1 /*
2 * Copyright 2006 The Android Open Source Project
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8 #ifndef SkScalar_DEFINED
9 #define SkScalar_DEFINED
10
11 #include "SkFixed.h"
12 #include "../private/SkFloatingPoint.h"
13
14 // TODO: move this sort of check into SkPostConfig.h
15 #define SK_SCALAR_IS_DOUBLE 0
16 #undef SK_SCALAR_IS_FLOAT
17 #define SK_SCALAR_IS_FLOAT 1
18
19
20 #if SK_SCALAR_IS_FLOAT
21
22 typedef float SkScalar;
23
24 #define SK_Scalar1 1.0f
25 #define SK_ScalarHalf 0.5f
26 #define SK_ScalarSqrt2 1.41421356f
27 #define SK_ScalarPI 3.14159265f
28 #define SK_ScalarTanPIOver8 0.414213562f
29 #define SK_ScalarRoot2Over2 0.707106781f
30 #define SK_ScalarMax 3.402823466e+38f
31 #define SK_ScalarInfinity SK_FloatInfinity
32 #define SK_ScalarNegativeInfinity SK_FloatNegativeInfinity
33 #define SK_ScalarNaN SK_FloatNaN
34
35 #define SkFixedToScalar(x) SkFixedToFloat(x)
36 #define SkScalarToFixed(x) SkFloatToFixed(x)
37
38 #define SkScalarFloorToScalar(x) sk_float_floor(x)
39 #define SkScalarCeilToScalar(x) sk_float_ceil(x)
40 #define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f)
41
42 #define SkScalarFloorToInt(x) sk_float_floor2int(x)
43 #define SkScalarCeilToInt(x) sk_float_ceil2int(x)
44 #define SkScalarRoundToInt(x) sk_float_round2int(x)
45
46 #define SkScalarAbs(x) sk_float_abs(x)
47 #define SkScalarCopySign(x, y) sk_float_copysign(x, y)
48 #define SkScalarMod(x, y) sk_float_mod(x,y)
49 #define SkScalarFraction(x) sk_float_mod(x, 1.0f)
50 #define SkScalarSqrt(x) sk_float_sqrt(x)
51 #define SkScalarPow(b, e) sk_float_pow(b, e)
52
53 #define SkScalarSin(radians) (float)sk_float_sin(radians)
54 #define SkScalarCos(radians) (float)sk_float_cos(radians)
55 #define SkScalarTan(radians) (float)sk_float_tan(radians)
56 #define SkScalarASin(val) (float)sk_float_asin(val)
57 #define SkScalarACos(val) (float)sk_float_acos(val)
58 #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x)
59 #define SkScalarExp(x) (float)sk_float_exp(x)
60 #define SkScalarLog(x) (float)sk_float_log(x)
61 #define SkScalarLog2(x) (float)sk_float_log2(x)
62
63 #else // SK_SCALAR_IS_DOUBLE
64
65 typedef double SkScalar;
66
67 #define SK_Scalar1 1.0
68 #define SK_ScalarHalf 0.5
69 #define SK_ScalarSqrt2 1.414213562373095
70 #define SK_ScalarPI 3.141592653589793
71 #define SK_ScalarTanPIOver8 0.4142135623731
72 #define SK_ScalarRoot2Over2 0.70710678118655
73 #define SK_ScalarMax 1.7976931348623157+308
74 #define SK_ScalarInfinity SK_DoubleInfinity
75 #define SK_ScalarNegativeInfinity SK_DoubleNegativeInfinity
76 #define SK_ScalarNaN SK_DoubleNaN
77
78 #define SkFixedToScalar(x) SkFixedToDouble(x)
79 #define SkScalarToFixed(x) SkDoubleToFixed(x)
80
81 #define SkScalarFloorToScalar(x) floor(x)
