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* Copyright 2006 The Android Open Source Project
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
#ifndef SkFloatingPoint_DEFINED
#define SkFloatingPoint_DEFINED
#include "include/core/SkTypes.h"
#include "include/private/SkFloatBits.h"
#include "include/private/SkSafe_math.h"
#include <float.h>
#include <math.h>
#include <cmath>
#include <cstring>
#include <limits>
#include <xmmintrin.h>
#elif defined(SK_ARM_HAS_NEON)
#include <arm_neon.h>
#if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
#include <unistd.h>
constexpr float SK_FloatSqrt2 = 1.41421356f;
constexpr float SK_FloatPI = 3.14159265f;
constexpr double SK_DoublePI = 3.14159265358979323846264338327950288;
// C++98 cmath std::pow seems to be the earliest portable way to get float pow.
// However, on Linux including cmath undefines isfinite.
static inline float sk_float_pow(float base, float exp) {
return powf(base, exp);
#define sk_float_sqrt(x) sqrtf(x)
#define sk_float_sin(x) sinf(x)
#define sk_float_cos(x) cosf(x)
#define sk_float_tan(x) tanf(x)
#define sk_float_floor(x) floorf(x)
#define sk_float_ceil(x) ceilf(x)
#define sk_float_trunc(x) truncf(x)
# define sk_float_acos(x) static_cast<float>(acos(x))
# define sk_float_asin(x) static_cast<float>(asin(x))
# define sk_float_acos(x) acosf(x)
# define sk_float_asin(x) asinf(x)
#define sk_float_atan2(y,x) atan2f(y,x)
#define sk_float_abs(x) fabsf(x)
#define sk_float_copysign(x, y) copysignf(x, y)
#define sk_float_mod(x,y) fmodf(x,y)
#define sk_float_exp(x) expf(x)
#define sk_float_log(x) logf(x)
constexpr float sk_float_degrees_to_radians(float degrees) {
return degrees * (SK_FloatPI / 180);
constexpr float sk_float_radians_to_degrees(float radians) {
return radians * (180 / SK_FloatPI);
#define sk_float_round(x) sk_float_floor((x) + 0.5f)
// can't find log2f on android, but maybe that just a tool bug?
static inline float sk_float_log2(float x) {
const double inv_ln_2 = 1.44269504088896;
return (float)(log(x) * inv_ln_2);
#define sk_float_log2(x) log2f(x)
static inline bool sk_float_isfinite(float x) {
return SkFloatBits_IsFinite(SkFloat2Bits(x));
static inline bool sk_floats_are_finite(float a, float b) {
return sk_float_isfinite(a) && sk_float_isfinite(b);
static inline bool sk_floats_are_finite(const float array[], int count) {
float prod = 0;
for (int i = 0; i < count; ++i) {
prod *= array[i];
// At this point, prod will either be NaN or 0
return prod == 0; // if prod is NaN, this check will return false
static inline bool sk_float_isinf(float x) {
return SkFloatBits_IsInf(SkFloat2Bits(x));
static inline bool sk_float_isnan(float x) {
return !(x == x);
#define sk_double_isnan(a) sk_float_isnan(a)
#define SK_MaxS32FitsInFloat 2147483520
#define SK_MinS32FitsInFloat -SK_MaxS32FitsInFloat
#define SK_MaxS64FitsInFloat (SK_MaxS64 >> (63-24) << (63-24)) // 0x7fffff8000000000
#define SK_MinS64FitsInFloat -SK_MaxS64FitsInFloat
* Return the closest int for the given float. Returns SK_MaxS32FitsInFloat for NaN.
static inline int sk_float_saturate2int(float x) {
x = x < SK_MaxS32FitsInFloat ? x : SK_MaxS32FitsInFloat;
x = x > SK_MinS32FitsInFloat ? x : SK_MinS32FitsInFloat;
return (int)x;
* Return the closest int for the given double. Returns SK_MaxS32 for NaN.
static inline int sk_double_saturate2int(double x) {
x = x < SK_MaxS32 ? x : SK_MaxS32;
x = x > SK_MinS32 ? x : SK_MinS32;
return (int)x;
* Return the closest int64_t for the given float. Returns SK_MaxS64FitsInFloat for NaN.
