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# 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} · @ref{Category: Evaluation flags}

Option variable: float2bf

  Default value: `true`

  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). The default value is `true`.

  ·

  @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.

  See also `bfloat` and `fpprintprec`.

  ·

  @ref{Category: Numerical evaluation}

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.

  ·

  @ref{Category: Numerical evaluation} · @ref{Category: Display flags and variables}

Option variable: numer_pbranch

  Default value: `false`

  The option variable `numer_pbranch` controls the numerical evaluation of the power of a negative integer, rational, or floating point number. When `numer_pbranch` is `true` and the exponent is a floating point number or the option variable `numer` is `true` too, Maxima evaluates the numerical result using the principal branch. Otherwise a simplified, but not an evaluated result is returned.

  Examples:

      (%i1) (-2)^0.75;
      (%o1) (-2)^0.75

      (%i2) (-2)^0.75,numer_pbranch:true;
      (%o2) 1.189207115002721*%i-1.189207115002721

      (%i3) (-2)^(3/4);
      (%o3) (-1)^(3/4)*2^(3/4)

      (%i4) (-2)^(3/4),numer;
      (%o4) 1.681792830507429*(-1)^0.75

      (%i5) (-2)^(3/4),numer,numer_pbranch:true;
      (%o5) 1.189207115002721*%i-1.189207115002721

  ·

  @ref{Category: Numerical evaluation}

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