Return first number with the sign of second number

x : float

The first number.

y : float

The second number whose sign is used.

Returns: float

The first number x with the sign of the second argument y.

LogRel(z) = log(1+z) with relative error accuracy near z = 0.

             June 1977 edition.   W. Fullerton, c3, Los Alamos Scientific Lab.
            
             series for alnr       on the interval -3.75000e-01 to  3.75000e-01
                                                    with weighted error   6.35e-32
                                                     log weighted error  31.20
                                           significant figures required  30.93
                                                decimal places required  32.01

x : float

The function argument.

Returns: float

LogRel(z) = log(1+z) with relative error accuracy near z = 0.

             June 1977 edition.   W. Fullerton, c3, Los Alamos Scientific Lab.
            
             series for alnr       on the interval -3.75000e-01 to  3.75000e-01
                                                    with weighted error   6.35e-32
                                                     log weighted error  31.20
                                           significant figures required  30.93
                                                decimal places required  32.01

x : float

The function argument.

bDebug : bool

If true, an exception will be thrown if errors occur, if false, double.NaN is returned in this case.

Returns: float

LogRel(z) = log(1+z) with relative error accuracy near z = 0.

             April 1977 version.  W. Fullerton, c3, Los Alamos Scientific Lab.
            
             let   rho = abs(z)  and
                   r**2 = abs(1+z)**2 = (1+x)**2 + y**2 = 1 + 2*x + rho**2 .
             now if rho is small we may evaluate LogRel(z) accurately by
                   log(1+z) = complex (log(r), arg(1+z))
                            = complex (0.5*log(r**2), arg(1+z))
                            = complex (0.5*LogRel(2*x+rho**2), arg(1+z))

z : Complex

The complex argument z.

Returns: Complex

Log(1+z) with relative error accuracy near z=0.

LogRel(z) = log(1+z) with relative error accuracy near z = 0.

             April 1977 version.  W. Fullerton, c3, Los Alamos Scientific Lab.
            
             let   rho = abs(z)  and
                   r**2 = abs(1+z)**2 = (1+x)**2 + y**2 = 1 + 2*x + rho**2 .
             now if rho is small we may evaluate LogRel(z) accurately by
                   log(1+z) = complex (log(r), arg(1+z))
                            = complex (0.5*log(r**2), arg(1+z))
                            = complex (0.5*LogRel(2*x+rho**2), arg(1+z))

z : Complex

The complex argument z.

bDebug : bool

If true, an exception will be thrown if errors occur, if false, double.NaN is returned in this case.

Returns: Complex

Log(1+z) with relative error accuracy near z=0.

Round to nearest integer.

d : float

The argument.

Returns: int

The nearest integer of the argument d.

Calculates the number of wraps w. This is the number of range wraps that must be taken to go from start to start+offset.

len : int

Length of the range.

start : int

Start point.

offset : int

Offset.

Returns: int

Number of range wraps when going from start to start+offset. In case offset is negative, the function returns a negative value.

Modulus x%y, but with result guaranted to be greater or equal to zero.

x : int

Nominator.

y : int

Denominator.

Returns: int

The remainder of the division x by y, but guaranted to be in the positive range.

The standard hypot() function for three arguments taking care of overflows and zerodivides.

x : float32

First argument.

y : float32

Second argument.

z : float32

Third argument.

Returns: float32

Square root of the sum of x-square, y-square and z-square.

The standard hypot() function for three arguments taking care of overflows and zerodivides.

x : float

First argument.

y : float

Second argument.

z : float

Third argument.

Returns: float

Square root of the sum of x-square, y-square and z-square.

Returns -1 if argument negative, 0 if argument zero, or 1 if argument is positive.

x : float

The number whose sign is returned.

Returns: int

-1 if the argument is negative, 0 if the argument is zero, or 1 if argument is positive.