SkPathOpsTypes.h revision dae6b97705fde08958b1a36fa6ce685d28fc692c
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 34dae6b97705fde08958b1a36fa6ce685d28fc692ccaryclark SkDEBUGPARAMS(bool debugSkipAssert) 35d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark SkDEBUGPARAMS(const char* testName)); 3654359294a7c9dc54802d512a5d891a35c1663392caryclark 3754359294a7c9dc54802d512a5d891a35c1663392caryclark enum Phase { 3854359294a7c9dc54802d512a5d891a35c1663392caryclark kIntersecting, 395b5ddd73b4baf22752924bf20d097e96236c36f8caryclark kWalking, 405b5ddd73b4baf22752924bf20d097e96236c36f8caryclark kFixWinding, 4154359294a7c9dc54802d512a5d891a35c1663392caryclark }; 4254359294a7c9dc54802d512a5d891a35c1663392caryclark 43624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark enum { 44624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark kMaxWindingTries = 10 45624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark }; 46624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 4726ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark bool angleCoincidence() const { 4854359294a7c9dc54802d512a5d891a35c1663392caryclark return fAngleCoincidence; 4954359294a7c9dc54802d512a5d891a35c1663392caryclark } 5054359294a7c9dc54802d512a5d891a35c1663392caryclark 514e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark void bumpNested() { 524e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark ++fNested; 534e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 544e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 554e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark void clearNested() { 564e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark fNested = 0; 574e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 584e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 5954359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpCoincidence* coincidence() { 6054359294a7c9dc54802d512a5d891a35c1663392caryclark return fCoincidence; 6154359294a7c9dc54802d512a5d891a35c1663392caryclark } 6254359294a7c9dc54802d512a5d891a35c1663392caryclark 63624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkOpContourHead* contourHead() { 64624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark return fContourHead; 65624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } 66624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 6754359294a7c9dc54802d512a5d891a35c1663392caryclark#ifdef SK_DEBUG 6854359294a7c9dc54802d512a5d891a35c1663392caryclark const struct SkOpAngle* debugAngle(int id) const; 6954359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpContour* debugContour(int id); 7054359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpPtT* debugPtT(int id) const; 7127c8eb8ffd7e221693d840c2b9279d53fe6f03d4caryclark bool debugRunFail() const; 7254359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpSegment* debugSegment(int id) const; 73dae6b97705fde08958b1a36fa6ce685d28fc692ccaryclark bool debugSkipAssert() const { return fDebugSkipAssert; } 7454359294a7c9dc54802d512a5d891a35c1663392caryclark const class SkOpSpanBase* debugSpan(int id) const; 75d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark const char* debugTestName() const { return fDebugTestName; } 764e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark#endif 774e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark 7826ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#if DEBUG_T_SECT_LOOP_COUNT 7926ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugAddLoopCount(SkIntersections* , const SkIntersectionHelper& , 8026ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark const SkIntersectionHelper& ); 8126ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugDoYourWorst(SkOpGlobalState* ); 8226ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugLoopReport(); 8326ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark void debugResetLoopCounts(); 8426ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#endif 8526ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark 864e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark int nested() const { 874e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark return fNested; 884e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark } 8954359294a7c9dc54802d512a5d891a35c1663392caryclark 904e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark#ifdef SK_DEBUG 9154359294a7c9dc54802d512a5d891a35c1663392caryclark int nextAngleID() { 9254359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fAngleID; 9354359294a7c9dc54802d512a5d891a35c1663392caryclark } 9454359294a7c9dc54802d512a5d891a35c1663392caryclark 9526ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark int nextCoinID() { 9626ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark return ++fCoinID; 9726ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark } 9826ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark 9954359294a7c9dc54802d512a5d891a35c1663392caryclark int nextContourID() { 10054359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fContourID; 10154359294a7c9dc54802d512a5d891a35c1663392caryclark } 10226ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark 10354359294a7c9dc54802d512a5d891a35c1663392caryclark int nextPtTID() { 10454359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fPtTID; 10554359294a7c9dc54802d512a5d891a35c1663392caryclark } 10654359294a7c9dc54802d512a5d891a35c1663392caryclark 10754359294a7c9dc54802d512a5d891a35c1663392caryclark int nextSegmentID() { 10854359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fSegmentID; 10954359294a7c9dc54802d512a5d891a35c1663392caryclark } 11054359294a7c9dc54802d512a5d891a35c1663392caryclark 11154359294a7c9dc54802d512a5d891a35c1663392caryclark int nextSpanID() { 11254359294a7c9dc54802d512a5d891a35c1663392caryclark return ++fSpanID; 11354359294a7c9dc54802d512a5d891a35c1663392caryclark } 11454359294a7c9dc54802d512a5d891a35c1663392caryclark#endif 11554359294a7c9dc54802d512a5d891a35c1663392caryclark 11654359294a7c9dc54802d512a5d891a35c1663392caryclark Phase phase() const { 11754359294a7c9dc54802d512a5d891a35c1663392caryclark return fPhase; 11854359294a7c9dc54802d512a5d891a35c1663392caryclark } 11954359294a7c9dc54802d512a5d891a35c1663392caryclark 12054359294a7c9dc54802d512a5d891a35c1663392caryclark void setAngleCoincidence() { 12154359294a7c9dc54802d512a5d891a35c1663392caryclark fAngleCoincidence = true; 12254359294a7c9dc54802d512a5d891a35c1663392caryclark } 12354359294a7c9dc54802d512a5d891a35c1663392caryclark 124624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark void setContourHead(SkOpContourHead* contourHead) { 125624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark fContourHead = contourHead; 126624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark } 127624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark 12854359294a7c9dc54802d512a5d891a35c1663392caryclark void setPhase(Phase phase) { 12954359294a7c9dc54802d512a5d891a35c1663392caryclark SkASSERT(fPhase != phase); 13054359294a7c9dc54802d512a5d891a35c1663392caryclark fPhase = phase; 13154359294a7c9dc54802d512a5d891a35c1663392caryclark } 13254359294a7c9dc54802d512a5d891a35c1663392caryclark 13354359294a7c9dc54802d512a5d891a35c1663392caryclark // called in very rare cases where angles are sorted incorrectly -- signfies op will fail 13454359294a7c9dc54802d512a5d891a35c1663392caryclark void setWindingFailed() { 13554359294a7c9dc54802d512a5d891a35c1663392caryclark fWindingFailed = true; 13654359294a7c9dc54802d512a5d891a35c1663392caryclark } 13754359294a7c9dc54802d512a5d891a35c1663392caryclark 13854359294a7c9dc54802d512a5d891a35c1663392caryclark bool windingFailed() const { 13954359294a7c9dc54802d512a5d891a35c1663392caryclark return fWindingFailed; 14054359294a7c9dc54802d512a5d891a35c1663392caryclark } 14154359294a7c9dc54802d512a5d891a35c1663392caryclark 14254359294a7c9dc54802d512a5d891a35c1663392caryclarkprivate: 14354359294a7c9dc54802d512a5d891a35c1663392caryclark SkOpCoincidence* fCoincidence; 144624637cc8ec22c000409704d0b403ac1b81ad4b0caryclark SkOpContourHead* fContourHead; 1454e1a4c9399b8bb0897218f3ec10c254d3bb97463caryclark int fNested; 14654359294a7c9dc54802d512a5d891a35c1663392caryclark bool fWindingFailed; 14754359294a7c9dc54802d512a5d891a35c1663392caryclark bool fAngleCoincidence; 14854359294a7c9dc54802d512a5d891a35c1663392caryclark Phase fPhase; 14954359294a7c9dc54802d512a5d891a35c1663392caryclark#ifdef SK_DEBUG 150d4349723fac9c0fd4dcf8c275fb7c756bdfdff7bcaryclark const char* fDebugTestName; 15154359294a7c9dc54802d512a5d891a35c1663392caryclark int fAngleID; 15226ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark int fCoinID; 15354359294a7c9dc54802d512a5d891a35c1663392caryclark int fContourID; 15454359294a7c9dc54802d512a5d891a35c1663392caryclark int fPtTID; 15554359294a7c9dc54802d512a5d891a35c1663392caryclark int fSegmentID; 15654359294a7c9dc54802d512a5d891a35c1663392caryclark int fSpanID; 157dae6b97705fde08958b1a36fa6ce685d28fc692ccaryclark bool fDebugSkipAssert; 15854359294a7c9dc54802d512a5d891a35c1663392caryclark#endif 15926ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#if DEBUG_T_SECT_LOOP_COUNT 16026ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark int fDebugLoopCount[3]; 16126ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark SkPath::Verb fDebugWorstVerb[6]; 16226ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark SkPoint fDebugWorstPts[24]; 16326ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark float fDebugWorstWeight[6]; 16426ad22ab61539e3d3b6bc5e0da8dcebbd52a53decaryclark#endif 16554359294a7c9dc54802d512a5d891a35c1663392caryclark}; 16654359294a7c9dc54802d512a5d891a35c1663392caryclark 167c3f63570c35a1e2bc84b33906c6401d6f3062bf2caryclark@google.com// Use Almost Equal when comparing coordinates. Use epsilon to compare T values. 1684fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool AlmostEqualUlps(float a, float b); 1694fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostEqualUlps(double a, double b) { 1704fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 17107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 173b669300a9753893ef900207c38aeff2d467764e5caryclarkbool AlmostEqualUlps_Pin(float a, float b); 174b669300a9753893ef900207c38aeff2d467764e5caryclarkinline bool AlmostEqualUlps_Pin(double a, double b) { 175b669300a9753893ef900207c38aeff2d467764e5caryclark return AlmostEqualUlps_Pin(SkDoubleToScalar(a), SkDoubleToScalar(b)); 176b669300a9753893ef900207c38aeff2d467764e5caryclark} 177b669300a9753893ef900207c38aeff2d467764e5caryclark 1787eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com// Use Almost Dequal when comparing should not special case denormalized values. 1797eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool AlmostDequalUlps(float a, float b); 1802db7fe7d3b7ee875e1099a22f0af17520696f5d7commit-bot@chromium.orgbool AlmostDequalUlps(double a, double b); 1817eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 182570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool NotAlmostEqualUlps(float a, float b); 183570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool NotAlmostEqualUlps(double a, double b) { 184570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return NotAlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 185570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 186570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 187b669300a9753893ef900207c38aeff2d467764e5caryclarkbool NotAlmostEqualUlps_Pin(float a, float b); 188b669300a9753893ef900207c38aeff2d467764e5caryclarkinline bool NotAlmostEqualUlps_Pin(double a, double b) { 189b669300a9753893ef900207c38aeff2d467764e5caryclark return NotAlmostEqualUlps_Pin(SkDoubleToScalar(a), SkDoubleToScalar(b)); 190b669300a9753893ef900207c38aeff2d467764e5caryclark} 191b669300a9753893ef900207c38aeff2d467764e5caryclark 1927eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool NotAlmostDequalUlps(float a, float b); 1937eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.cominline bool NotAlmostDequalUlps(double a, double b) { 1947eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return NotAlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 1957eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 1967eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 197570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com// Use Almost Bequal when comparing coordinates in conjunction with between. 