#include <algorithm>
#include <cmath>
#include <cstring>
#include <limits>
#include <typeinfo>
#include <type_traits>
#include <OpenImageIO/Imath.h>
#include <OpenImageIO/span.h>
#include <OpenImageIO/dassert.h>
#include <OpenImageIO/oiioversion.h>
#include <OpenImageIO/platform.h>
#include <OpenImageIO/simd.h>

Include dependency graph for fmath.h:

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Classes
struct	big_enough_float< T >

struct	big_enough_float< int >

struct	big_enough_float< unsigned int >

struct	big_enough_float< int64_t >

struct	big_enough_float< uint64_t >

struct	big_enough_float< double >

struct	DataProxy< I, E >

struct	ConstDataProxy< I, E >

struct	DataArrayProxy< I, E >

struct	ConstDataArrayProxy< I, E >

class	EightBitConverter< T >

Macros
#define	OIIO_FMATH_H 1

#define	OIIO_FMATH_SIMD_FRIENDLY 0

#define	M_PI 3.14159265358979323846264338327950288

#define	M_PI_2 1.57079632679489661923132169163975144

#define	M_PI_4 0.785398163397448309615660845819875721

#define	M_TWO_PI (M_PI * 2.0)

#define	M_1_PI 0.318309886183790671537767526745028724

#define	M_2_PI 0.636619772367581343075535053490057448

#define	M_SQRT2 1.41421356237309504880168872420969808

#define	M_SQRT1_2 0.707106781186547524400844362104849039

#define	M_LN2 0.69314718055994530941723212145817656

#define	M_LN10 2.30258509299404568401799145468436421

#define	M_E 2.71828182845904523536028747135266250

#define	M_LOG2E 1.44269504088896340735992468100189214

#define	OIIO_FMATH_HAS_SAFE_FMOD 1

Functions
template<typename T >
OIIO_HOSTDEVICE OIIO_CONSTEXPR14 bool	ispow2 (T x) noexcept

OIIO_HOSTDEVICE OIIO_CONSTEXPR14 int	ceil2 (int x) noexcept

OIIO_HOSTDEVICE OIIO_CONSTEXPR14 int	floor2 (int x) noexcept

OIIO_HOSTDEVICE int	pow2roundup (int x)

OIIO_HOSTDEVICE int	pow2rounddown (int x)

template<typename V , typename M >
OIIO_HOSTDEVICE V	round_to_multiple (V value, M multiple)

template<typename T >
OIIO_HOSTDEVICE T	round_to_multiple_of_pow2 (T x, T m)

template<typename V , typename M >
OIIO_HOSTDEVICE V	round_down_to_multiple (V value, M multiple)

OIIO_HOSTDEVICE uint32_t	clamped_mult32 (uint32_t a, uint32_t b)

OIIO_HOSTDEVICE uint64_t	clamped_mult64 (uint64_t a, uint64_t b)

template<class T >
OIIO_NODISCARD OIIO_FORCEINLINE OIIO_HOSTDEVICE T	rotl (T x, int s) noexcept

OIIO_FORCEINLINE OIIO_HOSTDEVICE uint32_t	rotl32 (uint32_t x, int k)

OIIO_FORCEINLINE OIIO_HOSTDEVICE uint64_t	rotl64 (uint64_t x, int k)

template<class T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_mod (T a, T b)

template<class T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	clamp (const T &a, const T &low, const T &high)
	clamp a to bounds [low,high]. More...

template<>
OIIO_FORCEINLINE simd::vfloat4	clamp (const simd::vfloat4 &a, const simd::vfloat4 &low, const simd::vfloat4 &high)

template<>
OIIO_FORCEINLINE simd::vfloat8	clamp (const simd::vfloat8 &a, const simd::vfloat8 &low, const simd::vfloat8 &high)

template<>
OIIO_FORCEINLINE simd::vfloat16	clamp (const simd::vfloat16 &a, const simd::vfloat16 &low, const simd::vfloat16 &high)

template<>
OIIO_FORCEINLINE simd::vint4	clamp (const simd::vint4 &a, const simd::vint4 &low, const simd::vint4 &high)

template<>
OIIO_FORCEINLINE simd::vint8	clamp (const simd::vint8 &a, const simd::vint8 &low, const simd::vint8 &high)

template<>
OIIO_FORCEINLINE simd::vint16	clamp (const simd::vint16 &a, const simd::vint16 &low, const simd::vint16 &high)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	madd (float a, float b, float c)
	Fused multiply and add: (a*b + c) More...

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	msub (float a, float b, float c)
	Fused multiply and subtract: (a*b - c) More...

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	nmadd (float a, float b, float c)
	Fused negative multiply and add: -(a*b) + c. More...

