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authorEric Anholt <[email protected]>2008-02-06 11:34:14 -0800
committerEric Anholt <[email protected]>2008-02-06 15:26:00 -0800
commitd98abcbef0bd4200fc0fd30fc0524bf452df3572 (patch)
treef053f350ece4c97bf6b4718d22edb3cfa65ea946 /src/mesa
parentc0e026c8090954ddb629a01cc1a93c61b2fc8298 (diff)
[915] Fix fp SIN function, and use a quadratic approximation instead of Taylor.
The Taylor series notably fails at producing sin(pi) == 0, which leads to discontinuity every 2*pi. The quadratic gets us sin(pi) == 0 behavior, at the expense of going from 2.4% THD with working Taylor series to 3.8% THD (easily seen on comparative graphs of the two). However, our previous implementation was producing sin(pi) < -1 and worse, so any reasonable approximation is an improvement. This also fixes the repeating behavior, where the previous implementation would repeat sin(x) for x>pi as sin(x % pi) and the opposite for x < -pi.
Diffstat (limited to 'src/mesa')
-rw-r--r--src/mesa/drivers/dri/i915/i915_fragprog.c99
1 files changed, 57 insertions, 42 deletions
diff --git a/src/mesa/drivers/dri/i915/i915_fragprog.c b/src/mesa/drivers/dri/i915/i915_fragprog.c
index bafc8f02b84..0a643719f88 100644
--- a/src/mesa/drivers/dri/i915/i915_fragprog.c
+++ b/src/mesa/drivers/dri/i915/i915_fragprog.c
@@ -43,9 +43,13 @@
#include "i915_context.h"
#include "i915_program.h"
+static const GLfloat sin_quad_constants[4] = {
+ 4.0,
+ -4.0,
+ 2.0,
+ -1.0
+};
-
-/* 1, -1/3!, 1/5!, -1/7! */
static const GLfloat sin_constants[4] = { 1.0,
-1.0 / (3 * 2 * 1),
1.0 / (5 * 4 * 3 * 2 * 1),
@@ -337,7 +341,7 @@ upload_program(struct i915_fragment_program *p)
while (1) {
GLuint src0, src1, src2, flags;
- GLuint tmp = 0;
+ GLuint tmp = 0, consts = 0;
switch (inst->Opcode) {
case OPCODE_ABS:
@@ -686,51 +690,62 @@ upload_program(struct i915_fragment_program *p)
case OPCODE_SIN:
src0 = src_vector(p, &inst->SrcReg[0], program);
tmp = i915_get_utemp(p);
+ consts = i915_emit_const4fv(p, sin_quad_constants);
+ /* Reduce range from repeating about [-pi,pi] to [-1,1] */
i915_emit_arith(p,
- A0_MUL,
- tmp, A0_DEST_CHANNEL_X, 0,
- src0, i915_emit_const1f(p, 1.0 / (M_PI)), 0);
-
- i915_emit_arith(p, A0_MOD, tmp, A0_DEST_CHANNEL_X, 0, tmp, 0, 0);
-
- /* By choosing different taylor constants, could get rid of this mul:
- */
- i915_emit_arith(p,
- A0_MUL,
+ A0_MAD,
tmp, A0_DEST_CHANNEL_X, 0,
- tmp, i915_emit_const1f(p, (M_PI)), 0);
-
- /*
- * t0.xy = MUL x.xx11, x.x1111 ; x^2, x, 1, 1
- * t0 = MUL t0.xyxy t0.xx11 ; x^4, x^3, x^2, x
- * t1 = MUL t0.xyyw t0.yz11 ; x^7 x^5 x^3 x
- * result = DP4 t1.wzyx, sin_constants
- */
- i915_emit_arith(p,
- A0_MUL,
- tmp, A0_DEST_CHANNEL_XY, 0,
- swizzle(tmp, X, X, ONE, ONE),
- swizzle(tmp, X, ONE, ONE, ONE), 0);
-
- i915_emit_arith(p,
- A0_MUL,
- tmp, A0_DEST_CHANNEL_ALL, 0,
- swizzle(tmp, X, Y, X, Y),
- swizzle(tmp, X, X, ONE, ONE), 0);
-
- i915_emit_arith(p,
- A0_MUL,
- tmp, A0_DEST_CHANNEL_ALL, 0,
- swizzle(tmp, X, Y, Y, W),
- swizzle(tmp, X, Z, ONE, ONE), 0);
-
+ src0,
+ i915_emit_const1f(p, 1.0 / (2.0 * M_PI)),
+ i915_emit_const1f(p, .5));
+
+ i915_emit_arith(p, A0_FRC, tmp, A0_DEST_CHANNEL_X, 0, tmp, 0, 0);
+
+ i915_emit_arith(p,
+ A0_MAD,
+ tmp, A0_DEST_CHANNEL_X, 0,
+ tmp,
+ swizzle(consts, Z, ZERO, ZERO, ZERO), /* 2 */
+ swizzle(consts, W, ZERO, ZERO, ZERO)); /* -1 */
+
+ /* Compute sin using a quadratic. While it has increased total
+ * error over the range, it does give continuity that the 4-component
+ * Taylor series lacks when repeating the range due to its
+ * sin(PI) != 0 behavior.
+ *
+ * The idea was described at:
+ * http://www.devmaster.net/forums/showthread.php?t=5784
+ *
+ * If we're concerned about the error of this approximation, we should
+ * probably incorporate a second pass to include a x**4 factor.
+ */
+
+ /* tmp.y = abs(tmp.x); {x, abs(x), 0, 0} */
+ i915_emit_arith(p,
+ A0_MAX,
+ tmp, A0_DEST_CHANNEL_Y, 0,
+ swizzle(tmp, ZERO, X, ZERO, ZERO),
+ negate(swizzle(tmp, ZERO, X, ZERO, ZERO), 0, 1, 0, 0),
+ 0);
+
+ /* tmp.y = tmp.y * tmp.x; {x, x * abs(x), 0, 0} */
+ i915_emit_arith(p,
+ A0_MUL,
+ tmp, A0_DEST_CHANNEL_Y, 0,
+ swizzle(tmp, ZERO, X, ZERO, ZERO),
+ tmp,
+ 0);
+
+ /* result = tmp.xy DP sin_quad_constants.xy */
i915_emit_arith(p,
- A0_DP4,
+ A0_DP3,
get_result_vector(p, inst),
get_result_flags(inst), 0,
- swizzle(tmp, W, Z, Y, X),
- i915_emit_const4fv(p, sin_constants), 0);
+ tmp,
+ swizzle(i915_emit_const4fv(p, sin_quad_constants),
+ X, Y, ZERO, ZERO),
+ 0);
break;
case OPCODE_SLT: