SkScalar.h revision b28b5e4e26183b6e14846fb00501cc445a4fdd7e 
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            (3.402823466e+38f)
54    /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar
55    */
56    #define SK_ScalarMin            (-SK_ScalarMax)
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    */
62    static inline bool SkScalarIsNaN(float x) { return x != x; }
63    /** Returns true if x is not NaN and not infinite */
64    static inline bool SkScalarIsFinite(float x) {
65        uint32_t bits = SkFloat2Bits(x);    // need unsigned for our shifts
66        int exponent = bits << 1 >> 24;
67        return exponent != 0xFF;
68    }
69#ifdef SK_DEBUG
70    /** SkIntToScalar(n) returns its integer argument as an SkScalar
71     *
72     * If we're compiling in DEBUG mode, and can thus afford some extra runtime
73     * cycles, check to make sure that the parameter passed in has not already
74     * been converted to SkScalar.  (A double conversion like this is harmless
75     * for SK_SCALAR_IS_FLOAT, but for SK_SCALAR_IS_FIXED this causes trouble.)
76     *
77     * Note that we need all of these method signatures to properly handle the
78     * various types that we pass into SkIntToScalar() to date:
79     * int, size_t, U8CPU, etc., even though what we really mean is "anything
80     * but a float".
81     */
82    static inline float SkIntToScalar(signed int param) {
83        return (float)param;
84    }
85    static inline float SkIntToScalar(unsigned int param) {
86        return (float)param;
87    }
88    static inline float SkIntToScalar(signed long param) {
89        return (float)param;
90    }
91    static inline float SkIntToScalar(unsigned long param) {
92        return (float)param;
93    }
94    static inline float SkIntToScalar(float param) {
95        /* If the parameter passed into SkIntToScalar is a float,
96         * one of two things has happened:
97         * 1. the parameter was an SkScalar (which is typedef'd to float)
98         * 2. the parameter was a float instead of an int
99         *
100         * Either way, it's not good.
101         */
102        SkASSERT(!"looks like you passed an SkScalar into SkIntToScalar");
103        return (float)0;
104    }
105#else  // not SK_DEBUG
106    /** SkIntToScalar(n) returns its integer argument as an SkScalar
107    */
108    #define SkIntToScalar(n)        ((float)(n))
109#endif // not SK_DEBUG
110    /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar
111    */
112    #define SkFixedToScalar(x)      SkFixedToFloat(x)
113    /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed
114    */
115    #define SkScalarToFixed(x)      SkFloatToFixed(x)
116
117    #define SkScalarToFloat(n)      (n)
118    #define SkFloatToScalar(n)      (n)
119
120    #define SkScalarToDouble(n)      (double)(n)
121    #define SkDoubleToScalar(n)      (float)(n)
122
123    /** SkScalarFraction(x) returns the signed fractional part of the argument
124    */
125    #define SkScalarFraction(x)     sk_float_mod(x, 1.0f)
126    /** Rounds the SkScalar to the nearest integer value
127    */
128    #define SkScalarRound(x)        sk_float_round2int(x)
129    /** Returns the smallest integer that is >= the specified SkScalar
130    */
131    #define SkScalarCeil(x)         sk_float_ceil2int(x)
132    /** Returns the largest integer that is <= the specified SkScalar
133    */
134    #define SkScalarFloor(x)        sk_float_floor2int(x)
135    /** Returns the absolute value of the specified SkScalar
136    */
137    #define SkScalarAbs(x)          sk_float_abs(x)
138    /** Return x with the sign of y
139     */
140    #define SkScalarCopySign(x, y)  sk_float_copysign(x, y)
141    /** Returns the value pinned between 0 and max inclusive
142    */
143    inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) {
144        return x < 0 ? 0 : x > max ? max : x;
145    }
146    /** Returns the value pinned between min and max inclusive
147    */
