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 "../private/SkFloatingPoint.h"
13
14// TODO: move this sort of check into SkPostConfig.h
15#define SK_SCALAR_IS_DOUBLE 0
16#undef SK_SCALAR_IS_FLOAT
17#define SK_SCALAR_IS_FLOAT  1
18
19
20#if SK_SCALAR_IS_FLOAT
21
22typedef float SkScalar;
23
24#define SK_Scalar1                  1.0f
25#define SK_ScalarHalf               0.5f
26#define SK_ScalarSqrt2              1.41421356f
27#define SK_ScalarPI                 3.14159265f
28#define SK_ScalarTanPIOver8         0.414213562f
29#define SK_ScalarRoot2Over2         0.707106781f
30#define SK_ScalarMax                3.402823466e+38f
31#define SK_ScalarInfinity           SK_FloatInfinity
32#define SK_ScalarNegativeInfinity   SK_FloatNegativeInfinity
33#define SK_ScalarNaN                SK_FloatNaN
34
35#define SkFixedToScalar(x)          SkFixedToFloat(x)
36#define SkScalarToFixed(x)          SkFloatToFixed(x)
37
38#define SkScalarFloorToScalar(x)    sk_float_floor(x)
39#define SkScalarCeilToScalar(x)     sk_float_ceil(x)
40#define SkScalarRoundToScalar(x)    sk_float_floor((x) + 0.5f)
41
42#define SkScalarFloorToInt(x)       sk_float_floor2int(x)
43#define SkScalarCeilToInt(x)        sk_float_ceil2int(x)
44#define SkScalarRoundToInt(x)       sk_float_round2int(x)
45
46#define SkScalarAbs(x)              sk_float_abs(x)
47#define SkScalarCopySign(x, y)      sk_float_copysign(x, y)
48#define SkScalarMod(x, y)           sk_float_mod(x,y)
49#define SkScalarFraction(x)         sk_float_mod(x, 1.0f)
50#define SkScalarSqrt(x)             sk_float_sqrt(x)
51#define SkScalarPow(b, e)           sk_float_pow(b, e)
52
53#define SkScalarSin(radians)        (float)sk_float_sin(radians)
54#define SkScalarCos(radians)        (float)sk_float_cos(radians)
55#define SkScalarTan(radians)        (float)sk_float_tan(radians)
56#define SkScalarASin(val)           (float)sk_float_asin(val)
57#define SkScalarACos(val)           (float)sk_float_acos(val)
58#define SkScalarATan2(y, x)         (float)sk_float_atan2(y,x)
59#define SkScalarExp(x)              (float)sk_float_exp(x)
60#define SkScalarLog(x)              (float)sk_float_log(x)
61#define SkScalarLog2(x)             (float)sk_float_log2(x)
62
63#else   // SK_SCALAR_IS_DOUBLE
64
65typedef double SkScalar;
66
67#define SK_Scalar1                  1.0
68#define SK_ScalarHalf               0.5
69#define SK_ScalarSqrt2              1.414213562373095
70#define SK_ScalarPI                 3.141592653589793
71#define SK_ScalarTanPIOver8         0.4142135623731
72#define SK_ScalarRoot2Over2         0.70710678118655
73#define SK_ScalarMax                1.7976931348623157+308
74#define SK_ScalarInfinity           SK_DoubleInfinity
75#define SK_ScalarNegativeInfinity   SK_DoubleNegativeInfinity
76#define SK_ScalarNaN                SK_DoubleNaN
77
78#define SkFixedToScalar(x)          SkFixedToDouble(x)
79#define SkScalarToFixed(x)          SkDoubleToFixed(x)
80
81#define SkScalarFloorToScalar(x)    floor(x)
82#define SkScalarCeilToScalar(x)     ceil(x)
83#define SkScalarRoundToScalar(x)    floor((x) + 0.5)
84
85#define SkScalarFloorToInt(x)       (int)floor(x)
86#define SkScalarCeilToInt(x)        (int)ceil(x)
87#define SkScalarRoundToInt(x)       (int)floor((x) + 0.5)
88
89#define SkScalarAbs(x)              abs(x)
90#define SkScalarCopySign(x, y)      copysign(x, y)
91#define SkScalarMod(x, y)           fmod(x,y)
92#define SkScalarFraction(x)         fmod(x, 1.0)
93#define SkScalarSqrt(x)             sqrt(x)
94#define SkScalarPow(b, e)           pow(b, e)
95
96#define SkScalarSin(radians)        sin(radians)
97#define SkScalarCos(radians)        cos(radians)
98#define SkScalarTan(radians)        tan(radians)
99#define SkScalarASin(val)           asin(val)
100#define SkScalarACos(val)           acos(val)
101#define SkScalarATan2(y, x)         atan2(y,x)
102#define SkScalarExp(x)              exp(x)
103#define SkScalarLog(x)              log(x)
104#define SkScalarLog2(x)             log2(x)
105
106#endif
107
108//////////////////////////////////////////////////////////////////////////////////////////////////
109
110#define SkIntToScalar(x)        static_cast<SkScalar>(x)
111#define SkScalarTruncToInt(x)   static_cast<int>(x)
112
113#define SkScalarToFloat(x)      static_cast<float>(x)
114#define SkFloatToScalar(x)      static_cast<SkScalar>(x)
115#define SkScalarToDouble(x)     static_cast<double>(x)
116#define SkDoubleToScalar(x)     static_cast<SkScalar>(x)
117
118#define SK_ScalarMin            (-SK_ScalarMax)
119
120static inline bool SkScalarIsNaN(SkScalar x) { return x != x; }
121
122/** Returns true if x is not NaN and not infinite
123 */
124static inline bool SkScalarIsFinite(SkScalar x) {
125    // We rely on the following behavior of infinities and nans
126    // 0 * finite --> 0
127    // 0 * infinity --> NaN
128    // 0 * NaN --> NaN
129    SkScalar prod = x * 0;
130    // At this point, prod will either be NaN or 0
131    return !SkScalarIsNaN(prod);
132}
133
134static inline bool SkScalarsAreFinite(SkScalar a, SkScalar b) {
135    SkScalar prod = 0;
136    prod *= a;
137    prod *= b;
138    // At this point, prod will either be NaN or 0
139    return !SkScalarIsNaN(prod);
140}
141
142static inline bool SkScalarsAreFinite(const SkScalar array[], int count) {
143    SkScalar prod = 0;
144    for (int i = 0; i < count; ++i) {
145        prod *= array[i];
146    }
147    // At this point, prod will either be NaN or 0
148    return !SkScalarIsNaN(prod);
149}
150
151/**
152 *  Variant of SkScalarRoundToInt, that performs the rounding step (adding 0.5) explicitly using
153 *  double, to avoid possibly losing the low bit(s) of the answer before calling floor().
