[comment {-*- tcl -*- doctools manpage}]
[manpage_begin math::decimal n 1.0.5]
[keywords decimal]
[keywords math]
[keywords tcl]
[copyright {2011 Mark Alston <mark at beernut dot com>}]
[moddesc   {Tcl Decimal Arithmetic Library}]
[titledesc {General decimal arithmetic}]
[category  Mathematics]
[require Tcl [opt "8.5 9"]]
[require math::decimal 1.0.3]

[description]
[para]
The decimal package provides decimal arithmetic support for both limited
precision floating point and arbitrary precision floating point.
Additionally, integer arithmetic is supported.
[para]
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:
[list_begin itemized]
[item]
A new data type decimal which is represented as a list containing sign,
mantissa and exponent.
[item]
Arithmetic operations on those decimal numbers such as addition, subtraction,
multiplication, etc...

[list_end]
[para]
Numbers are converted to decimal format using the operation ::math::decimal::fromstr.
[para]
Numbers are converted back to string format using the operation
::math::decimal::tostr.

[para]

[section "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.

[para]
[example_begin]
    package require math::decimal

    # Various operations on two numbers.
    # We first convert them to decimal format.
    set a [lb]::math::decimal::fromstr 8.2[rb]
    set b [lb]::math::decimal::fromstr .2[rb]

    # Then we perform our operations. Here we add
    set c [lb]::math::decimal::+ $a $b[rb]

    # Finally we convert back to string format for presentation to the user.
    puts [lb]::math::decimal::tostr $c[rb] ; # => will output 8.4

    # Other examples
    #
    # Subtraction
    set c [lb]::math::decimal::- $a $b[rb]
    puts [lb]::math::decimal::tostr $c[rb] ; # => will output 8.0

    # Why bother using this instead of simply expr?
    puts [lb]expr {8.2 + .2}[rb] ; # => will output 8.399999999999999
    puts [lb]expr {8.2 - .2}[rb] ; # => will output 7.999999999999999
    # See http://speleotrove.com/decimal to learn more about why this happens.
[example_end]

[section "API"]
[list_begin definitions]

[call [cmd ::math::decimal::fromstr] [arg string]]
Convert [emph string] into a decimal.

[call [cmd ::math::decimal::tostr] [arg decimal]]
Convert [emph decimal] into a string representing the number in base 10.

[call [cmd ::math::decimal::setVariable] [arg variable] [arg setting]]
Sets the [emph variable] to [emph setting]. Valid variables are:
[list_begin itemized]
[item][arg 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.
[item][arg precision] - Maximum number of digits allowed in mantissa.
[item][arg extended] - Set to 1 for extended mode. 0 for simplified mode.
[item][arg maxExponent] - Maximum value for the exponent. Defaults to 999.
[item][arg minExponent] - Minimum value for the exponent. Default to -998.
[list_end]
[call [cmd ::math::decimal::add] [arg a] [arg b]]
[call [cmd ::math::decimal::+] [arg a] [arg b]]
Return the sum of the two decimals [emph a] and [emph b].

[call [cmd ::math::decimal::subtract] [arg a] [arg b]]
[call [cmd ::math::decimal::-] [arg a] [arg b]]
Return the differnece of the two decimals [emph a] and [emph b].

[call [cmd ::math::decimal::multiply] [arg a] [arg b]]
[call [cmd ::math::decimal::*] [arg a] [arg b]]
Return the product of the two decimals [emph a] and [emph b].

[call [cmd ::math::decimal::divide] [arg a] [arg b]]
[call [cmd ::math::decimal::/] [arg a] [arg b]]
Return the quotient of the division between the two
decimals [emph a] and [emph b].

[call [cmd ::math::decimal::divideint] [arg a] [arg b]]
Return a the integer portion of the quotient of the division between
decimals [emph a] and [emph b]

[call [cmd ::math::decimal::remainder] [arg a] [arg b]]
Return the remainder of the division between the two
decimals [emph a] and [emph b].

