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#define SK_BUILD_WITH_CLANG_CL (defined(_MSC_VER) && defined(__clang__))
36#if (!SK_BUILD_WITH_CLANG_CL && __cplusplus >= 201103L) || (defined(_MSC_VER) && _MSC_VER >= 1800)
37    return copysign(x, y);
38
39// Posix has demanded 'float copysignf(float, float)' (from C99) since Issue 6.
40#elif defined(_POSIX_VERSION) && _POSIX_VERSION >= 200112L
41    return copysignf(x, y);
42
43// Visual studio prior to 13 only has 'double _copysign(double, double)'.
44#elif defined(_MSC_VER)
45    return (float)_copysign(x, y);
46
47// Otherwise convert to bits and extract sign.
48#else
49    int32_t xbits = SkFloat2Bits(x);
50    int32_t ybits = SkFloat2Bits(y);
51    return SkBits2Float((xbits & 0x7FFFFFFF) | (ybits & 0x80000000));
52#endif
53}
54
55#ifdef SK_BUILD_FOR_WINCE
56    #define sk_float_sqrt(x)        (float)::sqrt(x)
57    #define sk_float_sin(x)         (float)::sin(x)
58    #define sk_float_cos(x)         (float)::cos(x)
59    #define sk_float_tan(x)         (float)::tan(x)
60    #define sk_float_acos(x)        (float)::acos(x)
61    #define sk_float_asin(x)        (float)::asin(x)
62    #define sk_float_atan2(y,x)     (float)::atan2(y,x)
63    #define sk_float_abs(x)         (float)::fabs(x)
64    #define sk_float_mod(x,y)       (float)::fmod(x,y)
65    #define sk_float_exp(x)         (float)::exp(x)
66    #define sk_float_log(x)         (float)::log(x)
67    #define sk_float_floor(x)       (float)::floor(x)
68    #define sk_float_ceil(x)        (float)::ceil(x)
69#else
70    #define sk_float_sqrt(x)        sqrtf(x)
71    #define sk_float_sin(x)         sinf(x)
72    #define sk_float_cos(x)         cosf(x)
73    #define sk_float_tan(x)         tanf(x)
74    #define sk_float_floor(x)       floorf(x)
75    #define sk_float_ceil(x)        ceilf(x)
76#ifdef SK_BUILD_FOR_MAC
77    #define sk_float_acos(x)        static_cast<float>(acos(x))
78    #define sk_float_asin(x)        static_cast<float>(asin(x))
79#else
80    #define sk_float_acos(x)        acosf(x)
81    #define sk_float_asin(x)        asinf(x)
82#endif
83    #define sk_float_atan2(y,x)     atan2f(y,x)
84    #define sk_float_abs(x)         fabsf(x)
85    #define sk_float_mod(x,y)       fmodf(x,y)
86    #define sk_float_exp(x)         expf(x)
87    #define sk_float_log(x)         logf(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
115extern const uint32_t gIEEENotANumber;
116extern const uint32_t gIEEEInfinity;
117extern const uint32_t gIEEENegativeInfinity;
118
119#define SK_FloatNaN                 (*SkTCast<const float*>(&gIEEENotANumber))
120#define SK_FloatInfinity            (*SkTCast<const float*>(&gIEEEInfinity))
121#define SK_FloatNegativeInfinity    (*SkTCast<const float*>(&gIEEENegativeInfinity))
122
123#if defined(__SSE__)
124#include <xmmintrin.h>
125#elif defined(SK_ARM_HAS_NEON)
126#include <arm_neon.h>
127#endif
128
129// Fast, approximate inverse square root.
130// Compare to name-brand "1.0f / sk_float_sqrt(x)".  Should be around 10x faster on SSE, 2x on NEON.
131static inline float sk_float_rsqrt(const float x) {
132// We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
133// it at compile time.  This is going to be too fast to productively hide behind a function pointer.
134//
135// We do one step of Newton's method to refine the estimates in the NEON and null paths.  No
136// refinement is faster, but very innacurate.  Two steps is more accurate, but slower than 1/sqrt.
137#if defined(__SSE__)
138    float result;
139    _mm_store_ss(&result, _mm_rsqrt_ss(_mm_set_ss(x)));
140    return result;
141#elif defined(SK_ARM_HAS_NEON)
142    // Get initial estimate.
143    const float32x2_t xx = vdup_n_f32(x);  // Clever readers will note we're doing everything 2x.
144    float32x2_t estimate = vrsqrte_f32(xx);
145
146    // One step of Newton's method to refine.
147    const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
148    estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
149    return vget_lane_f32(estimate, 0);  // 1 will work fine too; the answer's in both places.
150#else
151    // Get initial estimate.
152    int i = *SkTCast<int*>(&x);
153    i = 0x5f3759df - (i>>1);
154    float estimate = *SkTCast<float*>(&i);
155
156    // One step of Newton's method to refine.
157    const float estimate_sq = estimate*estimate;
158    estimate *= (1.5f-0.5f*x*estimate_sq);
159    return estimate;
160#endif
161}
162
163#endif
164