/* * 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) { 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) { 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) { 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) { 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))) #define SkScalarToFixed48(x) SkFloatToFixed48(x) #endif