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 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 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) 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)) 129 130 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. 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