Mesa (master): gallivm: Updated lp_build_log2_approx to use a more accurate polynomial.
Jose Fonseca
jrfonseca at kemper.freedesktop.org
Thu Apr 5 19:40:38 UTC 2012
Module: Mesa
Branch: master
Commit: cf68959f99f372ef1c4f647e7a7438ab478314c9
URL: http://cgit.freedesktop.org/mesa/mesa/commit/?id=cf68959f99f372ef1c4f647e7a7438ab478314c9
Author: James Benton <jbenton at vmware.com>
Date: Thu Apr 5 20:34:11 2012 +0100
gallivm: Updated lp_build_log2_approx to use a more accurate polynomial.
Tested with lp_test_arit with 100% passes and piglit tests with 100%
pass for log but some tests still fail for pow.
Signed-off-by: José Fonseca <jfonseca at vmware.com>
---
src/gallium/auxiliary/gallivm/f.cpp | 8 ++--
src/gallium/auxiliary/gallivm/lp_bld_arit.c | 65 +++++++++++++++-----------
src/gallium/drivers/llvmpipe/lp_test_arit.c | 4 +-
3 files changed, 43 insertions(+), 34 deletions(-)
diff --git a/src/gallium/auxiliary/gallivm/f.cpp b/src/gallium/auxiliary/gallivm/f.cpp
index 7cb50f1..4b33e49 100644
--- a/src/gallium/auxiliary/gallivm/f.cpp
+++ b/src/gallium/auxiliary/gallivm/f.cpp
@@ -41,11 +41,11 @@
*
* and take the coefficients from the P = { ... } array.
*
- * - To compute log2 5th order polynomial between [1, 2] do:
+ * - To compute log2 4th order polynomial between [0, 1/9] do:
*
* variant 1
- * range 1 2
- * order 5 0
+ * range 0 0.111111112
+ * order 4 0
* step 200
* info
*
@@ -77,7 +77,7 @@ boost::math::ntl::RR f(const boost::math::ntl::RR& x, int variant)
return exp2(x);
case 1:
- return log2(x)/(x - 1.0);
+ return log2((1.0 + sqrt(x))/(1.0 - sqrt(x)))/sqrt(x);
}
return 0;
diff --git a/src/gallium/auxiliary/gallivm/lp_bld_arit.c b/src/gallium/auxiliary/gallivm/lp_bld_arit.c
index d07cf68..4ba4aa5 100644
--- a/src/gallium/auxiliary/gallivm/lp_bld_arit.c
+++ b/src/gallium/auxiliary/gallivm/lp_bld_arit.c
@@ -63,7 +63,7 @@
#define EXP_POLY_DEGREE 5
-#define LOG_POLY_DEGREE 5
+#define LOG_POLY_DEGREE 4
/**
@@ -2388,41 +2388,38 @@ lp_build_extract_mantissa(struct lp_build_context *bld,
/**
- * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
+ * Minimax polynomial fit of log2((1.0 + sqrt(x))/(1.0 - sqrt(x)))/sqrt(x) ,for x in range of [0, 1/9[
* These coefficients can be generate with
* http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
*/
const double lp_build_log2_polynomial[] = {
-#if LOG_POLY_DEGREE == 6
- 3.11578814719469302614,
- -3.32419399085241980044,
- 2.59883907202499966007,
- -1.23152682416275988241,
- 0.318212422185251071475,
- -0.0344359067839062357313
-#elif LOG_POLY_DEGREE == 5
- 2.8882704548164776201,
- -2.52074962577807006663,
- 1.48116647521213171641,
- -0.465725644288844778798,
- 0.0596515482674574969533
+#if LOG_POLY_DEGREE == 5
+ 2.88539008148777786488L,
+ 0.961796878841293367824L,
+ 0.577058946784739859012L,
+ 0.412914355135828735411L,
+ 0.308591899232910175289L,
+ 0.352376952300281371868L,
#elif LOG_POLY_DEGREE == 4
- 2.61761038894603480148,
- -1.75647175389045657003,
- 0.688243882994381274313,
- -0.107254423828329604454
+ 2.88539009343309178325L,
