SkPathOpsTypes.h revision 26ad22ab61539e3d3b6bc5e0da8dcebbd52a53de
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; 2826ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclarkclass SkIntersections; 2926ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclarkclass SkIntersectionHelper; 3054359294a7c9dc54802d512a5d891a35c1663392caryclark 3154359294a7c9dc54802d512a5d891a35c1663392caryclarkclass SkOpGlobalState { 3254359294a7c9dc54802d512a5d891a35c1663392caryclarkpublic: 33d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark SkOpGlobalState(SkOpCoincidence* coincidence, SkOpContourHead* head 34d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark SkDEBUGPARAMS(const char* testName)); 3554359294a7c9dc54802d512a5d891a35c1663392caryclark 3654359294a7c9dc54802d512a5d891a35c1663392caryclark enum Phase { 3754359294a7c9dc54802d512a5d891a35c1663392caryclark kIntersecting, 385b5ddd73b4baf22752924bf20d097e96236c36f8caryclark kWalking, 395b5ddd73b4baf22752924bf20d097e96236c36f8caryclark kFixWinding, 4054359294a7c9dc54802d512a5d891a35c1663392caryclark }; 4154359294a7c9dc54802d512a5d891a35c1663392caryclark 42624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark enum { 43624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark kMaxWindingTries = 10 44624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark }; 45624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 4626ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark bool angleCoincidence() const { 4754359294a7c9dc54802d512a5d891a35c1663392caryclark return fAngleCoincidence; 4854359294a7c9dc54802d512a5d891a35c1663392caryclark } 4954359294a7c9dc54802d512a5d891a35c1663392caryclark 504e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark void bumpNested() { 514e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark ++fNested; 524e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 534e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 544e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark void clearNested() { 554e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark fNested = 0; 564e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 574e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 5854359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpCoincidence* coincidence() { 5954359294a7c9dc54802d512a5d891a35c1663392caryclark return fCoincidence; 6054359294a7c9dc54802d512a5d891a35c1663392caryclark } 6154359294a7c9dc54802d512a5d891a35c1663392caryclark 62624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkOpContourHead* contourHead() { 63624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark return fContourHead; 64624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } 65624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 6654359294a7c9dc54802d512a5d891a35c1663392caryclark#ifdef SK_DEBUG 6754359294a7c9dc54802d512a5d891a35c1663392caryclark const struct SkOpAngle* debugAngle(int id) const; 6854359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpContour* debugContour(int id); 6954359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpPtT* debugPtT(int id) const; 7027c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark bool debugRunFail() const; 7154359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpSegment* debugSegment(int id) const; 7254359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpSpanBase* debugSpan(int id) const; 73d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark const char* debugTestName() const { return fDebugTestName; } 744e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark#endif 754e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 7626ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#if DEBUG_T_SECT_LOOP_COUNT 7726ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugAddLoopCount(SkIntersections* , const SkIntersectionHelper& , 7826ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark const SkIntersectionHelper& ); 7926ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugDoYourWorst(SkOpGlobalState* ); 8026ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugLoopReport(); 8126ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugResetLoopCounts(); 8226ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#endif 8326ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark 844e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark int nested() const { 854e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark return fNested; 864e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 8754359294a7c9dc54802d512a5d891a35c1663392caryclark 884e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark#ifdef SK_DEBUG 8954359294a7c9dc54802d512a5d891a35c1663392caryclark int nextAngleID() { 9054359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fAngleID; 9154359294a7c9dc54802d512a5d891a35c1663392caryclark } 9254359294a7c9dc54802d512a5d891a35c1663392caryclark 9326ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark int nextCoinID() { 9426ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark return ++fCoinID; 9526ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark } 9626ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark 9754359294a7c9dc54802d512a5d891a35c1663392caryclark int nextContourID() { 9854359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fContourID; 9954359294a7c9dc54802d512a5d891a35c1663392caryclark } 10026ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark 10154359294a7c9dc54802d512a5d891a35c1663392caryclark int nextPtTID() { 10254359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fPtTID; 10354359294a7c9dc54802d512a5d891a35c1663392caryclark } 10454359294a7c9dc54802d512a5d891a35c1663392caryclark 10554359294a7c9dc54802d512a5d891a35c1663392caryclark int nextSegmentID() { 10654359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fSegmentID; 10754359294a7c9dc54802d512a5d891a35c1663392caryclark } 10854359294a7c9dc54802d512a5d891a35c1663392caryclark 10954359294a7c9dc54802d512a5d891a35c1663392caryclark int nextSpanID() { 11054359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fSpanID; 11154359294a7c9dc54802d512a5d891a35c1663392caryclark } 11254359294a7c9dc54802d512a5d891a35c1663392caryclark#endif 11354359294a7c9dc54802d512a5d891a35c1663392caryclark 11454359294a7c9dc54802d512a5d891a35c1663392caryclark Phase phase() const { 11554359294a7c9dc54802d512a5d891a35c1663392caryclark return fPhase; 11654359294a7c9dc54802d512a5d891a35c1663392caryclark } 11754359294a7c9dc54802d512a5d891a35c1663392caryclark 11854359294a7c9dc54802d512a5d891a35c1663392caryclark void setAngleCoincidence() { 11954359294a7c9dc54802d512a5d891a35c1663392caryclark fAngleCoincidence = true; 12054359294a7c9dc54802d512a5d891a35c1663392caryclark } 12154359294a7c9dc54802d512a5d891a35c1663392caryclark 122624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark void setContourHead(SkOpContourHead* contourHead) { 123624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark fContourHead = contourHead; 124624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } 125624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 12654359294a7c9dc54802d512a5d891a35c1663392caryclark void setPhase(Phase phase) { 12754359294a7c9dc54802d512a5d891a35c1663392caryclark SkASSERT(fPhase != phase); 12854359294a7c9dc54802d512a5d891a35c1663392caryclark fPhase = phase; 12954359294a7c9dc54802d512a5d891a35c1663392caryclark } 13054359294a7c9dc54802d512a5d891a35c1663392caryclark 13154359294a7c9dc54802d512a5d891a35c1663392caryclark // called in very rare cases where angles are sorted incorrectly -- signfies op will fail 13254359294a7c9dc54802d512a5d891a35c1663392caryclark void setWindingFailed() { 13354359294a7c9dc54802d512a5d891a35c1663392caryclark fWindingFailed = true; 13454359294a7c9dc54802d512a5d891a35c1663392caryclark } 13554359294a7c9dc54802d512a5d891a35c1663392caryclark 13654359294a7c9dc54802d512a5d891a35c1663392caryclark bool windingFailed() const { 13754359294a7c9dc54802d512a5d891a35c1663392caryclark return fWindingFailed; 13854359294a7c9dc54802d512a5d891a35c1663392caryclark } 13954359294a7c9dc54802d512a5d891a35c1663392caryclark 14054359294a7c9dc54802d512a5d891a35c1663392caryclarkprivate: 14154359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpCoincidence* fCoincidence; 142624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkOpContourHead* fContourHead; 1434e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark int fNested; 14454359294a7c9dc54802d512a5d891a35c1663392caryclark bool fWindingFailed; 14554359294a7c9dc54802d512a5d891a35c1663392caryclark bool fAngleCoincidence; 14654359294a7c9dc54802d512a5d891a35c1663392caryclark Phase fPhase; 14754359294a7c9dc54802d512a5d891a35c1663392caryclark#ifdef SK_DEBUG 148d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark const char* fDebugTestName; 14954359294a7c9dc54802d512a5d891a35c1663392caryclark int fAngleID; 15026ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark int fCoinID; 15154359294a7c9dc54802d512a5d891a35c1663392caryclark int fContourID; 15254359294a7c9dc54802d512a5d891a35c1663392caryclark int fPtTID; 15354359294a7c9dc54802d512a5d891a35c1663392caryclark int fSegmentID; 15454359294a7c9dc54802d512a5d891a35c1663392caryclark int fSpanID; 15554359294a7c9dc54802d512a5d891a35c1663392caryclark#endif 15626ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#if DEBUG_T_SECT_LOOP_COUNT 15726ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark int fDebugLoopCount[3]; 15826ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark SkPath::Verb fDebugWorstVerb[6]; 15926ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark SkPoint fDebugWorstPts[24]; 16026ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark float fDebugWorstWeight[6]; 16126ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#endif 16254359294a7c9dc54802d512a5d891a35c1663392caryclark}; 16354359294a7c9dc54802d512a5d891a35c1663392caryclark 164c3f63570c35a1e2bc84b33906c6401d6f3062bf2caryclark@google.com// Use Almost Equal when comparing coordinates. Use epsilon to compare T values. 1654fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool AlmostEqualUlps(float a, float b); 1664fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostEqualUlps(double a, double b) { 1674fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 16807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1707eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com// Use Almost Dequal when comparing should not special case denormalized values. 1717eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool AlmostDequalUlps(float a, float b); 1722db7fe7d3b7ee875e1099a22f0af17520696f5d7commit-bot@chromium.orgbool AlmostDequalUlps(double a, double b); 1737eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 174570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool NotAlmostEqualUlps(float a, float b); 175570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool NotAlmostEqualUlps(double a, double b) { 176570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return NotAlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 177570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 178570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 1797eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool NotAlmostDequalUlps(float a, float b); 1807eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.cominline bool NotAlmostDequalUlps(double a, double b) { 1817eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return NotAlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 1827eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 1837eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 184570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com// Use Almost Bequal when comparing coordinates in conjunction with between. 185570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostBequalUlps(float a, float b); 186570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostBequalUlps(double a, double b) { 187570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostBequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 188570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 189570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 190a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.combool AlmostPequalUlps(float a, float b); 191a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.cominline bool AlmostPequalUlps(double a, double b) { 192a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return AlmostPequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 193a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com} 194a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com 1954fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool RoughlyEqualUlps(float a, float b); 1964fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool RoughlyEqualUlps(double a, double b) { 1974fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return RoughlyEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 19807e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 19907e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 200570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessUlps(float a, float b); 201570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessUlps(double a, double b) { 202570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 203570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 204570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 205570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessOrEqualUlps(float a, float b); 206570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessOrEqualUlps(double a, double b) { 207570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessOrEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 208570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 209570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 210fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c); 2114fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostBetweenUlps(double a, double b, double c) { 2124fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostBetweenUlps(SkDoubleToScalar(a), SkDoubleToScalar(b), SkDoubleToScalar(c)); 2134fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com} 2144fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 2154fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comint UlpsDistance(float a, float b); 2164fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline int UlpsDistance(double a, double b) { 2174fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return UlpsDistance(SkDoubleToScalar(a), SkDoubleToScalar(b)); 218fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 219fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 22007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23) 22107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// DBL_EPSILON == 2.22045e-16 22207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON; 