148    inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) {
149        return x < min ? min : x > max ? max : x;
150    }
151    /** Returns the specified SkScalar squared (x*x)
152    */
153    inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }
154    /** Returns the product of two SkScalars
155    */
156    #define SkScalarMul(a, b)       ((float)(a) * (b))
157    /** Returns the product of two SkScalars plus a third SkScalar
158    */
159    #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c))
160    /** Returns the product of a SkScalar and an int rounded to the nearest integer value
161    */
162    #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b))
163    /** Returns the product of a SkScalar and an int promoted to the next larger int
164    */
165    #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b))
166    /** Returns the product of a SkScalar and an int truncated to the next smaller int
167    */
168    #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b))
169    /** Returns the quotient of two SkScalars (a/b)
170    */
171    #define SkScalarDiv(a, b)       ((float)(a) / (b))
172    /** Returns the mod of two SkScalars (a mod b)
173    */
174    #define SkScalarMod(x,y)        sk_float_mod(x,y)
175    /** Returns the product of the first two arguments, divided by the third argument
176    */
177    #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c))
178    /** Returns the multiplicative inverse of the SkScalar (1/x)
179    */
180    #define SkScalarInvert(x)       (SK_Scalar1 / (x))
181    #define SkScalarFastInvert(x)   (SK_Scalar1 / (x))
182    /** Returns the square root of the SkScalar
183    */
184    #define SkScalarSqrt(x)         sk_float_sqrt(x)
185    /** Returns the average of two SkScalars (a+b)/2
186    */
187    #define SkScalarAve(a, b)       (((a) + (b)) * 0.5f)
188    /** Returns the geometric mean of two SkScalars
189    */
190    #define SkScalarMean(a, b)      sk_float_sqrt((float)(a) * (b))
191    /** Returns one half of the specified SkScalar
192    */
193    #define SkScalarHalf(a)         ((a) * 0.5f)
194
195    #define SK_ScalarSqrt2          1.41421356f
196    #define SK_ScalarPI             3.14159265f
197    #define SK_ScalarTanPIOver8     0.414213562f
198    #define SK_ScalarRoot2Over2     0.707106781f
199
200    #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
201    float SkScalarSinCos(SkScalar radians, SkScalar* cosValue);
202    #define SkScalarSin(radians)    (float)sk_float_sin(radians)
203    #define SkScalarCos(radians)    (float)sk_float_cos(radians)
204    #define SkScalarTan(radians)    (float)sk_float_tan(radians)
205    #define SkScalarASin(val)   (float)sk_float_asin(val)
206    #define SkScalarACos(val)   (float)sk_float_acos(val)
207    #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x)
208    #define SkScalarExp(x)  (float)sk_float_exp(x)
209    #define SkScalarLog(x)  (float)sk_float_log(x)
210
211    inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
212    inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
213
214    static inline bool SkScalarIsInt(SkScalar x) {
215        return x == (float)(int)x;
216    }
217#else
218    typedef SkFixed SkScalar;
219
220    #define SK_Scalar1              SK_Fixed1
221    #define SK_ScalarHalf           SK_FixedHalf
222    #define SK_ScalarInfinity   SK_FixedMax
223    #define SK_ScalarMax            SK_FixedMax
224    #define SK_ScalarMin            SK_FixedMin
225    #define SK_ScalarNaN            SK_FixedNaN
226    #define SkScalarIsNaN(x)        ((x) == SK_FixedNaN)
227    #define SkScalarIsFinite(x)     ((x) != SK_FixedNaN)
228
229    #define SkIntToScalar(n)        SkIntToFixed(n)
230    #define SkFixedToScalar(x)      (x)
231    #define SkScalarToFixed(x)      (x)
232    #ifdef SK_CAN_USE_FLOAT
233        #define SkScalarToFloat(n)  SkFixedToFloat(n)
234        #define SkFloatToScalar(n)  SkFloatToFixed(n)
235
236        #define SkScalarToDouble(n) SkFixedToDouble(n)