198570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostBequalUlps(float a, float b); 199570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostBequalUlps(double a, double b) { 200570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostBequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 201570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 202570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 203a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.combool AlmostPequalUlps(float a, float b); 204a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.cominline bool AlmostPequalUlps(double a, double b) { 205a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return AlmostPequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 206a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com} 207a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com 2084fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool RoughlyEqualUlps(float a, float b); 2094fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool RoughlyEqualUlps(double a, double b) { 2104fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return RoughlyEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 21107e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 21207e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 213570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessUlps(float a, float b); 214570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessUlps(double a, double b) { 215570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 216570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 217570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 218570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessOrEqualUlps(float a, float b); 219570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessOrEqualUlps(double a, double b) { 220570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessOrEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 221570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 222570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 223fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c); 2244fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostBetweenUlps(double a, double b, double c) { 2254fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostBetweenUlps(SkDoubleToScalar(a), SkDoubleToScalar(b), SkDoubleToScalar(c)); 2264fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com} 2274fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 2284fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comint UlpsDistance(float a, float b); 2294fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline int UlpsDistance(double a, double b) { 2304fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return UlpsDistance(SkDoubleToScalar(a), SkDoubleToScalar(b)); 231fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 232fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 23307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23) 23407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// DBL_EPSILON == 2.22045e-16 23507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON; 23607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_HALF = FLT_EPSILON / 2; 237cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double FLT_EPSILON_DOUBLE = FLT_EPSILON * 2; 2384431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orgconst double FLT_EPSILON_ORDERABLE_ERR = FLT_EPSILON * 16; 23907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON; 24007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON); 24107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON; 24207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double DBL_EPSILON_ERR = DBL_EPSILON * 4; // FIXME: tune -- allow a few bits of error 243cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double DBL_EPSILON_SUBDIVIDE_ERR = DBL_EPSILON * 16; 24407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double ROUGH_EPSILON = FLT_EPSILON * 64; 24507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double MORE_ROUGH_EPSILON = FLT_EPSILON * 256; 246dac1d17027dcaa5596885a9f333979418b35001ccaryclarkconst double WAY_ROUGH_EPSILON = FLT_EPSILON * 2048; 24754359294a7c9dc54802d512a5d891a35c1663392caryclarkconst double BUMP_EPSILON = FLT_EPSILON * 4096; 248dac1d17027dcaa5596885a9f333979418b35001ccaryclark 249dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool zero_or_one(double x) { 250dac1d17027dcaa5596885a9f333979418b35001ccaryclark return x == 0 || x == 1; 251dac1d17027dcaa5596885a9f333979418b35001ccaryclark} 25207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(double x) { 25407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 25507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 25607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_zero(double x) { 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < DBL_EPSILON_ERR; 25907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 261cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_zero(double x) { 262cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < DBL_EPSILON_SUBDIVIDE_ERR; 263cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 264cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 26507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(float x) { 26607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 26707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 26907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_cubed(double x) { 27007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_CUBED; 27107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_half(double x) { 27407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_HALF; 27507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 277cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_zero_double(double x) { 278cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < FLT_EPSILON_DOUBLE; 279cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 280cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 2814431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_orderable(double x) { 2824431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return fabs(x) < FLT_EPSILON_ORDERABLE_ERR; 2834431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2844431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 28507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_squared(double x) { 28607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQUARED; 28707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 28807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 28907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_sqrt(double