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| 1 /* | 1 /* |
| 2 * Copyright 2012 Google Inc. | 2 * Copyright 2012 Google Inc. |
| 3 * | 3 * |
| 4 * Use of this source code is governed by a BSD-style license that can be | 4 * Use of this source code is governed by a BSD-style license that can be |
| 5 * found in the LICENSE file. | 5 * found in the LICENSE file. |
| 6 */ | 6 */ |
| 7 #include "SkFloatBits.h" | 7 #include "SkFloatBits.h" |
| 8 #include "SkPathOpsTypes.h" | 8 #include "SkPathOpsTypes.h" |
| 9 | 9 |
| 10 | 10 |
| 11 | 11 |
| 12 // from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-num
bers-2012-edition/ | 12 // from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-num
bers-2012-edition/ |
| 13 // FIXME: move to SkFloatBits.h | 13 // FIXME: move to SkFloatBits.h |
| 14 static bool equal_ulps(float A, float B, int epsilon) { | 14 static bool equal_ulps(float a, float b, int epsilon) { |
| 15 SkFloatIntUnion floatIntA, floatIntB; | 15 SkFloatIntUnion floatIntA, floatIntB; |
| 16 floatIntA.fFloat = A; | 16 floatIntA.fFloat = a; |
| 17 floatIntB.fFloat = B; | 17 floatIntB.fFloat = b; |
| 18 // Different signs means they do not match. | 18 // Different signs means they do not match. |
| 19 if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) { | 19 if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) { |
| 20 // Check for equality to make sure +0 == -0 | 20 // Check for equality to make sure +0 == -0 |
| 21 return A == B; | 21 return a == b; |
| 22 } | 22 } |
| 23 // Find the difference in ULPs. | 23 // Find the difference in ULPs. |
| 24 int ulpsDiff = abs(floatIntA.fSignBitInt - floatIntB.fSignBitInt); | 24 int ulpsDiff = abs(floatIntA.fSignBitInt - floatIntB.fSignBitInt); |
| 25 return ulpsDiff <= epsilon; | 25 return ulpsDiff <= epsilon; |
| 26 } | 26 } |
| 27 | 27 |
| 28 static bool less_ulps(float A, float B, int epsilon) { | 28 static bool less_ulps(float a, float b, int epsilon) { |
| 29 SkFloatIntUnion floatIntA, floatIntB; | 29 SkFloatIntUnion floatIntA, floatIntB; |
| 30 floatIntA.fFloat = A; | 30 floatIntA.fFloat = a; |
| 31 floatIntB.fFloat = B; | 31 floatIntB.fFloat = b; |
| 32 // Check different signs with float epsilon since we only care if they're bo
th close to 0. | 32 // Check different signs with float epsilon since we only care if they're bo
th close to 0. |
| 33 if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) { | 33 if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) { |
| 34 return A <= B + FLT_EPSILON * epsilon; | 34 return a <= b + FLT_EPSILON * epsilon; |
| 35 } | 35 } |
| 36 // Find the difference in ULPs. | 36 // Find the difference in ULPs. |
| 37 return floatIntA.fSignBitInt <= floatIntB.fSignBitInt + epsilon; | 37 return floatIntA.fSignBitInt <= floatIntB.fSignBitInt + epsilon; |
| 38 } | 38 } |
| 39 | 39 |
| 40 bool AlmostEqualUlps(float A, float B) { | 40 bool AlmostEqualUlps(float a, float b) { |
| 41 const int UlpsEpsilon = 16; | 41 const int UlpsEpsilon = 16; |
| 42 return equal_ulps(A, B, UlpsEpsilon); | 42 return equal_ulps(a, b, UlpsEpsilon); |
| 43 } | 43 } |
| 44 | 44 |
| 45 bool RoughlyEqualUlps(float A, float B) { | 45 bool RoughlyEqualUlps(float a, float b) { |
| 46 const int UlpsEpsilon = 256; | 46 const int UlpsEpsilon = 256; |
| 47 return equal_ulps(A, B, UlpsEpsilon); | 47 return equal_ulps(a, b, UlpsEpsilon); |
| 48 } | 48 } |
| 49 | 49 |
| 50 bool AlmostBetweenUlps(float a, float b, float c) { | 50 bool AlmostBetweenUlps(float a, float b, float c) { |
| 51 const int UlpsEpsilon = 1; | 51 const int UlpsEpsilon = 1; |
| 52 return a <= c ? less_ulps(a, b, UlpsEpsilon) && less_ulps(b, c, UlpsEpsilon) | 52 return a <= c ? less_ulps(a, b, UlpsEpsilon) && less_ulps(b, c, UlpsEpsilon) |
| 53 : less_ulps(b, a, UlpsEpsilon) && less_ulps(c, b, UlpsEpsilon); | 53 : less_ulps(b, a, UlpsEpsilon) && less_ulps(c, b, UlpsEpsilon); |
| 54 } | 54 } |
| 55 | 55 |
| 56 int UlpsDistance(float a, float b) { |
| 57 SkFloatIntUnion floatIntA, floatIntB; |
| 58 floatIntA.fFloat = a; |
| 59 floatIntB.fFloat = b; |
| 60 // Different signs means they do not match. |
| 61 if ((floatIntA.fSignBitInt < 0) != (floatIntB.fSignBitInt < 0)) { |
| 62 // Check for equality to make sure +0 == -0 |
| 63 return a == b ? 0 : SK_MaxS32; |
| 64 } |
| 65 // Find the difference in ULPs. |
| 66 return abs(floatIntA.fSignBitInt - floatIntB.fSignBitInt); |
| 67 } |
| 68 |
| 56 // cube root approximation using bit hack for 64-bit float | 69 // cube root approximation using bit hack for 64-bit float |
| 57 // adapted from Kahan's cbrt | 70 // adapted from Kahan's cbrt |
| 58 static double cbrt_5d(double d) { | 71 static double cbrt_5d(double d) { |
| 59 const unsigned int B1 = 715094163; | 72 const unsigned int B1 = 715094163; |
| 60 double t = 0.0; | 73 double t = 0.0; |
| 61 unsigned int* pt = (unsigned int*) &t; | 74 unsigned int* pt = (unsigned int*) &t; |
| 62 unsigned int* px = (unsigned int*) &d; | 75 unsigned int* px = (unsigned int*) &d; |
| 63 pt[1] = px[1] / 3 + B1; | 76 pt[1] = px[1] / 3 + B1; |
| 64 return t; | 77 return t; |
| 65 } | 78 } |
| (...skipping 16 matching lines...) Expand all Loading... |
| 82 double SkDCubeRoot(double x) { | 95 double SkDCubeRoot(double x) { |
| 83 if (approximately_zero_cubed(x)) { | 96 if (approximately_zero_cubed(x)) { |
| 84 return 0; | 97 return 0; |
| 85 } | 98 } |
| 86 double result = halley_cbrt3d(fabs(x)); | 99 double result = halley_cbrt3d(fabs(x)); |
| 87 if (x < 0) { | 100 if (x < 0) { |
| 88 result = -result; | 101 result = -result; |
| 89 } | 102 } |
| 90 return result; | 103 return result; |
| 91 } | 104 } |
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