qlibs::ffmath Namespace Reference

Namespace for the Fast floating-point math library. More...

Classes
struct	numbers
	Provides several mathematical constants as single-precision floating-point numbers. More...

Enumerations
enum class	classification {   classification::FFP_ZERO , classification::FFP_SUBNORMAL , classification::FFP_NORMAL , classification::FFP_INFINITE ,   classification::FFP_NAN }
	Enum with the possible categorizations of a 32-bit floating-point number. More...

Functions
bool	isEqual (const float a, const float b, const float tol=1.175494351e-38F) noexcept
	Determines if the parameters given as floating-point values are approximately equal.
float	getInf (void)
	Returns positive infinity inf as a 32-bit floating point number.
float	getNan (void)
	Returns Not a Number ( NaN ) nan as a 32-bit floating point number.
classification	classify (const float f)
	Categorizes the floating-point number x. This function determines whether its argument is a normal floating-point number, or one of several special categories of values, including NaN (not a number), infinity, subnormal floating-point values or zero. To determine what category the argument belongs to, compare the return value with the any of the following number classification macros:
template<typename T , typename... Args>
T	Max (const T &first, const Args &... args)
	Finds the maximum value among the provided arguments.
template<typename T , typename... Args>
T	Min (const T &first, const Args &... args)
	Finds the minimum value among the provided arguments.
bool	isNan (const float x)
	Determine if x is Not-A-Number NaN.
bool	isInf (const float x)
	Determine if x is Infinity.
bool	isFinite (const float x)
	Determines if the given floating point number x has finite value i.e. it is normal, subnormal or zero, but not infinite or NaN.
bool	isNormal (const float x)
	Determines if the given floating point number x is normal, i.e. is neither zero, subnormal, infinite, or NaN.
float	copysign (float mag, float sgn)
	Composes a floating point value with the magnitude of mag and the sign of sgn.
float	sign (float x)
	Computes the sign function ( signum function).
float	absf (float x)
	Computes the absolute value of a floating point value x.
float	recip (float x)
	Computes the multiplicative inverse or reciprocal for the value x, denoted by 1/x or x^(−1)
float	sqrt (float x)
	Computes the square-root of x.
float	rSqrt (float x)
	Computes the reciprocal square-root of x denoted as 1/sqrt(x)
float	cbrt (float x)
	Computes the cubic-root of x.
float	rCbrt (float x)
	Computes the reciprocal cubic-root of x denoted as 1/cbrt(x)
float	rounding (float x)
	Computes the nearest integer value to x (in floating-point format), rounding halfway cases away from zero.
float	floor (float x)
	Computes the largest integer value not greater than x.
float	ceil (float x)
	Computes the smallest integer value not less than x.
float	trunc (float x)
	Computes the nearest integer not greater in magnitude than x.
float	frac (float x)
	Obtain the fractional part of x.
float	rem (float x, float y)
	Computes the floating point remainder after division of x by y, where x is the dividend and y is the divisor. This function is often called the remainder operation, which can be expressed as r=a-(b*trunc(a/b)) . This function follows the convention that rem(x,0) is nan.
float	mod (float x, float y)
	Computes the floating point remainder after division of x by y, where x is the dividend and y is the divisor. This function is often called the modulo operation, which can be expressed as b=a-m*floor(a/m) . This function follows the convention that mod(x,0) returns x.
float	sin (float x)
	Computes the sine of x (measured in radians).
float	cos (float x)
	Computes the cosine of x (measured in radians).
float	tan (float x)
	Computes the tangent of x (measured in radians).
float	asin (float x)
	Computes the principal value of the arc sine of x.
float	acos (float x)
	Computes the principal value of the arc cosine of x.
float	atan (float x)
	Computes the principal value of the arc tangent of x.
float	atan2 (float y, float x)
	Computes the arc tangent of y/x using the signs of arguments to determine the correct quadrant.
float	exp2 (float x)
	Computes 2 raised to the given power x.
float	log2 (float x)
	Computes the base 2 logarithm of x.
float	exp (float x)
	Computes the e ( Euler's number, 2.7182818 ) raised to the given power x.
float	expm1 (float x)
	Returns e raised to the given power minus one e^x-1 power x.
float	exp10 (float x)
	Computes the value of 10 raised to the power of x.
float	log (float x)
	Computes the natural (base e) logarithm of x.
float	log1p (float x)
	Computes the natural (base e) logarithm of 1 plus the given number x ln(1+x) .
float	log10 (float x)
	Computes the common (base-10) logarithm of x.
float	pow (float b, float e)
	Computes the value of b raised to the power e.
float	sinh (float x)
	Computes hyperbolic sine of x.
float	cosh (float x)
	Computes hyperbolic cosine of x.
float	tanh (float x)
	Computes hyperbolic tangent of x.
float	asinh (float x)
	Computes the inverse hyperbolic sine of x.
float	acosh (float x)
	Computes the inverse hyperbolic cosine of x.
float	atanh (float x)
	Computes the inverse hyperbolic tangent of x.
float	wrapToPi (float x)
	Wraps angle x, in radians, to the interval [−pi, pi] such that pi maps to pi and −pi maps to −pi. In general, odd, positive multiples of pi map to pi and odd, negative multiples of pi map to −pi.
