SkScalar.h revision e1e7d7a6b55504d97ce9f30202a179b63800093b
1ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com
28a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/*
3ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Copyright 2006 The Android Open Source Project
48a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com *
5ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * Use of this source code is governed by a BSD-style license that can be
6ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com * found in the LICENSE file.
78a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com */
88a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
9ec3ed6a5ebf6f2c406d7bcf94b6bc34fcaeb976eepoger@google.com
108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifndef SkScalar_DEFINED
118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#define SkScalar_DEFINED
128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#include "SkFixed.h"
1480afbf08eb82a99f8a2eeeb1741eb7ca1ccf957depoger@google.com#include "SkFloatingPoint.h"
158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** \file SkScalar.h
178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    Types and macros for the data type SkScalar. This is the fractional numeric type
198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    that, depending on the compile-time flag SK_SCALAR_IS_FLOAT, may be implemented
208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    either as an IEEE float, or as a 16.16 SkFixed. The macros in this file are written
218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    to allow the calling code to manipulate SkScalar values without knowing which representation
228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    is in effect.
238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/
248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#ifdef SK_SCALAR_IS_FLOAT
268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SkScalar is our type for fractional values and coordinates. Depending on
288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com        compile configurations, it is either represented as an IEEE float, or
298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com        as a 16.16 fixed point integer.
308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    typedef float   SkScalar;
328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    extern const uint32_t gIEEENotANumber;
338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    extern const uint32_t gIEEEInfinity;
348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar
368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_Scalar1              (1.0f)
388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar
398a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarHalf           (0.5f)
418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SK_ScalarInfinity is defined to be infinity as an SkScalar
428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
43373ebc634573364c27b1ebd35bb537ef1285cba4bsalomon@google.com    #define SK_ScalarInfinity           (*SkTCast<const float*>(&gIEEEInfinity))
448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SK_ScalarMax is defined to be the largest value representable as an SkScalar
458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
46c8ad63e5e42637c65c6b4e0adfacce55730b722dbsalomon@google.com    #define SK_ScalarMax            (3.402823466e+38f)
478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar
488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
49ee9aa304579b3d5314519372728187879456d49dbsalomon@google.com    #define SK_ScalarMin            (-SK_ScalarMax)
508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar
518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
52373ebc634573364c27b1ebd35bb537ef1285cba4bsalomon@google.com    #define SK_ScalarNaN      (*SkTCast<const float*>(&gIEEENotANumber))
538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SkScalarIsNaN(n) returns true if argument is not a number
548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    static inline bool SkScalarIsNaN(float x) { return x != x; }
569a323c98f6cd5d1dc002936588d182121231c69dreed@google.com
57077910e20cda41d7981084fbd047a108894bc8dfreed@google.com    /** Returns true if x is not NaN and not infinite */
58077910e20cda41d7981084fbd047a108894bc8dfreed@google.com    static inline bool SkScalarIsFinite(float x) {
599a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        // We rely on the following behavior of infinities and nans
609a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        // 0 * finite --> 0
619a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        // 0 * infinity --> NaN
629a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        // 0 * NaN --> NaN
639a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        float prod = x * 0;
649a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        // At this point, prod will either be NaN or 0
659a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        // Therefore we can return (prod == prod) or (0 == prod).
669a323c98f6cd5d1dc002936588d182121231c69dreed@google.com        return prod == prod;
67077910e20cda41d7981084fbd047a108894bc8dfreed@google.com    }
689a323c98f6cd5d1dc002936588d182121231c69dreed@google.com
69b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com#ifdef SK_DEBUG
70b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com    /** SkIntToScalar(n) returns its integer argument as an SkScalar
71b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     *
72b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * If we're compiling in DEBUG mode, and can thus afford some extra runtime
73b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * cycles, check to make sure that the parameter passed in has not already
74b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * been converted to SkScalar.  (A double conversion like this is harmless
75b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * for SK_SCALAR_IS_FLOAT, but for SK_SCALAR_IS_FIXED this causes trouble.)
76b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     *
77b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * Note that we need all of these method signatures to properly handle the
78b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * various types that we pass into SkIntToScalar() to date:
79b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * int, size_t, U8CPU, etc., even though what we really mean is "anything
80b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     * but a float".
