10. Floating Point

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10.1 Functions and Variables for Floating Point

Function: bffac (expr, n): Bigfloat version of the factorial (shifted gamma) function. The second argument is how many digits to retain and return, it's a good idea to request a couple of extra.

·
@ref{Category: Gamma and factorial functions} · @ref{Category: Numerical evaluation}

Option variable: algepsilon

Default value: 10^8

algepsilon is used by algsys.

@ref{Category: Algebraic equations}

Function: bfloat (expr)

Converts all numbers and functions of numbers in expr to bigfloat numbers. The number of significant digits in the resulting bigfloats is specified by the global variable fpprec.

When float2bf is false a warning message is printed when a floating point number is converted into a bigfloat number (since this may lead to loss of precision).

@ref{Category: Numerical evaluation}

Function: bfloatp (expr): Returns true if expr is a bigfloat number, otherwise false.

·
@ref{Category: Numerical evaluation} · @ref{Category: Predicate functions}

Function: bfpsi (n, z, fpprec)

Function: bfpsi0 (z, fpprec)

bfpsi is the polygamma function of real argument z and integer order n. bfpsi0 is the digamma function. bfpsi0 (z, fpprec) is equivalent to bfpsi (0, z, fpprec).

These functions return bigfloat values. fpprec is the bigfloat precision of the return value.

@ref{Category: Gamma and factorial functions} · @ref{Category: Numerical evaluation}

Option variable: bftorat

Default value: false

bftorat controls the conversion of bfloats to rational numbers. When bftorat is false, ratepsilon will be used to control the conversion (this results in relatively small rational numbers). When bftorat is true, the rational number generated will accurately represent the bfloat.

@ref{Category: Numerical evaluation}

Option variable: bftrunc

Default value: true

bftrunc causes trailing zeroes in non-zero bigfloat numbers not to be displayed. Thus, if bftrunc is false, bfloat (1) displays as 1.000000000000000B0. Otherwise, this is displayed as 1.0B0.

@ref{Category: Numerical evaluation}

Function: cbffac (z, fpprec)

Complex bigfloat factorial.

load ("bffac") loads this function.

@ref{Category: Gamma and factorial functions} · @ref{Category: Complex variables} · @ref{Category: Numerical evaluation}

Function: float (expr): Converts integers, rational numbers and bigfloats in expr to floating point numbers. It is also an evflag, float causes non-integral rational numbers and bigfloat numbers to be converted to floating point.

·
@ref{Category: Numerical evaluation}

Option variable: float2bf

Default value: false

When float2bf is false, a warning message is printed when a floating point number is converted into a bigfloat number (since this may lead to loss of precision).

@ref{Category: Numerical evaluation}

Function: floatnump (expr): Returns true if expr is a floating point number, otherwise false.

·
@ref{Category: Numerical evaluation} · @ref{Category: Predicate functions}

Option variable: fpprec

Default value: 16

fpprec is the number of significant digits for arithmetic on bigfloat numbers. fpprec does not affect computations on ordinary floating point numbers.