x) { 29007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQRT; 29107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 29207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 293cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool roughly_zero(double x) { 294cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < ROUGH_EPSILON; 295cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 296cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 29707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_inverse(double x) { 29807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) > FLT_EPSILON_INVERSE; 29907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// OPTIMIZATION: if called multiple times with the same denom, we want to pass 1/y instead 30207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_when_compared_to(double x, double y) { 3034431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x == 0 || fabs(x) < fabs(y * FLT_EPSILON); 30407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30654359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool precisely_zero_when_compared_to(double x, double y) { 30754359294a7c9dc54802d512a5d891a35c1663392caryclark return x == 0 || fabs(x) < fabs(y * DBL_EPSILON); 30854359294a7c9dc54802d512a5d891a35c1663392caryclark} 30954359294a7c9dc54802d512a5d891a35c1663392caryclark 31007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use 31107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// AlmostEqualUlps instead. 31207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal(double x, double y) { 31307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero(x - y); 31407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 31507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 31607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_equal(double x, double y) { 31707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return precisely_zero(x - y); 31807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 31907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 320cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_equal(double x, double y) { 321cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return precisely_subdivide_zero(x - y); 322cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 323cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 32407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_half(double x, double y) { 32507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero_half(x - y); 32607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 32707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 328cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_equal_double(double x, double y) { 329cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return approximately_zero_double(x - y); 330cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 331cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 3324431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_equal_orderable(double x, double y) { 3334431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return approximately_zero_orderable(x - y); 3344431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3354431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 33607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_squared(double x, double y) { 33707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_equal(x, y); 33807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 33907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 34007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater(double x, double y) { 34107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON >= y; 34207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 34307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3444431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_double(double x, double y) { 3454431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE >= y; 3464431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3474431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3484431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_orderable(double x, double y) { 3494431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR >= y; 3504431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3514431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 35207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_or_equal(double x, double y) { 35307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON > y; 35407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 35507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3564431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_double(double x, double y) { 3574431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE > y; 3584431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3594431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3604431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_orderable(double x, double y) { 3614431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR > y; 3624431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3634431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 36407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser(double x, double y) { 36507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON <= y; 36607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3684431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_double(double x, double y) { 3694431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE <= y; 3704431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3714431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3724431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_orderable(double x, double y) { 3734431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR <= y; 3744431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3754431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 37607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser_or_equal(double x, double y) { 37707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON < y; 37807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 37907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3804431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_double(double x, double y) { 3814431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE < y; 3824431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3834431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 3844431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_orderable(double x, double y) { 3854431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR < y; 3864431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 3874431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 38807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_than_one(double x) { 38907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - FLT_EPSILON; 39007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 39107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 39207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_greater_than_one(double x) { 39307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - DBL_EPSILON_ERR; 39407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 39507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 39607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_less_than_zero(double x) { 39707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 39807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 39907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 40007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_less_than_zero(double x) { 40107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 40207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 40307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 40407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_negative(double x) { 40507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 40607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 40707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4084431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_negative_orderable(double x) { 4094431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < FLT_EPSILON_ORDERABLE_ERR; 4104431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4114431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 41207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_negative(double x) { 41307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 41407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 41507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 41607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_one_or_less(double x) { 41707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < 1 + FLT_EPSILON; 41807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 41907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4204431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_one_or_less_double(double x) { 4214431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < 1 + FLT_EPSILON_DOUBLE; 4224431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4234431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 42407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive(double x) { 42507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 42607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 42707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 42807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive_squared(double x) { 42907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -(FLT_EPSILON_SQUARED); 43007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 43107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 43207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_or_more(double x) { 43307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 43407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 43507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 4364431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_or_more_double(double x) { 4374431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x > -FLT_EPSILON_DOUBLE; 4384431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4394431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 4404431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_between_orderable(double a, double b, double c) { 4414431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return a <= c 4424431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org ? approximately_negative_orderable(a - b) && approximately_negative_orderable(b - c) 4434431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org : approximately_negative_orderable(b - a) && approximately_negative_orderable(c - b); 4444431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 4454431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 44607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_between(double a, double b, double c) { 44707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return a <= c ? approximately_negative(a - b) && approximately_negative(b - c) 44807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : approximately_negative(b - a) && approximately_negative(c - b); 44907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 4500361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com 4510361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.cominline bool precisely_between(double a, double b, double c) { 4520361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com return a <= c ? precisely_negative(a - b) && precisely_negative(b - c) 4530361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com : precisely_negative(b - a) && precisely_negative(c - b); 4540361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com} 45507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 45607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// returns true if (a <= b <= c) || (a >= b >= c) 45707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool between(double a, double b, double c) { 45854359294a7c9dc54802d512a5d891a35c1663392caryclark SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0) 45954359294a7c9dc54802d512a5d891a35c1663392caryclark || (precisely_zero(a) && precisely_zero(b) && precisely_zero(c))); 46007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (a - b) * (c - b) <= 0; 46107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 46207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 463dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool roughly_equal(double x, double y) { 464dac1d17027dcaa5596885a9f333979418b35001ccaryclark return fabs(x - y) < ROUGH_EPSILON; 