81b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com     */
82dd8dd8f77b5802bdcb7b980761b54a055586b351reed@google.com    static inline float SkIntToScalar(signed int param) {
83b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com        return (float)param;
84b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com    }
85b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com    static inline float SkIntToScalar(unsigned int param) {
86b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com        return (float)param;
87b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com    }
88a030818936aa8f56db3cbf2d7fa14c1e5a543055reed@google.com    static inline float SkIntToScalar(signed long param) {
89b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com        return (float)param;
90b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com    }
91a030818936aa8f56db3cbf2d7fa14c1e5a543055reed@google.com    static inline float SkIntToScalar(unsigned long param) {
92b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com        return (float)param;
93b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com    }
94d4144060731a94a5b057dfad407e6e3c294435cfrobertphillips@google.com    static inline float SkIntToScalar(float /* param */) {
95b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com        /* If the parameter passed into SkIntToScalar is a float,
96b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com         * one of two things has happened:
97b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com         * 1. the parameter was an SkScalar (which is typedef'd to float)
98b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com         * 2. the parameter was a float instead of an int
99b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com         *
100b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com         * Either way, it's not good.
101b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com         */
1020c00f21fee3f5cfa3aa7e5d46ff94cb8cf340451tomhudson@google.com        SkDEBUGFAIL("looks like you passed an SkScalar into SkIntToScalar");
103b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com        return (float)0;
104b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com    }
105b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com#else  // not SK_DEBUG
1068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SkIntToScalar(n) returns its integer argument as an SkScalar
1078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkIntToScalar(n)        ((float)(n))
109b28b5e4e26183b6e14846fb00501cc445a4fdd7eepoger@google.com#endif // not SK_DEBUG
1108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar
1118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkFixedToScalar(x)      SkFixedToFloat(x)
1138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed
1148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarToFixed(x)      SkFloatToFixed(x)
1168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
1178a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarToFloat(n)      (n)
1188a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkFloatToScalar(n)      (n)
1198a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
1208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarToDouble(n)      (double)(n)
1218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkDoubleToScalar(n)      (float)(n)
1228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
1238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** SkScalarFraction(x) returns the signed fractional part of the argument
1248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarFraction(x)     sk_float_mod(x, 1.0f)
1261b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
1271b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarFloorToScalar(x)    sk_float_floor(x)
1281b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarCeilToScalar(x)     sk_float_ceil(x)
12924569b5bad4156a1eb95da92c96fc96b41e11622reed@google.com    #define SkScalarRoundToScalar(x)    sk_float_floor((x) + 0.5f)
1301b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
1311b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarFloorToInt(x)       sk_float_floor2int(x)
1321b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarCeilToInt(x)        sk_float_ceil2int(x)
1331b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarRoundToInt(x)       sk_float_round2int(x)
1341b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
1358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the absolute value of the specified SkScalar
1368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarAbs(x)          sk_float_abs(x)
138eebf5cb6c0f5ed2630de2e7712d61b4ec1d49015reed@android.com    /** Return x with the sign of y
139eebf5cb6c0f5ed2630de2e7712d61b4ec1d49015reed@android.com     */
140eebf5cb6c0f5ed2630de2e7712d61b4ec1d49015reed@android.com    #define SkScalarCopySign(x, y)  sk_float_copysign(x, y)
1418a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the value pinned between 0 and max inclusive
1428a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1438a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) {
1448a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com        return x < 0 ? 0 : x > max ? max : x;
1458a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    }
1468a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the value pinned between min and max inclusive
1478a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1488a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) {
1498a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com        return x < min ? min : x > max ? max : x;
1508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    }
1518a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the specified SkScalar squared (x*x)
1528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }
1548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the product of two SkScalars
1558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMul(a, b)       ((float)(a) * (b))
1578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the product of two SkScalars plus a third SkScalar