static inline int64_t sk_float_saturate2int64(float x) {
x = x < SK_MaxS64FitsInFloat ? x : SK_MaxS64FitsInFloat;
x = x > SK_MinS64FitsInFloat ? x : SK_MinS64FitsInFloat;
return (int64_t)x;
#define sk_float_floor2int(x) sk_float_saturate2int(sk_float_floor(x))
#define sk_float_round2int(x) sk_float_saturate2int(sk_float_floor((x) + 0.5f))
#define sk_float_ceil2int(x) sk_float_saturate2int(sk_float_ceil(x))
#define sk_float_floor2int_no_saturate(x) (int)sk_float_floor(x)
#define sk_float_round2int_no_saturate(x) (int)sk_float_floor((x) + 0.5f)
#define sk_float_ceil2int_no_saturate(x) (int)sk_float_ceil(x)
#define sk_double_floor(x) floor(x)
#define sk_double_round(x) floor((x) + 0.5)
#define sk_double_ceil(x) ceil(x)
#define sk_double_floor2int(x) (int)floor(x)
#define sk_double_round2int(x) (int)floor((x) + 0.5)
#define sk_double_ceil2int(x) (int)ceil(x)
// Cast double to float, ignoring any warning about too-large finite values being cast to float.
// Clang thinks this is undefined, but it's actually implementation defined to return either
// the largest float or infinity (one of the two bracketing representable floats). Good enough!
static inline float sk_double_to_float(double x) {
return static_cast<float>(x);
#define SK_FloatNaN std::numeric_limits<float>::quiet_NaN()
#define SK_FloatInfinity (+std::numeric_limits<float>::infinity())
#define SK_FloatNegativeInfinity (-std::numeric_limits<float>::infinity())
#define SK_DoubleNaN std::numeric_limits<double>::quiet_NaN()
// Returns false if any of the floats are outside of [0...1]
// Returns true if count is 0
bool sk_floats_are_unit(const float array[], size_t count);
static inline float sk_float_rsqrt_portable(float x) {
// Get initial estimate.
int i;
memcpy(&i, &x, 4);
i = 0x5F1FFFF9 - (i>>1);
float estimate;
memcpy(&estimate, &i, 4);
// One step of Newton's method to refine.
const float estimate_sq = estimate*estimate;
estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
return estimate;
// Fast, approximate inverse square root.
// Compare to name-brand "1.0f / sk_float_sqrt(x)". Should be around 10x faster on SSE, 2x on NEON.
static inline float sk_float_rsqrt(float x) {
// We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
// it at compile time. This is going to be too fast to productively hide behind a function pointer.
// We do one step of Newton's method to refine the estimates in the NEON and portable paths. No
// refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt.
// Optimized constants in the portable path courtesy of
return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
#elif defined(SK_ARM_HAS_NEON)
// Get initial estimate.
const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doing everything 2x.
float32x2_t estimate = vrsqrte_f32(xx);
// One step of Newton's method to refine.
const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in both places.
return sk_float_rsqrt_portable(x);
// This is the number of significant digits we can print in a string such that when we read that
// string back we get the floating point number we expect. The minimum value C requires is 6, but
// most compilers support 9
// IEEE defines how float divide behaves for non-finite values and zero-denoms, but C does not
// so we have a helper that suppresses the possible undefined-behavior warnings.
static inline float sk_ieee_float_divide(float numer, float denom) {
return numer / denom;
static inline double sk_ieee_double_divide(double numer, double denom) {
return numer / denom;
// While we clean up divide by zero, we'll replace places that do divide by zero with this TODO.
static inline float sk_ieee_float_divide_TODO_IS_DIVIDE_BY_ZERO_SAFE_HERE(float n, float d) {
return sk_ieee_float_divide(n,d);
static inline float sk_ieee_double_divide_TODO_IS_DIVIDE_BY_ZERO_SAFE_HERE(double n, double d) {
return sk_ieee_double_divide(n,d);
static inline float sk_fmaf(float f, float m, float a) {
#if defined(FP_FAST_FMA)
return std::fmaf(f,m,a);
return f*m+a;