glsl: Improve precision of mod(x,y)

Currently, Mesa uses the lowering pass MOD_TO_FRACT to implement
mod(x,y) as y * fract(x/y). This implementation has a down side though:
it introduces precision errors due to the fract() operation. Even worse,
since the result of fract() is multiplied by y, the larger y gets the
larger the precision error we produce, so for large enough numbers the
precision loss is significant. Some examples on i965:

Operation                           Precision error
-----------------------------------------------------
mod(-1.951171875, 1.9980468750)      0.0000000447
mod(121.57, 13.29)                   0.0000023842
mod(3769.12, 321.99)                 0.0000762939
mod(3769.12, 1321.99)                0.0001220703
mod(-987654.125, 123456.984375)      0.0160663128
mod( 987654.125, 123456.984375)      0.0312500000

This patch replaces the current lowering pass with a different one
(MOD_TO_FLOOR) that follows the recommended implementation in the GLSL
man pages:

mod(x,y) = x - y * floor(x/y)

This implementation eliminates the precision errors at the expense of
an additional add instruction on some systems. On systems that can do
negate with multiply-add in a single operation this new implementation
would come at no additional cost.

v2 (Ian Romanick)
- Do not clone operands because when they are expressions we would be
duplicating them and that can lead to suboptimal code.

Fixes the following 16 dEQP tests:
dEQP-GLES3.functional.shaders.builtin_functions.precision.mod.mediump_*
dEQP-GLES3.functional.shaders.builtin_functions.precision.mod.highp_*

Reviewed-by: Ian Romanick <ian.d.romanick@intel.com>

1 files changed, 1 insertions, 1 deletions

diff --git a/src/mesa/drivers/dri/i965/brw_shader.cpp b/src/mesa/drivers/dri/i965/brw_shader.cpp
index be30d97..7321665 100644
--- a/src/mesa/drivers/dri/i965/brw_shader.cpp
+++ b/src/mesa/drivers/dri/i965/brw_shader.cpp
@@ -157,7 +157,7 @@ brw_link_shader(struct gl_context *ctx, struct gl_shader_program *shProg)
                                   ? BITFIELD_INSERT_TO_BFM_BFI
                                   : 0;
       lower_instructions(shader->base.ir,
-			 MOD_TO_FRACT |
+			 MOD_TO_FLOOR |
 			 DIV_TO_MUL_RCP |
 			 SUB_TO_ADD_NEG |
 			 EXP_TO_EXP2 |