[OpenSPARC-T2-SAM] / sam-t2 / devtools / amd64 / man / man3 / Math::BigRat.3

.\" Automatically generated by Pod::Man v1.37, Pod::Parser v1.32
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sh \" Subsection heading
.br
.if t .Sp
.ne 5
.PP
\fB\\$1\fR
.PP
..
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" Set up some character translations and predefined strings.  \*(-- will
.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
.\" double quote, and \*(R" will give a right double quote.  | will give a
.\" real vertical bar.  \*(C+ will give a nicer C++.  Capital omega is used to
.\" do unbreakable dashes and therefore won't be available.  \*(C` and \*(C'
.\" expand to `' in nroff, nothing in troff, for use with C<>.
.tr \(*W-|\(bv\*(Tr
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
.ie n \{\
.    ds -- \(*W-
.    ds PI pi
.    if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
.    if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\"  diablo 12 pitch
.    ds L" ""
.    ds R" ""
.    ds C` ""
.    ds C' ""
'br\}
.el\{\
.    ds -- \|\(em\|
.    ds PI \(*p
.    ds L" ``
.    ds R" ''
'br\}
.\"
.\" If the F register is turned on, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.Sh), items (.Ip), and index
.\" entries marked with X<> in POD.  Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.if \nF \{\
.    de IX
.    tm Index:\\$1\t\\n%\t"\\$2"
..
.    nr % 0
.    rr F
.\}
.\"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.hy 0
.if n .na
.\"
.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
.\" Fear.  Run.  Save yourself.  No user-serviceable parts.
.    \" fudge factors for nroff and troff
.if n \{\
.    ds #H 0
.    ds #V .8m
.    ds #F .3m
.    ds #[ \f1
.    ds #] \fP
.\}
.if t \{\
.    ds #H ((1u-(\\\\n(.fu%2u))*.13m)
.    ds #V .6m
.    ds #F 0
.    ds #[ \&
.    ds #] \&
.\}
.    \" simple accents for nroff and troff
.if n \{\
.    ds ' \&
.    ds ` \&
.    ds ^ \&
.    ds , \&
.    ds ~ ~
.    ds /
.\}
.if t \{\
.    ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
.    ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
.    ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
.    ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
.    ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
.    ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
.\}
.    \" troff and (daisy-wheel) nroff accents
.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
.ds ae a\h'-(\w'a'u*4/10)'e
.ds Ae A\h'-(\w'A'u*4/10)'E
.    \" corrections for vroff
.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
.    \" for low resolution devices (crt and lpr)
.if \n(.H>23 .if \n(.V>19 \
\{\
.    ds : e
.    ds 8 ss
.    ds o a
.    ds d- d\h'-1'\(ga
.    ds D- D\h'-1'\(hy
.    ds th \o'bp'
.    ds Th \o'LP'
.    ds ae ae
.    ds Ae AE
.\}
.rm #[ #] #H #V #F C
.\" ========================================================================
.\"
.IX Title "Math::BigRat 3"
.TH Math::BigRat 3 "2001-09-21" "perl v5.8.8" "Perl Programmers Reference Guide"
.SH "NAME"
Math::BigRat \- Arbitrary big rational numbers
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&        use Math::BigRat;
.Ve
.PP
.Vb 1
\&        my $x = Math::BigRat->new('3/7'); $x += '5/9';
.Ve
.PP
.Vb 2
\&        print $x->bstr(),"\en";
\&        print $x ** 2,"\en";
.Ve
.PP
.Vb 2
\&        my $y = Math::BigRat->new('inf');
\&        print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\en";
.Ve
.PP
.Vb 1
\&        my $z = Math::BigRat->new(144); $z->bsqrt();
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
Math::BigRat complements Math::BigInt and Math::BigFloat by providing support
for arbitrary big rational numbers.
