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 SkMath_DEFINED
11#define SkMath_DEFINED
12
13#include "SkTypes.h"
14
15/**
16 *  Computes numer1 * numer2 / denom in full 64 intermediate precision.
17 *  It is an error for denom to be 0. There is no special handling if
18 *  the result overflows 32bits.
19 */
20int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom);
21
22/**
23 *  Computes (numer1 << shift) / denom in full 64 intermediate precision.
24 *  It is an error for denom to be 0. There is no special handling if
25 *  the result overflows 32bits.
26 */
27int32_t SkDivBits(int32_t numer, int32_t denom, int shift);
28
29/**
30 *  Return the integer square root of value, with a bias of bitBias
31 */
32int32_t SkSqrtBits(int32_t value, int bitBias);
33
34/** Return the integer square root of n, treated as a SkFixed (16.16)
35 */
36#define SkSqrt32(n)         SkSqrtBits(n, 15)
37
38///////////////////////////////////////////////////////////////////////////////
39
40//! Returns the number of leading zero bits (0...32)
41int SkCLZ_portable(uint32_t);
42
43#ifndef SkCLZ
44    #if defined(_MSC_VER) && _MSC_VER >= 1400
45        #include <intrin.h>
46
47        static inline int SkCLZ(uint32_t mask) {
48            if (mask) {
49                DWORD index;
50                _BitScanReverse(&index, mask);
51                return index ^ 0x1F;
52            } else {
53                return 32;
54            }
55        }
56    #elif defined(SK_CPU_ARM) || defined(__GNUC__) || defined(__clang__)
57        static inline int SkCLZ(uint32_t mask) {
58            // __builtin_clz(0) is undefined, so we have to detect that case.
59            return mask ? __builtin_clz(mask) : 32;
60        }
61    #else
62        #define SkCLZ(x)    SkCLZ_portable(x)
63    #endif
64#endif
65
66/**
67 *  Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches)
68 */
69static inline int SkClampPos(int value) {
70    return value & ~(value >> 31);
71}
72
73/** Given an integer and a positive (max) integer, return the value
74 *  pinned against 0 and max, inclusive.
75 *  @param value    The value we want returned pinned between [0...max]
76 *  @param max      The positive max value
77 *  @return 0 if value < 0, max if value > max, else value
78 */
79static inline int SkClampMax(int value, int max) {
80    // ensure that max is positive
81    SkASSERT(max >= 0);
82    if (value < 0) {
83        value = 0;
84    }
85    if (value > max) {
86        value = max;
87    }
88    return value;
89}
90
91/**
92 *  Returns the smallest power-of-2 that is >= the specified value. If value
93 *  is already a power of 2, then it is returned unchanged. It is undefined
94 *  if value is <= 0.
95 */
96static inline int SkNextPow2(int value) {
97    SkASSERT(value > 0);
98    return 1 << (32 - SkCLZ(value - 1));
99}
100
101/**
102 *  Returns the log2 of the specified value, were that value to be rounded up
103 *  to the next power of 2. It is undefined to pass 0. Examples:
104 *  SkNextLog2(1) -> 0
105 *  SkNextLog2(2) -> 1
106 *  SkNextLog2(3) -> 2
107 *  SkNextLog2(4) -> 2
108 *  SkNextLog2(5) -> 3
109 */
110static inline int SkNextLog2(uint32_t value) {
111    SkASSERT(value != 0);
112    return 32 - SkCLZ(value - 1);
113}
114
115/**
116 *  Returns true if value is a power of 2. Does not explicitly check for
117 *  value <= 0.
118 */
119static inline bool SkIsPow2(int value) {
120    return (value & (value - 1)) == 0;
121}
122
123///////////////////////////////////////////////////////////////////////////////
124
125/**
126 *  SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t.
127 *  With this requirement, we can generate faster instructions on some
128 *  architectures.
129 */
130#ifdef SK_ARM_HAS_EDSP
131    static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
132        SkASSERT((int16_t)x == x);
133        SkASSERT((int16_t)y == y);
134        int32_t product;
135        asm("smulbb %0, %1, %2 \n"
136            : "=r"(product)
137            : "r"(x), "r"(y)
138            );
139        return product;
140    }
141#else
142    #ifdef SK_DEBUG
143        static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
144            SkASSERT((int16_t)x == x);
145            SkASSERT((int16_t)y == y);
146            return x * y;
147        }
148    #else
149        #define SkMulS16(x, y)  ((x) * (y))
150    #endif
151#endif
152
153/**
154 *  Return a*b/((1 << shift) - 1), rounding any fractional bits.
155 *  Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8
156 */
157static inline unsigned SkMul16ShiftRound(U16CPU a, U16CPU b, int shift) {
158    SkASSERT(a <= 32767);
159    SkASSERT(b <= 32767);
160    SkASSERT(shift > 0 && shift <= 8);
161    unsigned prod = SkMulS16(a, b) + (1 << (shift - 1));
162    return (prod + (prod >> shift)) >> shift;
163}
164
165/**
166 *  Return a*b/255, rounding any fractional bits.
167 *  Only valid if a and b are unsigned and <= 32767.
168 */
169static inline U8CPU SkMulDiv255Round(U16CPU a, U16CPU b) {
170    SkASSERT(a <= 32767);
171    SkASSERT(b <= 32767);
172    unsigned prod = SkMulS16(a, b) + 128;
173    return (prod + (prod >> 8)) >> 8;
174}
175
176/**
177 * Stores numer/denom and numer%denom into div and mod respectively.
178 */
179template <typename In, typename Out>
180inline void SkTDivMod(In numer, In denom, Out* div, Out* mod) {
181#ifdef SK_CPU_ARM
182    // If we wrote this as in the else branch, GCC won't fuse the two into one
183    // divmod call, but rather a div call followed by a divmod.  Silly!  This
184    // version is just as fast as calling __aeabi_[u]idivmod manually, but with
185    // prettier code.
186    //
187    // This benches as around 2x faster than the code in the else branch.
188    const In d = numer/denom;
189    *div = static_cast<Out>(d);
190    *mod = static_cast<Out>(numer-d*denom);
191#else
192    // On x86 this will just be a single idiv.
193    *div = static_cast<Out>(numer/denom);
194    *mod = static_cast<Out>(numer%denom);
195#endif  // SK_CPU_ARM
196}
197
198#endif
199