3 * Copyright 2006 The Android Open Source Project
5 * Use of this source code is governed by a BSD-style license that can be
6 * found in the LICENSE file.
10 #ifndef SkFloatingPoint_DEFINED
11 #define SkFloatingPoint_DEFINED
19 #if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
23 #include "SkFloatBits.h"
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
28 static inline float sk_float_pow(float base, float exp) {
29 return powf(base, exp);
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 #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);
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);
43 // Visual studio prior to 13 only has 'double _copysign(double, double)'.
44 #elif defined(_MSC_VER)
45 return (float)_copysign(x, y);
47 // Otherwise convert to bits and extract sign.
49 int32_t xbits = SkFloat2Bits(x);
50 int32_t ybits = SkFloat2Bits(y);
51 return SkBits2Float((xbits & 0x7FFFFFFF) | (ybits & 0x80000000));
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)
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))
80 #define sk_float_acos(x) acosf(x)
81 #define sk_float_asin(x) asinf(x)
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)
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);
98 #define sk_float_isfinite(x) isfinite(x)
99 #define sk_float_isnan(x) isnan(x)
100 #define sk_float_isinf(x) isinf(x)
103 #define sk_double_isnan(a) sk_float_isnan(a)
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)
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)
115 extern const uint32_t gIEEENotANumber;
116 extern const uint32_t gIEEEInfinity;
117 extern const uint32_t gIEEENegativeInfinity;
119 #define SK_FloatNaN (*SkTCast<const float*>(&gIEEENotANumber))
120 #define SK_FloatInfinity (*SkTCast<const float*>(&gIEEEInfinity))
121 #define SK_FloatNegativeInfinity (*SkTCast<const float*>(&gIEEENegativeInfinity))
124 #include <xmmintrin.h>
125 #elif defined(SK_ARM_HAS_NEON)
126 #include <arm_neon.h>
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.
131 static 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.
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.
139 _mm_store_ss(&result, _mm_rsqrt_ss(_mm_set_ss(x)));
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);
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.
151 // Get initial estimate.
152 int i = *SkTCast<int*>(&x);
153 i = 0x5f3759df - (i>>1);
154 float estimate = *SkTCast<float*>(&i);
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);