22307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_HALF = FLT_EPSILON / 2; 224cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double FLT_EPSILON_DOUBLE = FLT_EPSILON * 2; 2254431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orgconst double FLT_EPSILON_ORDERABLE_ERR = FLT_EPSILON * 16; 22607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON; 22707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON); 22807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON; 22907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double DBL_EPSILON_ERR = DBL_EPSILON * 4; // FIXME: tune -- allow a few bits of error 230cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double DBL_EPSILON_SUBDIVIDE_ERR = DBL_EPSILON * 16; 23107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double ROUGH_EPSILON = FLT_EPSILON * 64; 23207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double MORE_ROUGH_EPSILON = FLT_EPSILON * 256; 233dac1d17027dcaa5596885a9f333979418b35001ccaryclarkconst double WAY_ROUGH_EPSILON = FLT_EPSILON * 2048; 23454359294a7c9dc54802d512a5d891a35c1663392caryclarkconst double BUMP_EPSILON = FLT_EPSILON * 4096; 235dac1d17027dcaa5596885a9f333979418b35001ccaryclark 236dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool zero_or_one(double x) { 237dac1d17027dcaa5596885a9f333979418b35001ccaryclark return x == 0 || x == 1; 238dac1d17027dcaa5596885a9f333979418b35001ccaryclark} 23907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(double x) { 24107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 24207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_zero(double x) { 24507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < DBL_EPSILON_ERR; 24607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 248cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_zero(double x) { 249cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < DBL_EPSILON_SUBDIVIDE_ERR; 250cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 251cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 25207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(float x) { 25307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 25407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 25507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_cubed(double x) { 25707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_CUBED; 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 25907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 26007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_half(double x) { 26107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_HALF; 26207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 264cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_zero_double(double x) { 265cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < FLT_EPSILON_DOUBLE; 266cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 267cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 2684431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_orderable(double x) { 2694431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return fabs(x) < FLT_EPSILON_ORDERABLE_ERR; 2704431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2714431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_squared(double x) { 27307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQUARED; 27407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_sqrt(double x) { 27707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQRT; 27807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 280cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool roughly_zero(double x) { 281cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < ROUGH_EPSILON; 282cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 283cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 28407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_inverse(double x) { 28507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) > FLT_EPSILON_INVERSE; 28607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 28707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 28807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// OPTIMIZATION: if called multiple times with the same denom, we want to pass 1/y instead 28907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_when_compared_to(double x, double y) { 2904431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x == 0 || fabs(x) < fabs(y * FLT_EPSILON); 29107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 29207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 29354359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool precisely_zero_when_compared_to(double x, double y) { 29454359294a7c9dc54802d512a5d891a35c1663392caryclark return x == 0 || fabs(x) < fabs(y * DBL_EPSILON); 29554359294a7c9dc54802d512a5d891a35c1663392caryclark} 29654359294a7c9dc54802d512a5d891a35c1663392caryclark 29707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use 29807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// AlmostEqualUlps instead. 29907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal(double x, double y) { 30007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero(x - y); 30107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_equal(double x, double y) { 30407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return precisely_zero(x - y); 30507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 307cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_equal(double x, double y) { 308cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return precisely_subdivide_zero(x - y); 309cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 310cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 31107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_half(double x, double y) { 31207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero_half(x - y); 31307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 31407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 315cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_equal_double(double x, double y) { 316cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return approximately_zero_double(x - y); 317cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 318cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 3194431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_equal_orderable(double x, double y) { 3204431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return approximately_zero_orderable(x - y); 3214431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3224431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 32307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_squared(double x, double y) { 32407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_equal(x, y); 32507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 32607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 32707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater(double x, double y) { 32807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON >= y; 32907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 33007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3314431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_double(double x, double y) { 3324431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE >= y; 3334431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3344431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3354431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_orderable(double