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 #include "SkSafe_math.h"
15 #include <float.h>
16
17 #if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
18 #include <xmmintrin.h>
19 #elif defined(SK_ARM_HAS_NEON)
20 #include <arm_neon.h>
21 #endif
22
23 // For _POSIX_VERSION
24 #if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
25 #include <unistd.h>
26 #endif
27
28 #include "SkFloatBits.h"
29
30 // C++98 cmath std::pow seems to be the earliest portable way to get float pow.
31 // However, on Linux including cmath undefines isfinite.
32 // http://gcc.gnu.org/bugzilla/show_bug.cgi?id=14608
sk_float_pow(float base,float exp)33 static inline float sk_float_pow(float base, float exp) {
34 return powf(base, exp);
35 }
36
37 #define sk_float_sqrt(x) sqrtf(x)
38 #define sk_float_sin(x) sinf(x)
39 #define sk_float_cos(x) cosf(x)
40 #define sk_float_tan(x) tanf(x)
41 #define sk_float_floor(x) floorf(x)
42 #define sk_float_ceil(x) ceilf(x)
43 #define sk_float_trunc(x) truncf(x)
44 #ifdef SK_BUILD_FOR_MAC
45 # define sk_float_acos(x) static_cast<float>(acos(x))
46 # define sk_float_asin(x) static_cast<float>(asin(x))
47 #else
48 # define sk_float_acos(x) acosf(x)
49 # define sk_float_asin(x) asinf(x)
50 #endif
51 #define sk_float_atan2(y,x) atan2f(y,x)
52 #define sk_float_abs(x) fabsf(x)
53 #define sk_float_copysign(x, y) copysignf(x, y)
54 #define sk_float_mod(x,y) fmodf(x,y)
55 #define sk_float_exp(x) expf(x)
56 #define sk_float_log(x) logf(x)
57
58 #define sk_float_round(x) sk_float_floor((x) + 0.5f)
59
60 // can't find log2f on android, but maybe that just a tool bug?
61 #ifdef SK_BUILD_FOR_ANDROID
sk_float_log2(float x)62 static inline float sk_float_log2(float x) {
63 const double inv_ln_2 = 1.44269504088896;
64 return (float)(log(x) * inv_ln_2);
65 }
66 #else
67 #define sk_float_log2(x) log2f(x)
68 #endif
69
70 #ifdef SK_BUILD_FOR_WIN
71 #define sk_float_isfinite(x) _finite(x)
72 #define sk_float_isnan(x) _isnan(x)
sk_float_isinf(float x)73 static inline int sk_float_isinf(float x) {
74 int32_t bits = SkFloat2Bits(x);
75 return (bits << 1) == (0xFF << 24);
76 }
77 #else
78 #define sk_float_isfinite(x) isfinite(x)
79 #define sk_float_isnan(x) isnan(x)
80 #define sk_float_isinf(x) isinf(x)
81 #endif
82
83 #define sk_double_isnan(a) sk_float_isnan(a)
84
85 #ifdef SK_USE_FLOATBITS
86 #define sk_float_floor2int(x) SkFloatToIntFloor(x)
87 #define sk_float_round2int(x) SkFloatToIntRound(x)
88 #define sk_float_ceil2int(x) SkFloatToIntCeil(x)
89 #else
90 #define sk_float_floor2int(x) (int)sk_float_floor(x)
91 #define sk_float_round2int(x) (int)sk_float_floor((x) + 0.5f)
92 #define sk_float_ceil2int(x) (int)sk_float_ceil(x)
93 #endif
94
95 #define sk_double_floor(x) floor(x)
96 #define sk_double_round(x) floor((x) + 0.5)
97 #define sk_double_ceil(x) ceil(x)
98 #define sk_double_floor2int(x) (int)floor(x)
99 #define sk_double_round2int(x) (int)floor((x) + 0.5f)
100 #define sk_double_ceil2int(x) (int)ceil(x)
101
102 static const uint32_t kIEEENotANumber = 0x7fffffff;
103 #define SK_FloatNaN (*SkTCast<const float*>(&kIEEENotANumber))
104 #define SK_FloatInfinity (+(float)INFINITY)
105 #define SK_FloatNegativeInfinity (-(float)INFINITY)
106
sk_float_rsqrt_portable(float x)107 static inline float sk_float_rsqrt_portable(float x) {
108 // Get initial estimate.
109 int i;
110 memcpy(&i, &x, 4);
111 i = 0x5F1FFFF9 - (i>>1);
112 float estimate;
113 memcpy(&estimate, &i, 4);
114
115 // One step of Newton's method to refine.
116 const float estimate_sq = estimate*estimate;
117 estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
118 return estimate;
119 }
120
121 // Fast, approximate inverse square root.
122 // Compare to name-brand "1.0f / sk_float_sqrt(x)". Should be around 10x faster on SSE, 2x on NEON.
sk_float_rsqrt(float x)123 static inline float sk_float_rsqrt(float x) {
124 // We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
125 // it at compile time. This is going to be too fast to productively hide behind a function pointer.
126 //
127 // We do one step of Newton's method to refine the estimates in the NEON and portable paths. No
128 // refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt.
129 //
130 // Optimized constants in the portable path courtesy of http://rrrola.wz.cz/inv_sqrt.html
131 #if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
132 return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
133 #elif defined(SK_ARM_HAS_NEON)
134 // Get initial estimate.
135 const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doing everything 2x.
136 float32x2_t estimate = vrsqrte_f32(xx);
137
138 // One step of Newton's method to refine.
139 const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
140 estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
141 return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in both places.
142 #else
143 return sk_float_rsqrt_portable(x);
144 #endif
145 }
146
147 // This is the number of significant digits we can print in a string such that when we read that
148 // string back we get the floating point number we expect. The minimum value C requires is 6, but
149 // most compilers support 9
150 #ifdef FLT_DECIMAL_DIG
151 #define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG
152 #else
153 #define SK_FLT_DECIMAL_DIG 9
154 #endif
155
156 #endif
157