.Sh "\s-1MATH\s0 \s-1LIBRARY\s0"
.IX Subsection "MATH LIBRARY"
Math with the numbers is done (by default) by a module called
Math::BigInt::Calc. This is equivalent to saying:
.PP
.Vb 1
\&        use Math::BigRat lib => 'Calc';
.Ve
.PP
You can change this by using:
.PP
.Vb 1
\&        use Math::BigRat lib => 'BitVect';
.Ve
.PP
The following would first try to find Math::BigInt::Foo, then
Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
.PP
.Vb 1
\&        use Math::BigRat lib => 'Foo,Math::BigInt::Bar';
.Ve
.PP
Calc.pm uses as internal format an array of elements of some decimal base
(usually 1e7, but this might be different for some systems) with the least
significant digit first, while BitVect.pm uses a bit vector of base 2, most
significant bit first. Other modules might use even different means of
representing the numbers. See the respective module documentation for further
details.
.PP
Currently the following replacement libraries exist, search for them at \s-1CPAN:\s0
.PP
.Vb 4
\&        Math::BigInt::BitVect
\&        Math::BigInt::GMP
\&        Math::BigInt::Pari
\&        Math::BigInt::FastCalc
.Ve
.SH "METHODS"
.IX Header "METHODS"
Any methods not listed here are dervied from Math::BigFloat (or
Math::BigInt), so make sure you check these two modules for further
information.
.Sh "\fInew()\fP"
.IX Subsection "new()"
.Vb 1
\&        $x = Math::BigRat->new('1/3');
.Ve
.PP
Create a new Math::BigRat object. Input can come in various forms:
.PP
.Vb 9
\&        $x = Math::BigRat->new(123);                            # scalars
\&        $x = Math::BigRat->new('inf');                          # infinity
\&        $x = Math::BigRat->new('123.3');                        # float
\&        $x = Math::BigRat->new('1/3');                          # simple string
\&        $x = Math::BigRat->new('1 / 3');                        # spaced
\&        $x = Math::BigRat->new('1 / 0.1');                      # w/ floats
\&        $x = Math::BigRat->new(Math::BigInt->new(3));           # BigInt
\&        $x = Math::BigRat->new(Math::BigFloat->new('3.1'));     # BigFloat
\&        $x = Math::BigRat->new(Math::BigInt::Lite->new('2'));   # BigLite
.Ve
.PP
.Vb 5
\&        # You can also give D and N as different objects:
\&        $x = Math::BigRat->new(
\&                Math::BigInt->new(-123),
\&                Math::BigInt->new(7),
\&                );                      # => -123/7
.Ve
.Sh "\fInumerator()\fP"
.IX Subsection "numerator()"
.Vb 1
\&        $n = $x->numerator();
.Ve
.PP
Returns a copy of the numerator (the part above the line) as signed BigInt.
.Sh "\fIdenominator()\fP"
.IX Subsection "denominator()"
.Vb 1
\&        $d = $x->denominator();
.Ve
.PP
Returns a copy of the denominator (the part under the line) as positive BigInt.
.Sh "\fIparts()\fP"
.IX Subsection "parts()"
.Vb 1
\&        ($n,$d) = $x->parts();
.Ve
.PP
Return a list consisting of (signed) numerator and (unsigned) denominator as
BigInts.
.Sh "\fIas_int()\fP"
.IX Subsection "as_int()"
.Vb 2
\&        $x = Math::BigRat->new('13/7');
\&        print $x->as_int(),"\en";                # '1'
.Ve
.PP
Returns a copy of the object as BigInt, truncated to an integer.
.PP
\&\f(CW\*(C`as_number()\*(C'\fR is an alias for \f(CW\*(C`as_int()\*(C'\fR.
.Sh "\fIas_hex()\fP"
.IX Subsection "as_hex()"
.Vb 2
\&        $x = Math::BigRat->new('13');
\&        print $x->as_hex(),"\en";                # '0xd'
.Ve
.PP
Returns the BigRat as hexadecimal string. Works only for integers. 