float	wrapTo2Pi (float x)
	Wraps angle x, in radians, to the interval [0, 2*pi] such that 0 maps to 0 and 2*pi and 2*pi maps to 2*pi. In general, positive multiples of 2*pi map to 2*pi and negative multiples of 2*pi map to 0.
float	wrapTo180 (float x)
	Wraps angle x, in degrees, to the interval [–180, 180] such that 180 maps to 180 and –180 maps to –180. In general, odd, positive multiples of 180 map to 180 and odd, negative multiples of 180 map to –180.
float	wrapTo360 (float x)
	Wraps angle x, in degrees, to the interval [0, 360] such that 0 maps to 0 and 360 maps to 360. In general, positive multiples of 360 map to 360 and negative multiples of 360 map to zero.
float	midpoint (float a, float b)
	Computes the midpoint of the floating-points a and b.
float	lerp (float a, float b, float t)
	Computes the linear interpolation between a and b, if the parameter t is inside [0, 1] (the linear extrapolation otherwise), i.e. the result of a+t*(b-a) with accounting for floating-point calculation imprecision.
float	map (const float x, const float xMin, const float xMax, const float yMin, const float yMax) noexcept
	Scales the given input x in value range given by xMin and xMax to value range specified by the yMin and yMax.
real_t	normalize (const float x, const float xMin, const float xMax) noexcept
	Normalize the given input x in value range given by xMin and xMax to value range between 0 and 1.
bool	inRangeCoerce (float &x, const float lowerL, const float upperL) noexcept
	Determines if the value pointed by x falls within a range specified by the upper limit and lower limit inputs and coerces the value to fall within the range.
bool	inPolygon (const float x, const float y, const float *const px, const float *const py, const size_t p) noexcept
	Determines if the point at ( x, y ) is inside the polygon given by the set of points on px and py.
bool	inCircle (const float x, const float y, const float cx, const float cy, const float r) noexcept
	Determines if the point at ( x, y) is inside the circle with radius r located at cx and cy.
float	erf (float x)
	Computes the error function of x.
float	erfc (float x)
	Computes the complementary error function of x.
float	rexp (float x, int32_t *pw2)
	Decomposes given floating point value x into a normalized fraction and an integral power of two.
float	ldexp (float x, int32_t pw2)
	Multiplies a floating point value x by the number 2 raised to the pw2 power.
float	hypot (float x, float y)
	Computes the square root of the sum of the squares of x and y, without undue overflow or underflow at intermediate stages of the computation.
float	nextAfter (float x, float y)
	Returns the next representable value of x in the direction of y. If x equals to y, y is returned.
float	tgamma (float x)
	Computes the gamma function of x.
float	lgamma (float x)
	Computes the natural logarithm of the absolute value of the gamma function of x.
float	factorial (float x)
	Return the factorial of the integer part of x.
float	assoc_laguerre (size_t n, size_t m, float x)
	Computes the associated Laguerre polynomials of the degree n, order m, and argument x.
float	assoc_legendre (size_t n, size_t m, float x)
	Computes the associated Legendre polynomials of the degree n, order m, and argument x.
float	beta (float x, float y)
	Computes the Beta function of x and y.
float	comp_ellint_1 (float k)
	Computes the complete elliptic integral of the first kind of k.
float	comp_ellint_2 (float k)
	Computes the complete elliptic integral of the second kind of k.
float	comp_ellint_3 (float k, float nu)
	Computes the complete elliptic integral of the third kind of k and nu.
float	ellint_1 (float k, float phi)
	Computes the incomplete elliptic integral of the first kind of k and phi.
float	ellint_2 (float k, float phi)
	Computes the incomplete elliptic integral of the second kind of k and phi.
float	ellint_3 (float k, float nu, float phi)
	Computes the incomplete elliptic integral of the third kind of k, nu and phi.
float	expint (float num)
	Computes the Exponential integral of num.
float	hermite (size_t n, float x)
	Computes the (physicist's) Hermite polynomials of the degree n and argument x.
float	laguerre (size_t n, float x)
	Computes the non-associated Laguerre polynomials of the degree n, and argument x.
float	legendre (size_t n, float x)
	Computes the unassociated Legendre polynomials of the degree n, and argument x.
float	riemann_zeta (float s)
	Computes the Riemann zeta function of s.
float	sph_bessel (size_t n, float x)
	Computes the spherical Bessel function of the first kind n, and x.
float	sph_neumann (size_t n, float x)
	Computes the spherical Bessel function of the second kind also known as the spherical Neumann function of n and x.
float	cyl_bessel_i (float nu, float x)
	Computes the regular modified cylindrical Bessel function of nu and x.
float	cyl_bessel_j (float nu, float x)
	Computes the cylindrical Bessel function of the first kind of nu and x.
float	cyl_bessel_k (float nu, float x)
	Computes the irregular modified cylindrical Bessel function (also known as modified Bessel function of the second kind) of nu and x.
float	cyl_neumann (float nu, float x)
	Computes the cylindrical Neumann function ( also known as Bessel function of the second kind or Weber function) of nu and x.
float	sph_legendre (size_t l, size_t m, float theta)
	1-3) Computes the spherical associated Legendre function of degree l, order m, and polar angle theta

