SkPathOpsTypes.cpp revision b669300a9753893ef900207c38aeff2d467764e5
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" 827c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark#include "SkOpCoincidence.h" 907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOpsTypes.h" 1007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 117eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.comstatic bool arguments_denormalized(float a, float b, int epsilon) { 12a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com float denormalizedCheck = FLT_EPSILON * epsilon / 2; 13a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return fabsf(a) <= denormalizedCheck && fabsf(b) <= denormalizedCheck; 147eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 157eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 1607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ 17cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com// FIXME: move to SkFloatBits.h 18a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.comstatic bool equal_ulps(float a, float b, int epsilon, int depsilon) { 19b669300a9753893ef900207c38aeff2d467764e5caryclark if (arguments_denormalized(a, b, depsilon)) { 20b669300a9753893ef900207c38aeff2d467764e5caryclark return true; 21b669300a9753893ef900207c38aeff2d467764e5caryclark } 22b669300a9753893ef900207c38aeff2d467764e5caryclark int aBits = SkFloatAs2sCompliment(a); 23b669300a9753893ef900207c38aeff2d467764e5caryclark int bBits = SkFloatAs2sCompliment(b); 24b669300a9753893ef900207c38aeff2d467764e5caryclark // Find the difference in ULPs. 25b669300a9753893ef900207c38aeff2d467764e5caryclark return aBits < bBits + epsilon && bBits < aBits + epsilon; 26b669300a9753893ef900207c38aeff2d467764e5caryclark} 27b669300a9753893ef900207c38aeff2d467764e5caryclark 28b669300a9753893ef900207c38aeff2d467764e5caryclarkstatic bool equal_ulps_pin(float a, float b, int epsilon, int depsilon) { 29570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) { 30570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return false; 3107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 32a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com if (arguments_denormalized(a, b, depsilon)) { 337eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return true; 347eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com } 357eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com int aBits = SkFloatAs2sCompliment(a); 367eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com int bBits = SkFloatAs2sCompliment(b); 377eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com // Find the difference in ULPs. 387eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return aBits < bBits + epsilon && bBits < aBits + epsilon; 397eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 407eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 417eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.comstatic bool d_equal_ulps(float a, float b, int epsilon) { 42570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int aBits = SkFloatAs2sCompliment(a); 43570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int bBits = SkFloatAs2sCompliment(b); 4407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com // Find the difference in ULPs. 45570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return aBits < bBits + epsilon && bBits < aBits + epsilon; 46570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 47570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 48570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.comstatic bool not_equal_ulps(float a, float b, int epsilon) { 49b669300a9753893ef900207c38aeff2d467764e5caryclark if (arguments_denormalized(a, b, epsilon)) { 50b669300a9753893ef900207c38aeff2d467764e5caryclark return false; 51b669300a9753893ef900207c38aeff2d467764e5caryclark } 52b669300a9753893ef900207c38aeff2d467764e5caryclark int aBits = SkFloatAs2sCompliment(a); 53b669300a9753893ef900207c38aeff2d467764e5caryclark int bBits = SkFloatAs2sCompliment(b); 54b669300a9753893ef900207c38aeff2d467764e5caryclark // Find the difference in ULPs. 55b669300a9753893ef900207c38aeff2d467764e5caryclark return aBits >= bBits + epsilon || bBits >= aBits + epsilon; 56b669300a9753893ef900207c38aeff2d467764e5caryclark} 57b669300a9753893ef900207c38aeff2d467764e5caryclark 58b669300a9753893ef900207c38aeff2d467764e5caryclarkstatic bool not_equal_ulps_pin(float a, float b, int epsilon) { 59570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) { 60570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return false; 61570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 627eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com if (arguments_denormalized(a, b, epsilon)) { 637eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return false; 647eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com } 657eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com int aBits = SkFloatAs2sCompliment(a); 667eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com int bBits = SkFloatAs2sCompliment(b); 677eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com // Find the difference in ULPs. 687eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return aBits >= bBits + epsilon || bBits >= aBits + epsilon; 697eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 707eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 717eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.comstatic bool d_not_equal_ulps(float a, float b, int epsilon) { 72570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int aBits = SkFloatAs2sCompliment(a); 73570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int bBits = SkFloatAs2sCompliment(b); 74570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com // Find the difference in ULPs. 75570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return aBits >= bBits + epsilon || bBits >= aBits + epsilon; 7607e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 7707e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 784fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comstatic bool less_ulps(float a, float b, int epsilon) { 797eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com if (arguments_denormalized(a, b, epsilon)) { 807eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return a <= b - FLT_EPSILON * epsilon; 817eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com } 82570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int aBits = SkFloatAs2sCompliment(a); 83570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int bBits = SkFloatAs2sCompliment(b); 84fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com // Find the difference in ULPs. 85570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return aBits <= bBits - epsilon; 86570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 87570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 88570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.comstatic bool less_or_equal_ulps(float a, float b, int epsilon) { 897eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com if (arguments_denormalized(a, b, epsilon)) { 907eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return a < b + FLT_EPSILON * epsilon; 917eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com } 92570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int aBits = SkFloatAs2sCompliment(a); 93570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com int bBits = SkFloatAs2sCompliment(b); 94570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com // Find the difference in ULPs. 95570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return aBits < bBits + epsilon; 96570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 97570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 98570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com// equality using the same error term as between 99570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostBequalUlps(float a, float b) { 100570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com const int UlpsEpsilon = 2; 101a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon); 102a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com} 103a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com 104a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.combool AlmostPequalUlps(float a, float b) { 105a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com const int UlpsEpsilon = 8; 106a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon); 107fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 108fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 1097eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool AlmostDequalUlps(float a, float b) { 1107eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com const int UlpsEpsilon = 16; 1117eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return d_equal_ulps(a, b, UlpsEpsilon); 1127eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 1137eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 1142db7fe7d3b7ee875e1099a22f0af17520696f5d7commit-bot@chromium.orgbool AlmostDequalUlps(double a, double b) { 115b669300a9753893ef900207c38aeff2d467764e5caryclark return AlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 1162db7fe7d3b7ee875e1099a22f0af17520696f5d7commit-bot@chromium.org} 1172db7fe7d3b7ee875e1099a22f0af17520696f5d7commit-bot@chromium.org 1184fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool AlmostEqualUlps(float a, float b) { 11907e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com const int UlpsEpsilon = 16; 120a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon); 12107e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 12207e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 123b669300a9753893ef900207c38aeff2d467764e5caryclarkbool AlmostEqualUlps_Pin(float a, float b) { 124b669300a9753893ef900207c38aeff2d467764e5caryclark const int UlpsEpsilon = 16; 125b669300a9753893ef900207c38aeff2d467764e5caryclark return equal_ulps_pin(a, b, UlpsEpsilon, UlpsEpsilon); 126b669300a9753893ef900207c38aeff2d467764e5caryclark} 127b669300a9753893ef900207c38aeff2d467764e5caryclark 128570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool NotAlmostEqualUlps(float a, float b) { 129570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com const int UlpsEpsilon = 16; 130570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return not_equal_ulps(a, b, UlpsEpsilon); 131570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 132570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 133b669300a9753893ef900207c38aeff2d467764e5caryclarkbool NotAlmostEqualUlps_Pin(float a, float b) { 134b669300a9753893ef900207c38aeff2d467764e5caryclark const int UlpsEpsilon = 16; 135b669300a9753893ef900207c38aeff2d467764e5caryclark return not_equal_ulps_pin(a, b, UlpsEpsilon); 136b669300a9753893ef900207c38aeff2d467764e5caryclark} 137b669300a9753893ef900207c38aeff2d467764e5caryclark 1387eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool NotAlmostDequalUlps(float a, float b) { 1397eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com const int UlpsEpsilon = 16; 1407eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return d_not_equal_ulps(a, b, UlpsEpsilon); 1417eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 1427eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 1434fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool RoughlyEqualUlps(float a, float b) { 14407e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com const int UlpsEpsilon = 256; 145a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com const int DUlpsEpsilon = 1024; 146a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return equal_ulps(a, b, UlpsEpsilon, DUlpsEpsilon); 14707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 149fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c) { 150570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com const int UlpsEpsilon = 2; 151570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return a <= c ? less_or_equal_ulps(a, b, UlpsEpsilon) && less_or_equal_ulps(b, c, UlpsEpsilon) 152570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com : less_or_equal_ulps(b, a, UlpsEpsilon) && less_or_equal_ulps(c, b, UlpsEpsilon); 153570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 154570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 155570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessUlps(float a, float b) { 156570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com const int UlpsEpsilon = 16; 157570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return less_ulps(a, b, UlpsEpsilon); 