.Sh "\fIas_bin()\fP"
.IX Subsection "as_bin()"
.Vb 2
\&        $x = Math::BigRat->new('13');
\&        print $x->as_bin(),"\en";                # '0x1101'
.Ve
.PP
Returns the BigRat as binary string. Works only for integers. 
.Sh "\fIbfac()\fP"
.IX Subsection "bfac()"
.Vb 1
\&        $x->bfac();
.Ve
.PP
Calculates the factorial of \f(CW$x\fR. For instance:
.PP
.Vb 2
\&        print Math::BigRat->new('3/1')->bfac(),"\en";    # 1*2*3
\&        print Math::BigRat->new('5/1')->bfac(),"\en";    # 1*2*3*4*5
.Ve
.PP
Works currently only for integers.
.Sh "\fIblog()\fP"
.IX Subsection "blog()"
Is not yet implemented.
.Sh "\fIbround()\fP/\fIround()\fP/\fIbfround()\fP"
.IX Subsection "bround()/round()/bfround()"
Are not yet implemented.
.Sh "\fIbmod()\fP"
.IX Subsection "bmod()"
.Vb 4
\&        use Math::BigRat;
\&        my $x = Math::BigRat->new('7/4');
\&        my $y = Math::BigRat->new('4/3');
\&        print $x->bmod($y);
.Ve
.PP
Set \f(CW$x\fR to the remainder of the division of \f(CW$x\fR by \f(CW$y\fR.
.Sh "\fIis_one()\fP"
.IX Subsection "is_one()"
.Vb 1
\&        print "$x is 1\en" if $x->is_one();
.Ve
.PP
Return true if \f(CW$x\fR is exactly one, otherwise false.
.Sh "\fIis_zero()\fP"
.IX Subsection "is_zero()"
.Vb 1
\&        print "$x is 0\en" if $x->is_zero();
.Ve
.PP
Return true if \f(CW$x\fR is exactly zero, otherwise false.
.Sh "\fIis_pos()\fP"
.IX Subsection "is_pos()"
.Vb 1
\&        print "$x is >= 0\en" if $x->is_positive();
.Ve
.PP
Return true if \f(CW$x\fR is positive (greater than or equal to zero), otherwise
false. Please note that '+inf' is also positive, while 'NaN' and '\-inf' aren't.
.PP
\&\f(CW\*(C`is_positive()\*(C'\fR is an alias for \f(CW\*(C`is_pos()\*(C'\fR.
.Sh "\fIis_neg()\fP"
.IX Subsection "is_neg()"
.Vb 1
\&        print "$x is < 0\en" if $x->is_negative();
.Ve
.PP
Return true if \f(CW$x\fR is negative (smaller than zero), otherwise false. Please
note that '\-inf' is also negative, while 'NaN' and '+inf' aren't.
.PP
\&\f(CW\*(C`is_negative()\*(C'\fR is an alias for \f(CW\*(C`is_neg()\*(C'\fR.
.Sh "\fIis_int()\fP"
.IX Subsection "is_int()"
.Vb 1
\&        print "$x is an integer\en" if $x->is_int();
.Ve
.PP
Return true if \f(CW$x\fR has a denominator of 1 (e.g. no fraction parts), otherwise
false. Please note that '\-inf', 'inf' and 'NaN' aren't integer.
.Sh "\fIis_odd()\fP"
.IX Subsection "is_odd()"
.Vb 1
\&        print "$x is odd\en" if $x->is_odd();
.Ve
.PP
Return true if \f(CW$x\fR is odd, otherwise false.
.Sh "\fIis_even()\fP"
.IX Subsection "is_even()"
.Vb 1
\&        print "$x is even\en" if $x->is_even();
.Ve
.PP
Return true if \f(CW$x\fR is even, otherwise false.
.Sh "\fIbceil()\fP"
.IX Subsection "bceil()"
.Vb 1
\&        $x->bceil();
.Ve
.PP
Set \f(CW$x\fR to the next bigger integer value (e.g. truncate the number to integer
and then increment it by one).
