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 // 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 copysign(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 #ifdef SK_BUILD_FOR_WINCE 60 #define sk_float_sqrt(x) (float)::sqrt(x) 61 #define sk_float_sin(x) (float)::sin(x) 62 #define sk_float_cos(x) (float)::cos(x) 63 #define sk_float_tan(x) (float)::tan(x) 64 #define sk_float_acos(x) (float)::acos(x) 65 #define sk_float_asin(x) (float)::asin(x) 66 #define sk_float_atan2(y,x) (float)::atan2(y,x) 67 #define sk_float_abs(x) (float)::fabs(x) 68 #define sk_float_mod(x,y) (float)::fmod(x,y) 69 #define sk_float_exp(x) (float)::exp(x) 70 #define sk_float_log(x) (float)::log(x) 71 #define sk_float_floor(x) (float)::floor(x) 72 #define sk_float_ceil(x) (float)::ceil(x) 73 #else 74 #define sk_float_sqrt(x) sqrtf(x) 75 #define sk_float_sin(x) sinf(x) 76 #define sk_float_cos(x) cosf(x) 77 #define sk_float_tan(x) tanf(x) 78 #define sk_float_floor(x) floorf(x) 79 #define sk_float_ceil(x) ceilf(x) 80 #ifdef SK_BUILD_FOR_MAC 81 #define sk_float_acos(x) static_cast<float>(acos(x)) 82 #define sk_float_asin(x) static_cast<float>(asin(x)) 83 #else 84 #define sk_float_acos(x) acosf(x) 85 #define sk_float_asin(x) asinf(x) 86 #endif 87 #define sk_float_atan2(y,x) atan2f(y,x) 88 #define sk_float_abs(x) fabsf(x) 89 #define sk_float_mod(x,y) fmodf(x,y) 90 #define sk_float_exp(x) expf(x) 91 #define sk_float_log(x) logf(x) 92 #endif 93 94 // can't find log2f on android, but maybe that just a tool bug? 95 #ifdef SK_BUILD_FOR_ANDROID 96 static inline float sk_float_log2(float x) { 97 const double inv_ln_2 = 1.44269504088896; 98 return (float)(log(x) * inv_ln_2); 99 } 100 #else 101 #define sk_float_log2(x) log2f(x) 102 #endif 103 104 #ifdef SK_BUILD_FOR_WIN 105 #define sk_float_isfinite(x) _finite(x) 106 #define sk_float_isnan(x) _isnan(x) 107 static inline int sk_float_isinf(float x) { 108 int32_t bits = SkFloat2Bits(x); 109 return (bits << 1) == (0xFF << 24); 110 } 111 #else 112 #define sk_float_isfinite(x) isfinite(x) 113 #define sk_float_isnan(x) isnan(x) 114 #define sk_float_isinf(x) isinf(x) 115 #endif 116 117 #define sk_double_isnan(a) sk_float_isnan(a) 118 119 #ifdef SK_USE_FLOATBITS 120 #define sk_float_floor2int(x) SkFloatToIntFloor(x) 121 #define sk_float_round2int(x) SkFloatToIntRound(x) 122 #define sk_float_ceil2int(x) SkFloatToIntCeil(x) 123 #else 124 #define sk_float_floor2int(x) (int)sk_float_floor(x) 125 #define sk_float_round2int(x) (int)sk_float_floor((x) + 0.5f) 126 #define sk_float_ceil2int(x) (int)sk_float_ceil(x) 127 #endif 128 129 #define sk_double_floor(x) floor(x) 130 #define sk_double_round(x) floor((x) + 0.5) 131 #define sk_double_ceil(x) ceil(x) 132 #define sk_double_floor2int(x) (int)floor(x) 133 #define sk_double_round2int(x) (int)floor((x) + 0.5f) 134 #define sk_double_ceil2int(x) (int)ceil(x) 135 136 extern const uint32_t gIEEENotANumber; 137 extern const uint32_t gIEEEInfinity; 138 extern const uint32_t gIEEENegativeInfinity; 139 140 #define SK_FloatNaN (*SkTCast<const float*>(&gIEEENotANumber)) 141 #define SK_FloatInfinity (*SkTCast<const float*>(&gIEEEInfinity)) 142 #define SK_FloatNegativeInfinity (*SkTCast<const float*>(&gIEEENegativeInfinity)) 143 144 #if defined(__SSE__) 145 #include <xmmintrin.h> 146 #elif defined(SK_ARM_HAS_NEON) 147 #include <arm_neon.h> 148 #endif 149 150 // Fast, approximate inverse square root. 151 // Compare to name-brand "1.0f / sk_float_sqrt(x)". Should be around 10x faster on SSE, 2x on NEON. 152 static inline float sk_float_rsqrt(const float x) { 153 // We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got 154 // it at compile time. This is going to be too fast to productively hide behind a function pointer. 155 // 156 // We do one step of Newton's method to refine the estimates in the NEON and null paths. No 157 // refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt. 158 #if defined(__SSE__) 159 float result; 160 _mm_store_ss(&result, _mm_rsqrt_ss(_mm_set_ss(x))); 161 return result; 162 #elif defined(SK_ARM_HAS_NEON) 163 // Get initial estimate. 164 const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doing everything 2x. 165 float32x2_t estimate = vrsqrte_f32(xx); 166 167 // One step of Newton's method to refine. 168 const float32x2_t estimate_sq = vmul_f32(estimate, estimate); 169 estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq)); 170 return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in both places. 171 #else 172 // Get initial estimate. 173 int i = *SkTCast<int*>(&x); 174 i = 0x5f3759df - (i>>1); 175 float estimate = *SkTCast<float*>(&i); 176 177 // One step of Newton's method to refine. 178 const float estimate_sq = estimate*estimate; 179 estimate *= (1.5f-0.5f*x*estimate_sq); 180 return estimate; 181 #endif 182 } 183 184 #endif 185
