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| 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*>(&gIEEENegativeInfini
ty)) | |
| 129 | |
| 130 // We forward declare this to break an #include cycle. | |
| 131 // (SkScalar -> SkFloatingPoint -> SkOpts.h -> SkXfermode -> SkColor -> SkScalar
) | |
| 132 namespace SkOpts { extern float (*rsqrt)(float); } | |
| 133 | |
| 134 // Fast, approximate inverse square root. | |
| 135 // Compare to name-brand "1.0f / sk_float_sqrt(x)". Should be around 10x faster
on SSE, 2x on NEON. | |
| 136 static inline float sk_float_rsqrt(const float x) { | |
| 137 // We want all this inlined, so we'll inline SIMD and just take the hit when we
don't know we've got | |
| 138 // it at compile time. This is going to be too fast to productively hide behind
a function pointer. | |
| 139 // | |
| 140 // We do one step of Newton's method to refine the estimates in the NEON and nul
l paths. No | |
| 141 // refinement is faster, but very innacurate. Two steps is more accurate, but s
lower than 1/sqrt. | |
| 142 // | |
| 143 // Optimized constants in the null path courtesy of http://rrrola.wz.cz/inv_sqrt
.html | |
| 144 #if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1 | |
| 145 return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x))); | |
| 146 #elif defined(SK_ARM_HAS_NEON) | |
| 147 // Get initial estimate. | |
| 148 const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doi
ng everything 2x. | |
| 149 float32x2_t estimate = vrsqrte_f32(xx); | |
| 150 | |
| 151 // One step of Newton's method to refine. | |
| 152 const float32x2_t estimate_sq = vmul_f32(estimate, estimate); | |
| 153 estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq)); | |
| 154 return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in
both places. | |
| 155 #else | |
| 156 // Perhaps runtime-detected NEON, or a portable fallback. | |
| 157 return SkOpts::rsqrt(x); | |
| 158 #endif | |
| 159 } | |
| 160 | |
| 161 // This is the number of significant digits we can print in a string such that w
hen we read that | |
| 162 // string back we get the floating point number we expect. The minimum value C
requires is 6, but | |
| 163 // most compilers support 9 | |
| 164 #ifdef FLT_DECIMAL_DIG | |
| 165 #define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG | |
| 166 #else | |
| 167 #define SK_FLT_DECIMAL_DIG 9 | |
| 168 #endif | |
| 169 | |
| 170 #endif | |
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