.Sh "\fIbfloor()\fP"
.IX Subsection "bfloor()"
.Vb 1
\&        $x->bfloor();
.Ve
.PP
Truncate \f(CW$x\fR to an integer value.
.Sh "\fIbsqrt()\fP"
.IX Subsection "bsqrt()"
.Vb 1
\&        $x->bsqrt();
.Ve
.PP
Calculate the square root of \f(CW$x\fR.
.Sh "config"
.IX Subsection "config"
.Vb 1
\&        use Data::Dumper;
.Ve
.PP
.Vb 2
\&        print Dumper ( Math::BigRat->config() );
\&        print Math::BigRat->config()->{lib},"\en";
.Ve
.PP
Returns a hash containing the configuration, e.g. the version number, lib
loaded etc. The following hash keys are currently filled in with the
appropriate information.
.PP
.Vb 27
\&        key             RO/RW   Description
\&                                Example
\&        ============================================================
\&        lib             RO      Name of the Math library
\&                                Math::BigInt::Calc
\&        lib_version     RO      Version of 'lib'
\&                                0.30
\&        class           RO      The class of config you just called
\&                                Math::BigRat
\&        version         RO      version number of the class you used
\&                                0.10
\&        upgrade         RW      To which class numbers are upgraded
\&                                undef
\&        downgrade       RW      To which class numbers are downgraded
\&                                undef
\&        precision       RW      Global precision
\&                                undef
\&        accuracy        RW      Global accuracy
\&                                undef
\&        round_mode      RW      Global round mode
\&                                even
\&        div_scale       RW      Fallback acccuracy for div
\&                                40
\&        trap_nan        RW      Trap creation of NaN (undef = no)
\&                                undef
\&        trap_inf        RW      Trap creation of +inf/-inf (undef = no)
\&                                undef
.Ve
.PP
By passing a reference to a hash you may set the configuration values. This
works only for values that a marked with a \f(CW\*(C`RW\*(C'\fR above, anything else is
read\-only.
.SH "BUGS"
.IX Header "BUGS"
Some things are not yet implemented, or only implemented half\-way:
.IP "inf handling (partial)" 2
.IX Item "inf handling (partial)"
.PD 0
.IP "NaN handling (partial)" 2
.IX Item "NaN handling (partial)"
.IP "rounding (not implemented except for bceil/bfloor)" 2
.IX Item "rounding (not implemented except for bceil/bfloor)"
.ie n .IP "$x ** $y\fR where \f(CW$y is not an integer" 2
.el .IP "$x ** \f(CW$y\fR where \f(CW$y\fR is not an integer" 2
.IX Item "$x ** $y where $y is not an integer"
.IP "\fIbmod()\fR, \fIblog()\fR, \fIbmodinv()\fR and \fIbmodpow()\fR (partial)" 2
.IX Item "bmod(), blog(), bmodinv() and bmodpow() (partial)"
.PD
.SH "LICENSE"
.IX Header "LICENSE"
This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
Math::BigFloat and Math::Big as well as Math::BigInt::BitVect,
Math::BigInt::Pari and  Math::BigInt::GMP.
.PP
See <http://search.cpan.org/search?dist=bignum> for a way to use
Math::BigRat.
.PP
The package at <http://search.cpan.org/search?dist=Math%3A%3ABigRat>
may contain more documentation and examples as well as testcases.
.SH "AUTHORS"
.IX Header "AUTHORS"
(C) by Tels <http://bloodgate.com/> 2001 \- 2005.
Commit	Line	Data
920dae64 AT	1	.\" Automatically generated by Pod::Man v1.37, Pod::Parser v1.32
	2	.\"
	3	.\" Standard preamble:
	4	.\" ========================================================================
	5	.de Sh \" Subsection heading
	6	.br
	7	.if t .Sp
	8	.ne 5
	9	.PP
	10	\fB\\$1\fR
	11	.PP
	12	..
	13	.de Sp \" Vertical space (when we can't use .PP)
	14	.if t .sp .5v
	15	.if n .sp
	16	..