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	nmsub (float a, float b, float c)
	Negative fused multiply and subtract: -(a*b) - c. More...

template<class T , class Q >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	lerp (const T &v0, const T &v1, const Q &x)

template<class T , class Q >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	bilerp (const T &v0, const T &v1, const T &v2, const T &v3, const Q &s, const Q &t)

template<class T , class Q >
OIIO_HOSTDEVICE void	bilerp (const T v0, const T v1, const T v2, const T v3, Q s, Q t, int n, T *result)

template<class T , class Q >
OIIO_HOSTDEVICE void	bilerp_mad (const T v0, const T v1, const T v2, const T v3, Q s, Q t, Q scale, int n, T *result)

template<class T , class Q >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	trilerp (T v0, T v1, T v2, T v3, T v4, T v5, T v6, T v7, Q s, Q t, Q r)

template<class T , class Q >
OIIO_HOSTDEVICE void	trilerp (const T v0, const T v1, const T v2, const T v3, const T v4, const T v5, const T v6, const T v7, Q s, Q t, Q r, int n, T *result)

template<class T , class Q >
OIIO_HOSTDEVICE void	trilerp_mad (const T v0, const T v1, const T v2, const T v3, const T v4, const T v5, const T v6, const T v7, Q s, Q t, Q r, Q scale, int n, T *result)

template<typename T >
OIIO_HOSTDEVICE void	evalBSplineWeights (T w[4], T fraction)

template<typename T >
OIIO_HOSTDEVICE void	evalBSplineWeightDerivs (T dw[4], T fraction)

template<class T >
OIIO_HOSTDEVICE void	bicubic_interp (const T *val, T s, T t, int n, T result)

OIIO_FORCEINLINE OIIO_HOSTDEVICE int	ifloor (float x)
	Return floor(x) cast to an int. More...

OIIO_HOSTDEVICE float	floorfrac (float x, int *xint)

simd::vfloat4	floorfrac (const simd::vfloat4 &x, simd::vint4 *xint)

simd::vfloat8	floorfrac (const simd::vfloat8 &x, simd::vint8 *xint)

simd::vfloat16	floorfrac (const simd::vfloat16 &x, simd::vint16 *xint)

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	radians (T deg)
	Convert degrees to radians. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	degrees (T rad)
	Convert radians to degrees. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	fast_neg (const T &x)

OIIO_HOSTDEVICE void	sincos (float x, float sine, float cosine)

OIIO_HOSTDEVICE void	sincos (double x, double sine, double cosine)

OIIO_HOSTDEVICE float	sign (float x)

template<typename IN_TYPE , typename OUT_TYPE >
OIIO_FORCEINLINE OIIO_HOSTDEVICE OUT_TYPE	bit_cast (const IN_TYPE &in)

OIIO_FORCEINLINE OIIO_HOSTDEVICE int	bitcast_to_int (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	bitcast_to_float (int x)

template<class T >
OIIO_HOSTDEVICE void	swap_endian (T *f, int len=1)

template<typename S , typename D , typename F >
OIIO_HOSTDEVICE D	scaled_conversion (const S &src, F scale, F min, F max)

template<typename S , typename D >
void	convert_type (const S src, D dst, size_t n, D _min, D _max)

template<>
void	convert_type< uint8_t, float > (const uint8_t src, float dst, size_t n, float, float)

template<>
void	convert_type< uint16_t, float > (const uint16_t src, float dst, size_t n, float, float)

template<>
void	convert_type< float, uint16_t > (const float src, uint16_t dst, size_t n, uint16_t, uint16_t)

template<>
void	convert_type< float, uint8_t > (const float src, uint8_t dst, size_t n, uint8_t, uint8_t)

template<typename S , typename D >
void	convert_type (const S src, D dst, size_t n)

template<typename S , typename D >
D	convert_type (const S &src)

template<unsigned int FROM_BITS, unsigned int TO_BITS>
OIIO_HOSTDEVICE unsigned int	bit_range_convert (unsigned int in)

OIIO_HOSTDEVICE unsigned int	bit_range_convert (unsigned int in, unsigned int FROM_BITS, unsigned int TO_BITS)

template<typename T >
void	bitstring_add_n_bits (T *&out, int &filled, uint32_t val, int n)

template<typename T >
void	bit_pack (cspan< T > data, void *out, int outbits)

template<typename T >
void	bit_unpack (int n, const unsigned char in, int inbits, T out)

OIIO_HOSTDEVICE void	float_to_rational (float f, unsigned int &num, unsigned int &den)

OIIO_HOSTDEVICE void	float_to_rational (float f, int &num, int &den)

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_sqrt (T x)
	Safe (clamping) sqrt: safe_sqrt(x<0) returns 0, not NaN. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_inversesqrt (T x)
	Safe (clamping) inverse sqrt: safe_inversesqrt(x<=0) returns 0. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_asin (T x)
	Safe (clamping) arcsine: clamp to the valid domain. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_acos (T x)
	Safe (clamping) arccosine: clamp to the valid domain. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_log2 (T x)
	Safe log2: clamp to valid domain. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_log (T x)
	Safe log: clamp to valid domain. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_log10 (T x)
	Safe log10: clamp to valid domain. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_logb (T x)
	Safe logb: clamp to valid domain. More...