82 #define SkScalarCeilToScalar(x) ceil(x)
83 #define SkScalarRoundToScalar(x) floor((x) + 0.5)
84
85 #define SkScalarFloorToInt(x) (int)floor(x)
86 #define SkScalarCeilToInt(x) (int)ceil(x)
87 #define SkScalarRoundToInt(x) (int)floor((x) + 0.5)
88
89 #define SkScalarAbs(x) abs(x)
90 #define SkScalarCopySign(x, y) copysign(x, y)
91 #define SkScalarMod(x, y) fmod(x,y)
92 #define SkScalarFraction(x) fmod(x, 1.0)
93 #define SkScalarSqrt(x) sqrt(x)
94 #define SkScalarPow(b, e) pow(b, e)
95
96 #define SkScalarSin(radians) sin(radians)
97 #define SkScalarCos(radians) cos(radians)
98 #define SkScalarTan(radians) tan(radians)
99 #define SkScalarASin(val) asin(val)
100 #define SkScalarACos(val) acos(val)
101 #define SkScalarATan2(y, x) atan2(y,x)
102 #define SkScalarExp(x) exp(x)
103 #define SkScalarLog(x) log(x)
104 #define SkScalarLog2(x) log2(x)
105
106 #endif
107
108 //////////////////////////////////////////////////////////////////////////////////////////////////
109
110 #define SkIntToScalar(x) static_cast<SkScalar>(x)
111 #define SkScalarTruncToInt(x) static_cast<int>(x)
112
113 #define SkScalarToFloat(x) static_cast<float>(x)
114 #define SkFloatToScalar(x) static_cast<SkScalar>(x)
115 #define SkScalarToDouble(x) static_cast<double>(x)
116 #define SkDoubleToScalar(x) static_cast<SkScalar>(x)
117
118 #define SK_ScalarMin (-SK_ScalarMax)
119
SkScalarIsNaN(SkScalar x)120 static inline bool SkScalarIsNaN(SkScalar x) { return x != x; }
121
122 /** Returns true if x is not NaN and not infinite
123 */
SkScalarIsFinite(SkScalar x)124 static inline bool SkScalarIsFinite(SkScalar x) {
125 // We rely on the following behavior of infinities and nans
126 // 0 * finite --> 0
127 // 0 * infinity --> NaN
128 // 0 * NaN --> NaN
129 SkScalar prod = x * 0;
130 // At this point, prod will either be NaN or 0
131 return !SkScalarIsNaN(prod);
132 }
133
SkScalarsAreFinite(SkScalar a,SkScalar b)134 static inline bool SkScalarsAreFinite(SkScalar a, SkScalar b) {
135 SkScalar prod = 0;
136 prod *= a;
137 prod *= b;
138 // At this point, prod will either be NaN or 0
139 return !SkScalarIsNaN(prod);
140 }
141
SkScalarsAreFinite(const SkScalar array[],int count)142 static inline bool SkScalarsAreFinite(const SkScalar array[], int count) {
143 SkScalar prod = 0;
144 for (int i = 0; i < count; ++i) {
145 prod *= array[i];
146 }
147 // At this point, prod will either be NaN or 0
148 return !SkScalarIsNaN(prod);
149 }
150
151 /**
152 * Variant of SkScalarRoundToInt, that performs the rounding step (adding 0.5) explicitly using
153 * double, to avoid possibly losing the low bit(s) of the answer before calling floor().
154 *
155 * This routine will likely be slower than SkScalarRoundToInt(), and should only be used when the
156 * extra precision is known to be valuable.
