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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 "SkFloatBits.h"
#include "SkPathOpsTypes.h"
static bool arguments_denormalized(float a, float b, int epsilon) {
float denomalizedCheck = FLT_EPSILON * epsilon / 2;
return fabsf(a) <= denomalizedCheck && fabsf(b) <= denomalizedCheck;
}
// 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) {
if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
return false;
}
if (arguments_denormalized(a, b, epsilon)) {
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) {
if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
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(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) {
if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
return false;
}
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 (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
return false;
}
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 (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
return false;
}
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);
}
bool AlmostDequalUlps(float a, float b) {
const int UlpsEpsilon = 16;
return d_equal_ulps(a, b, UlpsEpsilon);
}
bool AlmostEqualUlps(float a, float b) {
const int UlpsEpsilon = 16;
return equal_ulps(a, b, UlpsEpsilon);
}
bool NotAlmostEqualUlps(float a, float b) {
const int UlpsEpsilon = 16;
return not_equal_ulps(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;
return equal_ulps(a, b, UlpsEpsilon);
}
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) {
if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) {
return SK_MaxS32;
}
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 abs(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;
}
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