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