1588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c))
1608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the product of a SkScalar and an int rounded to the nearest integer value
1618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b))
1638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the product of a SkScalar and an int promoted to the next larger int
1648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b))
1668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the product of a SkScalar and an int truncated to the next smaller int
1678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b))
1698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the quotient of two SkScalars (a/b)
1708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarDiv(a, b)       ((float)(a) / (b))
1728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the mod of two SkScalars (a mod b)
1738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMod(x,y)        sk_float_mod(x,y)
1758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the product of the first two arguments, divided by the third argument
1768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c))
1788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the multiplicative inverse of the SkScalar (1/x)
1798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarInvert(x)       (SK_Scalar1 / (x))
1818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarFastInvert(x)   (SK_Scalar1 / (x))
1828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the square root of the SkScalar
1838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarSqrt(x)         sk_float_sqrt(x)
1850567f222b92d17923c687bed5f54b31652150891bungeman@google.com    /** Returns b to the e
1860567f222b92d17923c687bed5f54b31652150891bungeman@google.com    */
1870567f222b92d17923c687bed5f54b31652150891bungeman@google.com    #define SkScalarPow(b, e)       sk_float_pow(b, e)
1888a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the average of two SkScalars (a+b)/2
1898a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1908a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarAve(a, b)       (((a) + (b)) * 0.5f)
1918a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns the geometric mean of two SkScalars
1928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMean(a, b)      sk_float_sqrt((float)(a) * (b))
1948a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    /** Returns one half of the specified SkScalar
1958a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    */
1968a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarHalf(a)         ((a) * 0.5f)
1978a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
1988a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarSqrt2          1.41421356f
1998a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarPI             3.14159265f
2008a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarTanPIOver8     0.414213562f
2018a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarRoot2Over2     0.707106781f
2028a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2038a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
2048a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    float SkScalarSinCos(SkScalar radians, SkScalar* cosValue);
2058a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarSin(radians)    (float)sk_float_sin(radians)
2068a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarCos(radians)    (float)sk_float_cos(radians)
2078a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarTan(radians)    (float)sk_float_tan(radians)
2088a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarASin(val)   (float)sk_float_asin(val)
2098a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarACos(val)   (float)sk_float_acos(val)
2108a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x)
2118a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarExp(x)  (float)sk_float_exp(x)
2128a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarLog(x)  (float)sk_float_log(x)
2138a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; }
2158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; }
2168a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
217185d3d016d1e493694e9aaf45b070f34ba456983reed@google.com    static inline bool SkScalarIsInt(SkScalar x) {
218185d3d016d1e493694e9aaf45b070f34ba456983reed@google.com        return x == (float)(int)x;
219185d3d016d1e493694e9aaf45b070f34ba456983reed@google.com    }
2208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#else
2218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    typedef SkFixed SkScalar;
2228a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2238a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_Scalar1              SK_Fixed1
2248a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarHalf           SK_FixedHalf
2258a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarInfinity   SK_FixedMax
2268a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarMax            SK_FixedMax
2278a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarMin            SK_FixedMin
2288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarNaN            SK_FixedNaN
2298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarIsNaN(x)        ((x) == SK_FixedNaN)
230077910e20cda41d7981084fbd047a108894bc8dfreed@google.com    #define SkScalarIsFinite(x)     ((x) != SK_FixedNaN)
231077910e20cda41d7981084fbd047a108894bc8dfreed@google.com
2328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkIntToScalar(n)        SkIntToFixed(n)
2338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkFixedToScalar(x)      (x)
2348a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarToFixed(x)      (x)
2357886ad3de1aa523d5c71f1fa9f355dfcb2412d1dreed@google.com    #define SkScalarToFloat(n)  SkFixedToFloat(n)
2367886ad3de1aa523d5c71f1fa9f355dfcb2412d1dreed@google.com    #define SkFloatToScalar(n)  SkFloatToFixed(n)
2378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2387886ad3de1aa523d5c71f1fa9f355dfcb2412d1dreed@google.com    #define SkScalarToDouble(n) SkFixedToDouble(n)
2397886ad3de1aa523d5c71f1fa9f355dfcb2412d1dreed@google.com    #define SkDoubleToScalar(n) SkDoubleToFixed(n)
