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 // 64bit -> 32bit utilities
16
17 /**
18 * Return true iff the 64bit value can exactly be represented in signed 32bits
19 */
sk_64_isS32(int64_t value)20 static inline bool sk_64_isS32(int64_t value) {
21 return (int32_t)value == value;
22 }
23
24 /**
25 * Return the 64bit argument as signed 32bits, asserting in debug that the arg
26 * exactly fits in signed 32bits. In the release build, no checks are preformed
27 * and the return value if the arg does not fit is undefined.
28 */
sk_64_asS32(int64_t value)29 static inline int32_t sk_64_asS32(int64_t value) {
30 SkASSERT(sk_64_isS32(value));
31 return (int32_t)value;
32 }
33
34 // Handy util that can be passed two ints, and will automatically promote to
35 // 64bits before the multiply, so the caller doesn't have to remember to cast
36 // e.g. (int64_t)a * b;
sk_64_mul(int64_t a,int64_t b)37 static inline int64_t sk_64_mul(int64_t a, int64_t b) {
38 return a * b;
39 }
40
41 ///////////////////////////////////////////////////////////////////////////////
42
43 /**
44 * Computes numer1 * numer2 / denom in full 64 intermediate precision.
45 * It is an error for denom to be 0. There is no special handling if
46 * the result overflows 32bits.
47 */
SkMulDiv(int32_t numer1,int32_t numer2,int32_t denom)48 static inline int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) {
49 SkASSERT(denom);
50
51 int64_t tmp = sk_64_mul(numer1, numer2) / denom;
52 return sk_64_asS32(tmp);
53 }
54
55 /**
56 * Computes (numer1 << shift) / denom in full 64 intermediate precision.
57 * It is an error for denom to be 0. There is no special handling if
58 * the result overflows 32bits.
59 */
60 int32_t SkDivBits(int32_t numer, int32_t denom, int shift);
61
62 /**
63 * Return the integer square root of value, with a bias of bitBias
64 */
65 int32_t SkSqrtBits(int32_t value, int bitBias);
66
67 /** Return the integer square root of n, treated as a SkFixed (16.16)
68 */
69 #define SkSqrt32(n) SkSqrtBits(n, 15)
70
71 //! Returns the number of leading zero bits (0...32)
72 int SkCLZ_portable(uint32_t);
73
74 #ifndef SkCLZ
75 #if defined(_MSC_VER) && _MSC_VER >= 1400
76 #include <intrin.h>
77
SkCLZ(uint32_t mask)78 static inline int SkCLZ(uint32_t mask) {
79 if (mask) {
80 DWORD index;
81 _BitScanReverse(&index, mask);
82 // Suppress this bogus /analyze warning. The check for non-zero
83 // guarantees that _BitScanReverse will succeed.
84 #pragma warning(suppress : 6102) // Using 'index' from failed function call
85 return index ^ 0x1F;
86 } else {
87 return 32;
88 }
89 }
90 #elif defined(SK_CPU_ARM32) || defined(__GNUC__) || defined(__clang__)
SkCLZ(uint32_t mask)91 static inline int SkCLZ(uint32_t mask) {
92 // __builtin_clz(0) is undefined, so we have to detect that case.
93 return mask ? __builtin_clz(mask) : 32;
94 }
95 #else
96 #define SkCLZ(x) SkCLZ_portable(x)
97 #endif
98 #endif
99
100 /**
101 * Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches)
102 */
SkClampPos(int value)103 static inline int SkClampPos(int value) {
104 return value & ~(value >> 31);
105 }
106
107 /** Given an integer and a positive (max) integer, return the value
108 * pinned against 0 and max, inclusive.
109 * @param value The value we want returned pinned between [0...max]
110 * @param max The positive max value
111 * @return 0 if value < 0, max if value > max, else value
112 */
SkClampMax(int value,int max)113 static inline int SkClampMax(int value, int max) {
114 // ensure that max is positive
115 SkASSERT(max >= 0);
116 if (value < 0) {
117 value = 0;
118 }
119 if (value > max) {
120 value = max;
121 }
122 return value;
123 }
124
125 /**
126 * Returns the smallest power-of-2 that is >= the specified value. If value
127 * is already a power of 2, then it is returned unchanged. It is undefined
128 * if value is <= 0.