[call [cmd ::math::decimal::abs] [arg decimal]]
Return the absolute value of the decimal.

[call [cmd ::math::decimal::compare] [arg a] [arg b]]
Compare the two decimals a and b, returning [emph 0] if [emph {a == b}],
[emph 1] if [emph {a > b}], and [emph -1] if [emph {a < b}].

[call [cmd ::math::decimal::max] [arg a] [arg b]]
Compare the two decimals a and b, and return [emph a] if [emph {a >= b}], and [emph b] if [emph {a < b}].

[call [cmd ::math::decimal::maxmag] [arg a] [arg b]]
Compare the two decimals a and b while ignoring their signs, and return [emph a] if [emph {abs(a) >= abs(b)}], and [emph b] if [emph {abs(a) < abs(b)}].

[call [cmd ::math::decimal::min] [arg a] [arg b]]
Compare the two decimals a and b, and return [emph a] if [emph {a <= b}], and [emph b] if [emph {a > b}].

[call [cmd ::math::decimal::minmag] [arg a] [arg b]]
Compare the two decimals a and b while ignoring their signs, and return [emph a] if [emph {abs(a) <= abs(b)}], and [emph b] if [emph {abs(a) > abs(b)}].

[call [cmd ::math::decimal::plus] [arg a]]
Return the result from [emph {::math::decimal::+ 0 $a}].

[call [cmd ::math::decimal::minus] [arg a]]
Return the result from [emph {::math::decimal::- 0 $a}].

[call [cmd ::math::decimal::copynegate] [arg a]]
Returns [emph a] with the sign flipped.

[call [cmd ::math::decimal::copysign] [arg a] [arg b]]
Returns [emph a] with the sign set to the sign of the [emph b].

[call [cmd ::math::decimal::is-signed] [arg decimal]]
Return the sign of the decimal.
The procedure returns 0 if the number is positive, 1 if it's negative.

[call [cmd ::math::decimal::is-zero] [arg decimal]]
Return true if [emph decimal] value is zero, otherwise false is returned.

[call [cmd ::math::decimal::is-NaN] [arg decimal]]
Return true if [emph decimal] value is NaN (not a number), otherwise false is returned.

[call [cmd ::math::decimal::is-infinite] [arg decimal]]
Return true if [emph decimal] value is Infinite, otherwise false is returned.

[call [cmd ::math::decimal::is-finite] [arg decimal]]
Return true if [emph decimal] value is finite, otherwise false is returned.

[call [cmd ::math::decimal::fma] [arg a] [arg b] [arg c]]
Return the result from first multiplying [emph a] by [emph b] and then adding [emph c]. Rescaling only occurs after completion of all operations. In this way the result may vary from that returned by performing the operations individually.

[call [cmd ::math::decimal::round_half_even] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph digits] number of decimal points with the following rules: Round to the nearest. If equidistant, round so the final digit is even.

[call [cmd ::math::decimal::round_half_up] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph digits] number of decimal points with the following rules: Round to the nearest. If equidistant, round up.

[call [cmd ::math::decimal::round_half_down] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph digits] number of decimal points with the following rules: Round to the nearest. If equidistant, round down.

[call [cmd ::math::decimal::round_down] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph digits] number of decimal points with the following rules: Round toward 0.  (Truncate)

[call [cmd ::math::decimal::round_up] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph digits] number of decimal points with the following rules: Round away from 0

[call [cmd ::math::decimal::round_floor] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph digits] number of decimal points with the following rules: Round toward -Infinity.

[call [cmd ::math::decimal::round_ceiling] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph digits] number of decimal points with the following rules: Round toward Infinity

[call [cmd ::math::decimal::round_05up] [arg decimal] [arg digits]]
Rounds [emph decimal] to [emph 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.

[list_end]
[para]

[vset CATEGORY decimal]
[include ../common-text/feedback.inc]
[manpage_end]
