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Update fallback rsqrt implementation to use optimal constants.

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Improves max relative error from 0.00175126 to 0.000650197.
Also add unit tests to check error bounds.

BUG=chromium:511458

Review URL: https://codereview.chromium.org/1251423002
This commit is contained in:
jvanverth 2015-07-23 11:14:29 -07:00 committed by Commit bot
parent 4765bdcd63
commit 29c69793f0
2 changed files with 39 additions and 2 deletions
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6
include/core/SkFloatingPoint.h
View File

@ -151,6 +151,8 @@ static inline float sk_float_rsqrt(const float x) {
//
// We do one step of Newton's method to refine the estimates in the NEON and null paths. No
// refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt.
//
// Optimized constants in the null path courtesy of http://rrrola.wz.cz/inv_sqrt.html
#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
#elif defined(SK_ARM_HAS_NEON)
@ -165,12 +167,12 @@ static inline float sk_float_rsqrt(const float x) {
#else
// Get initial estimate.
int i = *SkTCast<int*>(&x);
i = 0x5f3759df - (i>>1);
i = 0x5F1FFFF9 - (i>>1);
float estimate = *SkTCast<float*>(&i);
// One step of Newton's method to refine.
const float estimate_sq = estimate*estimate;
estimate *= (1.5f-0.5f*x*estimate_sq);
estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
return estimate;
#endif
}

35
tests/MathTest.cpp
View File

@ -382,6 +382,40 @@ static void unittest_half(skiatest::Reporter* reporter) {
}
static void test_rsqrt(skiatest::Reporter* reporter) {
const float maxRelativeError = 6.50196699e-4f;
// test close to 0 up to 1
float input = 0.000001f;
for (int i = 0; i < 1000; ++i) {
float exact = 1.0f/sk_float_sqrt(input);
float estimate = sk_float_rsqrt(input);
float relativeError = sk_float_abs(exact - estimate)/exact;
REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
input += 0.001f;
}
// test 1 to ~100
input = 1.0f;
for (int i = 0; i < 1000; ++i) {
float exact = 1.0f/sk_float_sqrt(input);
float estimate = sk_float_rsqrt(input);
float relativeError = sk_float_abs(exact - estimate)/exact;
REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
input += 0.01f;
}
// test some big numbers
input = 1000000.0f;
for (int i = 0; i < 100; ++i) {
float exact = 1.0f/sk_float_sqrt(input);
float estimate = sk_float_rsqrt(input);
float relativeError = sk_float_abs(exact - estimate)/exact;
REPORTER_ASSERT(reporter, relativeError <= maxRelativeError);
input += 754326.f;
}
}
static void test_muldiv255(skiatest::Reporter* reporter) {
for (int a = 0; a <= 255; a++) {
for (int b = 0; b <= 255; b++) {
@ -521,6 +555,7 @@ DEF_TEST(Math, reporter) {
unittest_fastfloat(reporter);
unittest_isfinite(reporter);
unittest_half(reporter);
test_rsqrt(reporter);
for (i = 0; i < 10000; i++) {
SkFixed numer = rand.nextS();