Variables
constexpr float	FFP_E
	The base of natural logarithms ( e ) given as a single-precision floating-point number.
constexpr float	FFP_LOG2E
	The base 2 logarithm of e ( log_2 e ) given as a single-precision floating-point number.
constexpr float	FFP_LOG10E
	The base 10 logarithm of e ( log_10 e ) given as a single-precision floating-point number.
constexpr float	FFP_LN2
	The natural logarithm of 2 ( ln 2 ) given as a single-precision floating-point number.
constexpr float	FFP_LN10
	The natural logarithm of 10 ( ln 10 ) given as a single-precision floating-point number.
constexpr float	FFP_PI
	The circumference of a circle with diameter 1, ( π ) given as a single-precision floating-point number.
constexpr float	FFP_2PI
	Twice circumference of a circle with diameter 1, ( 2π ) given as a single-precision floating-point number.
constexpr float	FFP_PI_2
	Half of π ( π/2 ) given as a single-precision floating-point number.
constexpr float	FFP_PI_4
	A quarter of π ( π/4 ) given as a single-precision floating-point number.
constexpr float	FFP_1_PI
	The inverse of π ( 1/π ) given as a single-precision floating-point number.
constexpr float	FFP_2_PI
	Twice the inverse of π ( 2/π ) given as a single-precision floating-point number.
constexpr float	FFP_1_SQRTPI
	The inverse of the square root of π ( 1/√π ) given as a single-precision floating-point number.
constexpr float	FFP_2_SQRTPI
	Twice the inverse of the square root of π ( 1/√π ) given as a single-precision floating-point number.
constexpr float	FFP_SQRT2
	The square root of 2 ( √2 ) given as a single-precision floating-point number.
constexpr float	FFP_SQRT3
	The square root of 3 ( √3 ) given as a single-precision floating-point number.
constexpr float	FFP_SQRT1_2
	The inverse of square root of 2 ( 1/√2 ) given as a single-precision floating-point number.
constexpr float	FFP_SQRT1_3
	The inverse of square root of 3 ( 1/√3 ) given as a single-precision floating-point number.
constexpr float	FFP_LN_SQRT_2PI
	The natural logarithm of the square root of 2π given as a single-precision floating-point number.
constexpr float	FFP_GAMMA_E
	Constant Euler-Mascheroni given as a single-precision floating-point number.
constexpr float	FFP_PHI
	The golden ratio, (1+√5)/2 given as a single-precision floating-point number.
constexpr float	FFP_RADIAN
	Radian, value of ( 180/π ) given as a single-precision floating-point number.
constexpr float	FFP_LOG10_2
	The base 10 logarithm of 2 ( log_10 2 ) given as a single-precision floating-point number.
constexpr float	FFP_LN_PI
	The natural logarithm of π ( ln(π) ) given as a single-precision floating-point number.

Detailed Description

Namespace for the Fast floating-point math library.