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	safe_pow (T x, T y)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	safe_fmod (float a, float b)

OIIO_FORCEINLINE OIIO_HOSTDEVICE int	fast_rint (float x)

OIIO_FORCEINLINE simd::vint4	fast_rint (const simd::vfloat4 &x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_sin (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_cos (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE void	fast_sincos (float x, float sine, float cosine)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_tan (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_sinpi (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_cospi (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_acos (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_asin (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_atan (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_atan2 (float y, float x)

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	fast_log2 (const T &xval)

template<>
OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_log2 (const float &xval)

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	fast_log (const T &x)

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	fast_log10 (const T &x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_logb (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_log1p (float x)

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	fast_exp2 (const T &xval)

template<>
OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_exp2 (const float &xval)

template<typename T >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	fast_exp (const T &x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_correct_exp (float x)
	Faster float exp than is in libm, but still 100% accurate. More...

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_exp10 (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_expm1 (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_sinh (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_cosh (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_tanh (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_safe_pow (float x, float y)

template<typename T , typename U >
OIIO_FORCEINLINE OIIO_HOSTDEVICE T	fast_pow_pos (const T &x, const U &y)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_cbrt (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_erf (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_erfc (float x)

OIIO_FORCEINLINE OIIO_HOSTDEVICE float	fast_ierf (float x)

template<class T , class Func >
OIIO_HOSTDEVICE T	invert (Func &func, T y, T xmin=0.0, T xmax=1.0, int maxiters=32, T eps=1.0e-6, bool *brack=0)

OIIO_HOSTDEVICE float	interpolate_linear (float x, span_strided< const float > y)

Detailed Description

A variety of floating-point math helper routines (and, slight misnomer, some int stuff as well).

Definition in file fmath.h.

Macro Definition Documentation

#define M_1_PI 0.318309886183790671537767526745028724

Definition at line 102 of file fmath.h.

#define M_2_PI 0.636619772367581343075535053490057448

Definition at line 105 of file fmath.h.

#define M_E 2.71828182845904523536028747135266250

Definition at line 120 of file fmath.h.

#define M_LN10 2.30258509299404568401799145468436421

Definition at line 117 of file fmath.h.

#define M_LN2 0.69314718055994530941723212145817656

Definition at line 114 of file fmath.h.

#define M_LOG2E 1.44269504088896340735992468100189214

Definition at line 123 of file fmath.h.

#define M_PI 3.14159265358979323846264338327950288

Examples:: CVEX/cvexsample.C, SOP/SOP_BouncyAgent.C, SOP/SOP_DualStar.C, SOP/SOP_PointWave.C, and TS/TS_cosKernel.C.

Definition at line 90 of file fmath.h.

#define M_PI_2 1.57079632679489661923132169163975144

Definition at line 93 of file fmath.h.

#define M_PI_4 0.785398163397448309615660845819875721

Definition at line 96 of file fmath.h.

#define M_SQRT1_2 0.707106781186547524400844362104849039

Examples:: RAY/RAY_DemoSprite.C.

Definition at line 111 of file fmath.h.

#define M_SQRT2 1.41421356237309504880168872420969808

Definition at line 108 of file fmath.h.

#define M_TWO_PI (M_PI * 2.0)

Definition at line 99 of file fmath.h.

#define OIIO_FMATH_H 1

Definition at line 31 of file fmath.h.

#define OIIO_FMATH_HAS_SAFE_FMOD 1

Definition at line 1586 of file fmath.h.

#define OIIO_FMATH_SIMD_FRIENDLY 0

Occasionally there may be a tradeoff where the best/fastest implementation of a math function in an ordinary scalar context does things that prevent autovectorization (or OMP pragma vectorization) of a loop containing that operation, and the only way to make it SIMD friendly slows it down as a scalar op.

By default, we always prefer doing it as correctly and quickly as possible in scalar mode, but if OIIO_FMATH_SIMD_FRIENDLY is defined to be nonzero, we prefer ensuring that the SIMD loops are as efficient as possible, even at the expense of scalar performance.

Because everything here consists of inline functions, and it doesn't really matter for OIIO internals themselves, this is primarily intended for the sake of 3rd party apps that happen to have OIIO as a dependency and use the fmath.h functions. Such a downstream dependency just needs to ensure that OIIO_FMATH_SIMD_FRIENDLY is defined to 1 prior to including fmath.h.