	17	.de Vb \" Begin verbatim text
	18	.ft CW
	19	.nf
	20	.ne \\$1
	21	..
	22	.de Ve \" End verbatim text
	23	.ft R
	24	.fi
	25	..
	26	.\" Set up some character translations and predefined strings. \*(-- will
	27	.\" give an unbreakable dash, \(PI will give pi, \(L" will give a left
	28	.\" double quote, and \*(R" will give a right double quote. \| will give a
	29	.\" real vertical bar. \*(C+ will give a nicer C++. Capital omega is used to
	30	.\" do unbreakable dashes and therefore won't be available. \(C` and \(C'
	31	.\" expand to `' in nroff, nothing in troff, for use with C<>.
	32	.tr \(W-\|\(bv\(Tr
	33	.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
	34	.ie n \{\
	35	. ds -- \(*W-
	36	. ds PI pi
	37	. if (\n(.H=4u)&(1m=24u) .ds -- \(W\h'-12u'\(W\h'-12u'-\" diablo 10 pitch
	38	. if (\n(.H=4u)&(1m=20u) .ds -- \(W\h'-12u'\(W\h'-8u'-\" diablo 12 pitch
	39	. ds L" ""
	40	. ds R" ""
	41	. ds C` ""
	42	. ds C' ""
	43	'br\}
	44	.el\{\
	45	. ds -- \\|\(em\\|
	46	. ds PI \(*p
	47	. ds L" ``
	48	. ds R" ''
	49	'br\}
	50	.\"
	51	.\" If the F register is turned on, we'll generate index entries on stderr for
	52	.\" titles (.TH), headers (.SH), subsections (.Sh), items (.Ip), and index
	53	.\" entries marked with X<> in POD. Of course, you'll have to process the
	54	.\" output yourself in some meaningful fashion.
	55	.if \nF \{\
	56	. de IX
	57	. tm Index:\\$1\t\\n%\t"\\$2"
	58	..
	59	. nr % 0
	60	. rr F
	61	.\}
	62	.\"
	63	.\" For nroff, turn off justification. Always turn off hyphenation; it makes
	64	.\" way too many mistakes in technical documents.
65	.hy 0
66	.if n .na
67	.\"
68	.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
69	.\" Fear. Run. Save yourself. No user-serviceable parts.
70	. \" fudge factors for nroff and troff
71	.if n \{\
72	. ds #H 0
73	. ds #V .8m
74	. ds #F .3m
75	. ds #[ \f1
76	. ds #] \fP
77	.\}
78	.if t \{\
79	. ds #H ((1u-(\\\\n(.fu%2u))*.13m)
80	. ds #V .6m
81	. ds #F 0
82	. ds #[ \&
83	. ds #] \&
84	.\}
85	. \" simple accents for nroff and troff
86	.if n \{\
87	. ds ' \&
88	. ds ` \&
89	. ds ^ \&
90	. ds , \&
91	. ds ~ ~
92	. ds /
93	.\}
94	.if t \{\
95	. ds ' \\k:\h'-(\\n(.wu8/10-\(#H)'\'\h"\|\\n:u"
96	. ds ` \\k:\h'-(\\n(.wu8/10-\(#H)'\`\h'\|\\n:u'
97	. ds ^ \\k:\h'-(\\n(.wu10/11-\(#H)'^\h'\|\\n:u'
98	. ds , \\k:\h'-(\\n(.wu*8/10)',\h'\|\\n:u'
99	. ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'\|\\n:u'
100	. ds / \\k:\h'-(\\n(.wu8/10-\(#H)'\z\(sl\h'\|\\n:u'
101	.\}
102	. \" troff and (daisy-wheel) nroff accents
103	.ds : \\k:\h'-(\\n(.wu8/10-\(#H+.1m+\(#F)'\v'-\(#V'\z.\h'.2m+\(#F'.\h'\|\\n:u'\v'\(#V'
104	.ds 8 \h'\(#H'\(b\h'-\*(#H'
105	.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\(#H)/2u'\v'-.3n'\(#[\z\(de\v'.3n'\h'\|\\n:u'\*(#]
