SkPathOpsTypes.h revision 4e1a4c9399b8bb0897218f3ec10c254d3bb97463
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 */ 707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#ifndef SkPathOpsTypes_DEFINED 807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#define SkPathOpsTypes_DEFINED 907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include <float.h> // for FLT_EPSILON 1107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include <math.h> // for fabs, sqrt 1207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkFloatingPoint.h" 14277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#include "SkPath.h" 1507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOps.h" 1607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOpsDebug.h" 1707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkScalar.h" 1807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comenum SkPathOpsMask { 2007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com kWinding_PathOpsMask = -1, 2107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com kNo_PathOpsMask = 0, 2207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com kEvenOdd_PathOpsMask = 1 2307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com}; 2407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2554359294a7c9dc54802d512a5d891a35c1663392caryclarkclass SkOpCoincidence; 2654359294a7c9dc54802d512a5d891a35c1663392caryclarkclass SkOpContour; 27624637cc8ec22c000409704d0b403ac1b81ad4b0caryclarkclass SkOpContourHead; 2854359294a7c9dc54802d512a5d891a35c1663392caryclark 2954359294a7c9dc54802d512a5d891a35c1663392caryclarkclass SkOpGlobalState { 3054359294a7c9dc54802d512a5d891a35c1663392caryclarkpublic: 31624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkOpGlobalState(SkOpCoincidence* coincidence, SkOpContourHead* head) 3254359294a7c9dc54802d512a5d891a35c1663392caryclark : fCoincidence(coincidence) 33624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark , fContourHead(head) 344e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark , fNested(0) 3554359294a7c9dc54802d512a5d891a35c1663392caryclark , fWindingFailed(false) 3654359294a7c9dc54802d512a5d891a35c1663392caryclark , fAngleCoincidence(false) 3754359294a7c9dc54802d512a5d891a35c1663392caryclark , fPhase(kIntersecting) 381049f1246e7be4ccb68001361efceb8933e6f81ccaryclark SkDEBUGPARAMS(fAngleID(0)) 391049f1246e7be4ccb68001361efceb8933e6f81ccaryclark SkDEBUGPARAMS(fContourID(0)) 401049f1246e7be4ccb68001361efceb8933e6f81ccaryclark SkDEBUGPARAMS(fPtTID(0)) 411049f1246e7be4ccb68001361efceb8933e6f81ccaryclark SkDEBUGPARAMS(fSegmentID(0)) 421049f1246e7be4ccb68001361efceb8933e6f81ccaryclark SkDEBUGPARAMS(fSpanID(0)) { 4354359294a7c9dc54802d512a5d891a35c1663392caryclark } 4454359294a7c9dc54802d512a5d891a35c1663392caryclark 4554359294a7c9dc54802d512a5d891a35c1663392caryclark enum Phase { 4654359294a7c9dc54802d512a5d891a35c1663392caryclark kIntersecting, 475b5ddd73b4baf22752924bf20d097e96236c36f8caryclark kWalking, 485b5ddd73b4baf22752924bf20d097e96236c36f8caryclark kFixWinding, 4954359294a7c9dc54802d512a5d891a35c1663392caryclark }; 5054359294a7c9dc54802d512a5d891a35c1663392caryclark 51624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark enum { 52624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark kMaxWindingTries = 10 53624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark }; 54624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 5554359294a7c9dc54802d512a5d891a35c1663392caryclark bool angleCoincidence() { 5654359294a7c9dc54802d512a5d891a35c1663392caryclark return fAngleCoincidence; 5754359294a7c9dc54802d512a5d891a35c1663392caryclark } 5854359294a7c9dc54802d512a5d891a35c1663392caryclark 594e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark void bumpNested() { 604e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark ++fNested; 614e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 624e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 634e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark void clearNested() { 644e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark fNested = 0; 654e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 664e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 6754359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpCoincidence* coincidence() { 6854359294a7c9dc54802d512a5d891a35c1663392caryclark return fCoincidence; 6954359294a7c9dc54802d512a5d891a35c1663392caryclark } 7054359294a7c9dc54802d512a5d891a35c1663392caryclark 71624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkOpContourHead* contourHead() { 72624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark return fContourHead; 73624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } 74624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 7554359294a7c9dc54802d512a5d891a35c1663392caryclark#ifdef SK_DEBUG 7654359294a7c9dc54802d512a5d891a35c1663392caryclark const struct SkOpAngle* debugAngle(int id) const; 7754359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpContour* debugContour(int id); 7854359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpPtT* debugPtT(int id) const; 7954359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpSegment* debugSegment(int id) const; 8054359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpSpanBase* debugSpan(int id) const; 814e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark#endif 824e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 834e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark int nested() const { 844e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark return fNested; 854e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 8654359294a7c9dc54802d512a5d891a35c1663392caryclark 874e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark#ifdef SK_DEBUG 8854359294a7c9dc54802d512a5d891a35c1663392caryclark int nextAngleID() { 8954359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fAngleID; 9054359294a7c9dc54802d512a5d891a35c1663392caryclark } 9154359294a7c9dc54802d512a5d891a35c1663392caryclark 9254359294a7c9dc54802d512a5d891a35c1663392caryclark int nextContourID() { 9354359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fContourID; 9454359294a7c9dc54802d512a5d891a35c1663392caryclark } 9554359294a7c9dc54802d512a5d891a35c1663392caryclark int nextPtTID() { 9654359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fPtTID; 9754359294a7c9dc54802d512a5d891a35c1663392caryclark } 9854359294a7c9dc54802d512a5d891a35c1663392caryclark 9954359294a7c9dc54802d512a5d891a35c1663392caryclark int nextSegmentID() { 10054359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fSegmentID; 10154359294a7c9dc54802d512a5d891a35c1663392caryclark } 10254359294a7c9dc54802d512a5d891a35c1663392caryclark 10354359294a7c9dc54802d512a5d891a35c1663392caryclark int nextSpanID() { 10454359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fSpanID; 10554359294a7c9dc54802d512a5d891a35c1663392caryclark } 10654359294a7c9dc54802d512a5d891a35c1663392caryclark#endif 10754359294a7c9dc54802d512a5d891a35c1663392caryclark 10854359294a7c9dc54802d512a5d891a35c1663392caryclark Phase phase() const { 10954359294a7c9dc54802d512a5d891a35c1663392caryclark return fPhase; 11054359294a7c9dc54802d512a5d891a35c1663392caryclark } 11154359294a7c9dc54802d512a5d891a35c1663392caryclark 11254359294a7c9dc54802d512a5d891a35c1663392caryclark void setAngleCoincidence() { 11354359294a7c9dc54802d512a5d891a35c1663392caryclark fAngleCoincidence = true; 11454359294a7c9dc54802d512a5d891a35c1663392caryclark } 11554359294a7c9dc54802d512a5d891a35c1663392caryclark 116624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark void setContourHead(SkOpContourHead* contourHead) { 117624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark fContourHead = contourHead; 118624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } 119624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 12054359294a7c9dc54802d512a5d891a35c1663392caryclark void setPhase(Phase phase) { 12154359294a7c9dc54802d512a5d891a35c1663392caryclark SkASSERT(fPhase != phase); 12254359294a7c9dc54802d512a5d891a35c1663392caryclark fPhase = phase; 12354359294a7c9dc54802d512a5d891a35c1663392caryclark } 12454359294a7c9dc54802d512a5d891a35c1663392caryclark 12554359294a7c9dc54802d512a5d891a35c1663392caryclark // called in very rare cases where angles are sorted incorrectly -- signfies op will fail 12654359294a7c9dc54802d512a5d891a35c1663392caryclark void setWindingFailed() { 12754359294a7c9dc54802d512a5d891a35c1663392caryclark fWindingFailed = true; 12854359294a7c9dc54802d512a5d891a35c1663392caryclark } 12954359294a7c9dc54802d512a5d891a35c1663392caryclark 13054359294a7c9dc54802d512a5d891a35c1663392caryclark bool windingFailed() const { 13154359294a7c9dc54802d512a5d891a35c1663392caryclark return fWindingFailed; 13254359294a7c9dc54802d512a5d891a35c1663392caryclark } 13354359294a7c9dc54802d512a5d891a35c1663392caryclark 13454359294a7c9dc54802d512a5d891a35c1663392caryclarkprivate: 13554359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpCoincidence* fCoincidence; 136624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkOpContourHead* fContourHead; 1374e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark int fNested; 13854359294a7c9dc54802d512a5d891a35c1663392caryclark bool fWindingFailed; 13954359294a7c9dc54802d512a5d891a35c1663392caryclark bool fAngleCoincidence; 14054359294a7c9dc54802d512a5d891a35c1663392caryclark Phase fPhase; 14154359294a7c9dc54802d512a5d891a35c1663392caryclark#ifdef SK_DEBUG 14254359294a7c9dc54802d512a5d891a35c1663392caryclark int fAngleID; 14354359294a7c9dc54802d512a5d891a35c1663392caryclark int fContourID; 14454359294a7c9dc54802d512a5d891a35c1663392caryclark int fPtTID; 14554359294a7c9dc54802d512a5d891a35c1663392caryclark int fSegmentID; 14654359294a7c9dc54802d512a5d891a35c1663392caryclark int fSpanID; 14754359294a7c9dc54802d512a5d891a35c1663392caryclark#endif 14854359294a7c9dc54802d512a5d891a35c1663392caryclark}; 14954359294a7c9dc54802d512a5d891a35c1663392caryclark 150c3f63570c35a1e2bc84b33906c6401d6f3062bf2caryclark@google.com// Use Almost Equal when comparing coordinates. Use epsilon to compare T values. 1514fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool AlmostEqualUlps(float a, float b); 1524fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostEqualUlps(double a, double b) { 1534fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 15407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1567eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com// Use Almost Dequal when comparing should not special case denormalized values. 1577eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool AlmostDequalUlps(float a, float b); 1582db7fe7d3b7ee875e1099a22f0af17520696f5d7commit-bot@chromium.orgbool AlmostDequalUlps(double a, double b); 1597eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 160570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool NotAlmostEqualUlps(float a, float b); 161570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool NotAlmostEqualUlps(double a, double b) { 162570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return NotAlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 163570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 164570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 1657eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool NotAlmostDequalUlps(float a, float b); 1667eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.cominline bool NotAlmostDequalUlps(double a, double b) { 1677eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return NotAlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 1687eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 1697eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 170570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com// Use Almost Bequal when comparing coordinates in conjunction with between. 171570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostBequalUlps(float a, float b); 172570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostBequalUlps(double a, double b) { 173570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostBequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 174570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 175570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 176a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.combool AlmostPequalUlps(float a, float b); 177a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.cominline bool AlmostPequalUlps(double a, double b) { 178a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return AlmostPequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 179a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com} 180a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com 1814fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool RoughlyEqualUlps(float a, float b); 1824fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool RoughlyEqualUlps(double a, double b) { 1834fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return RoughlyEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 18407e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 18507e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 186570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessUlps(float a, float b); 187570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessUlps(double a, double b) { 188570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 189570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 190570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 191570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessOrEqualUlps(float a, float b); 192570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessOrEqualUlps(double a, double b) { 193570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessOrEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 194570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 195570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 196fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c); 1974fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostBetweenUlps(double a, double b, double c) { 1984fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostBetweenUlps(SkDoubleToScalar(a), SkDoubleToScalar(b), SkDoubleToScalar(c)); 1994fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com} 2004fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 2014fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comint UlpsDistance(float a, float b); 2024fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline int UlpsDistance(double a, double b) { 2034fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return UlpsDistance(SkDoubleToScalar(a), SkDoubleToScalar(b)); 204fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 205fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 20607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23) 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// DBL_EPSILON == 2.22045e-16 20807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON; 20907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_HALF = FLT_EPSILON / 2; 210cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double FLT_EPSILON_DOUBLE = FLT_EPSILON * 2; 2114431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orgconst double FLT_EPSILON_ORDERABLE_ERR = FLT_EPSILON * 16; 21207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON; 21307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON); 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON; 21507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double DBL_EPSILON_ERR = DBL_EPSILON * 4; // FIXME: tune -- allow a few bits of error 216cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double DBL_EPSILON_SUBDIVIDE_ERR = DBL_EPSILON * 16; 21707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double ROUGH_EPSILON = FLT_EPSILON * 64; 21807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double MORE_ROUGH_EPSILON = FLT_EPSILON * 256; 219dac1d17027dcaa5596885a9f333979418b35001ccaryclarkconst double WAY_ROUGH_EPSILON = FLT_EPSILON * 2048; 22054359294a7c9dc54802d512a5d891a35c1663392caryclarkconst double BUMP_EPSILON = FLT_EPSILON * 4096; 221dac1d17027dcaa5596885a9f333979418b35001ccaryclark 222dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool zero_or_one(double x) { 223dac1d17027dcaa5596885a9f333979418b35001ccaryclark return x == 0 || x == 1; 224dac1d17027dcaa5596885a9f333979418b35001ccaryclark} 22507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 22607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(double x) { 22707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 22807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 22907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_zero(double x) { 23107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < DBL_EPSILON_ERR; 23207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 23307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 234cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_zero(double x) { 235cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < DBL_EPSILON_SUBDIVIDE_ERR; 236cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 237cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 23807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(float x) { 23907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 24007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_cubed(double x) { 24307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_CUBED; 24407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_half(double x) { 24707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_HALF; 24807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 250cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_zero_double(double x) { 251cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < FLT_EPSILON_DOUBLE; 252cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 253cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 2544431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_orderable(double x) { 2554431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return fabs(x) < FLT_EPSILON_ORDERABLE_ERR; 2564431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2574431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_squared(double x) { 25907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQUARED; 26007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 26207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_sqrt(double x) { 26307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQRT; 26407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 266cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool roughly_zero(double x) { 267cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < ROUGH_EPSILON; 268cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 269cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 27007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_inverse(double x) { 27107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) > FLT_EPSILON_INVERSE; 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// OPTIMIZATION: if called multiple times with the same denom, we want to pass 1/y instead 27507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_when_compared_to(double x, double y) { 2764431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x == 0 || fabs(x) < fabs(y * FLT_EPSILON); 27707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27954359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool precisely_zero_when_compared_to(double x, double y) { 28054359294a7c9dc54802d512a5d891a35c1663392caryclark return x == 0 || fabs(x) < fabs(y * DBL_EPSILON); 28154359294a7c9dc54802d512a5d891a35c1663392caryclark} 28254359294a7c9dc54802d512a5d891a35c1663392caryclark 28307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use 28407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// AlmostEqualUlps instead. 28507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal(double x, double y) { 28607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero(x - y); 28707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 28807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 28907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_equal(double x, double y) { 29007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return precisely_zero(x - y); 29107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 29207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 293cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_equal(double x, double y) { 294cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return precisely_subdivide_zero(x - y); 295cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 296cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 29707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_half(double x, double y) { 29807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero_half(x - y); 29907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 301cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_equal_double(double x, double y) { 302cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return approximately_zero_double(x - y); 303cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 304cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 3054431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_equal_orderable(double x, double y) { 3064431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return approximately_zero_orderable(x - y); 3074431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3084431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 30907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_squared(double x, double y) { 31007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_equal(x, y); 31107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 31207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 31307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater(double x, double y) { 31407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON >= y; 31507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 31607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3174431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_double(double x, double y) { 3184431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE >= y; 