Definition at line 69 of file fmath.h.

Function Documentation

template<class T >

OIIO_HOSTDEVICE void bicubic_interp	(	const T **	val,
		T	s,
		T	t,
		int	n,
		T *	result
	)

inline

Bicubically interoplate arrays of pointers arranged in a 4x4 pattern with val[0] pointing to the data in the upper left corner, val[15] pointing to the lower right) at coordinates (s,t), storing the results in 'result'. These are all vectors, so do it for each of 'n' contiguous values (using the same s,t interpolants).

Definition at line 599 of file fmath.h.

template<class T , class Q >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T bilerp	(	const T &	v0,
		const T &	v1,
		const T &	v2,
		const T &	v3,
		const Q &	s,
		const Q &	t
	)

Bilinearly interoplate values v0-v3 (v0 upper left, v1 upper right, v2 lower left, v3 lower right) at coordinates (s,t) and return the result. This is a template, and so should work for any types.

Definition at line 462 of file fmath.h.

template<class T , class Q >

OIIO_HOSTDEVICE void bilerp	(	const T *	v0,
		const T *	v1,
		const T *	v2,
		const T *	v3,
		Q	s,
		Q	t,
		int	n,
		T *	result
	)

inline

Bilinearly interoplate arrays of values v0-v3 (v0 upper left, v1 upper right, v2 lower left, v3 lower right) at coordinates (s,t), storing the results in 'result'. These are all vectors, so do it for each of 'n' contiguous values (using the same s,t interpolants).

Definition at line 477 of file fmath.h.

template<class T , class Q >

OIIO_HOSTDEVICE void bilerp_mad	(	const T *	v0,
		const T *	v1,
		const T *	v2,
		const T *	v3,
		Q	s,
		Q	t,
		Q	scale,
		int	n,
		T *	result
	)

inline

Bilinearly interoplate arrays of values v0-v3 (v0 upper left, v1 upper right, v2 lower left, v3 lower right) at coordinates (s,t), SCALING the interpolated value by 'scale' and then ADDING to 'result'. These are all vectors, so do it for each of 'n' contiguous values (using the same s,t interpolants).

Definition at line 496 of file fmath.h.

template<typename IN_TYPE , typename OUT_TYPE >

OIIO_FORCEINLINE OIIO_HOSTDEVICE OUT_TYPE bit_cast ( const IN_TYPE & in )

Definition at line 754 of file fmath.h.

template<typename T >

void bit_pack	(	cspan< T >	data,
		void *	out,
		int	outbits
	)

inline

Pack values from T in[0..n-1] (where T is expected to be a uint8, uint16, or uint32, into successive raw outbits-bit pieces of out[], where outbits is expected to be less than the number of bits in a T.

Definition at line 1273 of file fmath.h.

template<unsigned int FROM_BITS, unsigned int TO_BITS>

OIIO_HOSTDEVICE unsigned int bit_range_convert ( unsigned int in )

inline

Helper function to convert channel values between different bit depths. Roughly equivalent to:

out = round (in * (pow (2, TO_BITS) - 1) / (pow (2, FROM_BITS) - 1));

but utilizes an integer math trick for speed. It can be proven that the absolute error of this method is less or equal to 1, with an average error (with respect to the entire domain) below 0.2.

It is assumed that the original value is a valid FROM_BITS integer, i.e. shifted fully to the right.

Definition at line 1194 of file fmath.h.

OIIO_HOSTDEVICE unsigned int bit_range_convert	(	unsigned int	in,
		unsigned int	FROM_BITS,
		unsigned int	TO_BITS
	)

inline

Definition at line 1207 of file fmath.h.

template<typename T >

void bit_unpack	(	int	n,
		const unsigned char *	in,
		int	inbits,
		T *	out
	)

inline

Decode n packed inbits-bits values from in[...] into normal uint8, uint16, or uint32 representation of T out[0..n-1]. In other words, each successive inbits of in (allowing spanning of byte boundaries) will be stored in a successive out[i].

Definition at line 1293 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float bitcast_to_float ( int x )

Definition at line 801 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE int bitcast_to_int ( float x )

Definition at line 798 of file fmath.h.

template<typename T >

void bitstring_add_n_bits	(	T *&	out,
		int &	filled,
		uint32_t	val,
		int	n
	)

inline

Append the n LSB bits of val into a bit sting T out[], where the filled MSB bits of *out are already filled in. Increment out and adjust filled as required. Type T should be uint8_t, uint16_t, or uint32_t.

Definition at line 1225 of file fmath.h.

OIIO_HOSTDEVICE OIIO_CONSTEXPR14 int ceil2 ( int x )

inlinenoexcept

Round up to next higher power of 2 (return x if it's already a power of 2).