2408a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarFraction(x)     SkFixedFraction(x)
2411b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
2421b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarFloorToScalar(x)    SkFixedFloorToFixed(x)
2431b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarCeilToScalar(x)     SkFixedCeilToFixed(x)
2441b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarRoundToScalar(x)    SkFixedRoundToFixed(x)
2451b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
2461b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarFloorToInt(x)       SkFixedFloorToInt(x)
2471b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarCeilToInt(x)        SkFixedCeilToInt(x)
2481b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com    #define SkScalarRoundToInt(x)       SkFixedRoundToInt(x)
2491b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
2508a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarAbs(x)          SkFixedAbs(x)
251eebf5cb6c0f5ed2630de2e7712d61b4ec1d49015reed@android.com    #define SkScalarCopySign(x, y)  SkCopySign32(x, y)
2528a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarClampMax(x, max) SkClampMax(x, max)
2538a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarPin(x, min, max) SkPin32(x, min, max)
2548a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarSquare(x)       SkFixedSquare(x)
2558a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMul(a, b)       SkFixedMul(a, b)
2568a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c)
2578a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulRound(a, b)  SkFixedMulCommon(a, b, SK_FixedHalf)
2588a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulCeil(a, b)   SkFixedMulCommon(a, b, SK_Fixed1 - 1)
2598a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulFloor(a, b)  SkFixedMulCommon(a, b, 0)
2608a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarDiv(a, b)       SkFixedDiv(a, b)
2618a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMod(a, b)       SkFixedMod(a, b)
2628a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c)
2638a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarInvert(x)       SkFixedInvert(x)
2648a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarFastInvert(x)   SkFixedFastInvert(x)
2658a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarSqrt(x)         SkFixedSqrt(x)
2668a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarAve(a, b)       SkFixedAve(a, b)
2678a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarMean(a, b)      SkFixedMean(a, b)
2688a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarHalf(a)         ((a) >> 1)
2698a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2708a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarSqrt2          SK_FixedSqrt2
2718a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarPI             SK_FixedPI
2728a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarTanPIOver8     SK_FixedTanPIOver8
2738a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SK_ScalarRoot2Over2     SK_FixedRoot2Over2
2748a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkDegreesToRadians(degrees)     SkFractMul(degrees, SK_FractPIOver180)
2768a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr)
2778a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarSin(radians)    SkFixedSin(radians)
2788a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarCos(radians)    SkFixedCos(radians)
2798a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarTan(val)        SkFixedTan(val)
2808a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarASin(val)       SkFixedASin(val)
2818a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarACos(val)       SkFixedACos(val)
2828a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarATan2(y, x)     SkFixedATan2(y,x)
2838a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarExp(x)          SkFixedExp(x)
2848a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkScalarLog(x)          SkFixedLog(x)
2858a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2868a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkMaxScalar(a, b)       SkMax32(a, b)
2878a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    #define SkMinScalar(a, b)       SkMin32(a, b)
288185d3d016d1e493694e9aaf45b070f34ba456983reed@google.com
289185d3d016d1e493694e9aaf45b070f34ba456983reed@google.com    static inline bool SkScalarIsInt(SkFixed x) {
290185d3d016d1e493694e9aaf45b070f34ba456983reed@google.com        return 0 == (x & 0xffff);
291185d3d016d1e493694e9aaf45b070f34ba456983reed@google.com    }
2928a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif
2938a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
2941b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com// DEPRECATED : use ToInt or ToScalar variant
2951b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com#define SkScalarFloor(x)    SkScalarFloorToInt(x)
2961b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com#define SkScalarCeil(x)     SkScalarCeilToInt(x)
2971b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com#define SkScalarRound(x)    SkScalarRoundToInt(x)
2981b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
299647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com/**
300647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com *  Returns -1 || 0 || 1 depending on the sign of value:
301647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com *  -1 if x < 0
302647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com *   0 if x == 0
303647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com *   1 if x > 0
304647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com */
305647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.comstatic inline int SkScalarSignAsInt(SkScalar x) {
306647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com    return x < 0 ? -1 : (x > 0);
307647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com}
308647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com
309647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com// Scalar result version of above
