<div dir="ltr">On 21 January 2013 00:49, Chad Versace <<a href="mailto:chad.versace@linux.intel.com" target="_blank">chad.versace@linux.intel.com</a>> wrote: <div class="gmail_extra"><div class="gmail_quote"> <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">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 behavior is bia </blockquote><div> </div><div>Sentence fragment above. Did you lose your place while editing the commit message? </div><div>With the commit mesage fixed, this patch is: </div><div>Reviewed-by: Paul Berry <<a href="mailto:stereotype441@gmail.com">stereotype441@gmail.com</a>> </div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> 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. CC: Paul Berry <<a href="mailto:stereotype441@gmail.com" target="_blank">stereotype441@gmail.com</a>> Signed-off-by: Chad Versace <<a href="mailto:chad.versace@linux.intel.com" target="_blank">chad.versace@linux.intel.com</a>> --- src/mesa/main/imports.c | 66 +++++++++++++++++++++++++++---------------------- 1 file changed, 37 insertions(+), 29 deletions(-) diff --git a/src/mesa/main/imports.c b/src/mesa/main/imports.c index 26c91dc..e6f7542 100644 --- a/src/mesa/main/imports.c +++ b/src/mesa/main/imports.c @@ -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: - * <a href="http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html" target="_blank">http://www.opengl.org/discussion_boards/ubb/Forum3/HTML/008786.html</a> + * + * 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 */ - e = 0; - } - else if (new_exp < -14) { - /* this maps to a denorm */ - unsigned int exp_val = (unsigned int) (-14 - new_exp); /* 2^-exp_val*/ + 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; - 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; } -- 1.8.1.1 </blockquote></div> </div></div>