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- /*
- * Copyright 2012 Google Inc.
- *
- * Use of this source code is governed by a BSD-style license that can be
- * found in the LICENSE file.
- */
- #include "include/private/SkFloatBits.h"
- #include "src/core/SkArenaAlloc.h"
- #include "src/pathops/SkOpCoincidence.h"
- #include "src/pathops/SkPathOpsTypes.h"
- static bool arguments_denormalized(float a, float b, int epsilon) {
- float denormalizedCheck = FLT_EPSILON * epsilon / 2;
- return fabsf(a) <= denormalizedCheck && fabsf(b) <= denormalizedCheck;
- }
- // from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
- // FIXME: move to SkFloatBits.h
- static bool equal_ulps(float a, float b, int epsilon, int depsilon) {
- if (arguments_denormalized(a, b, depsilon)) {
- return true;
- }
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits < bBits + epsilon && bBits < aBits + epsilon;
- }
- static bool equal_ulps_no_normal_check(float a, float b, int epsilon, int depsilon) {
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits < bBits + epsilon && bBits < aBits + epsilon;
- }
- static bool equal_ulps_pin(float a, float b, int epsilon, int depsilon) {
- if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
- return false;
- }
- if (arguments_denormalized(a, b, depsilon)) {
- return true;
- }
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits < bBits + epsilon && bBits < aBits + epsilon;
- }
- static bool d_equal_ulps(float a, float b, int epsilon) {
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits < bBits + epsilon && bBits < aBits + epsilon;
- }
- static bool not_equal_ulps(float a, float b, int epsilon) {
- if (arguments_denormalized(a, b, epsilon)) {
- return false;
- }
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits >= bBits + epsilon || bBits >= aBits + epsilon;
- }
- static bool not_equal_ulps_pin(float a, float b, int epsilon) {
- if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
- return false;
- }
- if (arguments_denormalized(a, b, epsilon)) {
- return false;
- }
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits >= bBits + epsilon || bBits >= aBits + epsilon;
- }
- static bool d_not_equal_ulps(float a, float b, int epsilon) {
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits >= bBits + epsilon || bBits >= aBits + epsilon;
- }
- static bool less_ulps(float a, float b, int epsilon) {
- if (arguments_denormalized(a, b, epsilon)) {
- return a <= b - FLT_EPSILON * epsilon;
- }
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits <= bBits - epsilon;
- }
- static bool less_or_equal_ulps(float a, float b, int epsilon) {
- if (arguments_denormalized(a, b, epsilon)) {
- return a < b + FLT_EPSILON * epsilon;
- }
- int aBits = SkFloatAs2sCompliment(a);
- int bBits = SkFloatAs2sCompliment(b);
- // Find the difference in ULPs.
- return aBits < bBits + epsilon;
- }
- // equality using the same error term as between
- bool AlmostBequalUlps(float a, float b) {
- const int UlpsEpsilon = 2;
- return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon);
- }
- bool AlmostPequalUlps(float a, float b) {
- const int UlpsEpsilon = 8;
- return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon);
- }
- bool AlmostDequalUlps(float a, float b) {
- const int UlpsEpsilon = 16;
- return d_equal_ulps(a, b, UlpsEpsilon);
- }
- bool AlmostDequalUlps(double a, double b) {
- if (fabs(a) < SK_ScalarMax && fabs(b) < SK_ScalarMax) {
- return AlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b));
- }
- return fabs(a - b) / SkTMax(fabs(a), fabs(b)) < FLT_EPSILON * 16;
- }
- bool AlmostEqualUlps(float a, float b) {
