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 "SkFloatingPoint.h"
13
14 //#define SK_SUPPORT_DEPRECATED_SCALARROUND
15
16 typedef float SkScalar;
17
18 /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar
19 */
20 #define SK_Scalar1 (1.0f)
21 /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar
22 */
23 #define SK_ScalarHalf (0.5f)
24 /** SK_ScalarInfinity is defined to be infinity as an SkScalar
25 */
26 #define SK_ScalarInfinity SK_FloatInfinity
27 /** SK_ScalarNegativeInfinity is defined to be negative infinity as an SkScalar
28 */
29 #define SK_ScalarNegativeInfinity SK_FloatNegativeInfinity
30 /** SK_ScalarMax is defined to be the largest value representable as an SkScalar
31 */
32 #define SK_ScalarMax (3.402823466e+38f)
33 /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar
34 */
35 #define SK_ScalarMin (-SK_ScalarMax)
36 /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar
37 */
38 #define SK_ScalarNaN SK_FloatNaN
39 /** SkScalarIsNaN(n) returns true if argument is not a number
40 */
SkScalarIsNaN(float x)41 static inline bool SkScalarIsNaN(float x) { return x != x; }
42
43 /** Returns true if x is not NaN and not infinite */
SkScalarIsFinite(float x)44 static inline bool SkScalarIsFinite(float x) {
45 // We rely on the following behavior of infinities and nans
46 // 0 * finite --> 0
47 // 0 * infinity --> NaN
48 // 0 * NaN --> NaN
49 float prod = x * 0;
50 // At this point, prod will either be NaN or 0
51 // Therefore we can return (prod == prod) or (0 == prod).
52 return prod == prod;
53 }
54
55 /** SkIntToScalar(n) returns its integer argument as an SkScalar
56 */
57 #define SkIntToScalar(n) ((float)(n))
58 /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar
59 */
60 #define SkFixedToScalar(x) SkFixedToFloat(x)
61 /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed
62 */
63 #define SkScalarToFixed(x) SkFloatToFixed(x)
64
65 #define SkScalarToFloat(n) (n)
66 #ifndef SK_SCALAR_TO_FLOAT_EXCLUDED
67 #define SkFloatToScalar(n) (n)
68 #endif
69
70 #define SkScalarToDouble(n) (double)(n)
71 #define SkDoubleToScalar(n) (float)(n)
72
73 /** SkScalarFraction(x) returns the signed fractional part of the argument
74 */
75 #define SkScalarFraction(x) sk_float_mod(x, 1.0f)
76
77 #define SkScalarFloorToScalar(x) sk_float_floor(x)
78 #define SkScalarCeilToScalar(x) sk_float_ceil(x)
79 #define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f)
80
81 #define SkScalarFloorToInt(x) sk_float_floor2int(x)
82 #define SkScalarCeilToInt(x) sk_float_ceil2int(x)
83 #define SkScalarRoundToInt(x) sk_float_round2int(x)
84 #define SkScalarTruncToInt(x) static_cast<int>(x)
85
86 /**
87 * Variant of SkScalarRoundToInt, that performs the rounding step (adding 0.5) explicitly using
88 * double, to avoid possibly losing the low bit(s) of the answer before calling floor().
89 *
90 * This routine will likely be slower than SkScalarRoundToInt(), and should only be used when the
91 * extra precision is known to be valuable.
92 *
93 * In particular, this catches the following case:
94 * SkScalar x = 0.49999997;
95 * int ix = SkScalarRoundToInt(x);
96 * SkASSERT(0 == ix); // <--- fails
97 * ix = SkDScalarRoundToInt(x);
98 * SkASSERT(0 == ix); // <--- succeeds
99 */
SkDScalarRoundToInt(SkScalar x)100 static inline int SkDScalarRoundToInt(SkScalar x) {
101 double xx = x;
102 xx += 0.5;
103 return (int)floor(xx);
104 }
105
106 /** Returns the absolute value of the specified SkScalar
107 */
108 #define SkScalarAbs(x) sk_float_abs(x)
109 /** Return x with the sign of y
110 */
111 #define SkScalarCopySign(x, y) sk_float_copysign(x, y)
112 /** Returns the value pinned between 0 and max inclusive
113 */
SkScalarClampMax(SkScalar x,SkScalar max)114 inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) {
115 return x < 0 ? 0 : x > max ? max : x;
116 }
117 /** Returns the value pinned between min and max inclusive
118 */
SkScalarPin(SkScalar x,SkScalar min,SkScalar max)119 inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) {
120 return x < min ? min : x > max ? max : x;
121 }
122 /** Returns the specified SkScalar squared (x*x)
123 */
SkScalarSquare(SkScalar x)124 inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }
125 /** Returns the product of two SkScalars
126 */
127 #define SkScalarMul(a, b) ((float)(a) * (b))
128 /** Returns the product of two SkScalars plus a third SkScalar
129 */
130 #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c))
131 /** Returns the quotient of two SkScalars (a/b)
132 */
133 #define SkScalarDiv(a, b) ((float)(a) / (b))