106	.ds d- \h'\(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\(#H'
107	.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'\|\\n:u'
108	.ds th \(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u2/3)'\s-1o\s+1\*(#]
109	.ds Th \(#[\s+2I\s-2\h'-\w'I'u3/5'\v'-.3m'o\v'.3m'\*(#]
110	.ds ae a\h'-(\w'a'u*4/10)'e
111	.ds Ae A\h'-(\w'A'u*4/10)'E
112	. \" corrections for vroff
113	.if v .ds ~ \\k:\h'-(\\n(.wu9/10-\(#H)'\s-2\u~\d\s+2\h'\|\\n:u'
114	.if v .ds ^ \\k:\h'-(\\n(.wu10/11-\(#H)'\v'-.4m'^\v'.4m'\h'\|\\n:u'
115	. \" for low resolution devices (crt and lpr)
116	.if \n(.H>23 .if \n(.V>19 \
117	\{\
118	. ds : e
119	. ds 8 ss
120	. ds o a
121	. ds d- d\h'-1'\(ga
122	. ds D- D\h'-1'\(hy
123	. ds th \o'bp'
124	. ds Th \o'LP'
125	. ds ae ae
126	. ds Ae AE
127	.\}
128	.rm #[ #] #H #V #F C
129	.\" ========================================================================
130	.\"
131	.IX Title "Math::BigRat 3"
132	.TH Math::BigRat 3 "2001-09-21" "perl v5.8.8" "Perl Programmers Reference Guide"
133	.SH "NAME"
134	Math::BigRat \- Arbitrary big rational numbers
135	.SH "SYNOPSIS"
136	.IX Header "SYNOPSIS"
137	.Vb 1
138	\& use Math::BigRat;
139	.Ve
140	.PP
141	.Vb 1
142	\& my $x = Math::BigRat->new('3/7'); $x += '5/9';
143	.Ve
144	.PP
145	.Vb 2
146	\& print $x->bstr(),"\en";
147	\& print $x ** 2,"\en";
148	.Ve
149	.PP
150	.Vb 2
151	\& my $y = Math::BigRat->new('inf');
152	\& print "$y ", ($y->is_inf ? 'is' : 'is not') , " infinity\en";
153	.Ve
154	.PP
155	.Vb 1
156	\& my $z = Math::BigRat->new(144); $z->bsqrt();
157	.Ve
158	.SH "DESCRIPTION"
159	.IX Header "DESCRIPTION"
160	Math::BigRat complements Math::BigInt and Math::BigFloat by providing support
161	for arbitrary big rational numbers.
162	.Sh "\s-1MATH\s0 \s-1LIBRARY\s0"
163	.IX Subsection "MATH LIBRARY"
164	Math with the numbers is done (by default) by a module called
165	Math::BigInt::Calc. This is equivalent to saying:
166	.PP
167	.Vb 1
168	\& use Math::BigRat lib => 'Calc';
169	.Ve
170	.PP
171	You can change this by using:
172	.PP
173	.Vb 1
174	\& use Math::BigRat lib => 'BitVect';
175	.Ve
176	.PP
177	The following would first try to find Math::BigInt::Foo, then
178	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
179	.PP
180	.Vb 1
181	\& use Math::BigRat lib => 'Foo,Math::BigInt::Bar';
182	.Ve
183	.PP
184	Calc.pm uses as internal format an array of elements of some decimal base
185	(usually 1e7, but this might be different for some systems) with the least
186	significant digit first, while BitVect.pm uses a bit vector of base 2, most
187	significant bit first. Other modules might use even different means of
188	representing the numbers. See the respective module documentation for further
189	details.
