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281 lines
9.6 KiB
281 lines
9.6 KiB
/*
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* Copyright 2006 The Android Open Source Project
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#ifndef SkFloatingPoint_DEFINED
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#define SkFloatingPoint_DEFINED
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#include "include/core/SkTypes.h"
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#include "include/private/SkFloatBits.h"
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#include "include/private/SkSafe_math.h"
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#include <float.h>
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#include <math.h>
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#include <cmath>
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#include <cstring>
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#include <limits>
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#if defined(SK_LEGACY_FLOAT_RSQRT)
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#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
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#include <xmmintrin.h>
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#elif defined(SK_ARM_HAS_NEON)
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#include <arm_neon.h>
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#endif
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#endif
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// For _POSIX_VERSION
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#if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
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#include <unistd.h>
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#endif
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constexpr float SK_FloatSqrt2 = 1.41421356f;
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constexpr float SK_FloatPI = 3.14159265f;
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constexpr double SK_DoublePI = 3.14159265358979323846264338327950288;
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// C++98 cmath std::pow seems to be the earliest portable way to get float pow.
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// However, on Linux including cmath undefines isfinite.
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// http://gcc.gnu.org/bugzilla/show_bug.cgi?id=14608
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static inline float sk_float_pow(float base, float exp) {
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return powf(base, exp);
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}
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#define sk_float_sqrt(x) sqrtf(x)
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#define sk_float_sin(x) sinf(x)
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#define sk_float_cos(x) cosf(x)
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#define sk_float_tan(x) tanf(x)
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#define sk_float_floor(x) floorf(x)
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#define sk_float_ceil(x) ceilf(x)
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#define sk_float_trunc(x) truncf(x)
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#ifdef SK_BUILD_FOR_MAC
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# define sk_float_acos(x) static_cast<float>(acos(x))
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# define sk_float_asin(x) static_cast<float>(asin(x))
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#else
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# define sk_float_acos(x) acosf(x)
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# define sk_float_asin(x) asinf(x)
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#endif
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#define sk_float_atan2(y,x) atan2f(y,x)
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#define sk_float_abs(x) fabsf(x)
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#define sk_float_copysign(x, y) copysignf(x, y)
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#define sk_float_mod(x,y) fmodf(x,y)
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#define sk_float_exp(x) expf(x)
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#define sk_float_log(x) logf(x)
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constexpr float sk_float_degrees_to_radians(float degrees) {
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return degrees * (SK_FloatPI / 180);
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}
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constexpr float sk_float_radians_to_degrees(float radians) {
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return radians * (180 / SK_FloatPI);
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}
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#define sk_float_round(x) sk_float_floor((x) + 0.5f)
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// can't find log2f on android, but maybe that just a tool bug?
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#ifdef SK_BUILD_FOR_ANDROID
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static inline float sk_float_log2(float x) {
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const double inv_ln_2 = 1.44269504088896;
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return (float)(log(x) * inv_ln_2);
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}
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#else
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#define sk_float_log2(x) log2f(x)
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#endif
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static inline bool sk_float_isfinite(float x) {
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return SkFloatBits_IsFinite(SkFloat2Bits(x));
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}
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static inline bool sk_floats_are_finite(float a, float b) {
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return sk_float_isfinite(a) && sk_float_isfinite(b);
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}
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static inline bool sk_floats_are_finite(const float array[], int count) {
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float prod = 0;
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for (int i = 0; i < count; ++i) {
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prod *= array[i];
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}
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// At this point, prod will either be NaN or 0
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return prod == 0; // if prod is NaN, this check will return false
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}
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static inline bool sk_float_isinf(float x) {
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return SkFloatBits_IsInf(SkFloat2Bits(x));
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}
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static inline bool sk_float_isnan(float x) {
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return !(x == x);
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}
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#define sk_double_isnan(a) sk_float_isnan(a)
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#define SK_MaxS32FitsInFloat 2147483520
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#define SK_MinS32FitsInFloat -SK_MaxS32FitsInFloat
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#define SK_MaxS64FitsInFloat (SK_MaxS64 >> (63-24) << (63-24)) // 0x7fffff8000000000
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#define SK_MinS64FitsInFloat -SK_MaxS64FitsInFloat
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/**
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* Return the closest int for the given float. Returns SK_MaxS32FitsInFloat for NaN.
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*/
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static inline int sk_float_saturate2int(float x) {
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x = x < SK_MaxS32FitsInFloat ? x : SK_MaxS32FitsInFloat;
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x = x > SK_MinS32FitsInFloat ? x : SK_MinS32FitsInFloat;
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return (int)x;
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}
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/**
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* Return the closest int for the given double. Returns SK_MaxS32 for NaN.
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*/
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static inline int sk_double_saturate2int(double x) {
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x = x < SK_MaxS32 ? x : SK_MaxS32;
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x = x > SK_MinS32 ? x : SK_MinS32;
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return (int)x;
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}
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/**
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* Return the closest int64_t for the given float. Returns SK_MaxS64FitsInFloat for NaN.