134 /** Returns the mod of two SkScalars (a mod b)
135 */
136 #define SkScalarMod(x,y) sk_float_mod(x,y)
137 /** Returns the product of the first two arguments, divided by the third argument
138 */
139 #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c))
140 /** Returns the multiplicative inverse of the SkScalar (1/x)
141 */
142 #define SkScalarInvert(x) (SK_Scalar1 / (x))
143 #define SkScalarFastInvert(x) (SK_Scalar1 / (x))
144 /** Returns the square root of the SkScalar
145 */
146 #define SkScalarSqrt(x) sk_float_sqrt(x)
147 /** Returns b to the e
148 */
149 #define SkScalarPow(b, e) sk_float_pow(b, e)
150 /** Returns the average of two SkScalars (a+b)/2
151 */
152 #define SkScalarAve(a, b) (((a) + (b)) * 0.5f)
153 /** Returns one half of the specified SkScalar
154 */
155 #define SkScalarHalf(a) ((a) * 0.5f)
156
157 #define SK_ScalarSqrt2 1.41421356f
158 #define SK_ScalarPI 3.14159265f
159 #define SK_ScalarTanPIOver8 0.414213562f
160 #define SK_ScalarRoot2Over2 0.707106781f
161
162 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
163 #define SkRadiansToDegrees(radians) ((radians) * (180 / SK_ScalarPI))
164 float SkScalarSinCos(SkScalar radians, SkScalar* cosValue);
165 #define SkScalarSin(radians) (float)sk_float_sin(radians)
166 #define SkScalarCos(radians) (float)sk_float_cos(radians)
167 #define SkScalarTan(radians) (float)sk_float_tan(radians)
168 #define SkScalarASin(val) (float)sk_float_asin(val)
169 #define SkScalarACos(val) (float)sk_float_acos(val)
170 #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x)
171 #define SkScalarExp(x) (float)sk_float_exp(x)
172 #define SkScalarLog(x) (float)sk_float_log(x)
173
SkMaxScalar(SkScalar a,SkScalar b)174 inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
SkMinScalar(SkScalar a,SkScalar b)175 inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
176
SkScalarIsInt(SkScalar x)177 static inline bool SkScalarIsInt(SkScalar x) {
178 return x == (float)(int)x;
179 }
180
181 // DEPRECATED : use ToInt or ToScalar variant
182 #ifdef SK_SUPPORT_DEPRECATED_SCALARROUND
183 # define SkScalarFloor(x) SkScalarFloorToInt(x)
184 # define SkScalarCeil(x) SkScalarCeilToInt(x)
185 # define SkScalarRound(x) SkScalarRoundToInt(x)
186 #endif
187
188 /**
189 * Returns -1 || 0 || 1 depending on the sign of value:
190 * -1 if x < 0
191 * 0 if x == 0
192 * 1 if x > 0
193 */
SkScalarSignAsInt(SkScalar x)194 static inline int SkScalarSignAsInt(SkScalar x) {
195 return x < 0 ? -1 : (x > 0);
196 }
197
198 // Scalar result version of above
SkScalarSignAsScalar(SkScalar x)199 static inline SkScalar SkScalarSignAsScalar(SkScalar x) {
200 return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0);
201 }
202
203 #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12))
204
205 static inline bool SkScalarNearlyZero(SkScalar x,
206 SkScalar tolerance = SK_ScalarNearlyZero) {
207 SkASSERT(tolerance >= 0);
208 return SkScalarAbs(x) <= tolerance;
209 }
210
211 static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y,
212 SkScalar tolerance = SK_ScalarNearlyZero) {
213 SkASSERT(tolerance >= 0);
214 return SkScalarAbs(x-y) <= tolerance;
215 }
216
217 /** Linearly interpolate between A and B, based on t.
218 If t is 0, return A
219 If t is 1, return B
220 else interpolate.
221 t must be [0..SK_Scalar1]
222 */
SkScalarInterp(SkScalar A,SkScalar B,SkScalar t)223 static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
224 SkASSERT(t >= 0 && t <= SK_Scalar1);
225 return A + (B - A) * t;
226 }
227
228 /** Interpolate along the function described by (keys[length], values[length])
229 for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length]
230 clamp to the min or max value. This function was inspired by a desire
231 to change the multiplier for thickness in fakeBold; therefore it assumes
232 the number of pairs (length) will be small, and a linear search is used.
233 Repeated keys are allowed for discontinuous functions (so long as keys is
234 monotonically increasing), and if key is the value of a repeated scalar in
235 keys, the first one will be used. However, that may change if a binary
236 search is used.
237 */
238 SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[],
239 const SkScalar values[], int length);
240
241 /*
242 * Helper to compare an array of scalars.
243 */
SkScalarsEqual(const SkScalar a[],const SkScalar b[],int n)244 static inline bool SkScalarsEqual(const SkScalar a[], const SkScalar b[], int n) {
245 SkASSERT(n >= 0);
246 for (int i = 0; i < n; ++i) {
247 if (a[i] != b[i]) {
248 return false;
249 }
250 }
251 return true;
252 }
253
254 #endif
255