1 /* 2 * Copyright 2006 The Android Open Source Project 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 8 9 #ifndef SkFDot6_DEFINED 10 #define SkFDot6_DEFINED 11 12 #include "SkFixed.h" 13 #include "SkScalar.h" 14 #include "SkMath.h" 15 16 typedef int32_t SkFDot6; 17 18 /* This uses the magic number approach suggested here: 19 * http://stereopsis.com/sree/fpu2006.html and used in 20 * _cairo_fixed_from_double. It does banker's rounding 21 * (i.e. round to nearest even) 22 */ 23 inline SkFDot6 SkScalarRoundToFDot6(SkScalar x, int shift = 0) 24 { 25 union { 26 double fDouble; 27 int32_t fBits[2]; 28 } tmp; 29 int fractionalBits = 6 + shift; 30 double magic = (1LL << (52 - (fractionalBits))) * 1.5; 31 32 tmp.fDouble = SkScalarToDouble(x) + magic; 33 #ifdef SK_CPU_BENDIAN 34 return tmp.fBits[1]; 35 #else 36 return tmp.fBits[0]; 37 #endif 38 } 39 40 #define SK_FDot6One (64) 41 #define SK_FDot6Half (32) 42 43 #ifdef SK_DEBUG 44 inline SkFDot6 SkIntToFDot6(S16CPU x) { 45 SkASSERT(SkToS16(x) == x); 46 return x << 6; 47 } 48 #else 49 #define SkIntToFDot6(x) ((x) << 6) 50 #endif 51 52 #define SkFDot6Floor(x) ((x) >> 6) 53 #define SkFDot6Ceil(x) (((x) + 63) >> 6) 54 #define SkFDot6Round(x) (((x) + 32) >> 6) 55 56 #define SkFixedToFDot6(x) ((x) >> 10) 57 58 inline SkFixed SkFDot6ToFixed(SkFDot6 x) { 59 SkASSERT((SkLeftShift(x, 10) >> 10) == x); 60 61 return SkLeftShift(x, 10); 62 } 63 64 #define SkScalarToFDot6(x) (SkFDot6)((x) * 64) 65 #define SkFDot6ToScalar(x) ((SkScalar)(x) * 0.015625f) 66 #define SkFDot6ToFloat SkFDot6ToScalar 67 68 inline SkFixed SkFDot6Div(SkFDot6 a, SkFDot6 b) { 69 SkASSERT(b != 0); 70 71 if (a == (int16_t)a) { 72 return SkLeftShift(a, 16) / b; 73 } else { 74 return SkFixedDiv(a, b); 75 } 76 } 77 78 #include "SkFDot6Constants.h" 79 80 class QuickFDot6Inverse { 81 public: 82 inline static SkFixed Lookup(SkFDot6 x) { 83 SkASSERT(SkAbs32(x) < kInverseTableSize); 84 return gFDot6INVERSE[kInverseTableSize + x]; 85 } 86 }; 87 88 static inline SkFixed QuickSkFDot6Div(SkFDot6 a, SkFDot6 b) { 89 const int kMinBits = 3; // abs(b) should be at least (1 << kMinBits) for quick division 90 const int kMaxBits = 31; // Number of bits available in signed int 91 // Given abs(b) <= (1 << kMinBits), the inverse of abs(b) is at most 1 << (22 - kMinBits) in 92 // SkFixed format. Hence abs(a) should be less than kMaxAbsA 93 const int kMaxAbsA = 1 << (kMaxBits - (22 - kMinBits)); 94 SkFDot6 abs_a = SkAbs32(a); 95 SkFDot6 abs_b = SkAbs32(b); 96 if (abs_b >= (1 << kMinBits) && abs_b < kInverseTableSize && abs_a < kMaxAbsA) { 97 SkASSERT((int64_t)a * QuickFDot6Inverse::Lookup(b) <= SK_MaxS32 98 && (int64_t)a * QuickFDot6Inverse::Lookup(b) >= SK_MinS32); 99 SkFixed ourAnswer = (a * QuickFDot6Inverse::Lookup(b)) >> 6; 100 #ifdef SK_DEBUG 101 SkFixed directAnswer = SkFDot6Div(a, b); 102 SkASSERT( 103 (directAnswer == 0 && ourAnswer == 0) || 104 SkFixedDiv(SkAbs32(directAnswer - ourAnswer), SkAbs32(directAnswer)) <= 1 << 10 105 ); 106 #endif 107 return ourAnswer; 108 } else { 109 return SkFDot6Div(a, b); 110 } 111 } 112 113 #endif 114