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 #include "SkSafe_math.h" 15 #include <float.h> 16 17 #if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1 18 #include <xmmintrin.h> 19 #elif defined(SK_ARM_HAS_NEON) 20 #include <arm_neon.h> 21 #endif 22 23 // For _POSIX_VERSION 24 #if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__)) 25 #include <unistd.h> 26 #endif 27 28 #include "SkFloatBits.h" 29 30 // C++98 cmath std::pow seems to be the earliest portable way to get float pow. 31 // However, on Linux including cmath undefines isfinite. 32 // http://gcc.gnu.org/bugzilla/show_bug.cgi?id=14608 33 static inline float sk_float_pow(float base, float exp) { 34 return powf(base, exp); 35 } 36 37 #define sk_float_sqrt(x) sqrtf(x) 38 #define sk_float_sin(x) sinf(x) 39 #define sk_float_cos(x) cosf(x) 40 #define sk_float_tan(x) tanf(x) 41 #define sk_float_floor(x) floorf(x) 42 #define sk_float_ceil(x) ceilf(x) 43 #define sk_float_trunc(x) truncf(x) 44 #ifdef SK_BUILD_FOR_MAC 45 # define sk_float_acos(x) static_cast<float>(acos(x)) 46 # define sk_float_asin(x) static_cast<float>(asin(x)) 47 #else 48 # define sk_float_acos(x) acosf(x) 49 # define sk_float_asin(x) asinf(x) 50 #endif 51 #define sk_float_atan2(y,x) atan2f(y,x) 52 #define sk_float_abs(x) fabsf(x) 53 #define sk_float_copysign(x, y) copysignf(x, y) 54 #define sk_float_mod(x,y) fmodf(x,y) 55 #define sk_float_exp(x) expf(x) 56 #define sk_float_log(x) logf(x) 57 58 #define sk_float_round(x) sk_float_floor((x) + 0.5f) 59 60 // can't find log2f on android, but maybe that just a tool bug? 61 #ifdef SK_BUILD_FOR_ANDROID 62 static inline float sk_float_log2(float x) { 63 const double inv_ln_2 = 1.44269504088896; 64 return (float)(log(x) * inv_ln_2); 65 } 66 #else 67 #define sk_float_log2(x) log2f(x) 68 #endif 69 70 #ifdef SK_BUILD_FOR_WIN 71 #define sk_float_isfinite(x) _finite(x) 72 #define sk_float_isnan(x) _isnan(x) 73 static inline int sk_float_isinf(float x) { 74 int32_t bits = SkFloat2Bits(x); 75 return (bits << 1) == (0xFF << 24); 76 } 77 #else 78 #define sk_float_isfinite(x) isfinite(x) 79 #define sk_float_isnan(x) isnan(x) 80 #define sk_float_isinf(x) isinf(x) 81 #endif 82 83 #define sk_double_isnan(a) sk_float_isnan(a) 84 85 #ifdef SK_USE_FLOATBITS 86 #define sk_float_floor2int(x) SkFloatToIntFloor(x) 87 #define sk_float_round2int(x) SkFloatToIntRound(x) 88 #define sk_float_ceil2int(x) SkFloatToIntCeil(x) 89 #else 90 #define sk_float_floor2int(x) (int)sk_float_floor(x) 91 #define sk_float_round2int(x) (int)sk_float_floor((x) + 0.5f) 92 #define sk_float_ceil2int(x) (int)sk_float_ceil(x) 93 #endif 94 95 #define sk_double_floor(x) floor(x) 96 #define sk_double_round(x) floor((x) + 0.5) 97 #define sk_double_ceil(x) ceil(x) 98 #define sk_double_floor2int(x) (int)floor(x) 99 #define sk_double_round2int(x) (int)floor((x) + 0.5f) 100 #define sk_double_ceil2int(x) (int)ceil(x) 101 102 static const uint32_t kIEEENotANumber = 0x7fffffff; 103 #define SK_FloatNaN (*SkTCast<const float*>(&kIEEENotANumber)) 104 #define SK_FloatInfinity (+(float)INFINITY) 105 #define SK_FloatNegativeInfinity (-(float)INFINITY) 106 107 static inline float sk_float_rsqrt_portable(float x) { 108 // Get initial estimate. 109 int i; 110 memcpy(&i, &x, 4); 111 i = 0x5F1FFFF9 - (i>>1); 112 float estimate; 113 memcpy(&estimate, &i, 4); 114 115 // One step of Newton's method to refine. 116 const float estimate_sq = estimate*estimate; 117 estimate *= 0.703952253f*(2.38924456f-x*estimate_sq); 118 return estimate; 119 } 120 121 // Fast, approximate inverse square root. 122 // Compare to name-brand "1.0f / sk_float_sqrt(x)". Should be around 10x faster on SSE, 2x on NEON. 123 static inline float sk_float_rsqrt(float x) { 124 // We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got 125 // it at compile time. This is going to be too fast to productively hide behind a function pointer. 126 // 127 // We do one step of Newton's method to refine the estimates in the NEON and portable paths. No 128 // refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt. 129 // 130 // Optimized constants in the portable path courtesy of http://rrrola.wz.cz/inv_sqrt.html 131 #if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1 132 return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x))); 133 #elif defined(SK_ARM_HAS_NEON) 134 // Get initial estimate. 135 const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doing everything 2x. 136 float32x2_t estimate = vrsqrte_f32(xx); 137 138 // One step of Newton's method to refine. 139 const float32x2_t estimate_sq = vmul_f32(estimate, estimate); 140 estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq)); 141 return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in both places. 142 #else 143 return sk_float_rsqrt_portable(x); 144 #endif 145 } 146 147 // This is the number of significant digits we can print in a string such that when we read that 148 // string back we get the floating point number we expect. The minimum value C requires is 6, but 149 // most compilers support 9 150 #ifdef FLT_DECIMAL_DIG 151 #define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG 152 #else 153 #define SK_FLT_DECIMAL_DIG 9 154 #endif 155 156 #endif 157
