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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 SkFixed_DEFINED
#define SkFixed_DEFINED
#include "SkTypes.h"
/** \file SkFixed.h
Types and macros for 16.16 fixed point
*/
/** 32 bit signed integer used to represent fractions values with 16 bits to the right of the decimal point
*/
typedef int32_t SkFixed;
#define SK_Fixed1 (1 << 16)
#define SK_FixedHalf (1 << 15)
#define SK_FixedMax (0x7FFFFFFF)
#define SK_FixedMin (-SK_FixedMax)
#define SK_FixedNaN ((int) 0x80000000)
#define SK_FixedPI (0x3243F)
#define SK_FixedSqrt2 (92682)
#define SK_FixedTanPIOver8 (0x6A0A)
#define SK_FixedRoot2Over2 (0xB505)
#define SkFixedToFloat(x) ((x) * 1.5258789e-5f)
#if 1
#define SkFloatToFixed(x) ((SkFixed)((x) * SK_Fixed1))
#else
// pins over/under flows to max/min int32 (slower than just a cast)
static inline SkFixed SkFloatToFixed(float x) {
int64_t n = x * SK_Fixed1;
return (SkFixed)n;
}
#endif
#ifdef SK_DEBUG
static inline SkFixed SkFloatToFixed_Check(float x) {
int64_t n64 = (int64_t)(x * SK_Fixed1);
SkFixed n32 = (SkFixed)n64;
SkASSERT(n64 == n32);
return n32;
}
#else
#define SkFloatToFixed_Check(x) SkFloatToFixed(x)
#endif
#define SkFixedToDouble(x) ((x) * 1.5258789e-5)
#define SkDoubleToFixed(x) ((SkFixed)((x) * SK_Fixed1))
/** 32 bit signed integer used to represent fractions values with 30 bits to the right of the decimal point
*/
typedef int32_t SkFract;
#define SK_Fract1 (1 << 30)
#define Sk_FracHalf (1 << 29)
#define SK_FractPIOver180 (0x11DF46A)
#define SkFractToFloat(x) ((float)(x) * 0.00000000093132257f)
#define SkFloatToFract(x) ((SkFract)((x) * SK_Fract1))
/** Converts an integer to a SkFixed, asserting that the result does not overflow
a 32 bit signed integer
*/
#ifdef SK_DEBUG
inline SkFixed SkIntToFixed(int n)
{
SkASSERT(n >= -32768 && n <= 32767);
return n << 16;
}
#else
// force the cast to SkFixed to ensure that the answer is signed (like the debug version)
#define SkIntToFixed(n) (SkFixed)((n) << 16)
#endif
/** Converts a SkFixed to a SkFract, asserting that the result does not overflow
a 32 bit signed integer
*/
#ifdef SK_DEBUG
inline SkFract SkFixedToFract(SkFixed x)
{
SkASSERT(x >= (-2 << 16) && x <= (2 << 16) - 1);
return x << 14;
}
#else
#define SkFixedToFract(x) ((x) << 14)
#endif
/** Returns the signed fraction of a SkFixed
*/
inline SkFixed SkFixedFraction(SkFixed x)
{
SkFixed mask = x >> 31 << 16;
return (x & 0xFFFF) | mask;
}
/** Converts a SkFract to a SkFixed
*/
#define SkFractToFixed(x) ((x) >> 14)
#define SkFixedRoundToInt(x) (((x) + SK_FixedHalf) >> 16)
#define SkFixedCeilToInt(x) (((x) + SK_Fixed1 - 1) >> 16)
#define SkFixedFloorToInt(x) ((x) >> 16)
#define SkFixedRoundToFixed(x) (((x) + SK_FixedHalf) & 0xFFFF0000)
#define SkFixedCeilToFixed(x) (((x) + SK_Fixed1 - 1) & 0xFFFF0000)
#define SkFixedFloorToFixed(x) ((x) & 0xFFFF0000)
// DEPRECATED
#define SkFixedFloor(x) SkFixedFloorToInt(x)
#define SkFixedCeil(x) SkFixedCeilToInt(x)
#define SkFixedRound(x) SkFixedRoundToInt(x)
#define SkFixedAbs(x) SkAbs32(x)
#define SkFixedAve(a, b) (((a) + (b)) >> 1)
SkFixed SkFixedMul_portable(SkFixed, SkFixed);
SkFract SkFractMul_portable(SkFract, SkFract);
inline SkFixed SkFixedSquare_portable(SkFixed value)
{
uint32_t a = SkAbs32(value);
uint32_t ah = a >> 16;
uint32_t al = a & 0xFFFF;
SkFixed result = ah * a + al * ah + (al * al >> 16);
if (result >= 0)
return result;
else // Overflow.