157 *
158 * In particular, this catches the following case:
159 * SkScalar x = 0.49999997;
160 * int ix = SkScalarRoundToInt(x);
161 * SkASSERT(0 == ix); // <--- fails
162 * ix = SkDScalarRoundToInt(x);
163 * SkASSERT(0 == ix); // <--- succeeds
164 */
SkDScalarRoundToInt(SkScalar x)165 static inline int SkDScalarRoundToInt(SkScalar x) {
166 double xx = x;
167 xx += 0.5;
168 return (int)floor(xx);
169 }
170
SkScalarClampMax(SkScalar x,SkScalar max)171 static inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) {
172 x = SkTMin(x, max);
173 x = SkTMax<SkScalar>(x, 0);
174 return x;
175 }
176
SkScalarPin(SkScalar x,SkScalar min,SkScalar max)177 static inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) {
178 return SkTPin(x, min, max);
179 }
180
181 SkScalar SkScalarSinCos(SkScalar radians, SkScalar* cosValue);
182
SkScalarSquare(SkScalar x)183 static inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }
184
185 #define SkScalarMul(a, b) ((SkScalar)(a) * (b))
186 #define SkScalarMulAdd(a, b, c) ((SkScalar)(a) * (b) + (c))
187 #define SkScalarMulDiv(a, b, c) ((SkScalar)(a) * (b) / (c))
188 #define SkScalarInvert(x) (SK_Scalar1 / (x))
189 #define SkScalarFastInvert(x) (SK_Scalar1 / (x))
190 #define SkScalarAve(a, b) (((a) + (b)) * SK_ScalarHalf)
191 #define SkScalarHalf(a) ((a) * SK_ScalarHalf)
192
193 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
194 #define SkRadiansToDegrees(radians) ((radians) * (180 / SK_ScalarPI))
195
SkMaxScalar(SkScalar a,SkScalar b)196 static inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
SkMinScalar(SkScalar a,SkScalar b)197 static inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
198
SkScalarIsInt(SkScalar x)199 static inline bool SkScalarIsInt(SkScalar x) {
200 return x == (SkScalar)(int)x;
201 }
202
203 /**
204 * Returns -1 || 0 || 1 depending on the sign of value:
205 * -1 if x < 0
206 * 0 if x == 0
207 * 1 if x > 0
208 */
SkScalarSignAsInt(SkScalar x)209 static inline int SkScalarSignAsInt(SkScalar x) {
210 return x < 0 ? -1 : (x > 0);
211 }
212
213 // Scalar result version of above
SkScalarSignAsScalar(SkScalar x)214 static inline SkScalar SkScalarSignAsScalar(SkScalar x) {
215 return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0);
216 }
217
218 #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12))
219
220 static inline bool SkScalarNearlyZero(SkScalar x,
221 SkScalar tolerance = SK_ScalarNearlyZero) {
222 SkASSERT(tolerance >= 0);
223 return SkScalarAbs(x) <= tolerance;
224 }
225
226 static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y,
227 SkScalar tolerance = SK_ScalarNearlyZero) {
228 SkASSERT(tolerance >= 0);
229 return SkScalarAbs(x-y) <= tolerance;
230 }
231
232 /** Linearly interpolate between A and B, based on t.
233 If t is 0, return A
234 If t is 1, return B
235 else interpolate.
236 t must be [0..SK_Scalar1]
237 */
SkScalarInterp(SkScalar A,SkScalar B,SkScalar t)238 static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
239 SkASSERT(t >= 0 && t <= SK_Scalar1);
240 return A + (B - A) * t;
241 }
242
243 /** Interpolate along the function described by (keys[length], values[length])
244 for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length]
245 clamp to the min or max value. This function was inspired by a desire
246 to change the multiplier for thickness in fakeBold; therefore it assumes
247 the number of pairs (length) will be small, and a linear search is used.
248 Repeated keys are allowed for discontinuous functions (so long as keys is
249 monotonically increasing), and if key is the value of a repeated scalar in
250 keys, the first one will be used. However, that may change if a binary
251 search is used.
252 */
253 SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[],
254 const SkScalar values[], int length);
255
256 /*
257 * Helper to compare an array of scalars.
258 */
SkScalarsEqual(const SkScalar a[],const SkScalar b[],int n)259 static inline bool SkScalarsEqual(const SkScalar a[], const SkScalar b[], int n) {
260 SkASSERT(n >= 0);
261 for (int i = 0; i < n; ++i) {
262 if (a[i] != b[i]) {
263 return false;
264 }
265 }
266 return true;
267 }
268
269 #endif
270