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
16typedef 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 */
23inline 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
58inline 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
68inline 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
80class QuickFDot6Inverse {
81public:
82    inline static SkFixed Lookup(SkFDot6 x) {
83        SkASSERT(SkAbs32(x) < kInverseTableSize);
84        return gFDot6INVERSE[kInverseTableSize + x];
85    }
86};
87
88static 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