+ 0.961791550404184197881L,
+ 0.577440339438736392009L,
+ 0.403343858251329912514L,
+ 0.406718052498846252698L,
#elif LOG_POLY_DEGREE == 3
- 2.28330284476918490682,
- -1.04913055217340124191,
- 0.204446009836232697516
+ 2.88538959748872753838L,
+ 0.961932915889597772928L,
+ 0.571118517972136195241L,
+ 0.493997535084709500285L,
#else
#error
#endif
};
-
/**
* See http://www.devmaster.net/forums/showthread.php?p=43580
+ * http://en.wikipedia.org/wiki/Logarithm#Calculation
+ * http://www.nezumi.demon.co.uk/consult/logx.htm
*/
void
lp_build_log2_approx(struct lp_build_context *bld,
@@ -2441,6 +2438,8 @@ lp_build_log2_approx(struct lp_build_context *bld,
LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
LLVMValueRef i = NULL;
+ LLVMValueRef y = NULL;
+ LLVMValueRef z = NULL;
LLVMValueRef exp = NULL;
LLVMValueRef mant = NULL;
LLVMValueRef logexp = NULL;
@@ -2478,18 +2477,28 @@ lp_build_log2_approx(struct lp_build_context *bld,
}
if(p_log2) {
- /* mant = (float) mantissa(x) */
+ /* mant = 1 + (float) mantissa(x) */
mant = LLVMBuildAnd(builder, i, mantmask, "");
mant = LLVMBuildOr(builder, mant, one, "");
mant = LLVMBuildBitCast(builder, mant, vec_type, "");
- logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
+ /* y = (mant - 1) / (mant + 1) */
+ y = lp_build_div(bld,
+ lp_build_sub(bld, mant, bld->one),
+ lp_build_add(bld, mant, bld->one)
+ );
+
+ /* z = y^2 */
+ z = lp_build_mul(bld, y, y);
+
+ /* compute P(z) */
+ logmant = lp_build_polynomial(bld, z, lp_build_log2_polynomial,
Elements(lp_build_log2_polynomial));
- /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
- logmant = LLVMBuildFMul(builder, logmant, LLVMBuildFSub(builder, mant, bld->one, ""), "");
+ /* logmant = y * P(z) */
+ logmant = lp_build_mul(bld, y, logmant);
- res = LLVMBuildFAdd(builder, logmant, logexp, "");
+ res = lp_build_add(bld, logmant, logexp);
}
if(p_exp) {
diff --git a/src/gallium/drivers/llvmpipe/lp_test_arit.c b/src/gallium/drivers/llvmpipe/lp_test_arit.c
index 3030426..9b34efe 100644
--- a/src/gallium/drivers/llvmpipe/lp_test_arit.c
+++ b/src/gallium/drivers/llvmpipe/lp_test_arit.c
@@ -177,9 +177,9 @@ static const struct unary_test_t
unary_tests[] = {
{"neg", &lp_build_negate, &negf, exp2_values, Elements(exp2_values), 20.0 },
{"exp2", &lp_build_exp2, &exp2f, exp2_values, Elements(exp2_values), 20.0 },
- {"log2", &lp_build_log2, &log2f, log2_values, Elements(log2_values), 10.0 }, // FIXME
+ {"log2", &lp_build_log2, &log2f, log2_values, Elements(log2_values), 20.0 },
{"exp", &lp_build_exp, &expf, exp2_values, Elements(exp2_values), 18.0 },
- {"log", &lp_build_log, &logf, log2_values, Elements(log2_values), 10.0 }, // FIXME
+ {"log", &lp_build_log, &logf, log2_values, Elements(log2_values), 20.0 },
{"rsqrt", &lp_build_rsqrt, &rsqrtf, rsqrt_values, Elements(rsqrt_values), 20.0 },
{"sin", &lp_build_sin, &sinf, sincos_values, Elements(sincos_values), 20.0 },
{"cos", &lp_build_cos, &cosf, sincos_values, Elements(sincos_values), 20.0 },
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