Commit: 1e4d99368bba53edb6f903036b49edda92f27e31 Author: Sergey Sharybin Date: Fri Oct 3 18:27:08 2014 +0600 Branches: master https://developer.blender.org/rB1e4d99368bba53edb6f903036b49edda92f27e31
Cycles: Use more accurate implementation of erf() and erfinv() This functions are orders of magnitude more accurate than the old ones, and they're around the same complexity to compute. =================================================================== M intern/cycles/kernel/closure/bsdf_microfacet.h =================================================================== diff --git a/intern/cycles/kernel/closure/bsdf_microfacet.h b/intern/cycles/kernel/closure/bsdf_microfacet.h index a0c59e6..c6aed12 100644 --- a/intern/cycles/kernel/closure/bsdf_microfacet.h +++ b/intern/cycles/kernel/closure/bsdf_microfacet.h @@ -35,139 +35,38 @@ CCL_NAMESPACE_BEGIN -/* Approximate erf and erfinv implementations +/* Approximate erf and erfinv implementations. + * Implementation comes stright from the wikipedia: * - * Adapted from code (C) Copyright John Maddock 2006. - * Use, modification and distribution are subject to the - * Boost Software License, Version 1.0. (See accompanying file - * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) */ - -ccl_device float approx_erff_impl(float z) -{ - float result; - - if(z < 0.5f) { - if(z < 1e-10f) { - if(z == 0) { - result = 0; - } - else { - float c = 0.0033791670f; - result = z * 1.125f + z * c; - } - } - else { - float Y = 1.044948577f; - - float zz = z * z; - float num = (((-0.007727583f * zz) + -0.050999073f)*zz + -0.338165134f)*zz + 0.083430589f; - float denom = (((0.000370900f * zz) + 0.008585719f)*zz + 0.087522260f)*zz + 0.455004033f; - result = z * (Y + num / denom); - } - } - else if(z < 2.5f) { - if(z < 1.5f) { - float Y = 0.4059357643f; - float fz = z - 0.5f; - - float num = (((0.088890036f * fz) + 0.191003695f)*fz + 0.178114665f)*fz + -0.098090592f; - float denom = (((0.123850974f * fz) + 0.578052804f)*fz + 1.426280048f)*fz + 1.847590709f; - - result = Y + num / denom; - result *= expf(-z * z) / z; - } - else { - float Y = 0.506728172f; - float fz = z - 1.5f; - float num = (((0.017567943f * fz) + 0.043948189f)*fz + 0.038654037f)*fz + -0.024350047f; - float denom = (((0.325732924f * fz) + 0.982403709f)*fz + 1.539914949f)*fz + 1; - - result = Y + num / denom; - result *= expf(-z * z) / z; - } - - result = 1 - result; - } - else { - result = 1; - } - - return result; -} + * http://en.wikipedia.org/wiki/Error_function + * + * Some constants are baked into the code. + */ -ccl_device float approx_erff(float z) +ccl_device_inline float approx_erff(float x) { float s = 1.0f; - - if(z < 0.0f) { + if(x < 0.0f) { s = -1.0f; - z = -z; - } - - return s * approx_erff_impl(z); -} - -ccl_device float approx_erfinvf_impl(float p, float q) -{ - float result = 0; - - if(p <= 0.5f) { - float Y = 0.089131474f; - float g = p * (p + 10); - float num = (((-0.012692614f * p) + 0.033480662f)*p + -0.008368748f)*p + -0.000508781f; - float denom = (((1.562215583f * p) + -1.565745582f)*p + -0.970005043f)*p + 1.0f; - float r = num / denom; - result = g * Y + g * r; + x = -x; } - else if(q >= 0.25f) { - float Y = 2.249481201f; - float g = sqrtf(-2 * logf(q)); - float xs = q - 0.25f; - float num = (((17.644729840f * xs) + 8.370503283f)*xs + 0.105264680f)*xs + -0.202433508f; - float denom = (((-28.660818049f * xs) + 3.971343795f)*xs + 6.242641248f)*xs + 1.0f; - float r = num / denom; - result = g / (Y + r); + /* Such a clamp doesn't give much distortion to the output value + * and gives quite a few of the speedup. + */ + if(x > 3.0f) { + return s; } - else { - float x = sqrtf(-logf(q)); - - if(x < 3) { - float Y = 0.807220458f; - float xs = x - 1.125f; - float num = (((0.387079738f * xs) + 0.117030156f)*xs + -0.163794047f)*xs + -0.131102781f; - float denom = (((4.778465929f * xs) + 5.381683457f)*xs + 3.466254072f)*xs + 1.0f; - float R = num / denom; - result = Y * x + R * x; - } - else { - float Y = 0.939955711f; - float xs = x - 3; - float num = (((0.009508047f * xs) + 0.018557330f)*xs + -0.002224265f)*xs + -0.035035378f; - float denom = (((0.220091105f * xs) + 0.762059164f)*xs + 1.365334981f)*xs + 1.0f; - float R = num / denom; - result = Y * x + R * x; - } - } - - return result; + float t = 1.0f / (1.0f + 0.47047f*x); + return s * (1.0f - + t*(0.3480242f + t*(-0.0958798f + t*0.7478556f)) * expf(-x*x)); } -ccl_device float approx_erfinvf(float z) +ccl_device_inline float approx_erfinvf(float x) { - float p, q, s; - - if(z < 0) { - p = -z; - q = 1 - p; - s = -1; - } - else { - p = z; - q = 1 - z; - s = 1; - } - - return s * approx_erfinvf_impl(p, q); + float ln1_x2 = logf(1.0f - x*x); + float term = 4.546884979448f + ln1_x2 * 0.5f; + return copysignf(1.0f, x) * + sqrtf(sqrtf(term*term - ln1_x2 * 7.142230224076f) - term); } /* Beckmann and GGX microfacet importance sampling from: _______________________________________________ Bf-blender-cvs mailing list [email protected] http://lists.blender.org/mailman/listinfo/bf-blender-cvs
