SkFloatingPoint.h revision d3fbd34099a530b5415c95b1f2f8149ac417b9b3 
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#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1800)
35    return copysign(x, y);
36
37// Posix has demanded 'float copysignf(float, float)' (from C99) since Issue 6.
38#elif defined(_POSIX_VERSION) && _POSIX_VERSION >= 200112L
39    return copysignf(x, y);
40
41// Visual studio prior to 13 only has 'double _copysign(double, double)'.
42#elif defined(_MSC_VER)
43    return _copysign(x, y);
44
45// Otherwise convert to bits and extract sign.
46#else
47    int32_t xbits = SkFloat2Bits(x);
48    int32_t ybits = SkFloat2Bits(y);
49    return SkBits2Float((xbits & 0x7FFFFFFF) | (ybits & 0x80000000));
50#endif
51}
52
53#ifdef SK_BUILD_FOR_WINCE
54    #define sk_float_sqrt(x)        (float)::sqrt(x)
55    #define sk_float_sin(x)         (float)::sin(x)
56    #define sk_float_cos(x)         (float)::cos(x)
57    #define sk_float_tan(x)         (float)::tan(x)
58    #define sk_float_acos(x)        (float)::acos(x)
59    #define sk_float_asin(x)        (float)::asin(x)
60    #define sk_float_atan2(y,x)     (float)::atan2(y,x)
61    #define sk_float_abs(x)         (float)::fabs(x)
62    #define sk_float_mod(x,y)       (float)::fmod(x,y)
63    #define sk_float_exp(x)         (float)::exp(x)
64    #define sk_float_log(x)         (float)::log(x)
65    #define sk_float_floor(x)       (float)::floor(x)
66    #define sk_float_ceil(x)        (float)::ceil(x)
67#else
68    #define sk_float_sqrt(x)        sqrtf(x)
69    #define sk_float_sin(x)         sinf(x)
70    #define sk_float_cos(x)         cosf(x)
71    #define sk_float_tan(x)         tanf(x)
72    #define sk_float_floor(x)       floorf(x)
73    #define sk_float_ceil(x)        ceilf(x)
74#ifdef SK_BUILD_FOR_MAC
75    #define sk_float_acos(x)        static_cast<float>(acos(x))
76    #define sk_float_asin(x)        static_cast<float>(asin(x))
77#else
78    #define sk_float_acos(x)        acosf(x)
79    #define sk_float_asin(x)        asinf(x)
80#endif
81    #define sk_float_atan2(y,x)     atan2f(y,x)
82    #define sk_float_abs(x)         fabsf(x)
83    #define sk_float_mod(x,y)       fmodf(x,y)
84    #define sk_float_exp(x)         expf(x)
85    #define sk_float_log(x)         logf(x)
86#endif
87
88#ifdef SK_BUILD_FOR_WIN
89    #define sk_float_isfinite(x)    _finite(x)
90    #define sk_float_isnan(x)       _isnan(x)
91    static inline int sk_float_isinf(float x) {
92        int32_t bits = SkFloat2Bits(x);
93        return (bits << 1) == (0xFF << 24);
94    }
95#else
96    #define sk_float_isfinite(x)    isfinite(x)
97    #define sk_float_isnan(x)       isnan(x)
98    #define sk_float_isinf(x)       isinf(x)
99#endif
100
101#define sk_double_isnan(a)          sk_float_isnan(a)
102
103#ifdef SK_USE_FLOATBITS
104    #define sk_float_floor2int(x)   SkFloatToIntFloor(x)
105    #define sk_float_round2int(x)   SkFloatToIntRound(x)
106    #define sk_float_ceil2int(x)    SkFloatToIntCeil(x)
107#else
108    #define sk_float_floor2int(x)   (int)sk_float_floor(x)
109    #define sk_float_round2int(x)   (int)sk_float_floor((x) + 0.5f)
110    #define sk_float_ceil2int(x)    (int)sk_float_ceil(x)
111#endif
112
113extern const uint32_t gIEEENotANumber;
114extern const uint32_t gIEEEInfinity;
115extern const uint32_t gIEEENegativeInfinity;
116
117#define SK_FloatNaN                 (*SkTCast<const float*>(&gIEEENotANumber))
118#define SK_FloatInfinity            (*SkTCast<const float*>(&gIEEEInfinity))
119#define SK_FloatNegativeInfinity    (*SkTCast<const float*>(&gIEEENegativeInfinity))
120
121#if defined(__SSE__)
122#include <xmmintrin.h>
123#elif defined(__ARM_NEON__)
124#include <arm_neon.h>
125#endif
126
127// Fast, approximate inverse square root.
128// Compare to name-brand "1.0f / sk_float_sqrt(x)".  Should be around 10x faster on SSE, 2x on NEON.
129static inline float sk_float_rsqrt(const float x) {
130// We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
131// it at compile time.  This is going to be too fast to productively hide behind a function pointer.
132//
133// We do one step of Newton's method to refine the estimates in the NEON and null paths.  No
134// refinement is faster, but very innacurate.  Two steps is more accurate, but slower than 1/sqrt.
135#if defined(__SSE__)
136    float result;
137    _mm_store_ss(&result, _mm_rsqrt_ss(_mm_set_ss(x)));
138    return result;
139#elif defined(__ARM_NEON__)
140    // Get initial estimate.
141    const float32x2_t xx = vdup_n_f32(x);  // Clever readers will note we're doing everything 2x.
142    float32x2_t estimate = vrsqrte_f32(xx);
143
144    // One step of Newton's method to refine.
145    const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
146    estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
147    return vget_lane_f32(estimate, 0);  // 1 will work fine too; the answer's in both places.
148#else
149    // Get initial estimate.
150    int i = *SkTCast<int*>(&x);
151    i = 0x5f3759df - (i>>1);
152    float estimate = *SkTCast<float*>(&i);
153
154    // One step of Newton's method to refine.
155    const float estimate_sq = estimate*estimate;
156    estimate *= (1.5f-0.5f*x*estimate_sq);
157    return estimate;
158#endif
159}
160
161#endif
162