1
2 /*
3 * Copyright 2006 The Android Open Source Project
4 *
5 * Use of this source code is governed by a BSD-style license that can be
6 * found in the LICENSE file.
7 */
8
9
10 #ifndef SkScalar_DEFINED
11 #define SkScalar_DEFINED
12
13 #include "SkFixed.h"
14 #include "SkFloatingPoint.h"
15
16 /** \file SkScalar.h
17
18 Types and macros for the data type SkScalar. This is the fractional numeric type
19 that, depending on the compile-time flag SK_SCALAR_IS_FLOAT, may be implemented
20 either as an IEEE float, or as a 16.16 SkFixed. The macros in this file are written
21 to allow the calling code to manipulate SkScalar values without knowing which representation
22 is in effect.
23 */
24
25 #ifdef SK_SCALAR_IS_FLOAT
26
27 /** SkScalar is our type for fractional values and coordinates. Depending on
28 compile configurations, it is either represented as an IEEE float, or
29 as a 16.16 fixed point integer.
30 */
31 typedef float SkScalar;
32 extern const uint32_t gIEEENotANumber;
33 extern const uint32_t gIEEEInfinity;
34
35 /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar
36 */
37 #define SK_Scalar1 (1.0f)
38 /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar
39 */
40 #define SK_ScalarHalf (0.5f)
41 /** SK_ScalarInfinity is defined to be infinity as an SkScalar
42 */
43 #define SK_ScalarInfinity (*(const float*)&gIEEEInfinity)
44 /** SK_ScalarMax is defined to be the largest value representable as an SkScalar
45 */
46 #define SK_ScalarMax (3.402823466e+38f)
47 /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar
48 */
49 #define SK_ScalarMin (-SK_ScalarMax)
50 /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar
51 */
52 #define SK_ScalarNaN (*(const float*)(const void*)&gIEEENotANumber)
53 /** SkScalarIsNaN(n) returns true if argument is not a number
54 */
SkScalarIsNaN(float x)55 static inline bool SkScalarIsNaN(float x) { return x != x; }
56 /** Returns true if x is not NaN and not infinite */
SkScalarIsFinite(float x)57 static inline bool SkScalarIsFinite(float x) {
58 uint32_t bits = SkFloat2Bits(x); // need unsigned for our shifts
59 int exponent = bits << 1 >> 24;
60 return exponent != 0xFF;
61 }
62 #ifdef SK_DEBUG
63 /** SkIntToScalar(n) returns its integer argument as an SkScalar
64 *
65 * If we're compiling in DEBUG mode, and can thus afford some extra runtime
66 * cycles, check to make sure that the parameter passed in has not already
67 * been converted to SkScalar. (A double conversion like this is harmless
68 * for SK_SCALAR_IS_FLOAT, but for SK_SCALAR_IS_FIXED this causes trouble.)
69 *
70 * Note that we need all of these method signatures to properly handle the
71 * various types that we pass into SkIntToScalar() to date:
72 * int, size_t, U8CPU, etc., even though what we really mean is "anything
73 * but a float".
74 */
SkIntToScalar(signed int param)75 static inline float SkIntToScalar(signed int param) {
76 return (float)param;
77 }
SkIntToScalar(unsigned int param)78 static inline float SkIntToScalar(unsigned int param) {
79 return (float)param;
80 }
SkIntToScalar(signed long param)81 static inline float SkIntToScalar(signed long param) {
82 return (float)param;
83 }
SkIntToScalar(unsigned long param)84 static inline float SkIntToScalar(unsigned long param) {
85 return (float)param;
86 }
SkIntToScalar(float param)87 static inline float SkIntToScalar(float param) {
88 /* If the parameter passed into SkIntToScalar is a float,
89 * one of two things has happened:
90 * 1. the parameter was an SkScalar (which is typedef'd to float)
91 * 2. the parameter was a float instead of an int
92 *
93 * Either way, it's not good.
94 */
95 SkDEBUGFAIL("looks like you passed an SkScalar into SkIntToScalar");
96 return (float)0;
97 }
98 #else // not SK_DEBUG
99 /** SkIntToScalar(n) returns its integer argument as an SkScalar
100 */
101 #define SkIntToScalar(n) ((float)(n))
102 #endif // not SK_DEBUG
103 /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar
104 */
105 #define SkFixedToScalar(x) SkFixedToFloat(x)
106 /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed
107 */
108 #define SkScalarToFixed(x) SkFloatToFixed(x)
109
110 #define SkScalarToFloat(n) (n)
111 #define SkFloatToScalar(n) (n)
112
113 #define SkScalarToDouble(n) (double)(n)
114 #define SkDoubleToScalar(n) (float)(n)
115
116 /** SkScalarFraction(x) returns the signed fractional part of the argument
117 */
118 #define SkScalarFraction(x) sk_float_mod(x, 1.0f)
119
120 #define SkScalarFloorToScalar(x) sk_float_floor(x)
121 #define SkScalarCeilToScalar(x) sk_float_ceil(x)
122 #define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f)
123
124 #define SkScalarFloorToInt(x) sk_float_floor2int(x)
125 #define SkScalarCeilToInt(x) sk_float_ceil2int(x)
126 #define SkScalarRoundToInt(x) sk_float_round2int(x)
127
128 /** Returns the absolute value of the specified SkScalar
129 */
130 #define SkScalarAbs(x) sk_float_abs(x)
131 /** Return x with the sign of y
132 */
133 #define SkScalarCopySign(x, y) sk_float_copysign(x, y)
134 /** Returns the value pinned between 0 and max inclusive
135 */
SkScalarClampMax(SkScalar x,SkScalar max)136 inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) {
137 return x < 0 ? 0 : x > max ? max : x;
138 }
139 /** Returns the value pinned between min and max inclusive
140 */
SkScalarPin(SkScalar x,SkScalar min,SkScalar max)141 inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) {
142 return x < min ? min : x > max ? max : x;
143 }
144 /** Returns the specified SkScalar squared (x*x)
145 */
SkScalarSquare(SkScalar x)146 inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }
147 /** Returns the product of two SkScalars
148 */
149 #define SkScalarMul(a, b) ((float)(a) * (b))
150 /** Returns the product of two SkScalars plus a third SkScalar
151 */
152 #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c))
153 /** Returns the product of a SkScalar and an int rounded to the nearest integer value
154 */
155 #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b))
156 /** Returns the product of a SkScalar and an int promoted to the next larger int
157 */
158 #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b))
159 /** Returns the product of a SkScalar and an int truncated to the next smaller int
160 */
161 #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b))
162 /** Returns the quotient of two SkScalars (a/b)
163 */
164 #define SkScalarDiv(a, b) ((float)(a) / (b))
165 /** Returns the mod of two SkScalars (a mod b)
166 */
167 #define SkScalarMod(x,y) sk_float_mod(x,y)
168 /** Returns the product of the first two arguments, divided by the third argument
169 */
170 #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c))
171 /** Returns the multiplicative inverse of the SkScalar (1/x)
172 */
173 #define SkScalarInvert(x) (SK_Scalar1 / (x))
174 #define SkScalarFastInvert(x) (SK_Scalar1 / (x))
175 /** Returns the square root of the SkScalar
176 */
177 #define SkScalarSqrt(x) sk_float_sqrt(x)
178 /** Returns the average of two SkScalars (a+b)/2
179 */
180 #define SkScalarAve(a, b) (((a) + (b)) * 0.5f)
181 /** Returns the geometric mean of two SkScalars
182 */
183 #define SkScalarMean(a, b) sk_float_sqrt((float)(a) * (b))
184 /** Returns one half of the specified SkScalar
185 */
186 #define SkScalarHalf(a) ((a) * 0.5f)
187
188 #define SK_ScalarSqrt2 1.41421356f
189 #define SK_ScalarPI 3.14159265f
190 #define SK_ScalarTanPIOver8 0.414213562f
191 #define SK_ScalarRoot2Over2 0.707106781f
192
193 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
194 float SkScalarSinCos(SkScalar radians, SkScalar* cosValue);
195 #define SkScalarSin(radians) (float)sk_float_sin(radians)
196 #define SkScalarCos(radians) (float)sk_float_cos(radians)
197 #define SkScalarTan(radians) (float)sk_float_tan(radians)
198 #define SkScalarASin(val) (float)sk_float_asin(val)
199 #define SkScalarACos(val) (float)sk_float_acos(val)
200 #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x)
201 #define SkScalarExp(x) (float)sk_float_exp(x)
202 #define SkScalarLog(x) (float)sk_float_log(x)
203
SkMaxScalar(SkScalar a,SkScalar b)204 inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
SkMinScalar(SkScalar a,SkScalar b)205 inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
206
SkScalarIsInt(SkScalar x)207 static inline bool SkScalarIsInt(SkScalar x) {
208 return x == (float)(int)x;
209 }
210 #else
211 typedef SkFixed SkScalar;
212
213 #define SK_Scalar1 SK_Fixed1
214 #define SK_ScalarHalf SK_FixedHalf
215 #define SK_ScalarInfinity SK_FixedMax
216 #define SK_ScalarMax SK_FixedMax
217 #define SK_ScalarMin SK_FixedMin
218 #define SK_ScalarNaN SK_FixedNaN
219 #define SkScalarIsNaN(x) ((x) == SK_FixedNaN)
220 #define SkScalarIsFinite(x) ((x) != SK_FixedNaN)
221
222 #define SkIntToScalar(n) SkIntToFixed(n)
223 #define SkFixedToScalar(x) (x)
224 #define SkScalarToFixed(x) (x)
225 #ifdef SK_CAN_USE_FLOAT
226 #define SkScalarToFloat(n) SkFixedToFloat(n)
227 #define SkFloatToScalar(n) SkFloatToFixed(n)
228
229 #define SkScalarToDouble(n) SkFixedToDouble(n)
230 #define SkDoubleToScalar(n) SkDoubleToFixed(n)
231 #endif
232 #define SkScalarFraction(x) SkFixedFraction(x)
233
234 #define SkScalarFloorToScalar(x) SkFixedFloorToFixed(x)
235 #define SkScalarCeilToScalar(x) SkFixedCeilToFixed(x)
236 #define SkScalarRoundToScalar(x) SkFixedRoundToFixed(x)
237
238 #define SkScalarFloorToInt(x) SkFixedFloorToInt(x)
239 #define SkScalarCeilToInt(x) SkFixedCeilToInt(x)
240 #define SkScalarRoundToInt(x) SkFixedRoundToInt(x)
241
242 #define SkScalarAbs(x) SkFixedAbs(x)
243 #define SkScalarCopySign(x, y) SkCopySign32(x, y)
244 #define SkScalarClampMax(x, max) SkClampMax(x, max)
245 #define SkScalarPin(x, min, max) SkPin32(x, min, max)
246 #define SkScalarSquare(x) SkFixedSquare(x)
247 #define SkScalarMul(a, b) SkFixedMul(a, b)
248 #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c)
249 #define SkScalarMulRound(a, b) SkFixedMulCommon(a, b, SK_FixedHalf)
250 #define SkScalarMulCeil(a, b) SkFixedMulCommon(a, b, SK_Fixed1 - 1)
251 #define SkScalarMulFloor(a, b) SkFixedMulCommon(a, b, 0)
252 #define SkScalarDiv(a, b) SkFixedDiv(a, b)
253 #define SkScalarMod(a, b) SkFixedMod(a, b)
254 #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c)
255 #define SkScalarInvert(x) SkFixedInvert(x)
256 #define SkScalarFastInvert(x) SkFixedFastInvert(x)
257 #define SkScalarSqrt(x) SkFixedSqrt(x)
