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mesa: Remove rounding bias in _mesa_float_to_half() 

Not all float32 values can be exactly represented as a float16.
_mesa_float_to_half() rounded such intermediate float32 values to zero by
truncating unrepresentable bits in the mantissa.

This patch improves _mesa_float_to_half() by rounding intermediate float32
values to the nearest float16; when the float32 is exactly between two
float16 values we round to the one with an even mantissa. This behavior is
preferred over the old behavior because:
  - It has reduced bias relative to the old behavior.

  - 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.

Reviewed-by: Ian Romanick <ian.d.romanick@intel.com>
Reviewed-by: Paul Berry <stereotype441@gmail.com>
Signed-off-by: Chad Versace <chad.versace@linux.intel.com>
This commit is contained in:
Chad Versace 2013-01-16 19:58:42 -08:00
parent eac030e38e
commit 529b6d1f3d
1 changed files with 37 additions and 29 deletions
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66
src/mesa/main/imports.c
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@ -336,8 +336,21 @@ _mesa_round_to_even(float val)
/**
* Convert a 4-byte float to a 2-byte half float.
* Based on code from:
* http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html
*
* 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.
*/
GLhalfARB
_mesa_float_to_half(float val)
@ -376,32 +389,13 @@ _mesa_float_to_half(float val)
else {
/* regular number */
const int new_exp = flt_e - 127;
if (new_exp < -24) {
/* this maps to 0 */
/* m = 0; - already set */
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;
}
else if (new_exp < -14) {
/* this maps to a denorm */
unsigned int exp_val = (unsigned int) (-14 - new_exp); /* 2^-exp_val*/
e = 0;
switch (exp_val) {
case 0:
_mesa_warning(NULL,
"float_to_half: logical error in denorm creation!\n");
/* m = 0; - already set */
break;
case 1: m = 512 + (flt_m >> 14); break;
case 2: m = 256 + (flt_m >> 15); break;
case 3: m = 128 + (flt_m >> 16); break;
case 4: m = 64 + (flt_m >> 17); break;
case 5: m = 32 + (flt_m >> 18); break;
case 6: m = 16 + (flt_m >> 19); break;
case 7: m = 8 + (flt_m >> 20); break;
case 8: m = 4 + (flt_m >> 21); break;
case 9: m = 2 + (flt_m >> 22); break;
case 10: m = 1; break;
}
m = _mesa_round_to_even((1 << 24) * fabsf(fi.f));
}
else if (new_exp > 15) {
/* map this value to infinity */
@ -409,12 +403,26 @@ _mesa_float_to_half(float val)
e = 31;
}
else {
/* regular */
/* 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 = flt_m >> 13;
m = _mesa_round_to_even(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;
}