3194431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3204431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3214431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_orderable(double x, double y) { 3224431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR >= y; 3234431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3244431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 32507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_or_equal(double x, double y) { 32607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON > y; 32707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 32807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3294431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_double(double x, double y) { 3304431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE > y; 3314431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3324431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3334431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_orderable(double x, double y) { 3344431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR > y; 3354431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3364431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 33707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser(double x, double y) { 33807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON <= y; 33907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 34007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3414431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_double(double x, double y) { 3424431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE <= y; 3434431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3444431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3454431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_orderable(double x, double y) { 3464431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR <= y; 3474431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3484431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 34907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser_or_equal(double x, double y) { 35007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON < y; 35107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 35207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3534431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_double(double x, double y) { 3544431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE < y; 3554431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3564431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3574431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_orderable(double x, double y) { 3584431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR < y; 3594431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3604431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 36107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_than_one(double x) { 36207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - FLT_EPSILON; 36307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 36507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_greater_than_one(double x) { 36607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - DBL_EPSILON_ERR; 36707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 36907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_less_than_zero(double x) { 37007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 37107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 37207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 37307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_less_than_zero(double x) { 37407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 37507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 37607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 37707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_negative(double x) { 37807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 37907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 38007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3814431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_negative_orderable(double x) { 3824431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < FLT_EPSILON_ORDERABLE_ERR; 3834431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3844431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 38507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_negative(double x) { 38607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 38707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 38807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 38907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_one_or_less(double x) { 39007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < 1 + FLT_EPSILON; 39107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 39207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3934431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_one_or_less_double(double x) { 3944431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < 1 + FLT_EPSILON_DOUBLE; 3954431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3964431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 39707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive(double x) { 39807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 39907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 40007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 40107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive_squared(double x) { 40207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -(FLT_EPSILON_SQUARED); 40307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 40407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 40507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_or_more(double x) { 40607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 40707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 40807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4094431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_or_more_double(double x) { 4104431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x > -FLT_EPSILON_DOUBLE; 4114431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4124431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 4134431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_between_orderable(double a, double b, double c) { 4144431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return a <= c 4154431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org ? approximately_negative_orderable(a - b) && approximately_negative_orderable(b - c) 4164431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org : approximately_negative_orderable(b - a) && approximately_negative_orderable(c - b); 4174431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4184431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 41907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_between(double a, double b, double c) { 42007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return a <= c ? approximately_negative(a - b) && approximately_negative(b - c) 42107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : approximately_negative(b - a) && approximately_negative(c - b); 42207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 4230361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com 4240361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.cominline bool precisely_between(double a, double b, double c) { 4250361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com return a <= c ? precisely_negative(a - b) && precisely_negative(b - c) 4260361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com : precisely_negative(b - a) && precisely_negative(c - b); 4270361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com} 42807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 42907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// returns true if (a <= b <= c) || (a >= b >= c) 43007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool between(double a, double b, double c) { 43154359294a7c9dc54802d512a5d891a35c1663392caryclark SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0) 43254359294a7c9dc54802d512a5d891a35c1663392caryclark || (precisely_zero(a) && precisely_zero(b) && precisely_zero(c))); 43307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (a - b) * (c - b) <= 0; 43407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 43507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 436dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool roughly_equal(double x, double y) { 437dac1d17027dcaa5596885a9f333979418b35001ccaryclark return fabs(x - y) < ROUGH_EPSILON; 438dac1d17027dcaa5596885a9f333979418b35001ccaryclark} 439dac1d17027dcaa5596885a9f333979418b35001ccaryclark 44054359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool roughly_negative(double x) { 44154359294a7c9dc54802d512a5d891a35c1663392caryclark return x < ROUGH_EPSILON; 44254359294a7c9dc54802d512a5d891a35c1663392caryclark} 44354359294a7c9dc54802d512a5d891a35c1663392caryclark 44454359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool roughly_between(double a, double b, double c) { 44554359294a7c9dc54802d512a5d891a35c1663392caryclark return a <= c ? roughly_negative(a - b) && roughly_negative(b - c) 44654359294a7c9dc54802d512a5d891a35c1663392caryclark : roughly_negative(b - a) && roughly_negative(c - b); 44754359294a7c9dc54802d512a5d891a35c1663392caryclark} 44854359294a7c9dc54802d512a5d891a35c1663392caryclark 44907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool more_roughly_equal(double x, double y) { 45007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < MORE_ROUGH_EPSILON; 45107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 45207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 453dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool way_roughly_equal(double x, double y) { 454dac1d17027dcaa5596885a9f333979418b35001ccaryclark return fabs(x - y) < WAY_ROUGH_EPSILON; 45507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 45607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 45707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDPoint; 45807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDVector; 45907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDLine; 46007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDQuad; 4611049f1246e7be4ccb68001361efceb8933e6f81ccaryclarkstruct SkDConic; 46207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDCubic; 46307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDRect; 46407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 465277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline SkPath::Verb SkPathOpsPointsToVerb(int points) { 466277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int verb = (1 << points) >> 1; 467277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 468277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (points) { 469277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 0: SkASSERT(SkPath::kMove_Verb == verb); break; 470277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 1: SkASSERT(SkPath::kLine_Verb == verb); break; 471277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 2: SkASSERT(SkPath::kQuad_Verb == verb); break; 472277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 3: SkASSERT(SkPath::kCubic_Verb == verb); break; 473330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not be here"); 474277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 475277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 476277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return (SkPath::Verb)verb; 477277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 478277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 479277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline int SkPathOpsVerbToPoints(SkPath::Verb verb) { 4801049f1246e7be4ccb68001361efceb8933e6f81ccaryclark int points = (int) verb - (((int) verb + 1) >> 2); 481277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 482277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (verb) { 483277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kLine_Verb: SkASSERT(1 == points); break; 484277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kQuad_Verb: SkASSERT(2 == points); break; 4851049f1246e7be4ccb68001361efceb8933e6f81ccaryclark case SkPath::kConic_Verb: SkASSERT(2 == points); break; 486277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kCubic_Verb: SkASSERT(3 == points); break; 487330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not get here"); 488277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 489277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 490277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return points; 491277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 492277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 49307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline double SkDInterp(double A, double B, double t) { 49407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A + (B - A) * t; 49507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 49607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 49707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x); 49807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 49907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns -1 if negative, 0 if zero, 1 if positive 50007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 50107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSign(double x) { 50207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) - (x < 0); 50307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 50407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 50507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 0 if negative, 1 if zero, 2 if positive 50607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 50707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SKDSide(double x) { 50807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) + (x >= 0); 50907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 51007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 51107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 1 if negative, 2 if zero, 4 if positive 51207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 51307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSideBit(double x) { 51407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 1 << SKDSide(x); 51507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 51607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 517fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline double SkPinT(double t) { 518fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return precisely_less_than_zero(t) ? 0 : precisely_greater_than_one(t) ? 1 : t; 519fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 520fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 52107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#endif 522