- const int UlpsEpsilon = 16;
- return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon);
- }
- bool AlmostEqualUlpsNoNormalCheck(float a, float b) {
- const int UlpsEpsilon = 16;
- return equal_ulps_no_normal_check(a, b, UlpsEpsilon, UlpsEpsilon);
- }
- bool AlmostEqualUlps_Pin(float a, float b) {
- const int UlpsEpsilon = 16;
- return equal_ulps_pin(a, b, UlpsEpsilon, UlpsEpsilon);
- }
- bool NotAlmostEqualUlps(float a, float b) {
- const int UlpsEpsilon = 16;
- return not_equal_ulps(a, b, UlpsEpsilon);
- }
- bool NotAlmostEqualUlps_Pin(float a, float b) {
- const int UlpsEpsilon = 16;
- return not_equal_ulps_pin(a, b, UlpsEpsilon);
- }
- bool NotAlmostDequalUlps(float a, float b) {
- const int UlpsEpsilon = 16;
- return d_not_equal_ulps(a, b, UlpsEpsilon);
- }
- bool RoughlyEqualUlps(float a, float b) {
- const int UlpsEpsilon = 256;
- const int DUlpsEpsilon = 1024;
- return equal_ulps(a, b, UlpsEpsilon, DUlpsEpsilon);
- }
- bool AlmostBetweenUlps(float a, float b, float c) {
- const int UlpsEpsilon = 2;
- return a <= c ? less_or_equal_ulps(a, b, UlpsEpsilon) && less_or_equal_ulps(b, c, UlpsEpsilon)
- : less_or_equal_ulps(b, a, UlpsEpsilon) && less_or_equal_ulps(c, b, UlpsEpsilon);
- }
- bool AlmostLessUlps(float a, float b) {
- const int UlpsEpsilon = 16;
- return less_ulps(a, b, UlpsEpsilon);
- }
- bool AlmostLessOrEqualUlps(float a, float b) {
- const int UlpsEpsilon = 16;
- return less_or_equal_ulps(a, b, UlpsEpsilon);
- }
- int UlpsDistance(float a, float b) {
- SkFloatIntUnion floatIntA, floatIntB;
- floatIntA.fFloat = a;
- floatIntB.fFloat = b;
- // Different signs means they do not match.
- if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) {
- // Check for equality to make sure +0 == -0
- return a == b ? 0 : SK_MaxS32;
- }
- // Find the difference in ULPs.
- return SkTAbs(floatIntA.fSignBitInt - floatIntB.fSignBitInt);
- }
- // cube root approximation using bit hack for 64-bit float
- // adapted from Kahan's cbrt
- static double cbrt_5d(double d) {
- const unsigned int B1 = 715094163;
- double t = 0.0;
- unsigned int* pt = (unsigned int*) &t;
- unsigned int* px = (unsigned int*) &d;
- pt[1] = px[1] / 3 + B1;
- return t;
- }
- // iterative cube root approximation using Halley's method (double)
- static double cbrta_halleyd(const double a, const double R) {
- const double a3 = a * a * a;
- const double b = a * (a3 + R + R) / (a3 + a3 + R);
- return b;
- }
- // cube root approximation using 3 iterations of Halley's method (double)
- static double halley_cbrt3d(double d) {
- double a = cbrt_5d(d);
- a = cbrta_halleyd(a, d);
- a = cbrta_halleyd(a, d);
- return cbrta_halleyd(a, d);
- }
- double SkDCubeRoot(double x) {
- if (approximately_zero_cubed(x)) {
- return 0;
- }
- double result = halley_cbrt3d(fabs(x));
- if (x < 0) {
- result = -result;
- }
- return result;
- }
- SkOpGlobalState::SkOpGlobalState(SkOpContourHead* head,
- SkArenaAlloc* allocator
- SkDEBUGPARAMS(bool debugSkipAssert)
- SkDEBUGPARAMS(const char* testName))
- : fAllocator(allocator)
- , fCoincidence(nullptr)
- , fContourHead(head)
- , fNested(0)
- , fWindingFailed(false)
- , fPhase(SkOpPhase::kIntersecting)
- SkDEBUGPARAMS(fDebugTestName(testName))
- SkDEBUGPARAMS(fAngleID(0))
- SkDEBUGPARAMS(fCoinID(0))
- SkDEBUGPARAMS(fContourID(0))
- SkDEBUGPARAMS(fPtTID(0))
- SkDEBUGPARAMS(fSegmentID(0))
- SkDEBUGPARAMS(fSpanID(0))
- SkDEBUGPARAMS(fDebugSkipAssert(debugSkipAssert)) {
- #if DEBUG_T_SECT_LOOP_COUNT
- debugResetLoopCounts();
- #endif
- #if DEBUG_COIN
- fPreviousFuncName = nullptr;
- #endif
- }
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