n - 15)
* which is the FP16 form with e = 14 - n
*/
int e = 14 - n;
assert(e >= 1 && e <= 30);
assert(m >= 0 && m < 0x400);
return (e << 10) | m;
}
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