10. Floating Point

10.1 Definitions 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.

load ("bffac") loads this function.

Option variable: algepsilon

Default value: 10^8

algepsilon is used by algsys.

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).

Function: bfloatp (expr)

Returns true if expr is a bigfloat number, otherwise false.

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.

load ("bffac") loads these functions.

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.

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.

Function: cbffac (z, fpprec)

Complex bigfloat factorial.

load ("bffac") loads this function.

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.

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).

Function: floatnump (expr)

Returns true if expr is a floating point number, otherwise false.

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.

See also bfloat and fpprintprec.

Option variable: fpprintprec

Default value: 0

fpprintprec is the number of digits to print when printing an ordinary float or bigfloat number.

For ordinary floating point numbers, when fpprintprec has a value between 2 and 16 (inclusive), the number of digits printed is equal to fpprintprec. Otherwise, fpprintprec is 0, or greater than 16, and the number of digits printed is 16.

For bigfloat numbers, when fpprintprec has a value between 2 and fpprec (inclusive), the number of digits printed is equal to fpprintprec. Otherwise, fpprintprec is 0, or greater than fpprec, and the number of digits printed is equal to fpprec.

fpprintprec cannot be 1.

Lisp function: ?round (x)

Lisp function: ?round (x, divisor)

Round the floating point x to the nearest integer. The argument must be an ordinary float, not a bigfloat. The ? beginning the name indicates this is a Lisp function.

(%i1) ?round (-2.8); (%o1) - 3

Lisp function: ?truncate (x)

Lisp function: ?truncate (x, divisor)

Truncate the floating point x towards 0, to become an integer. The argument must be an ordinary float, not a bigfloat. The ? beginning the name indicates this is a Lisp function.

(%i1) ?truncate (-2.8); (%o1) - 2 (%i2) ?truncate (2.4); (%o2) 2 (%i3) ?truncate (2.8); (%o3) 2

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