1 /*
2 * Copyright (C) 2006 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 * http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17 #ifndef SkScalar_DEFINED
18 #define SkScalar_DEFINED
19
20 #include "SkFixed.h"
21
22 /** \file SkScalar.h
23
24 Types and macros for the data type SkScalar. This is the fractional numeric type
25 that, depending on the compile-time flag SK_SCALAR_IS_FLOAT, may be implemented
26 either as an IEEE float, or as a 16.16 SkFixed. The macros in this file are written
27 to allow the calling code to manipulate SkScalar values without knowing which representation
28 is in effect.
29 */
30
31 #ifdef SK_SCALAR_IS_FLOAT
32 #include "SkFloatingPoint.h"
33
34 /** SkScalar is our type for fractional values and coordinates. Depending on
35 compile configurations, it is either represented as an IEEE float, or
36 as a 16.16 fixed point integer.
37 */
38 typedef float SkScalar;
39 extern const uint32_t gIEEENotANumber;
40 extern const uint32_t gIEEEInfinity;
41
42 /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar
43 */
44 #define SK_Scalar1 (1.0f)
45 /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar
46 */
47 #define SK_ScalarHalf (0.5f)
48 /** SK_ScalarInfinity is defined to be infinity as an SkScalar
49 */
50 #define SK_ScalarInfinity (*(const float*)&gIEEEInfinity)
51 /** SK_ScalarMax is defined to be the largest value representable as an SkScalar
52 */
53 #define SK_ScalarMax (3.4028235e+38f)
54 /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar
55 */
56 #define SK_ScalarMin (1.1754944e-38f)
57 /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar
58 */
59 #define SK_ScalarNaN (*(const float*)(const void*)&gIEEENotANumber)
60 /** SkScalarIsNaN(n) returns true if argument is not a number
61 */
SkScalarIsNaN(float x)62 static inline bool SkScalarIsNaN(float x) { return x != x; }
63 /** SkIntToScalar(n) returns its integer argument as an SkScalar
64 */
65 #define SkIntToScalar(n) ((float)(n))
66 /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar
67 */
68 #define SkFixedToScalar(x) SkFixedToFloat(x)
69 /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed
70 */
71 #define SkScalarToFixed(x) SkFloatToFixed(x)
72
73 #define SkScalarToFloat(n) (n)
74 #define SkFloatToScalar(n) (n)
75
76 #define SkScalarToDouble(n) (double)(n)
77 #define SkDoubleToScalar(n) (float)(n)
78
79 /** SkScalarFraction(x) returns the signed fractional part of the argument
80 */
81 #define SkScalarFraction(x) sk_float_mod(x, 1.0f)
82 /** Rounds the SkScalar to the nearest integer value
83 */
84 #define SkScalarRound(x) sk_float_round2int(x)
85 /** Returns the smallest integer that is >= the specified SkScalar
86 */
87 #define SkScalarCeil(x) sk_float_ceil2int(x)
88 /** Returns the largest integer that is <= the specified SkScalar
89 */
90 #define SkScalarFloor(x) sk_float_floor2int(x)
91 /** Returns the absolute value of the specified SkScalar
92 */
93 #define SkScalarAbs(x) sk_float_abs(x)
94 /** Return x with the sign of y
95 */
96 #define SkScalarCopySign(x, y) sk_float_copysign(x, y)
97 /** Returns the value pinned between 0 and max inclusive
98 */
SkScalarClampMax(SkScalar x,SkScalar max)99 inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) {
100 return x < 0 ? 0 : x > max ? max : x;
101 }
102 /** Returns the value pinned between min and max inclusive
103 */
SkScalarPin(SkScalar x,SkScalar min,SkScalar max)104 inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) {
105 return x < min ? min : x > max ? max : x;
106 }
107 /** Returns the specified SkScalar squared (x*x)
108 */
SkScalarSquare(SkScalar x)109 inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }
110 /** Returns the product of two SkScalars
111 */
112 #define SkScalarMul(a, b) ((float)(a) * (b))
113 /** Returns the product of two SkScalars plus a third SkScalar
114 */
115 #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c))
116 /** Returns the product of a SkScalar and an int rounded to the nearest integer value
117 */
118 #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b))
119 /** Returns the product of a SkScalar and an int promoted to the next larger int
120 */
121 #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b))
122 /** Returns the product of a SkScalar and an int truncated to the next smaller int
123 */
124 #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b))
125 /** Returns the quotient of two SkScalars (a/b)
126 */
127 #define SkScalarDiv(a, b) ((float)(a) / (b))
128 /** Returns the mod of two SkScalars (a mod b)
129 */
130 #define SkScalarMod(x,y) sk_float_mod(x,y)
131 /** Returns the product of the first two arguments, divided by the third argument
132 */
133 #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c))
134 /** Returns the multiplicative inverse of the SkScalar (1/x)
135 */
136 #define SkScalarInvert(x) (SK_Scalar1 / (x))