Definition at line 153 of file fmath.h.

template<class T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T clamp	(	const T &	a,
		const T &	low,
		const T &	high
	)

clamp a to bounds [low,high].

Definition at line 340 of file fmath.h.

template<>

OIIO_FORCEINLINE simd::vfloat4 clamp	(	const simd::vfloat4 &	a,
		const simd::vfloat4 &	low,
		const simd::vfloat4 &	high
	)

Definition at line 366 of file fmath.h.

template<>

OIIO_FORCEINLINE simd::vfloat8 clamp	(	const simd::vfloat8 &	a,
		const simd::vfloat8 &	low,
		const simd::vfloat8 &	high
	)

Definition at line 372 of file fmath.h.

template<>

OIIO_FORCEINLINE simd::vfloat16 clamp	(	const simd::vfloat16 &	a,
		const simd::vfloat16 &	low,
		const simd::vfloat16 &	high
	)

Definition at line 378 of file fmath.h.

template<>

OIIO_FORCEINLINE simd::vint4 clamp	(	const simd::vint4 &	a,
		const simd::vint4 &	low,
		const simd::vint4 &	high
	)

Definition at line 385 of file fmath.h.

template<>

OIIO_FORCEINLINE simd::vint8 clamp	(	const simd::vint8 &	a,
		const simd::vint8 &	low,
		const simd::vint8 &	high
	)

Definition at line 391 of file fmath.h.

template<>

OIIO_FORCEINLINE simd::vint16 clamp	(	const simd::vint16 &	a,
		const simd::vint16 &	low,
		const simd::vint16 &	high
	)

Definition at line 397 of file fmath.h.

OIIO_HOSTDEVICE uint32_t clamped_mult32	(	uint32_t	a,
		uint32_t	b
	)

inline

Multiply two unsigned 32-bit ints safely, carefully checking for overflow, and clamping to uint32_t's maximum value.

Definition at line 240 of file fmath.h.

OIIO_HOSTDEVICE uint64_t clamped_mult64	(	uint64_t	a,
		uint64_t	b
	)

inline

Multiply two unsigned 64-bit ints safely, carefully checking for overflow, and clamping to uint64_t's maximum value.

Definition at line 252 of file fmath.h.

template<typename S , typename D >

void convert_type	(	const S *	src,
		D *	dst,
		size_t	n,
		D	_min,
		D	_max
	)

Convert n consecutive values from the type of S to the type of D. The conversion is not a simple cast, but correctly remaps the 0.0->1.0 range from and to the full positive range of integral types. Take a memcpy shortcut if both types are the same and no conversion is necessary. Optional arguments can give nonstandard quantizations.

Definition at line 945 of file fmath.h.

template<typename S , typename D >

void convert_type	(	const S *	src,
		D *	dst,
		size_t	n
	)

inline

Definition at line 1141 of file fmath.h.

template<typename S , typename D >

D convert_type ( const S & src )

inline

Convert a single value from the type of S to the type of D. The conversion is not a simple cast, but correctly remaps the 0.0->1.0 range from and to the full positive range of integral types. Take a copy shortcut if both types are the same and no conversion is necessary.

Definition at line 1158 of file fmath.h.

template<>

void convert_type< float, uint16_t >	(	const float *	src,
		uint16_t *	dst,
		size_t	n,
		uint16_t	,
		uint16_t
	)

inline

Definition at line 1073 of file fmath.h.

template<>

void convert_type< float, uint8_t >	(	const float *	src,
		uint8_t *	dst,
		size_t	n,
		uint8_t	,
		uint8_t
	)

inline

Definition at line 1094 of file fmath.h.

template<>

void convert_type< uint16_t, float >	(	const uint16_t *	src,
		float *	dst,
		size_t	n,
		float	,
		float
	)

inline

Definition at line 1029 of file fmath.h.

template<>

void convert_type< uint8_t, float >	(	const uint8_t *	src,
		float *	dst,
		size_t	n,
		float	,
		float
	)

inline

Definition at line 1011 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T degrees ( T rad )

Convert radians to degrees.

Definition at line 673 of file fmath.h.

template<typename T >

OIIO_HOSTDEVICE void evalBSplineWeightDerivs	(	T	dw[4],
		T	fraction
	)

inline

Evaluate B-spline derivative weights in w[0..3] for the given fraction. This is an important component of performing a cubic interpolation with derivatives.

Definition at line 581 of file fmath.h.

template<typename T >

OIIO_HOSTDEVICE void evalBSplineWeights	(	T	w[4],
		T	fraction
	)

inline

Evaluate B-spline weights in w[0..3] for the given fraction. This is an important component of performing a cubic interpolation.