154 *
155 *  This routine will likely be slower than SkScalarRoundToInt(), and should only be used when the
156 *  extra precision is known to be valuable.
157 *
158 *  In particular, this catches the following case:
159 *      SkScalar x = 0.49999997;
160 *      int ix = SkScalarRoundToInt(x);
161 *      SkASSERT(0 == ix);    // <--- fails
162 *      ix = SkDScalarRoundToInt(x);
163 *      SkASSERT(0 == ix);    // <--- succeeds
164 */
165static inline int SkDScalarRoundToInt(SkScalar x) {
166    double xx = x;
167    xx += 0.5;
168    return (int)floor(xx);
169}
170
171static inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) {
172    x = SkTMin(x, max);
173    x = SkTMax<SkScalar>(x, 0);
174    return x;
175}
176
177static inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) {
178    return SkTPin(x, min, max);
179}
180
181SkScalar SkScalarSinCos(SkScalar radians, SkScalar* cosValue);
182
183static inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }
184
185#define SkScalarMul(a, b)       ((SkScalar)(a) * (b))
186#define SkScalarMulAdd(a, b, c) ((SkScalar)(a) * (b) + (c))
187#define SkScalarMulDiv(a, b, c) ((SkScalar)(a) * (b) / (c))
188#define SkScalarInvert(x)       (SK_Scalar1 / (x))
189#define SkScalarFastInvert(x)   (SK_Scalar1 / (x))
190#define SkScalarAve(a, b)       (((a) + (b)) * SK_ScalarHalf)
191#define SkScalarHalf(a)         ((a) * SK_ScalarHalf)
192
193#define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
194#define SkRadiansToDegrees(radians) ((radians) * (180 / SK_ScalarPI))
195
196static inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
197static inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
198
199static inline bool SkScalarIsInt(SkScalar x) {
200    return x == (SkScalar)(int)x;
201}
202
203/**
204 *  Returns -1 || 0 || 1 depending on the sign of value:
205 *  -1 if x < 0
206 *   0 if x == 0
207 *   1 if x > 0
208 */
209static inline int SkScalarSignAsInt(SkScalar x) {
210    return x < 0 ? -1 : (x > 0);
211}
212
213// Scalar result version of above
214static inline SkScalar SkScalarSignAsScalar(SkScalar x) {
215    return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0);
216}
217
218#define SK_ScalarNearlyZero         (SK_Scalar1 / (1 << 12))
219
220static inline bool SkScalarNearlyZero(SkScalar x,
221                                      SkScalar tolerance = SK_ScalarNearlyZero) {
222    SkASSERT(tolerance >= 0);
223    return SkScalarAbs(x) <= tolerance;
224}
225
226static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y,
227                                       SkScalar tolerance = SK_ScalarNearlyZero) {
228    SkASSERT(tolerance >= 0);
229    return SkScalarAbs(x-y) <= tolerance;
230}
231
232/** Linearly interpolate between A and B, based on t.
233    If t is 0, return A
234    If t is 1, return B
235    else interpolate.
236    t must be [0..SK_Scalar1]
237*/
238static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
239    SkASSERT(t >= 0 && t <= SK_Scalar1);
240    return A + (B - A) * t;
241}
242
243/** Interpolate along the function described by (keys[length], values[length])
244    for the passed searchKey.  SearchKeys outside the range keys[0]-keys[Length]
245    clamp to the min or max value.  This function was inspired by a desire
246    to change the multiplier for thickness in fakeBold; therefore it assumes
247    the number of pairs (length) will be small, and a linear search is used.
248    Repeated keys are allowed for discontinuous functions (so long as keys is
249    monotonically increasing), and if key is the value of a repeated scalar in
250    keys, the first one will be used.  However, that may change if a binary
251    search is used.
252*/
253SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[],
254                            const SkScalar values[], int length);
255
256/*
257 *  Helper to compare an array of scalars.
258 */
259static inline bool SkScalarsEqual(const SkScalar a[], const SkScalar b[], int n) {
260    SkASSERT(n >= 0);
261    for (int i = 0; i < n; ++i) {
262        if (a[i] != b[i]) {
263            return false;
264        }
265    }
266    return true;
267}
268
269#endif
270