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 #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 (float)_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)
sk_float_isinf(float 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
113 extern const uint32_t gIEEENotANumber;
114 extern const uint32_t gIEEEInfinity;
115 extern 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.
sk_float_rsqrt(const float x)129 static 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