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[915] Fix fp SIN function, and use a quadratic approximation instead of Taylor.

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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.
This commit is contained in:
Eric Anholt
2008-02-06 11:34:14 -08:00
parent c0e026c809
commit d98abcbef0
1 changed files with 55 additions and 40 deletions
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95
src/mesa/drivers/dri/i915/i915_fragprog.c
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@@ -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,
A0_MAD,
tmp, A0_DEST_CHANNEL_X, 0,
src0, i915_emit_const1f(p, 1.0 / (M_PI)), 0);
src0,
i915_emit_const1f(p, 1.0 / (2.0 * M_PI)),
i915_emit_const1f(p, .5));
i915_emit_arith(p, A0_MOD, tmp, A0_DEST_CHANNEL_X, 0, tmp, 0, 0);
i915_emit_arith(p, A0_FRC, 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_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_MUL,
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);
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: