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 : */
55 0 : static inline bool SkScalarIsNaN(float x) { return x != x; }
56 : /** Returns true if x is not NaN and not infinite */
57 0 : static inline bool SkScalarIsFinite(float x) {
58 0 : uint32_t bits = SkFloat2Bits(x); // need unsigned for our shifts
59 0 : int exponent = bits << 1 >> 24;
60 0 : 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 : */
75 5856 : static inline float SkIntToScalar(signed int param) {
76 5856 : return (float)param;
77 : }
78 0 : static inline float SkIntToScalar(unsigned int param) {
79 0 : return (float)param;
80 : }
81 0 : static inline float SkIntToScalar(signed long param) {
82 0 : return (float)param;
83 : }
84 : static inline float SkIntToScalar(unsigned long param) {
85 : return (float)param;
86 : }
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 : */
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 : */
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 : */
146 0 : 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 :
204 0 : inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
205 0 : inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
206 :
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 :
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 : */
297 0 : static inline int SkScalarSignAsInt(SkScalar x) {
298 0 : return x < 0 ? -1 : (x > 0);
299 : }
300 :
301 : // Scalar result version of above
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 0 : static inline bool SkScalarNearlyZero(SkScalar x,
312 : SkScalar tolerance = SK_ScalarNearlyZero) {
313 0 : SkASSERT(tolerance > 0);
314 0 : 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 : */
329 0 : static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
330 0 : SkASSERT(t >= 0 && t <= SK_Scalar1);
331 0 : 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
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