1
2/*
3 * Copyright 2006 The Android Open Source Project
4 *
5 * Use of this source code is governed by a BSD-style license that can be
6 * found in the LICENSE file.
7 */
8
9
10#ifndef SkFloatingPoint_DEFINED
11#define SkFloatingPoint_DEFINED
12
13#include "SkTypes.h"
14
15#include <math.h>
16#include <float.h>
17
18// For _POSIX_VERSION
19#if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
20#include <unistd.h>
21#endif
22
23#include "SkFloatBits.h"
24
25// C++98 cmath std::pow seems to be the earliest portable way to get float pow.
26// However, on Linux including cmath undefines isfinite.
27// http://gcc.gnu.org/bugzilla/show_bug.cgi?id=14608
28static inline float sk_float_pow(float base, float exp) {
29    return powf(base, exp);
30}
31
32static inline float sk_float_copysign(float x, float y) {
33// c++11 contains a 'float copysign(float, float)' function in <cmath>.
34// clang-cl reports __cplusplus for clang, not the __cplusplus vc++ version _MSC_VER would report.
35#if (defined(_MSC_VER) && defined(__clang__))
36#    define SK_BUILD_WITH_CLANG_CL 1
37#else
38#    define SK_BUILD_WITH_CLANG_CL 0
39#endif
40#if (!SK_BUILD_WITH_CLANG_CL && __cplusplus >= 201103L) || (_MSC_VER >= 1800)
41    return copysignf(x, y);
42
43// Posix has demanded 'float copysignf(float, float)' (from C99) since Issue 6.
44#elif defined(_POSIX_VERSION) && _POSIX_VERSION >= 200112L
45    return copysignf(x, y);
46
47// Visual studio prior to 13 only has 'double _copysign(double, double)'.
48#elif defined(_MSC_VER)
49    return (float)_copysign(x, y);
50
51// Otherwise convert to bits and extract sign.
52#else
53    int32_t xbits = SkFloat2Bits(x);
54    int32_t ybits = SkFloat2Bits(y);
55    return SkBits2Float((xbits & 0x7FFFFFFF) | (ybits & 0x80000000));
56#endif
57}
58
59#define sk_float_sqrt(x)        sqrtf(x)
60#define sk_float_sin(x)         sinf(x)
61#define sk_float_cos(x)         cosf(x)
62#define sk_float_tan(x)         tanf(x)
63#define sk_float_floor(x)       floorf(x)
64#define sk_float_ceil(x)        ceilf(x)
65#ifdef SK_BUILD_FOR_MAC
66#    define sk_float_acos(x)    static_cast<float>(acos(x))
67#    define sk_float_asin(x)    static_cast<float>(asin(x))
68#else
69#    define sk_float_acos(x)    acosf(x)
70#    define sk_float_asin(x)    asinf(x)
71#endif
72#define sk_float_atan2(y,x)     atan2f(y,x)
73#define sk_float_abs(x)         fabsf(x)
74#define sk_float_mod(x,y)       fmodf(x,y)
75#define sk_float_exp(x)         expf(x)
76#define sk_float_log(x)         logf(x)
77
78#define sk_float_round(x) sk_float_floor((x) + 0.5f)
79
80// can't find log2f on android, but maybe that just a tool bug?
81#ifdef SK_BUILD_FOR_ANDROID
82    static inline float sk_float_log2(float x) {
83        const double inv_ln_2 = 1.44269504088896;
84        return (float)(log(x) * inv_ln_2);
85    }
86#else
87    #define sk_float_log2(x)        log2f(x)
88#endif
89
90#ifdef SK_BUILD_FOR_WIN
91    #define sk_float_isfinite(x)    _finite(x)
92    #define sk_float_isnan(x)       _isnan(x)
93    static inline int sk_float_isinf(float x) {
94        int32_t bits = SkFloat2Bits(x);
95        return (bits << 1) == (0xFF << 24);
96    }
97#else
98    #define sk_float_isfinite(x)    isfinite(x)
99    #define sk_float_isnan(x)       isnan(x)
100    #define sk_float_isinf(x)       isinf(x)
101#endif
102
103#define sk_double_isnan(a)          sk_float_isnan(a)
104
105#ifdef SK_USE_FLOATBITS
106    #define sk_float_floor2int(x)   SkFloatToIntFloor(x)
107    #define sk_float_round2int(x)   SkFloatToIntRound(x)
108    #define sk_float_ceil2int(x)    SkFloatToIntCeil(x)
109#else
110    #define sk_float_floor2int(x)   (int)sk_float_floor(x)
111    #define sk_float_round2int(x)   (int)sk_float_floor((x) + 0.5f)
112    #define sk_float_ceil2int(x)    (int)sk_float_ceil(x)
113#endif
114
115#define sk_double_floor(x)          floor(x)
116#define sk_double_round(x)          floor((x) + 0.5)
117#define sk_double_ceil(x)           ceil(x)
118#define sk_double_floor2int(x)      (int)floor(x)
119#define sk_double_round2int(x)      (int)floor((x) + 0.5f)
120#define sk_double_ceil2int(x)       (int)ceil(x)
121
122extern const uint32_t gIEEENotANumber;
123extern const uint32_t gIEEEInfinity;
124extern const uint32_t gIEEENegativeInfinity;
125
126#define SK_FloatNaN                 (*SkTCast<const float*>(&gIEEENotANumber))
127#define SK_FloatInfinity            (*SkTCast<const float*>(&gIEEEInfinity))
128#define SK_FloatNegativeInfinity    (*SkTCast<const float*>(&gIEEENegativeInfinity))
129
130static inline float sk_float_rsqrt_portable(float x) {
131    // Get initial estimate.
132    int i = *SkTCast<int*>(&x);
133    i = 0x5F1FFFF9 - (i>>1);
134    float estimate = *SkTCast<float*>(&i);
135
136    // One step of Newton's method to refine.
137    const float estimate_sq = estimate*estimate;
138    estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
139    return estimate;
140}
141
142// Fast, approximate inverse square root.
143// Compare to name-brand "1.0f / sk_float_sqrt(x)".  Should be around 10x faster on SSE, 2x on NEON.
144static inline float sk_float_rsqrt(float x) {
145// We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
146// it at compile time.  This is going to be too fast to productively hide behind a function pointer.
147//
148// We do one step of Newton's method to refine the estimates in the NEON and portable paths.  No
149// refinement is faster, but very innacurate.  Two steps is more accurate, but slower than 1/sqrt.
150//
151// Optimized constants in the portable path courtesy of http://rrrola.wz.cz/inv_sqrt.html
152#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
153    return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
154#elif defined(SK_ARM_HAS_NEON)
155    // Get initial estimate.
156    const float32x2_t xx = vdup_n_f32(x);  // Clever readers will note we're doing everything 2x.
157    float32x2_t estimate = vrsqrte_f32(xx);
158
159    // One step of Newton's method to refine.
160    const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
161    estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
162    return vget_lane_f32(estimate, 0);  // 1 will work fine too; the answer's in both places.
163#else
164    return sk_float_rsqrt_portable(x);
165#endif
166}
167
168// This is the number of significant digits we can print in a string such that when we read that
169// string back we get the floating point number we expect.  The minimum value C requires is 6, but
170// most compilers support 9
171#ifdef FLT_DECIMAL_DIG
172#define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG
173#else
174#define SK_FLT_DECIMAL_DIG 9
175#endif
176
177#endif
178