158570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 159570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 160570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessOrEqualUlps(float a, float b) { 161570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com const int UlpsEpsilon = 16; 162570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return less_or_equal_ulps(a, b, UlpsEpsilon); 163fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 164fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 1654fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comint UlpsDistance(float a, float b) { 1664fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com SkFloatIntUnion floatIntA, floatIntB; 1674fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com floatIntA.fFloat = a; 1684fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com floatIntB.fFloat = b; 1694fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com // Different signs means they do not match. 1704fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) { 1714fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com // Check for equality to make sure +0 == -0 1724fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return a == b ? 0 : SK_MaxS32; 1734fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com } 1744fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com // Find the difference in ULPs. 17560e0fee6d4acff638ccc9670c4055aced529a7a0bungeman return SkTAbs(floatIntA.fSignBitInt - floatIntB.fSignBitInt); 1764fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com} 1774fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 17807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// cube root approximation using bit hack for 64-bit float 17907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// adapted from Kahan's cbrt 180cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comstatic double cbrt_5d(double d) { 18107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const unsigned int B1 = 715094163; 18207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double t = 0.0; 18307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com unsigned int* pt = (unsigned int*) &t; 18407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com unsigned int* px = (unsigned int*) &d; 18507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com pt[1] = px[1] / 3 + B1; 18607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return t; 18707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// iterative cube root approximation using Halley's method (double) 190cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comstatic double cbrta_halleyd(const double a, const double R) { 19107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const double a3 = a * a * a; 19207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com const double b = a * (a3 + R + R) / (a3 + a3 + R); 19307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return b; 19407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// cube root approximation using 3 iterations of Halley's method (double) 19707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstatic double halley_cbrt3d(double d) { 19807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double a = cbrt_5d(d); 19907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com a = cbrta_halleyd(a, d); 20007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com a = cbrta_halleyd(a, d); 20107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return cbrta_halleyd(a, d); 20207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x) { 20507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (approximately_zero_cubed(x)) { 20607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 0; 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 20807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com double result = halley_cbrt3d(fabs(x)); 20907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com if (x < 0) { 21007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com result = -result; 21107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com } 21207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return result; 21307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 21427c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark 215d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclarkSkOpGlobalState::SkOpGlobalState(SkOpCoincidence* coincidence, SkOpContourHead* head 216d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark SkDEBUGPARAMS(const char* testName)) 21727c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark : fCoincidence(coincidence) 21827c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark , fContourHead(head) 21927c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark , fNested(0) 22027c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark , fWindingFailed(false) 22127c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark , fAngleCoincidence(false) 22227c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark , fPhase(kIntersecting) 223d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark SkDEBUGPARAMS(fDebugTestName(testName)) 22427c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark SkDEBUGPARAMS(fAngleID(0)) 22526ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark SkDEBUGPARAMS(fCoinID(0)) 22627c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark SkDEBUGPARAMS(fContourID(0)) 22727c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark SkDEBUGPARAMS(fPtTID(0)) 22827c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark SkDEBUGPARAMS(fSegmentID(0)) 22927c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark SkDEBUGPARAMS(fSpanID(0)) { 23027c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark if (coincidence) { 23127c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark coincidence->debugSetGlobalState(this); 23227c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark } 23326ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#if DEBUG_T_SECT_LOOP_COUNT 23426ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark debugResetLoopCounts(); 23526ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#endif 23627c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark} 23727c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark 238