x, double y) { 3364431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR >= y; 3374431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3384431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 33907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_or_equal(double x, double y) { 34007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON > y; 34107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 34207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3434431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_double(double x, double y) { 3444431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE > y; 3454431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3464431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3474431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_orderable(double x, double y) { 3484431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR > y; 3494431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3504431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 35107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser(double x, double y) { 35207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON <= y; 35307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 35407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3554431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_double(double x, double y) { 3564431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE <= y; 3574431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3584431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3594431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_orderable(double x, double y) { 3604431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR <= y; 3614431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3624431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 36307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser_or_equal(double x, double y) { 36407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON < y; 36507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3674431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_double(double x, double y) { 3684431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE < y; 3694431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3704431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3714431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_orderable(double x, double y) { 3724431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR < y; 3734431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3744431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 37507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_than_one(double x) { 37607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - FLT_EPSILON; 37707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 37807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 37907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_greater_than_one(double x) { 38007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - DBL_EPSILON_ERR; 38107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 38207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 38307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_less_than_zero(double x) { 38407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 38507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 38607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 38707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_less_than_zero(double x) { 38807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 38907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 39007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 39107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_negative(double x) { 39207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 39307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 39407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3954431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_negative_orderable(double x) { 3964431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < FLT_EPSILON_ORDERABLE_ERR; 3974431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3984431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 39907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_negative(double x) { 40007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 40107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 40207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 40307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_one_or_less(double x) { 40407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < 1 + FLT_EPSILON; 40507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 40607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4074431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_one_or_less_double(double x) { 4084431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < 1 + FLT_EPSILON_DOUBLE; 4094431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4104431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 41107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive(double x) { 41207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 41307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 41407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 41507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive_squared(double x) { 41607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -(FLT_EPSILON_SQUARED); 41707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 41807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 41907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_or_more(double x) { 42007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 42107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 42207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4234431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_or_more_double(double x) { 4244431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x > -FLT_EPSILON_DOUBLE; 4254431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4264431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 4274431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_between_orderable(double a, double b, double c) { 4284431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return a <= c 4294431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org ? approximately_negative_orderable(a - b) && approximately_negative_orderable(b - c) 4304431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org : approximately_negative_orderable(b - a) && approximately_negative_orderable(c - b); 4314431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4324431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 43307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_between(double a, double b, double c) { 43407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return a <= c ? approximately_negative(a - b) && approximately_negative(b - c) 43507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : approximately_negative(b - a) && approximately_negative(c - b); 43607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 4370361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com 4380361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.cominline bool precisely_between(double a, double b, double c) { 4390361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com return a <= c ? precisely_negative(a - b) && precisely_negative(b - c) 4400361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com : precisely_negative(b - a) && precisely_negative(c - b); 4410361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com} 44207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 44307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// returns true if (a <= b <= c) || (a >= b >= c) 44407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool between(double a, double b, double c) { 44554359294a7c9dc54802d512a5d891a35c1663392caryclark SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0) 44654359294a7c9dc54802d512a5d891a35c1663392caryclark || (precisely_zero(a) && precisely_zero(b) && precisely_zero(c))); 44707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (a - b) * (c - b) <= 0; 44807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 44907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 450dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool roughly_equal(double x, double y) { 451dac1d17027dcaa5596885a9f333979418b35001ccaryclark return fabs(x - y) < ROUGH_EPSILON; 452dac1d17027dcaa5596885a9f333979418b35001ccaryclark} 453dac1d17027dcaa5596885a9f333979418b35001ccaryclark 45454359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool roughly_negative(double x) { 45554359294a7c9dc54802d512a5d891a35c1663392caryclark return x < ROUGH_EPSILON; 45654359294a7c9dc54802d512a5d891a35c1663392caryclark} 45754359294a7c9dc54802d512a5d891a35c1663392caryclark 45854359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool roughly_between(double a, double b, double c) { 45954359294a7c9dc54802d512a5d891a35c1663392caryclark return a <= c ? roughly_negative(a - b) && roughly_negative(b - c) 46054359294a7c9dc54802d512a5d891a35c1663392caryclark : roughly_negative(b - a) && roughly_negative(c - b); 46154359294a7c9dc54802d512a5d891a35c1663392caryclark} 46254359294a7c9dc54802d512a5d891a35c1663392caryclark 46307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool more_roughly_equal(double x, double y) { 46407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < MORE_ROUGH_EPSILON; 46507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 46607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 467dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool way_roughly_equal(double x, double y) { 468dac1d17027dcaa5596885a9f333979418b35001ccaryclark return fabs(x - y) < WAY_ROUGH_EPSILON; 46907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 47007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 47107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDPoint; 47207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDVector; 47307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDLine; 47407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDQuad; 4751049f1246e7be4ccb68001361efceb8933e6f81ccaryclarkstruct SkDConic; 47607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDCubic; 47707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDRect; 47807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 479277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline SkPath::Verb SkPathOpsPointsToVerb(int points) { 480277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int verb = (1 << points) >> 1; 481277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 482277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (points) { 483277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 0: SkASSERT(SkPath::kMove_Verb == verb); break; 484277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 1: SkASSERT(SkPath::kLine_Verb == verb); break; 485277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 2: SkASSERT(SkPath::kQuad_Verb == verb); break; 486277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 3: SkASSERT(SkPath::kCubic_Verb == verb); break; 487330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not be here"); 488277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 489277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 490277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return (SkPath::Verb)verb; 491277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 492277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 493277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline int SkPathOpsVerbToPoints(SkPath::Verb verb) { 4941049f1246e7be4ccb68001361efceb8933e6f81ccaryclark int points = (int) verb - (((int) verb + 1) >> 2); 495277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 496277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (verb) { 497277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kLine_Verb: SkASSERT(1 == points); break; 498277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kQuad_Verb: SkASSERT(2 == points); break; 4991049f1246e7be4ccb68001361efceb8933e6f81ccaryclark case SkPath::kConic_Verb: SkASSERT(2 == points); break; 500277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kCubic_Verb: SkASSERT(3 == points); break; 501330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not get here"); 502277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 503277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 504277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return points; 505277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 506277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 50707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline double SkDInterp(double A, double B, double t) { 50807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A + (B - A) * t; 50907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 51007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 51107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x); 51207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 51307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns -1 if negative, 0 if zero, 1 if positive 51407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 51507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSign(double x) { 51607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) - (x < 0); 51707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 51807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 51907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 0 if negative, 1 if zero, 2 if positive 52007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 52107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SKDSide(double x) { 52207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) + (x >= 0); 52307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 52407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 52507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 1 if negative, 2 if zero, 4 if positive 52607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 52707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSideBit(double x) { 52807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 1 << SKDSide(x); 52907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 53007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 531fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline double SkPinT(double t) { 532fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return precisely_less_than_zero(t) ? 0 : precisely_greater_than_one(t) ? 1 : t; 533fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 534fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 53507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#endif 536