310647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.comstatic inline SkScalar SkScalarSignAsScalar(SkScalar x) {
311647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com    return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0);
312647a804c3dd53b6743091ec97dd12111f90efec3bsalomon@google.com}
3131b20280f9b2e95fdcf4a2ee6f7f9d5a92c5b94c2reed@google.com
3148a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#define SK_ScalarNearlyZero         (SK_Scalar1 / (1 << 12))
3158a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
316187d5595901d1120d9425851e5afdd773f574502reed@android.comstatic inline bool SkScalarNearlyZero(SkScalar x,
3171fd56dc6e189ea0e94b5df9af959c243573f8883epoger@google.com                                    SkScalar tolerance = SK_ScalarNearlyZero) {
3189b5ca29af81b93faea040daa25a620bee99d6c38reed@google.com    SkASSERT(tolerance >= 0);
3199b5ca29af81b93faea040daa25a620bee99d6c38reed@google.com    return SkScalarAbs(x) <= tolerance;
3208a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com}
3218a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
3221fd56dc6e189ea0e94b5df9af959c243573f8883epoger@google.comstatic inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y,
3231fd56dc6e189ea0e94b5df9af959c243573f8883epoger@google.com                                     SkScalar tolerance = SK_ScalarNearlyZero) {
3249b5ca29af81b93faea040daa25a620bee99d6c38reed@google.com    SkASSERT(tolerance >= 0);
3259b5ca29af81b93faea040daa25a620bee99d6c38reed@google.com    return SkScalarAbs(x-y) <= tolerance;
3261fd56dc6e189ea0e94b5df9af959c243573f8883epoger@google.com}
3271fd56dc6e189ea0e94b5df9af959c243573f8883epoger@google.com
3288a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com/** Linearly interpolate between A and B, based on t.
3298a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    If t is 0, return A
3308a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    If t is 1, return B
3318a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    else interpolate.
3328a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    t must be [0..SK_Scalar1]
3338a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com*/
334187d5595901d1120d9425851e5afdd773f574502reed@android.comstatic inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) {
3358a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    SkASSERT(t >= 0 && t <= SK_Scalar1);
3368a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com    return A + SkScalarMul(B - A, t);
3378a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com}
3388a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com
339f4959ab11827bef99e8985031feb457cae1f987akeyar@chromium.orgstatic inline SkScalar SkScalarLog2(SkScalar x) {
340f4959ab11827bef99e8985031feb457cae1f987akeyar@chromium.org    static const SkScalar log2_conversion_factor = SkScalarDiv(1, SkScalarLog(2));
341f4959ab11827bef99e8985031feb457cae1f987akeyar@chromium.org
342f4959ab11827bef99e8985031feb457cae1f987akeyar@chromium.org    return SkScalarMul(SkScalarLog(x), log2_conversion_factor);
343f4959ab11827bef99e8985031feb457cae1f987akeyar@chromium.org}
344f4959ab11827bef99e8985031feb457cae1f987akeyar@chromium.org
34528be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org/** Interpolate along the function described by (keys[length], values[length])
34628be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    for the passed searchKey.  SearchKeys outside the range keys[0]-keys[Length]
34728be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    clamp to the min or max value.  This function was inspired by a desire
34828be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    to change the multiplier for thickness in fakeBold; therefore it assumes
34928be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    the number of pairs (length) will be small, and a linear search is used.
35028be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    Repeated keys are allowed for discontinuous functions (so long as keys is
35128be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    monotonically increasing), and if key is the value of a repeated scalar in
35228be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    keys, the first one will be used.  However, that may change if a binary
35328be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org    search is used.
35428be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org*/
35528be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.orgSkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[],
35628be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org                            const SkScalar values[], int length);
35728be72b63e457c680c192a34fb9f58e1c693363fvandebo@chromium.org
358e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com/*
359e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com *  Helper to compare an array of scalars.
360e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com */
361e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.comstatic inline bool SkScalarsEqual(const SkScalar a[], const SkScalar b[], int n) {
362e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com#ifdef SK_SCALAR_IS_FLOAT
363e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com    SkASSERT(n >= 0);
364e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com    for (int i = 0; i < n; ++i) {
365e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com        if (a[i] != b[i]) {
366e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com            return false;
367e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com        }
368e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com    }
369e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com    return true;
370e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com#else
371e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com    return 0 == memcmp(a, b, n * sizeof(SkScalar));
372e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com#endif
373e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com}
374e1e7d7a6b55504d97ce9f30202a179b63800093breed@google.com
3758a1c16ff38322f0210116fa7293eb8817c7e477ereed@android.com#endif
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