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 28 static inline float sk_float_pow(float base, float exp) { 29 return powf(base, exp); 30 } 31 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) 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. 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
