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# math::decimal(n) 1.0.3 tcllib "Tcl Decimal Arithmetic Library"

## Name

math::decimal - General decimal arithmetic

## Synopsis

- package require Tcl ?8.5?
- package require math::decimal 1.0.3

- ::math::decimal::fromstr string
- ::math::decimal::tostr decimal
- ::math::decimal::setVariable variable setting
- ::math::decimal::add a b
- ::math::decimal::+ a b
- ::math::decimal::subtract a b
- ::math::decimal::- a b
- ::math::decimal::multiply a b
- ::math::decimal::* a b
- ::math::decimal::divide a b
- ::math::decimal::/ a b
- ::math::decimal::divideint a b
- ::math::decimal::remainder a b
- ::math::decimal::abs decimal
- ::math::decimal::compare a b
- ::math::decimal::max a b
- ::math::decimal::maxmag a b
- ::math::decimal::min a b
- ::math::decimal::minmag a b
- ::math::decimal::plus a
- ::math::decimal::minus a
- ::math::decimal::copynegate a
- ::math::decimal::copysign a b
- ::math::decimal::is-signed decimal
- ::math::decimal::is-zero decimal
- ::math::decimal::is-NaN decimal
- ::math::decimal::is-infinite decimal
- ::math::decimal::is-finite decimal
- ::math::decimal::fma a b c
- ::math::decimal::round_half_even decimal digits
- ::math::decimal::round_half_up decimal digits
- ::math::decimal::round_half_down decimal digits
- ::math::decimal::round_down decimal digits
- ::math::decimal::round_up decimal digits
- ::math::decimal::round_floor decimal digits
- ::math::decimal::round_ceiling decimal digits
- ::math::decimal::round_05up decimal digits

## Description

The decimal package provides decimal arithmetic support for both limited precision floating point and arbitrary precision floating point. Additionally, integer arithmetic is supported.

More information and the specifications on which this package depends can be found on the general decimal arithmetic page at http://speleotrove.com/decimal This package provides for:

- A new data type decimal which is represented as a list containing sign, mantissa and exponent.

- Arithmetic operations on those decimal numbers such as addition, subtraction, multiplication, etc...

Numbers are converted to decimal format using the operation ::math::decimal::fromstr.

Numbers are converted back to string format using the operation ::math::decimal::tostr.

## EXAMPLES

This section shows some simple examples. Since the purpose of this library is to perform decimal math operations, examples may be the simplest way to learn how to work with it and to see the difference between using this package and sticking with expr. Consult the API section of this man page for information about individual procedures.

        package require math::decimal
        # Various operations on two numbers.
        # We first convert them to decimal format.
        set a [::math::decimal::fromstr 8.2]
        set b [::math::decimal::fromstr .2]
        # Then we perform our operations. Here we add
        set c [::math::decimal::+ $a $b]
        # Finally we convert back to string format for presentation to the user.
        puts [::math::decimal::tostr $c] ; # => will output 8.4
        # Other examples
        #
        # Subtraction
        set c [::math::decimal::- $a $b]
        puts [::math::decimal::tostr $c] ; # => will output 8.0
        # Why bother using this instead of simply expr?
        puts [expr {8.2 + .2}] ; # => will output 8.399999999999999
        puts [expr {8.2 - .2}] ; # => will output 7.999999999999999
        # See http://speleotrove.com/decimal to learn more about why this happens.

## API

::math::decimal::fromstr string

  Convert string into a decimal.

::math::decimal::tostr decimal

  Convert decimal into a string representing the number in base 10.

::math::decimal::setVariable variable setting

  Sets the variable to setting. Valid variables are:

  - rounding - Method of rounding to use during rescale. Valid methods are round_half_even, round_half_up, round_half_down, round_down, round_up, round_floor, round_ceiling.

  - precision - Maximum number of digits allowed in mantissa.

  - extended - Set to 1 for extended mode. 0 for simplified mode.

  - maxExponent - Maximum value for the exponent. Defaults to 999.

  - minExponent - Minimum value for the exponent. Default to -998.

::math::decimal::add a b
::math::decimal::+ a b

  Return the sum of the two decimals a and b.

::math::decimal::subtract a b
::math::decimal::- a b

  Return the differnece of the two decimals a and b.

::math::decimal::multiply a b
::math::decimal::* a b

  Return the product of the two decimals a and b.

::math::decimal::divide a b
::math::decimal::/ a b

  Return the quotient of the division between the two decimals a and b.

::math::decimal::divideint a b

  Return a the integer portion of the quotient of the division between decimals a and b

::math::decimal::remainder a b

  Return the remainder of the division between the two decimals a and b.

::math::decimal::abs decimal

  Return the absolute value of the decimal.

::math::decimal::compare a b

  Compare the two decimals a and b, returning 0 if a == b, 1 if a > b, and -1 if a < b.

::math::decimal::max a b

  Compare the two decimals a and b, and return a if a >= b, and b if a < b.

::math::decimal::maxmag a b

  Compare the two decimals a and b while ignoring their signs, and return a if abs(a) >= abs(b), and b if abs(a) < abs(b).

::math::decimal::min a b

  Compare the two decimals a and b, and return a if a <= b, and b if a > b.

::math::decimal::minmag a b

  Compare the two decimals a and b while ignoring their signs, and return a if abs(a) <= abs(b), and b if abs(a) > abs(b).

::math::decimal::plus a

  Return the result from ::math::decimal::+ 0 $a.

::math::decimal::minus a

  Return the result from ::math::decimal::- 0 $a.

::math::decimal::copynegate a

  Returns a with the sign flipped.

::math::decimal::copysign a b

  Returns a with the sign set to the sign of the b.

::math::decimal::is-signed decimal

  Return the sign of the decimal. The procedure returns 0 if the number is positive, 1 if it's negative.

::math::decimal::is-zero decimal

  Return true if decimal value is zero, otherwise false is returned.

::math::decimal::is-NaN decimal

  Return true if decimal value is NaN (not a number), otherwise false is returned.

::math::decimal::is-infinite decimal

  Return true if decimal value is Infinite, otherwise false is returned.

::math::decimal::is-finite decimal

  Return true if decimal value is finite, otherwise false is returned.

::math::decimal::fma a b c

  Return the result from first multiplying a by b and then adding c. Rescaling only occurs after completion of all operations. In this way the result may vary from that returned by performing the operations individually.

::math::decimal::round_half_even decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round to the nearest. If equidistant, round so the final digit is even.

::math::decimal::round_half_up decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round to the nearest. If equidistant, round up.

::math::decimal::round_half_down decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round to the nearest. If equidistant, round down.

::math::decimal::round_down decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round toward 0. (Truncate)

::math::decimal::round_up decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round away from 0

::math::decimal::round_floor decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round toward -Infinity.

::math::decimal::round_ceiling decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round toward Infinity

::math::decimal::round_05up decimal digits

  Rounds decimal to digits number of decimal points with the following rules: Round zero or five away from 0. The same as round-up, except that rounding up only occurs if the digit to be rounded up is 0 or 5, and after overflow the result is the same as for round-down.

## Bugs, Ideas, Feedback

This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category decimal of the Tcllib Trackers. Please also report any ideas for enhancements you may have for either package and/or documentation.

When proposing code changes, please provide unified diffs, i.e the output of diff -u.

Note further that attachments are strongly preferred over inlined patches. Attachments can be made by going to the Edit form of the ticket immediately after its creation, and then using the left-most button in the secondary navigation bar.

## Keywords

decimal, math, tcl

## Category

Mathematics

## Copyright

Copyright © 2011 Mark Alston <mark at beernut dot com>