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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 //! Returns the number of leading zero bits (0...32)
16 int SkCLZ_portable(uint32_t);
17 
18 /** Computes the 64bit product of a * b, and then shifts the answer down by
19     shift bits, returning the low 32bits. shift must be [0..63]
20     e.g. to perform a fixedmul, call SkMulShift(a, b, 16)
21 */
22 int32_t SkMulShift(int32_t a, int32_t b, unsigned shift);
23 
24 /** Computes numer1 * numer2 / denom in full 64 intermediate precision.
25     It is an error for denom to be 0. There is no special handling if
26     the result overflows 32bits.
27 */
28 int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom);
29 
30 /** Computes (numer1 << shift) / denom in full 64 intermediate precision.
31     It is an error for denom to be 0. There is no special handling if
32     the result overflows 32bits.
33 */
34 int32_t SkDivBits(int32_t numer, int32_t denom, int shift);
35 
36 /** Return the integer square root of value, with a bias of bitBias
37 */
38 int32_t SkSqrtBits(int32_t value, int bitBias);
39 
40 /** Return the integer square root of n, treated as a SkFixed (16.16)
41 */
42 #define SkSqrt32(n)         SkSqrtBits(n, 15)
43 
44 /** Return the integer cube root of value, with a bias of bitBias
45  */
46 int32_t SkCubeRootBits(int32_t value, int bitBias);
47 
48 /** Returns -1 if n < 0, else returns 0
49 */
50 #define SkExtractSign(n)    ((int32_t)(n) >> 31)
51 
52 /** If sign == -1, returns -n, else sign must be 0, and returns n.
53     Typically used in conjunction with SkExtractSign().
54 */
SkApplySign(int32_t n,int32_t sign)55 static inline int32_t SkApplySign(int32_t n, int32_t sign) {
56     SkASSERT(sign == 0 || sign == -1);
57     return (n ^ sign) - sign;
58 }
59 
60 /** Return x with the sign of y */
SkCopySign32(int32_t x,int32_t y)61 static inline int32_t SkCopySign32(int32_t x, int32_t y) {
62     return SkApplySign(x, SkExtractSign(x ^ y));
63 }
64 
65 /** Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches)
66 */
SkClampPos(int value)67 static inline int SkClampPos(int value) {
68     return value & ~(value >> 31);
69 }
70 
71 /** Given an integer and a positive (max) integer, return the value
72     pinned against 0 and max, inclusive.
73     @param value    The value we want returned pinned between [0...max]
74     @param max      The positive max value
75     @return 0 if value < 0, max if value > max, else value
76 */
SkClampMax(int value,int max)77 static inline int SkClampMax(int value, int max) {
78     // ensure that max is positive
79     SkASSERT(max >= 0);
80     if (value < 0) {
81         value = 0;
82     }
83     if (value > max) {
84         value = max;
85     }
86     return value;
87 }
88 
89 /** Given a positive value and a positive max, return the value
90     pinned against max.
91     Note: only works as long as max - value doesn't wrap around
92     @return max if value >= max, else value
93 */
SkClampUMax(unsigned value,unsigned max)94 static inline unsigned SkClampUMax(unsigned value, unsigned max) {
95 #ifdef SK_CPU_HAS_CONDITIONAL_INSTR
96     if (value > max) {
97         value = max;
98     }
99     return value;
100 #else
101     int diff = max - value;
102     // clear diff if diff is positive
103     diff &= diff >> 31;
104 
105     return value + diff;
106 #endif
107 }
108 
109 ///////////////////////////////////////////////////////////////////////////////
110 
111 #if defined(__arm__)
112     #define SkCLZ(x)    __builtin_clz(x)
113 #endif
114 
115 #ifndef SkCLZ
116     #define SkCLZ(x)    SkCLZ_portable(x)
117 #endif
118 
119 ///////////////////////////////////////////////////////////////////////////////
120 
121 /** Returns the smallest power-of-2 that is >= the specified value. If value
122     is already a power of 2, then it is returned unchanged. It is undefined
123     if value is <= 0.
