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/*
* Copyright 2006 The Android Open Source Project
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#ifndef SkMath_DEFINED
#define SkMath_DEFINED
#include "SkTypes.h"
//! Returns the number of leading zero bits (0...32)
int SkCLZ_portable(uint32_t);
/** Computes the 64bit product of a * b, and then shifts the answer down by
shift bits, returning the low 32bits. shift must be [0..63]
e.g. to perform a fixedmul, call SkMulShift(a, b, 16)
*/
int32_t SkMulShift(int32_t a, int32_t b, unsigned shift);
/** Computes numer1 * numer2 / denom in full 64 intermediate precision.
It is an error for denom to be 0. There is no special handling if
the result overflows 32bits.
*/
int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom);
/** Computes (numer1 << shift) / denom in full 64 intermediate precision.
It is an error for denom to be 0. There is no special handling if
the result overflows 32bits.
*/
int32_t SkDivBits(int32_t numer, int32_t denom, int shift);
/** Return the integer square root of value, with a bias of bitBias
*/
int32_t SkSqrtBits(int32_t value, int bitBias);
/** Return the integer square root of n, treated as a SkFixed (16.16)
*/
#define SkSqrt32(n) SkSqrtBits(n, 15)
/** Return the integer cube root of value, with a bias of bitBias
*/
int32_t SkCubeRootBits(int32_t value, int bitBias);
/** Returns -1 if n < 0, else returns 0
*/
#define SkExtractSign(n) ((int32_t)(n) >> 31)
/** If sign == -1, returns -n, else sign must be 0, and returns n.
Typically used in conjunction with SkExtractSign().
*/
static inline int32_t SkApplySign(int32_t n, int32_t sign) {
SkASSERT(sign == 0 || sign == -1);
return (n ^ sign) - sign;
}
/** Return x with the sign of y */
static inline int32_t SkCopySign32(int32_t x, int32_t y) {
return SkApplySign(x, SkExtractSign(x ^ y));
}
/** Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches)
*/
static inline int SkClampPos(int value) {
return value & ~(value >> 31);
}
/** Given an integer and a positive (max) integer, return the value
pinned against 0 and max, inclusive.
@param value The value we want returned pinned between [0...max]
@param max The positive max value
@return 0 if value < 0, max if value > max, else value
*/
static inline int SkClampMax(int value, int max) {
// ensure that max is positive
SkASSERT(max >= 0);
if (value < 0) {
value = 0;
}
if (value > max) {
value = max;
}
return value;
}
/** Given a positive value and a positive max, return the value
pinned against max.
Note: only works as long as max - value doesn't wrap around
@return max if value >= max, else value
*/
static inline unsigned SkClampUMax(unsigned value, unsigned max) {
#ifdef SK_CPU_HAS_CONDITIONAL_INSTR
if (value > max) {
value = max;
}
return value;
#else
int diff = max - value;
// clear diff if diff is positive
diff &= diff >> 31;
return value + diff;
#endif
}
///////////////////////////////////////////////////////////////////////////////
#if defined(__arm__)
#define SkCLZ(x) __builtin_clz(x)
#endif
#ifndef SkCLZ
#define SkCLZ(x) SkCLZ_portable(x)
#endif
///////////////////////////////////////////////////////////////////////////////
/** Returns the smallest power-of-2 that is >= the specified value. If value
is already a power of 2, then it is returned unchanged. It is undefined
if value is <= 0.
*/
static inline int SkNextPow2(int value) {
SkASSERT(value > 0);
return 1 << (32 - SkCLZ(value - 1));
}
/** Returns the log2 of the specified value, were that value to be rounded up
to the next power of 2. It is undefined to pass 0. Examples:
SkNextLog2(1) -> 0
SkNextLog2(2) -> 1
SkNextLog2(3) -> 2
SkNextLog2(4) -> 2
SkNextLog2(5) -> 3
*/
static inline int SkNextLog2(uint32_t value) {
SkASSERT(value != 0);
return 32 - SkCLZ(value - 1);
}
/** Returns true if value is a power of 2. Does not explicitly check for
value <= 0.
*/
static inline bool SkIsPow2(int value) {
return (value & (value - 1)) == 0;
}
///////////////////////////////////////////////////////////////////////////////
/** SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t.
With this requirement, we can generate faster instructions on some
architectures.
*/
#if defined(__arm__) \
&& !defined(__thumb__) \
&& !defined(__ARM_ARCH_4T__) \
&& !defined(__ARM_ARCH_5T__)
static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
SkASSERT((int16_t)x == x);
SkASSERT((int16_t)y == y);
int32_t product;
asm("smulbb %0, %1, %2 \n"
: "=r"(product)
: "r"(x), "r"(y)
);
return product;
}
#else
#ifdef SK_DEBUG
static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
SkASSERT((int16_t)x == x);
SkASSERT((int16_t)y == y);
return x * y;
}
#else
#define SkMulS16(x, y) ((x) * (y))
#endif
#endif
/** Return a*b/255, truncating away any fractional bits. Only valid if both
a and b are 0..255
*/
static inline U8CPU SkMulDiv255Trunc(U8CPU a, U8CPU b) {
SkASSERT((uint8_t)a == a);
SkASSERT((uint8_t)b == b);
unsigned prod = SkMulS16(a, b) + 1;
return (prod + (prod >> 8)) >> 8;
}
/** Return a*b/255, rounding any fractional bits. Only valid if both
a and b are 0..255
*/
static inline U8CPU SkMulDiv255Round(U8CPU a, U8CPU b) {
SkASSERT((uint8_t)a == a);
SkASSERT((uint8_t)b == b);
unsigned prod = SkMulS16(a, b) + 128;
return (prod + (prod >> 8)) >> 8;
}
/** Return (a*b)/255, taking the ceiling of any fractional bits. Only valid if
both a and b are 0..255. The expected result equals (a * b + 254) / 255.
*/
static inline U8CPU SkMulDiv255Ceiling(U8CPU a, U8CPU b) {
SkASSERT((uint8_t)a == a);
SkASSERT((uint8_t)b == b);
unsigned prod = SkMulS16(a, b) + 255;
return (prod + (prod >> 8)) >> 8;
}
/** Return a*b/((1 << shift) - 1), rounding any fractional bits.
Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8
*/
static inline unsigned SkMul16ShiftRound(unsigned a, unsigned b, int shift) {
SkASSERT(a <= 32767);
SkASSERT(b <= 32767);
SkASSERT(shift > 0 && shift <= 8);
unsigned prod = SkMulS16(a, b) + (1 << (shift - 1));
return (prod + (prod >> shift)) >> shift;
}
/** Just the rounding step in SkDiv255Round: round(value / 255)
*/
static inline unsigned SkDiv255Round(unsigned prod) {
prod += 128;
return (prod + (prod >> 8)) >> 8;
}
#endif
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