465dac1d17027dcaa5596885a9f333979418b35001ccaryclark} 466dac1d17027dcaa5596885a9f333979418b35001ccaryclark 46754359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool roughly_negative(double x) { 46854359294a7c9dc54802d512a5d891a35c1663392caryclark return x < ROUGH_EPSILON; 46954359294a7c9dc54802d512a5d891a35c1663392caryclark} 47054359294a7c9dc54802d512a5d891a35c1663392caryclark 47154359294a7c9dc54802d512a5d891a35c1663392caryclarkinline bool roughly_between(double a, double b, double c) { 47254359294a7c9dc54802d512a5d891a35c1663392caryclark return a <= c ? roughly_negative(a - b) && roughly_negative(b - c) 47354359294a7c9dc54802d512a5d891a35c1663392caryclark : roughly_negative(b - a) && roughly_negative(c - b); 47454359294a7c9dc54802d512a5d891a35c1663392caryclark} 47554359294a7c9dc54802d512a5d891a35c1663392caryclark 47607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool more_roughly_equal(double x, double y) { 47707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < MORE_ROUGH_EPSILON; 47807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 47907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 480dac1d17027dcaa5596885a9f333979418b35001ccaryclarkinline bool way_roughly_equal(double x, double y) { 481dac1d17027dcaa5596885a9f333979418b35001ccaryclark return fabs(x - y) < WAY_ROUGH_EPSILON; 48207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 48307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 48407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDPoint; 48507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDVector; 48607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDLine; 48707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDQuad; 4881049f1246e7be4ccb68001361efceb8933e6f81ccaryclarkstruct SkDConic; 48907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDCubic; 49007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDRect; 49107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 492277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline SkPath::Verb SkPathOpsPointsToVerb(int points) { 493277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int verb = (1 << points) >> 1; 494277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 495277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (points) { 496277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 0: SkASSERT(SkPath::kMove_Verb == verb); break; 497277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 1: SkASSERT(SkPath::kLine_Verb == verb); break; 498277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 2: SkASSERT(SkPath::kQuad_Verb == verb); break; 499277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 3: SkASSERT(SkPath::kCubic_Verb == verb); break; 500330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not be here"); 501277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 502277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 503277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return (SkPath::Verb)verb; 504277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 505277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 506277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline int SkPathOpsVerbToPoints(SkPath::Verb verb) { 5071049f1246e7be4ccb68001361efceb8933e6f81ccaryclark int points = (int) verb - (((int) verb + 1) >> 2); 508277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 509277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (verb) { 510277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kLine_Verb: SkASSERT(1 == points); break; 511277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kQuad_Verb: SkASSERT(2 == points); break; 5121049f1246e7be4ccb68001361efceb8933e6f81ccaryclark case SkPath::kConic_Verb: SkASSERT(2 == points); break; 513277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kCubic_Verb: SkASSERT(3 == points); break; 514330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not get here"); 515277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 516277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 517277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return points; 518277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 519277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 52007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline double SkDInterp(double A, double B, double t) { 52107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A + (B - A) * t; 52207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 52307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 52407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x); 52507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 52607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns -1 if negative, 0 if zero, 1 if positive 52707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 52807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSign(double x) { 52907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) - (x < 0); 53007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 53107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 53207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 0 if negative, 1 if zero, 2 if positive 53307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 53407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SKDSide(double x) { 53507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) + (x >= 0); 53607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 53707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 53807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 1 if negative, 2 if zero, 4 if positive 53907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 54007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSideBit(double x) { 54107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 1 << SKDSide(x); 54207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 54307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 544fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline double SkPinT(double t) { 545fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return precisely_less_than_zero(t) ? 0 : precisely_greater_than_one(t) ? 1 : t; 546fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 547fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 54807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#endif 549