AIPS++ interface to <math.h>. You should include this file rather than <math.h> directly. It will be used to cover up any deficiencies in the system <math.h>.
This file does not include things like element-by-element array operations. See the ArrayMath functions for these functions.
This file includes the standard math library. Hence besides the functions defined here the following functions are also available.
Double sin(Double x) Sine function
Double cos(Double x) Cosine function
Double tan(Double x) Tangent function
Double asin(Double x) Inverse sine function
Double acos(Double x) Inverse cosine function
Double atan(Double x) Inverse tangent function
Double atan2(Double y, Double x) Four quandrant inverse tangent function
Double hypot(Double y, Double x) Euclidean distance sqrt(x*x+y*y)
Double sinh(Double x) Hyperbolic sine
Double cosh(Double x) Hyperbolic cosine
Double tanh(Double x) Hyperbolic tangent
Double acosh(Double x) Inverse hyperbolic sine
Double asinh(Double x) Inverse hyperbolic cosine
Double atanh(Double x) Inverse hyperbolic tangent
Double sqrt(Double x) Square root
Double cbrt(Double x) Cube root
Double pow(Double x, Double y) x raised to the power of y
Double exp(Double x) Exponental function
Double expm1(Double x) exp(x)-1. Use when x is small.
Double log(Double x) Natural logarithm
Double log10(Double x) Base ten logarithm
Double log1p(Double x) log(x+1). Use when x is small
Double j0(Double x) Bessel function of the first kind, zeroth order
Double j1(Double x) Bessel function of the first kind, first order
Double jn(Int n, Double x) Bessel function of the first kind nth order
Double y0(Double x) Bessel function of the second kind, zeroth order
Double y1(Double x) Bessel function of the second kind, first order
Double yn(Int n, Double x) Bessel function of the second kind, nth order
Double lgamma(Double x) Natural Log of the absolute value of the gamma
function
Double lgamma_r(Double x, Int* sign) Same as lgamma. The sign of the gamma
function is returned in the second argument.
Double erf(Double x) Error function
Double erfc(Double x) Complementary error function (1 - erf(x)).
Use for large x.
Double ceil(Double x) Returns the least integral value greater than or
equal to x
Double floor(Double x) Returns the least integral value than than or
equal to x
Double rint(Double x) Round to an integer using the current direction.
Double fabs(Double x) Absolute value of x
Double remainder(Double x, Double y) the remainder. x - y*Int(x/y)
Double fmod(Double x, Double y) As above. May differ by +/- y
Int isNaN(Double x) Returns 1 if x is a NaN, zero otherwise
Int ilogb(Double x) Unbiased exponent of x
Double logb(Double x) As above but returns floating point result
Double scalbn(Double x, Int n) x*2**n. Uses exponent manipulation.
Double scalb(Double x, Double n) x*2**n. As above but n is a Double
Double significand(Double x) Returns the fractional part of x
(between 1 and 2)
Double copysign(Double x, Double y) returns a value with the magnitude of
x and the sign bit of y.
Double nextafter(Double x, Double y) Returns the next machine representable
number after x in the direction specified by y
This file also includes the standard C library (stdlib.h). This is to obtain a definition of the following functions.
Int abs(Int x) absolute value function
Returns f1**f2. The Double precision version is defined in the standard library. But many compilers are not good enough to automatically do the type promotion. Hence these functions are explicitly defined.
Return the integer "less than" point (i.e. the one further from zero if "point" is negative.
Functions to get the max or min of two numbers.
Get the absolute value of uInt. Should already be defined for integers in <stdlib.h>. Define it for uInts so that certain compilers can resolve the ambiguity when used in a templated class.
Return the square of a value.
Return the cube of a value.
Functions to return whether a value is "relatively" near another. Returns tol > abs(val2 - val1)/max(abs(val1),(val2)). If tol <= 0, returns val1 == val2. If either val is 0.0, take care of area around the minimum number that can be represented.
The "allNear" versions are aliases for the normal "near" versions. They exist to make template functions that work for both arrays and scalars easier to write. These functions should be moved to ArrayMath.h
Functions to return whether a value is "absolutely" near another. Returns tol > abs(val2 - val1)
The "allNearAbs" versions are aliases for the normal "nearAbs" versions. They exist to make template functions that work for both arrays and scalars easier to write. These functions should be in ArrayMath.h
Functions to test if a floating point number is finite. It is if it is NaN nor infinity.
Functions to test for IEEE NaN's. The Float variant uses an in-line Macro examining the bit pattern (for portability and efficiency). The Double version invokes the IEEE function isnan found in ieeefp.h or math.h
Functions that return IEEE NaN's. The specific NaN returned has all bits set. This is 'quiet' NaN, and because the sign bit is set it may be considered a negative number (but NaN's are not numbers!).
Functions to test for IEEE Infinity's. Should work for positive or negative infinity.
Functions that return an IEEE Infinity, (positive infinity).