237        #define SkDoubleToScalar(n) SkDoubleToFixed(n)
238    #endif
239    #define SkScalarFraction(x)     SkFixedFraction(x)
240    #define SkScalarRound(x)        SkFixedRound(x)
241    #define SkScalarCeil(x)         SkFixedCeil(x)
242    #define SkScalarFloor(x)        SkFixedFloor(x)
243    #define SkScalarAbs(x)          SkFixedAbs(x)
244    #define SkScalarCopySign(x, y)  SkCopySign32(x, y)
245    #define SkScalarClampMax(x, max) SkClampMax(x, max)
246    #define SkScalarPin(x, min, max) SkPin32(x, min, max)
247    #define SkScalarSquare(x)       SkFixedSquare(x)
248    #define SkScalarMul(a, b)       SkFixedMul(a, b)
249    #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c)
250    #define SkScalarMulRound(a, b)  SkFixedMulCommon(a, b, SK_FixedHalf)
251    #define SkScalarMulCeil(a, b)   SkFixedMulCommon(a, b, SK_Fixed1 - 1)
252    #define SkScalarMulFloor(a, b)  SkFixedMulCommon(a, b, 0)
253    #define SkScalarDiv(a, b)       SkFixedDiv(a, b)
254    #define SkScalarMod(a, b)       SkFixedMod(a, b)
255    #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c)
256    #define SkScalarInvert(x)       SkFixedInvert(x)
257    #define SkScalarFastInvert(x)   SkFixedFastInvert(x)
258    #define SkScalarSqrt(x)         SkFixedSqrt(x)
259    #define SkScalarAve(a, b)       SkFixedAve(a, b)
260    #define SkScalarMean(a, b)      SkFixedMean(a, b)
261    #define SkScalarHalf(a)         ((a) >> 1)
262
263    #define SK_ScalarSqrt2          SK_FixedSqrt2
264    #define SK_ScalarPI             SK_FixedPI
265    #define SK_ScalarTanPIOver8     SK_FixedTanPIOver8
266    #define SK_ScalarRoot2Over2     SK_FixedRoot2Over2
267
268    #define SkDegreesToRadians(degrees)     SkFractMul(degrees, SK_FractPIOver180)
269    #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr)
270    #define SkScalarSin(radians)    SkFixedSin(radians)
271    #define SkScalarCos(radians)    SkFixedCos(radians)
272    #define SkScalarTan(val)        SkFixedTan(val)
273    #define SkScalarASin(val)       SkFixedASin(val)
274    #define SkScalarACos(val)       SkFixedACos(val)
275    #define SkScalarATan2(y, x)     SkFixedATan2(y,x)
276    #define SkScalarExp(x)          SkFixedExp(x)
277    #define SkScalarLog(x)          SkFixedLog(x)
278
279    #define SkMaxScalar(a, b)       SkMax32(a, b)
280    #define SkMinScalar(a, b)       SkMin32(a, b)
281
282    static inline bool SkScalarIsInt(SkFixed x) {
283        return 0 == (x & 0xffff);
284    }
285#endif
286
287#define SK_ScalarNearlyZero         (SK_Scalar1 / (1 << 12))
288
289/*  <= is slower than < for floats, so we use < for our tolerance test
290*/
291
292static inline bool SkScalarNearlyZero(SkScalar x,
293                                  SkScalar tolerance = SK_ScalarNearlyZero) {
294    SkASSERT(tolerance > 0);
295    return SkScalarAbs(x) < tolerance;
296}
297
298/** Linearly interpolate between A and B, based on t.
299    If t is 0, return A
300    If t is 1, return B
301    else interpolate.
302    t must be [0..SK_Scalar1]
303*/
304static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
305    SkASSERT(t >= 0 && t <= SK_Scalar1);
306    return A + SkScalarMul(B - A, t);
307}
308
309/** Interpolate along the function described by (keys[length], values[length])
310    for the passed searchKey.  SearchKeys outside the range keys[0]-keys[Length]
311    clamp to the min or max value.  This function was inspired by a desire
312    to change the multiplier for thickness in fakeBold; therefore it assumes
313    the number of pairs (length) will be small, and a linear search is used.
314    Repeated keys are allowed for discontinuous functions (so long as keys is
315    monotonically increasing), and if key is the value of a repeated scalar in
316    keys, the first one will be used.  However, that may change if a binary
317    search is used.
318*/
319SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[],
320                            const SkScalar values[], int length);
321
322#endif
323