diff options
| -rw-r--r-- | include/core/SkFloatingPoint.h | 6 | ||||
| -rw-r--r-- | tests/MathTest.cpp | 35 |
2 files changed, 39 insertions, 2 deletions
diff --git a/include/core/SkFloatingPoint.h b/include/core/SkFloatingPoint.h index 7c34706f7a..13e8963c14 100644 --- a/include/core/SkFloatingPoint.h +++ b/include/core/SkFloatingPoint.h @@ -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 } diff --git a/tests/MathTest.cpp b/tests/MathTest.cpp index 772bade185..3c2bc64407 100644 --- a/tests/MathTest.cpp +++ b/tests/MathTest.cpp @@ -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(); |