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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 static bool arguments_denormalized(float a, float b, int epsilon) { | 10 static bool arguments_denormalized(float a, float b, int epsilon) { |
11 float denomalizedCheck = FLT_EPSILON * epsilon / 2; | 11 float denormalizedCheck = FLT_EPSILON * epsilon / 2; |
12 return fabsf(a) <= denomalizedCheck && fabsf(b) <= denomalizedCheck; | 12 return fabsf(a) <= denormalizedCheck && fabsf(b) <= denormalizedCheck; |
13 } | 13 } |
14 | 14 |
15 // from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-num
bers-2012-edition/ | 15 // from http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-num
bers-2012-edition/ |
16 // FIXME: move to SkFloatBits.h | 16 // FIXME: move to SkFloatBits.h |
17 static bool equal_ulps(float a, float b, int epsilon) { | 17 static bool equal_ulps(float a, float b, int epsilon, int depsilon) { |
18 if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) { | 18 if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) { |
19 return false; | 19 return false; |
20 } | 20 } |
21 if (arguments_denormalized(a, b, epsilon)) { | 21 if (arguments_denormalized(a, b, depsilon)) { |
22 return true; | 22 return true; |
23 } | 23 } |
24 int aBits = SkFloatAs2sCompliment(a); | 24 int aBits = SkFloatAs2sCompliment(a); |
25 int bBits = SkFloatAs2sCompliment(b); | 25 int bBits = SkFloatAs2sCompliment(b); |
26 // Find the difference in ULPs. | 26 // Find the difference in ULPs. |
27 return aBits < bBits + epsilon && bBits < aBits + epsilon; | 27 return aBits < bBits + epsilon && bBits < aBits + epsilon; |
28 } | 28 } |
29 | 29 |
30 static bool d_equal_ulps(float a, float b, int epsilon) { | 30 static bool d_equal_ulps(float a, float b, int epsilon) { |
31 if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) { | 31 if (!SkScalarIsFinite(a) || !SkScalarIsFinite(b)) { |
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82 } | 82 } |
83 int aBits = SkFloatAs2sCompliment(a); | 83 int aBits = SkFloatAs2sCompliment(a); |
84 int bBits = SkFloatAs2sCompliment(b); | 84 int bBits = SkFloatAs2sCompliment(b); |
85 // Find the difference in ULPs. | 85 // Find the difference in ULPs. |
86 return aBits < bBits + epsilon; | 86 return aBits < bBits + epsilon; |
87 } | 87 } |
88 | 88 |
89 // equality using the same error term as between | 89 // equality using the same error term as between |
90 bool AlmostBequalUlps(float a, float b) { | 90 bool AlmostBequalUlps(float a, float b) { |
91 const int UlpsEpsilon = 2; | 91 const int UlpsEpsilon = 2; |
92 return equal_ulps(a, b, UlpsEpsilon); | 92 return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon); |
| 93 } |
| 94 |
| 95 bool AlmostPequalUlps(float a, float b) { |
| 96 const int UlpsEpsilon = 8; |
| 97 return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon); |
93 } | 98 } |
94 | 99 |
95 bool AlmostDequalUlps(float a, float b) { | 100 bool AlmostDequalUlps(float a, float b) { |
96 const int UlpsEpsilon = 16; | 101 const int UlpsEpsilon = 16; |
97 return d_equal_ulps(a, b, UlpsEpsilon); | 102 return d_equal_ulps(a, b, UlpsEpsilon); |
98 } | 103 } |
99 | 104 |
100 bool AlmostEqualUlps(float a, float b) { | 105 bool AlmostEqualUlps(float a, float b) { |
101 const int UlpsEpsilon = 16; | 106 const int UlpsEpsilon = 16; |
102 return equal_ulps(a, b, UlpsEpsilon); | 107 return equal_ulps(a, b, UlpsEpsilon, UlpsEpsilon); |
103 } | 108 } |
104 | 109 |
105 bool NotAlmostEqualUlps(float a, float b) { | 110 bool NotAlmostEqualUlps(float a, float b) { |
106 const int UlpsEpsilon = 16; | 111 const int UlpsEpsilon = 16; |
107 return not_equal_ulps(a, b, UlpsEpsilon); | 112 return not_equal_ulps(a, b, UlpsEpsilon); |
108 } | 113 } |
109 | 114 |
110 bool NotAlmostDequalUlps(float a, float b) { | 115 bool NotAlmostDequalUlps(float a, float b) { |
111 const int UlpsEpsilon = 16; | 116 const int UlpsEpsilon = 16; |
112 return d_not_equal_ulps(a, b, UlpsEpsilon); | 117 return d_not_equal_ulps(a, b, UlpsEpsilon); |
113 } | 118 } |
114 | 119 |
115 bool RoughlyEqualUlps(float a, float b) { | 120 bool RoughlyEqualUlps(float a, float b) { |
116 const int UlpsEpsilon = 256; | 121 const int UlpsEpsilon = 256; |
117 return equal_ulps(a, b, UlpsEpsilon); | 122 const int DUlpsEpsilon = 1024; |
| 123 return equal_ulps(a, b, UlpsEpsilon, DUlpsEpsilon); |
118 } | 124 } |
119 | 125 |
120 bool AlmostBetweenUlps(float a, float b, float c) { | 126 bool AlmostBetweenUlps(float a, float b, float c) { |
121 const int UlpsEpsilon = 2; | 127 const int UlpsEpsilon = 2; |
122 return a <= c ? less_or_equal_ulps(a, b, UlpsEpsilon) && less_or_equal_ulps(
b, c, UlpsEpsilon) | 128 return a <= c ? less_or_equal_ulps(a, b, UlpsEpsilon) && less_or_equal_ulps(
b, c, UlpsEpsilon) |
123 : less_or_equal_ulps(b, a, UlpsEpsilon) && less_or_equal_ulps(c, b, Ulps
Epsilon); | 129 : less_or_equal_ulps(b, a, UlpsEpsilon) && less_or_equal_ulps(c, b, Ulps
Epsilon); |
124 } | 130 } |
125 | 131 |
126 bool AlmostLessUlps(float a, float b) { | 132 bool AlmostLessUlps(float a, float b) { |
127 const int UlpsEpsilon = 16; | 133 const int UlpsEpsilon = 16; |
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178 double SkDCubeRoot(double x) { | 184 double SkDCubeRoot(double x) { |
179 if (approximately_zero_cubed(x)) { | 185 if (approximately_zero_cubed(x)) { |
180 return 0; | 186 return 0; |
181 } | 187 } |
182 double result = halley_cbrt3d(fabs(x)); | 188 double result = halley_cbrt3d(fabs(x)); |
183 if (x < 0) { | 189 if (x < 0) { |
184 result = -result; | 190 result = -result; |
185 } | 191 } |
186 return result; | 192 return result; |
187 } | 193 } |
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