Definition at line 567 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_acos ( float x )

Definition at line 1820 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_asin ( float x )

Definition at line 1835 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_atan ( float x )

Definition at line 1848 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_atan2	(	float	y,
		float	x
	)

Definition at line 1867 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_cbrt ( float x )

Definition at line 2221 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_correct_exp ( float x )

Faster float exp than is in libm, but still 100% accurate.

Definition at line 2100 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_cos ( float x )

Definition at line 1680 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_cosh ( float x )

Definition at line 2156 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_cospi ( float x )

Fast approximate cos(x*M_PI) with ~0.1% absolute error. Note that this is MUCH faster, but much less accurate than fast_cos.

Definition at line 1811 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_erf ( float x )

Definition at line 2238 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_erfc ( float x )

Definition at line 2262 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T fast_exp ( const T & x )

Definition at line 2085 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_exp10 ( float x )

Definition at line 2112 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T fast_exp2 ( const T & xval )

Definition at line 2014 of file fmath.h.

template<>

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_exp2 ( const float & xval )

Definition at line 2047 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_expm1 ( float x )

Definition at line 2121 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_ierf ( float x )

Definition at line 2274 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T fast_log ( const T & x )

Definition at line 1957 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T fast_log10 ( const T & x )

Definition at line 1972 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_log1p ( float x )

Definition at line 1998 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T fast_log2 ( const T & xval )

Definition at line 1906 of file fmath.h.

template<>

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_log2 ( const float & xval )

Definition at line 1927 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_logb ( float x )

Definition at line 1985 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T fast_neg ( const T & x )

Faster floating point negation, in cases where you aren't too picky about the difference between +0 and -0. (Courtesy of Alex Wells, Intel, via code in OSL.)

Beware: fast_neg(0.0f) returns 0.0f, NOT -0.0f. All other values, including -0.0 and +/- Inf, work identically to -x. For many use cases, that's fine. (When was the last time you wanted a -0.0f anyway?)

The reason it's faster is that -x (for float x) is implemented by compilers by xor'ing x against a bitmask that flips the sign bit, and that bitmask had to come from somewhere – memory! – which can be expensive, depending on whether/where it is in cache. But 0 - x generates a zero in a register (with xor, no memory access needed) and then subtracts, so that's sometimes faster because there is no memory read. This works for SIMD types as well!

It's also safe (though pointless) to use fast_neg for integer types, where both -x and 0-x are implemented as a neg instruction.

Definition at line 696 of file fmath.h.

template<typename T , typename U >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T fast_pow_pos	(	const T &	x,
		const U &	y
	)

Definition at line 2215 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE int fast_rint ( float x )

Round to nearest integer, returning as an int. Note that this differs from std::rint, which returns a float; it's more akin to std::lrint, which returns a long (int). Sorry for the naming confusion.

Definition at line 1630 of file fmath.h.

OIIO_FORCEINLINE simd::vint4 fast_rint ( const simd::vfloat4 & x )

Definition at line 1642 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_safe_pow	(	float	x,
		float	y
	)

Definition at line 2177 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_sin ( float x )

Definition at line 1648 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE void fast_sincos	(	float	x,
		float *	sine,
		float *	cosine
	)

Definition at line 1707 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_sinh ( float x )

Definition at line 2133 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_sinpi ( float x )

Fast, approximate sin(x*M_PI) with maximum absolute error of 0.000918954611. Adapted from http://devmaster.net/posts/9648/fast-and-accurate-sine-cosine#comment-76773 Note that this is MUCH faster, but much less accurate than fast_sin.

Definition at line 1773 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_tan ( float x )

Definition at line 1741 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float fast_tanh ( float x )

Definition at line 2166 of file fmath.h.

OIIO_HOSTDEVICE void float_to_rational	(	float	f,
		unsigned int &	num,
		unsigned int &	den
	)

inline

Simple conversion of a (presumably non-negative) float into a rational. This does not attempt to find the simplest fraction that approximates the float, for example 52.83 will simply return 5283/100. This does not attempt to gracefully handle floats that are out of range that could be easily int/int.

Definition at line 1432 of file fmath.h.

OIIO_HOSTDEVICE void float_to_rational	(	float	f,
		int &	num,
		int &	den
	)

inline

Simple conversion of a float into a rational. This does not attempt to find the simplest fraction that approximates the float, for example 52.83 will simply return 5283/100. This does not attempt to gracefully handle floats that are out of range that could be easily int/int.

Definition at line 1459 of file fmath.h.

OIIO_HOSTDEVICE OIIO_CONSTEXPR14 int floor2 ( int x )

inlinenoexcept

Round down to next lower power of 2 (return x if it's already a power of 2).

Definition at line 176 of file fmath.h.