129 */
SkNextPow2(int value)130 static inline int SkNextPow2(int value) {
131 SkASSERT(value > 0);
132 return 1 << (32 - SkCLZ(value - 1));
133 }
134
135 /**
136 * Returns the log2 of the specified value, were that value to be rounded up
137 * to the next power of 2. It is undefined to pass 0. Examples:
138 * SkNextLog2(1) -> 0
139 * SkNextLog2(2) -> 1
140 * SkNextLog2(3) -> 2
141 * SkNextLog2(4) -> 2
142 * SkNextLog2(5) -> 3
143 */
SkNextLog2(uint32_t value)144 static inline int SkNextLog2(uint32_t value) {
145 SkASSERT(value != 0);
146 return 32 - SkCLZ(value - 1);
147 }
148
149 /**
150 * Returns true if value is a power of 2. Does not explicitly check for
151 * value <= 0.
152 */
SkIsPow2(int value)153 static inline bool SkIsPow2(int value) {
154 return (value & (value - 1)) == 0;
155 }
156
157 ///////////////////////////////////////////////////////////////////////////////
158
159 /**
160 * SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t.
161 * With this requirement, we can generate faster instructions on some
162 * architectures.
163 */
164 #ifdef SK_ARM_HAS_EDSP
SkMulS16(S16CPU x,S16CPU y)165 static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
166 SkASSERT((int16_t)x == x);
167 SkASSERT((int16_t)y == y);
168 int32_t product;
169 asm("smulbb %0, %1, %2 \n"
170 : "=r"(product)
171 : "r"(x), "r"(y)
172 );
173 return product;
174 }
175 #else
176 #ifdef SK_DEBUG
SkMulS16(S16CPU x,S16CPU y)177 static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
178 SkASSERT((int16_t)x == x);
179 SkASSERT((int16_t)y == y);
180 return x * y;
181 }
182 #else
183 #define SkMulS16(x, y) ((x) * (y))
184 #endif
185 #endif
186
187 /**
188 * Return a*b/((1 << shift) - 1), rounding any fractional bits.
189 * Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8
190 */
SkMul16ShiftRound(U16CPU a,U16CPU b,int shift)191 static inline unsigned SkMul16ShiftRound(U16CPU a, U16CPU b, int shift) {
192 SkASSERT(a <= 32767);
193 SkASSERT(b <= 32767);
194 SkASSERT(shift > 0 && shift <= 8);
195 unsigned prod = SkMulS16(a, b) + (1 << (shift - 1));
196 return (prod + (prod >> shift)) >> shift;
197 }
198
199 /**
200 * Return a*b/255, rounding any fractional bits.
201 * Only valid if a and b are unsigned and <= 32767.
202 */
SkMulDiv255Round(U16CPU a,U16CPU b)203 static inline U8CPU SkMulDiv255Round(U16CPU a, U16CPU b) {
204 SkASSERT(a <= 32767);
205 SkASSERT(b <= 32767);
206 unsigned prod = SkMulS16(a, b) + 128;
207 return (prod + (prod >> 8)) >> 8;
208 }
209
210 /**
211 * Stores numer/denom and numer%denom into div and mod respectively.
212 */
213 template <typename In, typename Out>
SkTDivMod(In numer,In denom,Out * div,Out * mod)214 inline void SkTDivMod(In numer, In denom, Out* div, Out* mod) {
215 #ifdef SK_CPU_ARM32
216 // If we wrote this as in the else branch, GCC won't fuse the two into one
217 // divmod call, but rather a div call followed by a divmod. Silly! This
218 // version is just as fast as calling __aeabi_[u]idivmod manually, but with
219 // prettier code.
220 //
221 // This benches as around 2x faster than the code in the else branch.
222 const In d = numer/denom;
223 *div = static_cast<Out>(d);
224 *mod = static_cast<Out>(numer-d*denom);
225 #else
226 // On x86 this will just be a single idiv.
227 *div = static_cast<Out>(numer/denom);
228 *mod = static_cast<Out>(numer%denom);
229 #endif
230 }
231
232 #endif
233