return SK_FixedMax;
}
#define SkFixedDiv(numer, denom) SkDivBits(numer, denom, 16)
SkFixed SkFixedDivInt(int32_t numer, int32_t denom);
SkFixed SkFixedMod(SkFixed numer, SkFixed denom);
#define SkFixedInvert(n) SkDivBits(SK_Fixed1, n, 16)
SkFixed SkFixedFastInvert(SkFixed n);
#define SkFixedSqrt(n) SkSqrtBits(n, 23)
SkFixed SkFixedMean(SkFixed a, SkFixed b); //*< returns sqrt(x*y)
int SkFixedMulCommon(SkFixed, int , int bias); // internal used by SkFixedMulFloor, SkFixedMulCeil, SkFixedMulRound
#define SkFractDiv(numer, denom) SkDivBits(numer, denom, 30)
#define SkFractSqrt(n) SkSqrtBits(n, 30)
SkFixed SkFixedSinCos(SkFixed radians, SkFixed* cosValueOrNull);
#define SkFixedSin(radians) SkFixedSinCos(radians, NULL)
inline SkFixed SkFixedCos(SkFixed radians)
{
SkFixed cosValue;
(void)SkFixedSinCos(radians, &cosValue);
return cosValue;
}
SkFixed SkFixedTan(SkFixed radians);
SkFixed SkFixedASin(SkFixed);
SkFixed SkFixedACos(SkFixed);
SkFixed SkFixedATan2(SkFixed y, SkFixed x);
SkFixed SkFixedExp(SkFixed);
SkFixed SkFixedLog(SkFixed);
#define SK_FixedNearlyZero (SK_Fixed1 >> 12)
inline bool SkFixedNearlyZero(SkFixed x, SkFixed tolerance = SK_FixedNearlyZero)
{
SkASSERT(tolerance > 0);
return SkAbs32(x) < tolerance;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////
// Now look for ASM overrides for our portable versions (should consider putting this in its own file)
#ifdef SkLONGLONG
inline SkFixed SkFixedMul_longlong(SkFixed a, SkFixed b)
{
return (SkFixed)((SkLONGLONG)a * b >> 16);
}
inline SkFract SkFractMul_longlong(SkFract a, SkFract b)
{
return (SkFract)((SkLONGLONG)a * b >> 30);
}
inline SkFixed SkFixedSquare_longlong(SkFixed value)
{
return (SkFixed)((SkLONGLONG)value * value >> 16);
}
#define SkFixedMul(a,b) SkFixedMul_longlong(a,b)
#define SkFractMul(a,b) SkFractMul_longlong(a,b)
#define SkFixedSquare(a) SkFixedSquare_longlong(a)
#endif
#if defined(SK_CPU_ARM)
/* This guy does not handle NaN or other obscurities, but is faster than
than (int)(x*65536)
*/
inline SkFixed SkFloatToFixed_arm(float x)
{
register int32_t y, z;
asm("movs %1, %3, lsl #1 \n"
"mov %2, #0x8E \n"
"sub %1, %2, %1, lsr #24 \n"
"mov %2, %3, lsl #8 \n"
"orr %2, %2, #0x80000000 \n"
"mov %1, %2, lsr %1 \n"
"it cs \n"
"rsbcs %1, %1, #0 \n"
: "=r"(x), "=&r"(y), "=&r"(z)
: "r"(x)
: "cc"
);
return y;
}
inline SkFixed SkFixedMul_arm(SkFixed x, SkFixed y)
{
register int32_t t;
asm("smull %0, %2, %1, %3 \n"
"mov %0, %0, lsr #16 \n"
"orr %0, %0, %2, lsl #16 \n"
: "=r"(x), "=&r"(y), "=r"(t)
: "r"(x), "1"(y)
:
);
return x;
}
inline SkFixed SkFixedMulAdd_arm(SkFixed x, SkFixed y, SkFixed a)
{
register int32_t t;
asm("smull %0, %3, %1, %4 \n"
"add %0, %2, %0, lsr #16 \n"
"add %0, %0, %3, lsl #16 \n"
: "=r"(x), "=&r"(y), "=&r"(a), "=r"(t)
: "%r"(x), "1"(y), "2"(a)
:
);
return x;
}
inline SkFixed SkFractMul_arm(SkFixed x, SkFixed y)
{
register int32_t t;
asm("smull %0, %2, %1, %3 \n"
"mov %0, %0, lsr #30 \n"
"orr %0, %0, %2, lsl #2 \n"
: "=r"(x), "=&r"(y), "=r"(t)
: "r"(x), "1"(y)
:
);
return x;
}
#undef SkFixedMul
#undef SkFractMul
#define SkFixedMul(x, y) SkFixedMul_arm(x, y)
#define SkFractMul(x, y) SkFractMul_arm(x, y)
#define SkFixedMulAdd(x, y, a) SkFixedMulAdd_arm(x, y, a)
#undef SkFloatToFixed
#define SkFloatToFixed(x) SkFloatToFixed_arm(x)
#endif
/////////////////////// Now define our macros to the portable versions if they weren't overridden
#ifndef SkFixedSquare
#define SkFixedSquare(x) SkFixedSquare_portable(x)
#endif
#ifndef SkFixedMul
#define SkFixedMul(x, y) SkFixedMul_portable(x, y)
#endif
#ifndef SkFractMul
#define SkFractMul(x, y) SkFractMul_portable(x, y)
#endif
#ifndef SkFixedMulAdd
#define SkFixedMulAdd(x, y, a) (SkFixedMul(x, y) + (a))
#endif
///////////////////////////////////////////////////////////////////////////////
typedef int64_t SkFixed48;
#define SkIntToFixed48(x) ((SkFixed48)(x) << 48)
#define SkFixed48ToInt(x) ((int)((x) >> 48))
#define SkFixedToFixed48(x) ((SkFixed48)(x) << 32)
#define SkFixed48ToFixed(x) ((SkFixed)((x) >> 32))
#define SkFloatToFixed48(x) ((SkFixed48)((x) * (65536.0f * 65536.0f * 65536.0f)))
#ifdef SK_SCALAR_IS_FLOAT
#define SkScalarToFixed48(x) SkFloatToFixed48(x)
#else
#define SkScalarToFixed48(x) SkFixedToFixed48(x)
#endif
#endif
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