OIIO_HOSTDEVICE float floorfrac	(	float	x,
		int *	xint
	)

inline

Return (x-floor(x)) and put (int)floor(x) in *xint. This is similar to the built-in modf, but returns a true int, always rounds down (compared to modf which rounds toward 0), and always returns frac >= 0 (comapred to modf which can return <0 if x<0).

Definition at line 630 of file fmath.h.

simd::vfloat4 floorfrac	(	const simd::vfloat4 &	x,
		simd::vint4 *	xint
	)

inline

Definition at line 645 of file fmath.h.

simd::vfloat8 floorfrac	(	const simd::vfloat8 &	x,
		simd::vint8 *	xint
	)

inline

Definition at line 651 of file fmath.h.

simd::vfloat16 floorfrac	(	const simd::vfloat16 &	x,
		simd::vint16 *	xint
	)

inline

Definition at line 657 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE int ifloor ( float x )

Return floor(x) cast to an int.

Definition at line 618 of file fmath.h.

OIIO_HOSTDEVICE float interpolate_linear	(	float	x,
		span_strided< const float >	y
	)

inline

Linearly interpolate a list of evenly-spaced knots y[0..len-1] with y[0] corresponding to the value at x==0.0 and y[len-1] corresponding to x==1.0.

Definition at line 2381 of file fmath.h.

template<class T , class Func >

OIIO_HOSTDEVICE T invert	(	Func &	func,
		T	y,
		T	xmin = `0.0`,
		T	xmax = `1.0`,
		int	maxiters = `32`,
		T	eps = `1.0e-6`,
		bool *	brack = `0`
	)

Solve for the x for which func(x) == y on the interval [xmin,xmax]. Use a maximum of maxiter iterations, and stop any time the remaining search interval or the function evaluations <= eps. If brack is non-NULL, set it to true if y is in [f(xmin), f(xmax)], otherwise false (in which case the caller should know that the results may be unreliable. Results are undefined if the function is not monotonic on that interval or if there are multiple roots in the interval (it may not converge, or may converge to any of the roots without telling you that there are more than one).

Definition at line 2329 of file fmath.h.

template<typename T >

OIIO_HOSTDEVICE OIIO_CONSTEXPR14 bool ispow2 ( T x )

inlinenoexcept

Quick test for whether an integer is a power of 2.

Definition at line 140 of file fmath.h.

template<class T , class Q >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T lerp	(	const T &	v0,
		const T &	v1,
		const Q &	x
	)

Linearly interpolate values v0-v1 at x: v0*(1-x) + v1*x. This is a template, and so should work for any types.

Definition at line 449 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float madd	(	float	a,
		float	b,
		float	c
	)

Fused multiply and add: (a*b + c)

Definition at line 413 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float msub	(	float	a,
		float	b,
		float	c
	)

Fused multiply and subtract: (a*b - c)

Definition at line 422 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float nmadd	(	float	a,
		float	b,
		float	c
	)

Fused negative multiply and add: -(a*b) + c.

Definition at line 430 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float nmsub	(	float	a,
		float	b,
		float	c
	)

Negative fused multiply and subtract: -(a*b) - c.

Definition at line 438 of file fmath.h.

OIIO_HOSTDEVICE int pow2rounddown ( int x )

inline

Definition at line 192 of file fmath.h.

OIIO_HOSTDEVICE int pow2roundup ( int x )

inline

Definition at line 191 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T radians ( T deg )

Convert degrees to radians.

Definition at line 669 of file fmath.h.

template<class T >

OIIO_NODISCARD OIIO_FORCEINLINE OIIO_HOSTDEVICE T rotl	(	T	x,
		int	s
	)

noexcept

Bitwise circular rotation left by s bits (for any unsigned integer type). For info on the C++20 std::rotl(), see http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p0553r4.html

Definition at line 273 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE uint32_t rotl32	(	uint32_t	x,
		int	k
	)

Definition at line 298 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE uint64_t rotl64	(	uint64_t	x,
		int	k
	)

Definition at line 308 of file fmath.h.

template<typename V , typename M >

OIIO_HOSTDEVICE V round_down_to_multiple	(	V	value,
		M	multiple
	)

inline

Round value down to a whole multiple of multiple. For example, round_down_to_multiple(10,10) == 10, round_down_to_multiple(17,10) == 10, and round_down_to_multiple(-17,10) == -20.

Definition at line 228 of file fmath.h.

template<typename V , typename M >

OIIO_HOSTDEVICE V round_to_multiple	(	V	value,
		M	multiple
	)

inline

Round value up to the next whole multiple. For example, round_to_multiple(10,10) == 10, round_to_multiple(17,10) == 20, and round_to_multiple(-17,10) == -10.

