SkPathOpsTypes.cpp revision cffbcc3b9665f2c928544b6fc6b8a0e22a4210fb
107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* 207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * Copyright 2012 Google Inc. 307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * 407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * Use of this source code is governed by a BSD-style license that can be 507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * found in the LICENSE file. 607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com */ 7cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com#include "SkFloatBits.h" 807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOpsTypes.h" 907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst int UlpsEpsilon = 16; 1107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ 13cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com// FIXME: move to SkFloatBits.h 1407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.combool AlmostEqualUlps(float A, float B) { 15cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com SkFloatIntUnion floatIntA, floatIntB; 16cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com floatIntA.fFloat = A; 17cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com floatIntB.fFloat = B; 1807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com // Different signs means they do not match. 19cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) 2007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com { 2107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com // Check for equality to make sure +0 == -0 2207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A == B; 2307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 2407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com // Find the difference in ULPs. 25cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com int ulpsDiff = abs(floatIntA.fSignBitInt - floatIntB.fSignBitInt); 2607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return ulpsDiff <= UlpsEpsilon; 2707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 2807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// cube root approximation using bit hack for 64-bit float 3007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// adapted from Kahan's cbrt 31cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comstatic double cbrt_5d(double d) { 3207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const unsigned int B1 = 715094163; 3307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double t = 0.0; 3407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com unsigned int* pt = (unsigned int*) &t; 3507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com unsigned int* px = (unsigned int*) &d; 3607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com pt[1] = px[1] / 3 + B1; 3707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return t; 3807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 3907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// iterative cube root approximation using Halley's method (double) 41cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comstatic double cbrta_halleyd(const double a, const double R) { 4207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const double a3 = a * a * a; 4307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const double b = a * (a3 + R + R) / (a3 + a3 + R); 4407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return b; 4507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 4607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// cube root approximation using 3 iterations of Halley's method (double) 4807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstatic double halley_cbrt3d(double d) { 4907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double a = cbrt_5d(d); 5007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com a = cbrta_halleyd(a, d); 5107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com a = cbrta_halleyd(a, d); 5207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return cbrta_halleyd(a, d); 5307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 5407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 5507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x) { 5607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (approximately_zero_cubed(x)) { 5707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 0; 5807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 5907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double result = halley_cbrt3d(fabs(x)); 6007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (x < 0) { 6107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com result = -result; 6207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 6307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return result; 6407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 65