258 #define SkScalarAve(a, b) SkFixedAve(a, b)
259 #define SkScalarMean(a, b) SkFixedMean(a, b)
260 #define SkScalarHalf(a) ((a) >> 1)
261
262 #define SK_ScalarSqrt2 SK_FixedSqrt2
263 #define SK_ScalarPI SK_FixedPI
264 #define SK_ScalarTanPIOver8 SK_FixedTanPIOver8
265 #define SK_ScalarRoot2Over2 SK_FixedRoot2Over2
266
267 #define SkDegreesToRadians(degrees) SkFractMul(degrees, SK_FractPIOver180)
268 #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr)
269 #define SkScalarSin(radians) SkFixedSin(radians)
270 #define SkScalarCos(radians) SkFixedCos(radians)
271 #define SkScalarTan(val) SkFixedTan(val)
272 #define SkScalarASin(val) SkFixedASin(val)
273 #define SkScalarACos(val) SkFixedACos(val)
274 #define SkScalarATan2(y, x) SkFixedATan2(y,x)
275 #define SkScalarExp(x) SkFixedExp(x)
276 #define SkScalarLog(x) SkFixedLog(x)
277
278 #define SkMaxScalar(a, b) SkMax32(a, b)
279 #define SkMinScalar(a, b) SkMin32(a, b)
280
SkScalarIsInt(SkFixed x)281 static inline bool SkScalarIsInt(SkFixed x) {
282 return 0 == (x & 0xffff);
283 }
284 #endif
285
286 // DEPRECATED : use ToInt or ToScalar variant
287 #define SkScalarFloor(x) SkScalarFloorToInt(x)
288 #define SkScalarCeil(x) SkScalarCeilToInt(x)
289 #define SkScalarRound(x) SkScalarRoundToInt(x)
290
291 /**
292 * Returns -1 || 0 || 1 depending on the sign of value:
293 * -1 if x < 0
294 * 0 if x == 0
295 * 1 if x > 0
296 */
SkScalarSignAsInt(SkScalar x)297 static inline int SkScalarSignAsInt(SkScalar x) {
298 return x < 0 ? -1 : (x > 0);
299 }
300
301 // Scalar result version of above
SkScalarSignAsScalar(SkScalar x)302 static inline SkScalar SkScalarSignAsScalar(SkScalar x) {
303 return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0);
304 }
305
306 #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12))
307
308 /* <= is slower than < for floats, so we use < for our tolerance test
309 */
310
311 static inline bool SkScalarNearlyZero(SkScalar x,
312 SkScalar tolerance = SK_ScalarNearlyZero) {
313 SkASSERT(tolerance > 0);
314 return SkScalarAbs(x) < tolerance;
315 }
316
317 static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y,
318 SkScalar tolerance = SK_ScalarNearlyZero) {
319 SkASSERT(tolerance > 0);
320 return SkScalarAbs(x-y) < tolerance;
321 }
322
323 /** Linearly interpolate between A and B, based on t.
324 If t is 0, return A
325 If t is 1, return B
326 else interpolate.
327 t must be [0..SK_Scalar1]
328 */
SkScalarInterp(SkScalar A,SkScalar B,SkScalar t)329 static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
330 SkASSERT(t >= 0 && t <= SK_Scalar1);
331 return A + SkScalarMul(B - A, t);
332 }
333
334 /** Interpolate along the function described by (keys[length], values[length])
335 for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length]
336 clamp to the min or max value. This function was inspired by a desire
337 to change the multiplier for thickness in fakeBold; therefore it assumes
338 the number of pairs (length) will be small, and a linear search is used.
339 Repeated keys are allowed for discontinuous functions (so long as keys is
340 monotonically increasing), and if key is the value of a repeated scalar in
341 keys, the first one will be used. However, that may change if a binary
342 search is used.
343 */
344 SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[],
345 const SkScalar values[], int length);
346
347 #endif
348