Definition at line 200 of file fmath.h.

template<typename T >

OIIO_HOSTDEVICE T round_to_multiple_of_pow2	(	T	x,
		T	m
	)

inline

Round up to the next whole multiple of m, for the special case where m is definitely a power of 2 (somewhat simpler than the more general round_to_multiple). This is a template that should work for any integer type.

Definition at line 215 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_acos ( T x )

Safe (clamping) arccosine: clamp to the valid domain.

Definition at line 1509 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_asin ( T x )

Safe (clamping) arcsine: clamp to the valid domain.

Definition at line 1501 of file fmath.h.

OIIO_FORCEINLINE OIIO_HOSTDEVICE float safe_fmod	(	float	a,
		float	b
	)

Safe fmod: guard against b==0.0 (in which case, return 0.0). Also, it seems that this is much faster than std::fmod!

Definition at line 1567 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_inversesqrt ( T x )

Safe (clamping) inverse sqrt: safe_inversesqrt(x<=0) returns 0.

Definition at line 1494 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_log ( T x )

Safe log: clamp to valid domain.

Definition at line 1527 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_log10 ( T x )

Safe log10: clamp to valid domain.

Definition at line 1536 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_log2 ( T x )

Safe log2: clamp to valid domain.

Definition at line 1518 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_logb ( T x )

Safe logb: clamp to valid domain.

Definition at line 1545 of file fmath.h.

template<class T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_mod	(	T	a,
		T	b
	)

Definition at line 318 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_pow	(	T	x,
		T	y
	)

Safe pow: clamp the domain so it never returns Inf or NaN or has divide by zero error.

Definition at line 1552 of file fmath.h.

template<typename T >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T safe_sqrt ( T x )

Safe (clamping) sqrt: safe_sqrt(x<0) returns 0, not NaN.

Definition at line 1488 of file fmath.h.

template<typename S , typename D , typename F >

OIIO_HOSTDEVICE D scaled_conversion	(	const S &	src,
		F	scale,
		F	min,
		F	max
	)

inline

Multiply src by scale, clamp to [min,max], and round to the nearest D (presumed to be integer). This is just a helper for the convert_type templates, it probably has no other use.

Definition at line 922 of file fmath.h.

OIIO_HOSTDEVICE float sign ( float x )

inline

Definition at line 732 of file fmath.h.

OIIO_HOSTDEVICE void sincos	(	float	x,
		float *	sine,
		float *	cosine
	)

inline

Definition at line 703 of file fmath.h.

OIIO_HOSTDEVICE void sincos	(	double	x,
		double *	sine,
		double *	cosine
	)

inline

Definition at line 717 of file fmath.h.

template<class T >

OIIO_HOSTDEVICE void swap_endian	(	T *	f,
		int	len = `1`
	)

inline

Change endian-ness of one or more data items that are each 2, 4, or 8 bytes. This should work for any of short, unsigned short, int, unsigned int, float, long long, pointers.

Definition at line 812 of file fmath.h.

template<class T , class Q >

OIIO_FORCEINLINE OIIO_HOSTDEVICE T trilerp	(	T	v0,
		T	v1,
		T	v2,
		T	v3,
		T	v4,
		T	v5,
		T	v6,
		T	v7,
		Q	s,
		Q	t,
		Q	r
	)

Trilinearly interoplate arrays of values v0-v7 (v0 upper left top, v1 upper right top, ...) at coordinates (s,t,r), and return the result. This is a template, and so should work for any types.

Definition at line 514 of file fmath.h.

template<class T , class Q >

OIIO_HOSTDEVICE void trilerp	(	const T *	v0,
		const T *	v1,
		const T *	v2,
		const T *	v3,
		const T *	v4,
		const T *	v5,
		const T *	v6,
		const T *	v7,
		Q	s,
		Q	t,
		Q	r,
		int	n,
		T *	result
	)

inline

Trilinearly interoplate arrays of values v0-v7 (v0 upper left top, v1 upper right top, ...) at coordinates (s,t,r), storing the results in 'result'. These are all vectors, so do it for each of 'n' contiguous values (using the same s,t,r interpolants).

Definition at line 532 of file fmath.h.

template<class T , class Q >

OIIO_HOSTDEVICE void trilerp_mad	(	const T *	v0,
		const T *	v1,
		const T *	v2,
		const T *	v3,
		const T *	v4,
		const T *	v5,
		const T *	v6,
		const T *	v7,
		Q	s,
		Q	t,
		Q	r,
		Q	scale,
		int	n,
		T *	result
	)

inline

Trilinearly interoplate arrays of values v0-v7 (v0 upper left top, v1 upper right top, ...) at coordinates (s,t,r), SCALING the interpolated value by 'scale' and then ADDING to 'result'. These are all vectors, so do it for each of 'n' contiguous values (using the same s,t,r interpolants).

Definition at line 553 of file fmath.h.

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