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
sk_float_pow(float base,float exp)28 static inline float sk_float_pow(float base, float exp) {
29     return powf(base, exp);
30 }
31 
sk_float_copysign(float x,float y)32 static 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 copysign(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 #ifdef SK_BUILD_FOR_WINCE
60     #define sk_float_sqrt(x)        (float)::sqrt(x)
61     #define sk_float_sin(x)         (float)::sin(x)
62     #define sk_float_cos(x)         (float)::cos(x)
63     #define sk_float_tan(x)         (float)::tan(x)
64     #define sk_float_acos(x)        (float)::acos(x)
65     #define sk_float_asin(x)        (float)::asin(x)
66     #define sk_float_atan2(y,x)     (float)::atan2(y,x)
67     #define sk_float_abs(x)         (float)::fabs(x)
68     #define sk_float_mod(x,y)       (float)::fmod(x,y)
69     #define sk_float_exp(x)         (float)::exp(x)
70     #define sk_float_log(x)         (float)::log(x)
71     #define sk_float_floor(x)       (float)::floor(x)
72     #define sk_float_ceil(x)        (float)::ceil(x)
73 #else
74     #define sk_float_sqrt(x)        sqrtf(x)
75     #define sk_float_sin(x)         sinf(x)
76     #define sk_float_cos(x)         cosf(x)
77     #define sk_float_tan(x)         tanf(x)
78     #define sk_float_floor(x)       floorf(x)
79     #define sk_float_ceil(x)        ceilf(x)
80 #ifdef SK_BUILD_FOR_MAC
81     #define sk_float_acos(x)        static_cast<float>(acos(x))
82     #define sk_float_asin(x)        static_cast<float>(asin(x))
83 #else
84     #define sk_float_acos(x)        acosf(x)
85     #define sk_float_asin(x)        asinf(x)
86 #endif
87     #define sk_float_atan2(y,x)     atan2f(y,x)
88     #define sk_float_abs(x)         fabsf(x)
89     #define sk_float_mod(x,y)       fmodf(x,y)
90     #define sk_float_exp(x)         expf(x)
91     #define sk_float_log(x)         logf(x)
92 #endif
93 
94 // can't find log2f on android, but maybe that just a tool bug?
95 #ifdef SK_BUILD_FOR_ANDROID
sk_float_log2(float x)96     static inline float sk_float_log2(float x) {
97         const double inv_ln_2 = 1.44269504088896;
98         return (float)(log(x) * inv_ln_2);
99     }
100 #else
101     #define sk_float_log2(x)        log2f(x)
102 #endif
103 
104 #ifdef SK_BUILD_FOR_WIN
105     #define sk_float_isfinite(x)    _finite(x)
106     #define sk_float_isnan(x)       _isnan(x)
sk_float_isinf(float x)107     static inline int sk_float_isinf(float x) {
108         int32_t bits = SkFloat2Bits(x);
109         return (bits << 1) == (0xFF << 24);
110     }
111 #else
112     #define sk_float_isfinite(x)    isfinite(x)
113     #define sk_float_isnan(x)       isnan(x)
114     #define sk_float_isinf(x)       isinf(x)
115 #endif
116 
117 #define sk_double_isnan(a)          sk_float_isnan(a)
118 
119 #ifdef SK_USE_FLOATBITS
120     #define sk_float_floor2int(x)   SkFloatToIntFloor(x)
121     #define sk_float_round2int(x)   SkFloatToIntRound(x)
122     #define sk_float_ceil2int(x)    SkFloatToIntCeil(x)
123 #else
124     #define sk_float_floor2int(x)   (int)sk_float_floor(x)
125     #define sk_float_round2int(x)   (int)sk_float_floor((x) + 0.5f)
126     #define sk_float_ceil2int(x)    (int)sk_float_ceil(x)
127 #endif
128 
129 #define sk_double_floor(x)          floor(x)
130 #define sk_double_round(x)          floor((x) + 0.5)
131 #define sk_double_ceil(x)           ceil(x)
132 #define sk_double_floor2int(x)      (int)floor(x)
133 #define sk_double_round2int(x)      (int)floor((x) + 0.5f)
134 #define sk_double_ceil2int(x)       (int)ceil(x)
135 
136 extern const uint32_t gIEEENotANumber;
137 extern const uint32_t gIEEEInfinity;
138 extern const uint32_t gIEEENegativeInfinity;
139 
140 #define SK_FloatNaN                 (*SkTCast<const float*>(&gIEEENotANumber))
141 #define SK_FloatInfinity            (*SkTCast<const float*>(&gIEEEInfinity))
142 #define SK_FloatNegativeInfinity    (*SkTCast<const float*>(&gIEEENegativeInfinity))
143 
144 #if defined(__SSE__)
145 #include <xmmintrin.h>
146 #elif defined(SK_ARM_HAS_NEON)
147 #include <arm_neon.h>
148 #endif
149 
150 // Fast, approximate inverse square root.
151 // Compare to name-brand "1.0f / sk_float_sqrt(x)".  Should be around 10x faster on SSE, 2x on NEON.
sk_float_rsqrt(const float x)152 static inline float sk_float_rsqrt(const float x) {
153 // We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
154 // it at compile time.  This is going to be too fast to productively hide behind a function pointer.
155 //
156 // We do one step of Newton's method to refine the estimates in the NEON and null paths.  No
157 // refinement is faster, but very innacurate.  Two steps is more accurate, but slower than 1/sqrt.
158 #if defined(__SSE__)
159     float result;
160     _mm_store_ss(&result, _mm_rsqrt_ss(_mm_set_ss(x)));
161     return result;
162 #elif defined(SK_ARM_HAS_NEON)
163     // Get initial estimate.
164     const float32x2_t xx = vdup_n_f32(x);  // Clever readers will note we're doing everything 2x.
165     float32x2_t estimate = vrsqrte_f32(xx);
166 
167     // One step of Newton's method to refine.
168     const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
169     estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
170     return vget_lane_f32(estimate, 0);  // 1 will work fine too; the answer's in both places.
171 #else
172     // Get initial estimate.
173     int i = *SkTCast<int*>(&x);
174     i = 0x5f3759df - (i>>1);
175     float estimate = *SkTCast<float*>(&i);
176 
177     // One step of Newton's method to refine.
178     const float estimate_sq = estimate*estimate;
179     estimate *= (1.5f-0.5f*x*estimate_sq);
180     return estimate;
181 #endif
182 }
183 
184 #endif
185