DXR is a code search and navigation tool aimed at making sense of large projects. It supports full-text and regex searches as well as structural queries.

Header

Mercurial (d8847129d134)

VCS Links

Line Code
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
/*
 * 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 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 (!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) {
    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, 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 (SkScalarIsFinite(a) || SkScalarIsFinite(b)) {
        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 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;
    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) {
    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;
}