124 */
SkNextPow2(int value)125 static inline int SkNextPow2(int value) {
126     SkASSERT(value > 0);
127     return 1 << (32 - SkCLZ(value - 1));
128 }
129 
130 /** Returns the log2 of the specified value, were that value to be rounded up
131     to the next power of 2. It is undefined to pass 0. Examples:
132          SkNextLog2(1) -> 0
133          SkNextLog2(2) -> 1
134          SkNextLog2(3) -> 2
135          SkNextLog2(4) -> 2
136          SkNextLog2(5) -> 3
137 */
SkNextLog2(uint32_t value)138 static inline int SkNextLog2(uint32_t value) {
139     SkASSERT(value != 0);
140     return 32 - SkCLZ(value - 1);
141 }
142 
143 /** Returns true if value is a power of 2. Does not explicitly check for
144     value <= 0.
145  */
SkIsPow2(int value)146 static inline bool SkIsPow2(int value) {
147     return (value & (value - 1)) == 0;
148 }
149 
150 ///////////////////////////////////////////////////////////////////////////////
151 
152 /** SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t.
153     With this requirement, we can generate faster instructions on some
154     architectures.
155 */
156 #if defined(__arm__) \
157   && !defined(__thumb__) \
158   && !defined(__ARM_ARCH_4T__) \
159   && !defined(__ARM_ARCH_5T__)
SkMulS16(S16CPU x,S16CPU y)160     static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
161         SkASSERT((int16_t)x == x);
162         SkASSERT((int16_t)y == y);
163         int32_t product;
164         asm("smulbb %0, %1, %2 \n"
165             : "=r"(product)
166             : "r"(x), "r"(y)
167             );
168         return product;
169     }
170 #else
171     #ifdef SK_DEBUG
SkMulS16(S16CPU x,S16CPU y)172         static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
173             SkASSERT((int16_t)x == x);
174             SkASSERT((int16_t)y == y);
175             return x * y;
176         }
177     #else
178         #define SkMulS16(x, y)  ((x) * (y))
179     #endif
180 #endif
181 
182 /** Return a*b/255, truncating away any fractional bits. Only valid if both
183     a and b are 0..255
184 */
SkMulDiv255Trunc(U8CPU a,U8CPU b)185 static inline U8CPU SkMulDiv255Trunc(U8CPU a, U8CPU b) {
186     SkASSERT((uint8_t)a == a);
187     SkASSERT((uint8_t)b == b);
188     unsigned prod = SkMulS16(a, b) + 1;
189     return (prod + (prod >> 8)) >> 8;
190 }
191 
192 /** Return a*b/255, rounding any fractional bits. Only valid if both
193     a and b are 0..255
194  */
SkMulDiv255Round(U8CPU a,U8CPU b)195 static inline U8CPU SkMulDiv255Round(U8CPU a, U8CPU b) {
196     SkASSERT((uint8_t)a == a);
197     SkASSERT((uint8_t)b == b);
198     unsigned prod = SkMulS16(a, b) + 128;
199     return (prod + (prod >> 8)) >> 8;
200 }
201 
202 /** Return (a*b)/255, taking the ceiling of any fractional bits. Only valid if
203     both a and b are 0..255. The expected result equals (a * b + 254) / 255.
204  */
SkMulDiv255Ceiling(U8CPU a,U8CPU b)205 static inline U8CPU SkMulDiv255Ceiling(U8CPU a, U8CPU b) {
206     SkASSERT((uint8_t)a == a);
207     SkASSERT((uint8_t)b == b);
208     unsigned prod = SkMulS16(a, b) + 255;
209     return (prod + (prod >> 8)) >> 8;
210 }
211 
212 /** Return a*b/((1 << shift) - 1), rounding any fractional bits.
213     Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8
214 */
SkMul16ShiftRound(unsigned a,unsigned b,int shift)215 static inline unsigned SkMul16ShiftRound(unsigned a, unsigned b, int shift) {
216     SkASSERT(a <= 32767);
217     SkASSERT(b <= 32767);
218     SkASSERT(shift > 0 && shift <= 8);
219     unsigned prod = SkMulS16(a, b) + (1 << (shift - 1));
220     return (prod + (prod >> shift)) >> shift;
221 }
222 
223 /** Just the rounding step in SkDiv255Round: round(value / 255)
224  */
SkDiv255Round(unsigned prod)225 static inline unsigned SkDiv255Round(unsigned prod) {
226     prod += 128;
227     return (prod + (prod >> 8)) >> 8;
228 }
229 
230 #endif
231 
232