137 #define SkScalarFastInvert(x) (SK_Scalar1 / (x))
138 /** Returns the square root of the SkScalar
139 */
140 #define SkScalarSqrt(x) sk_float_sqrt(x)
141 /** Returns the average of two SkScalars (a+b)/2
142 */
143 #define SkScalarAve(a, b) (((a) + (b)) * 0.5f)
144 /** Returns the geometric mean of two SkScalars
145 */
146 #define SkScalarMean(a, b) sk_float_sqrt((float)(a) * (b))
147 /** Returns one half of the specified SkScalar
148 */
149 #define SkScalarHalf(a) ((a) * 0.5f)
150
151 #define SK_ScalarSqrt2 1.41421356f
152 #define SK_ScalarPI 3.14159265f
153 #define SK_ScalarTanPIOver8 0.414213562f
154 #define SK_ScalarRoot2Over2 0.707106781f
155
156 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
157 float SkScalarSinCos(SkScalar radians, SkScalar* cosValue);
158 #define SkScalarSin(radians) (float)sk_float_sin(radians)
159 #define SkScalarCos(radians) (float)sk_float_cos(radians)
160 #define SkScalarTan(radians) (float)sk_float_tan(radians)
161 #define SkScalarASin(val) (float)sk_float_asin(val)
162 #define SkScalarACos(val) (float)sk_float_acos(val)
163 #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x)
164 #define SkScalarExp(x) (float)sk_float_exp(x)
165 #define SkScalarLog(x) (float)sk_float_log(x)
166
SkMaxScalar(SkScalar a,SkScalar b)167 inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
SkMinScalar(SkScalar a,SkScalar b)168 inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
169
170 #else
171 typedef SkFixed SkScalar;
172
173 #define SK_Scalar1 SK_Fixed1
174 #define SK_ScalarHalf SK_FixedHalf
175 #define SK_ScalarInfinity SK_FixedMax
176 #define SK_ScalarMax SK_FixedMax
177 #define SK_ScalarMin SK_FixedMin
178 #define SK_ScalarNaN SK_FixedNaN
179 #define SkScalarIsNaN(x) ((x) == SK_FixedNaN)
180 #define SkIntToScalar(n) SkIntToFixed(n)
181 #define SkFixedToScalar(x) (x)
182 #define SkScalarToFixed(x) (x)
183 #ifdef SK_CAN_USE_FLOAT
184 #define SkScalarToFloat(n) SkFixedToFloat(n)
185 #define SkFloatToScalar(n) SkFloatToFixed(n)
186
187 #define SkScalarToDouble(n) SkFixedToDouble(n)
188 #define SkDoubleToScalar(n) SkDoubleToFixed(n)
189 #endif
190 #define SkScalarFraction(x) SkFixedFraction(x)
191 #define SkScalarRound(x) SkFixedRound(x)
192 #define SkScalarCeil(x) SkFixedCeil(x)
193 #define SkScalarFloor(x) SkFixedFloor(x)
194 #define SkScalarAbs(x) SkFixedAbs(x)
195 #define SkScalarCopySign(x, y) SkCopySign32(x, y)
196 #define SkScalarClampMax(x, max) SkClampMax(x, max)
197 #define SkScalarPin(x, min, max) SkPin32(x, min, max)
198 #define SkScalarSquare(x) SkFixedSquare(x)
199 #define SkScalarMul(a, b) SkFixedMul(a, b)
200 #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c)
201 #define SkScalarMulRound(a, b) SkFixedMulCommon(a, b, SK_FixedHalf)
202 #define SkScalarMulCeil(a, b) SkFixedMulCommon(a, b, SK_Fixed1 - 1)
203 #define SkScalarMulFloor(a, b) SkFixedMulCommon(a, b, 0)
204 #define SkScalarDiv(a, b) SkFixedDiv(a, b)
205 #define SkScalarMod(a, b) SkFixedMod(a, b)
206 #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c)
207 #define SkScalarInvert(x) SkFixedInvert(x)
208 #define SkScalarFastInvert(x) SkFixedFastInvert(x)
209 #define SkScalarSqrt(x) SkFixedSqrt(x)
210 #define SkScalarAve(a, b) SkFixedAve(a, b)
211 #define SkScalarMean(a, b) SkFixedMean(a, b)
212 #define SkScalarHalf(a) ((a) >> 1)
213
214 #define SK_ScalarSqrt2 SK_FixedSqrt2
215 #define SK_ScalarPI SK_FixedPI
216 #define SK_ScalarTanPIOver8 SK_FixedTanPIOver8
217 #define SK_ScalarRoot2Over2 SK_FixedRoot2Over2
218
219 #define SkDegreesToRadians(degrees) SkFractMul(degrees, SK_FractPIOver180)
220 #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr)
221 #define SkScalarSin(radians) SkFixedSin(radians)
222 #define SkScalarCos(radians) SkFixedCos(radians)
223 #define SkScalarTan(val) SkFixedTan(val)
224 #define SkScalarASin(val) SkFixedASin(val)
225 #define SkScalarACos(val) SkFixedACos(val)
226 #define SkScalarATan2(y, x) SkFixedATan2(y,x)
227 #define SkScalarExp(x) SkFixedExp(x)
228 #define SkScalarLog(x) SkFixedLog(x)
229
230 #define SkMaxScalar(a, b) SkMax32(a, b)
231 #define SkMinScalar(a, b) SkMin32(a, b)
232 #endif
233
234 #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12))
235
236 /* <= is slower than < for floats, so we use < for our tolerance test
237 */
238
239 static inline bool SkScalarNearlyZero(SkScalar x,
240 SkScalar tolerance = SK_ScalarNearlyZero) {
241 SkASSERT(tolerance > 0);
242 return SkScalarAbs(x) < tolerance;
243 }
244
245 /** Linearly interpolate between A and B, based on t.
246 If t is 0, return A
247 If t is 1, return B
248 else interpolate.
249 t must be [0..SK_Scalar1]
250 */
SkScalarInterp(SkScalar A,SkScalar B,SkScalar t)251 static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
252 SkASSERT(t >= 0 && t <= SK_Scalar1);
253 return A + SkScalarMul(B - A, t);
254 }
255
256 #endif
257
258