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
SkIntToFDot6(S16CPU x)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
SkFDot6ToFixed(SkFDot6 x)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
SkFDot6Div(SkFDot6 a,SkFDot6 b)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:
Lookup(SkFDot6 x)82 inline static SkFixed Lookup(SkFDot6 x) {
83 SkASSERT(SkAbs32(x) < kInverseTableSize);
84 return gFDot6INVERSE[kInverseTableSize + x];
85 }
86 };
87
QuickSkFDot6Div(SkFDot6 a,SkFDot6 b)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