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*/
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static inline int64_t sk_float_saturate2int64(float x) {
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x = x < SK_MaxS64FitsInFloat ? x : SK_MaxS64FitsInFloat;
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x = x > SK_MinS64FitsInFloat ? x : SK_MinS64FitsInFloat;
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return (int64_t)x;
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}
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#define sk_float_floor2int(x) sk_float_saturate2int(sk_float_floor(x))
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#define sk_float_round2int(x) sk_float_saturate2int(sk_float_floor((x) + 0.5f))
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#define sk_float_ceil2int(x) sk_float_saturate2int(sk_float_ceil(x))
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#define sk_float_floor2int_no_saturate(x) (int)sk_float_floor(x)
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#define sk_float_round2int_no_saturate(x) (int)sk_float_floor((x) + 0.5f)
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#define sk_float_ceil2int_no_saturate(x) (int)sk_float_ceil(x)
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#define sk_double_floor(x) floor(x)
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#define sk_double_round(x) floor((x) + 0.5)
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#define sk_double_ceil(x) ceil(x)
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#define sk_double_floor2int(x) (int)floor(x)
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#define sk_double_round2int(x) (int)floor((x) + 0.5)
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#define sk_double_ceil2int(x) (int)ceil(x)
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// Cast double to float, ignoring any warning about too-large finite values being cast to float.
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// Clang thinks this is undefined, but it's actually implementation defined to return either
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// the largest float or infinity (one of the two bracketing representable floats). Good enough!
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SK_ATTRIBUTE(no_sanitize("float-cast-overflow"))
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static inline float sk_double_to_float(double x) {
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return static_cast<float>(x);
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}
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#define SK_FloatNaN std::numeric_limits<float>::quiet_NaN()
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#define SK_FloatInfinity (+std::numeric_limits<float>::infinity())
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#define SK_FloatNegativeInfinity (-std::numeric_limits<float>::infinity())
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#define SK_DoubleNaN std::numeric_limits<double>::quiet_NaN()
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// Returns false if any of the floats are outside of [0...1]
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// Returns true if count is 0
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bool sk_floats_are_unit(const float array[], size_t count);
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#if defined(SK_LEGACY_FLOAT_RSQRT)
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static inline float sk_float_rsqrt_portable(float x) {
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// Get initial estimate.
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int i;
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memcpy(&i, &x, 4);
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i = 0x5F1FFFF9 - (i>>1);
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float estimate;
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memcpy(&estimate, &i, 4);
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// One step of Newton's method to refine.
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const float estimate_sq = estimate*estimate;
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estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
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return estimate;
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}
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// Fast, approximate inverse square root.
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// Compare to name-brand "1.0f / sk_float_sqrt(x)". Should be around 10x faster on SSE, 2x on NEON.
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static inline float sk_float_rsqrt(float x) {
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// We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
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// it at compile time. This is going to be too fast to productively hide behind a function pointer.
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//
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// We do one step of Newton's method to refine the estimates in the NEON and portable paths. No
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// refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt.
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//
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// Optimized constants in the portable path courtesy of http://rrrola.wz.cz/inv_sqrt.html
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#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
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return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
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#elif defined(SK_ARM_HAS_NEON)
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// Get initial estimate.
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const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doing everything 2x.
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float32x2_t estimate = vrsqrte_f32(xx);
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// One step of Newton's method to refine.
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const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
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estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
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return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in both places.
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#else
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return sk_float_rsqrt_portable(x);
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#endif
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}
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#else
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static inline float sk_float_rsqrt_portable(float x) { return 1.0f / sk_float_sqrt(x); }
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static inline float sk_float_rsqrt (float x) { return 1.0f / sk_float_sqrt(x); }
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#endif
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// Returns the log2 of the provided value, were that value to be rounded up to the next power of 2.
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// Returns 0 if value <= 0:
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// Never returns a negative number, even if value is NaN.
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//
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// sk_float_nextlog2((-inf..1]) -> 0
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// sk_float_nextlog2((1..2]) -> 1
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// sk_float_nextlog2((2..4]) -> 2
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// sk_float_nextlog2((4..8]) -> 3
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// ...
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static inline int sk_float_nextlog2(float x) {
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uint32_t bits = (uint32_t)SkFloat2Bits(x);
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bits += (1u << 23) - 1u; // Increment the exponent for non-powers-of-2.
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int exp = ((int32_t)bits >> 23) - 127;
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return exp & ~(exp >> 31); // Return 0 for negative or denormalized floats, and exponents < 0.
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}
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// This is the number of significant digits we can print in a string such that when we read that
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// string back we get the floating point number we expect. The minimum value C requires is 6, but
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// most compilers support 9
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#ifdef FLT_DECIMAL_DIG
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#define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG
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#else
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#define SK_FLT_DECIMAL_DIG 9
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#endif
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// IEEE defines how float divide behaves for non-finite values and zero-denoms, but C does not
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// so we have a helper that suppresses the possible undefined-behavior warnings.
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SK_ATTRIBUTE(no_sanitize("float-divide-by-zero"))
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static inline float sk_ieee_float_divide(float numer, float denom) {
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return numer / denom;
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}
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SK_ATTRIBUTE(no_sanitize("float-divide-by-zero"))
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static inline double sk_ieee_double_divide(double numer, double denom) {
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return numer / denom;
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}
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// While we clean up divide by zero, we'll replace places that do divide by zero with this TODO.
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static inline float sk_ieee_float_divide_TODO_IS_DIVIDE_BY_ZERO_SAFE_HERE(float n, float d) {
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return sk_ieee_float_divide(n,d);
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}
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static inline float sk_ieee_double_divide_TODO_IS_DIVIDE_BY_ZERO_SAFE_HERE(double n, double d) {
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return sk_ieee_double_divide(n,d);
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}
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static inline float sk_fmaf(float f, float m, float a) {
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#if defined(FP_FAST_FMA)
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return std::fmaf(f,m,a);
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#else
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return f*m+a;
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#endif
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}
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#endif
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