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 copysignf(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 #define sk_float_sqrt(x) sqrtf(x)
60 #define sk_float_sin(x) sinf(x)
61 #define sk_float_cos(x) cosf(x)
62 #define sk_float_tan(x) tanf(x)
63 #define sk_float_floor(x) floorf(x)
64 #define sk_float_ceil(x) ceilf(x)
65 #ifdef SK_BUILD_FOR_MAC
66 # define sk_float_acos(x) static_cast<float>(acos(x))
67 # define sk_float_asin(x) static_cast<float>(asin(x))
68 #else
69 # define sk_float_acos(x) acosf(x)
70 # define sk_float_asin(x) asinf(x)
71 #endif
72 #define sk_float_atan2(y,x) atan2f(y,x)
73 #define sk_float_abs(x) fabsf(x)
74 #define sk_float_mod(x,y) fmodf(x,y)
75 #define sk_float_exp(x) expf(x)
76 #define sk_float_log(x) logf(x)
77
78 #define sk_float_round(x) sk_float_floor((x) + 0.5f)
79
80 // can't find log2f on android, but maybe that just a tool bug?
81 #ifdef SK_BUILD_FOR_ANDROID
sk_float_log2(float x)82 static inline float sk_float_log2(float x) {
83 const double inv_ln_2 = 1.44269504088896;
84 return (float)(log(x) * inv_ln_2);
85 }
86 #else
87 #define sk_float_log2(x) log2f(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)
sk_float_isinf(float 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
115 #define sk_double_floor(x) floor(x)
116 #define sk_double_round(x) floor((x) + 0.5)
117 #define sk_double_ceil(x) ceil(x)
118 #define sk_double_floor2int(x) (int)floor(x)
119 #define sk_double_round2int(x) (int)floor((x) + 0.5f)
120 #define sk_double_ceil2int(x) (int)ceil(x)
121
122 extern const uint32_t gIEEENotANumber;
123 extern const uint32_t gIEEEInfinity;
124 extern const uint32_t gIEEENegativeInfinity;
125
126 #define SK_FloatNaN (*SkTCast<const float*>(&gIEEENotANumber))
127 #define SK_FloatInfinity (*SkTCast<const float*>(&gIEEEInfinity))
128 #define SK_FloatNegativeInfinity (*SkTCast<const float*>(&gIEEENegativeInfinity))
129
sk_float_rsqrt_portable(float x)130 static inline float sk_float_rsqrt_portable(float x) {
131 // Get initial estimate.
132 int i = *SkTCast<int*>(&x);
133 i = 0x5F1FFFF9 - (i>>1);
134 float estimate = *SkTCast<float*>(&i);
135
136 // One step of Newton's method to refine.
137 const float estimate_sq = estimate*estimate;
138 estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
139 return estimate;
140 }
141
142 // Fast, approximate inverse square root.
143 // 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)144 static inline float sk_float_rsqrt(float x) {
145 // We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
146 // it at compile time. This is going to be too fast to productively hide behind a function pointer.
147 //
148 // We do one step of Newton's method to refine the estimates in the NEON and portable paths. No
149 // refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt.
150 //
151 // Optimized constants in the portable path courtesy of http://rrrola.wz.cz/inv_sqrt.html
152 #if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
153 return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
154 #elif defined(SK_ARM_HAS_NEON)
155 // Get initial estimate.
156 const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doing everything 2x.
157 float32x2_t estimate = vrsqrte_f32(xx);
158
159 // One step of Newton's method to refine.
160 const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
161 estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
162 return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in both places.
163 #else
164 return sk_float_rsqrt_portable(x);
165 #endif
166 }
167
168 // This is the number of significant digits we can print in a string such that when we read that
169 // string back we get the floating point number we expect. The minimum value C requires is 6, but
170 // most compilers support 9
171 #ifdef FLT_DECIMAL_DIG
172 #define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG
173 #else
174 #define SK_FLT_DECIMAL_DIG 9
175 #endif
176
177 #endif
178