190	.PP
191	Currently the following replacement libraries exist, search for them at \s-1CPAN:\s0
192	.PP
193	.Vb 4
194	\& Math::BigInt::BitVect
195	\& Math::BigInt::GMP
196	\& Math::BigInt::Pari
197	\& Math::BigInt::FastCalc
198	.Ve
199	.SH "METHODS"
200	.IX Header "METHODS"
201	Any methods not listed here are dervied from Math::BigFloat (or
202	Math::BigInt), so make sure you check these two modules for further
203	information.
204	.Sh "\fInew()\fP"
205	.IX Subsection "new()"
206	.Vb 1
207	\& $x = Math::BigRat->new('1/3');
208	.Ve
209	.PP
210	Create a new Math::BigRat object. Input can come in various forms:
211	.PP
212	.Vb 9
213	\& $x = Math::BigRat->new(123); # scalars
214	\& $x = Math::BigRat->new('inf'); # infinity
215	\& $x = Math::BigRat->new('123.3'); # float
216	\& $x = Math::BigRat->new('1/3'); # simple string
217	\& $x = Math::BigRat->new('1 / 3'); # spaced
218	\& $x = Math::BigRat->new('1 / 0.1'); # w/ floats
219	\& $x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt
220	\& $x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat
221	\& $x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite
222	.Ve
223	.PP
224	.Vb 5
225	\& # You can also give D and N as different objects:
226	\& $x = Math::BigRat->new(
227	\& Math::BigInt->new(-123),
228	\& Math::BigInt->new(7),
229	\& ); # => -123/7
230	.Ve
231	.Sh "\fInumerator()\fP"
232	.IX Subsection "numerator()"
233	.Vb 1
234	\& $n = $x->numerator();
235	.Ve
236	.PP
237	Returns a copy of the numerator (the part above the line) as signed BigInt.
238	.Sh "\fIdenominator()\fP"
239	.IX Subsection "denominator()"
240	.Vb 1
241	\& $d = $x->denominator();
242	.Ve
243	.PP
244	Returns a copy of the denominator (the part under the line) as positive BigInt.
245	.Sh "\fIparts()\fP"
246	.IX Subsection "parts()"
247	.Vb 1
248	\& ($n,$d) = $x->parts();
249	.Ve
250	.PP
251	Return a list consisting of (signed) numerator and (unsigned) denominator as
252	BigInts.
253	.Sh "\fIas_int()\fP"
254	.IX Subsection "as_int()"
255	.Vb 2
256	\& $x = Math::BigRat->new('13/7');
257	\& print $x->as_int(),"\en"; # '1'
258	.Ve
259	.PP
260	Returns a copy of the object as BigInt, truncated to an integer.
261	.PP
262	\&\f(CW\(C`as_number()\(C'\fR is an alias for \f(CW\(C`as_int()\(C'\fR.
263	.Sh "\fIas_hex()\fP"
264	.IX Subsection "as_hex()"
265	.Vb 2
266	\& $x = Math::BigRat->new('13');
267	\& print $x->as_hex(),"\en"; # '0xd'
268	.Ve
269	.PP
270	Returns the BigRat as hexadecimal string. Works only for integers.
271	.Sh "\fIas_bin()\fP"
272	.IX Subsection "as_bin()"
273	.Vb 2
274	\& $x = Math::BigRat->new('13');
275	\& print $x->as_bin(),"\en"; # '0x1101'
276	.Ve
277	.PP
278	Returns the BigRat as binary string. Works only for integers.
279	.Sh "\fIbfac()\fP"
280	.IX Subsection "bfac()"
281	.Vb 1
282	\& $x->bfac();
283	.Ve
284	.PP
285	Calculates the factorial of \f(CW$x\fR. For instance:
286	.PP
287	.Vb 2
288	\& print Math::BigRat->new('3/1')->bfac(),"\en"; # 123
289	\& print Math::BigRat->new('5/1')->bfac(),"\en"; # 12345
290	.Ve
291	.PP
292	Works currently only for integers.
293	.Sh "\fIblog()\fP"
294	.IX Subsection "blog()"
295	Is not yet implemented.
296	.Sh "\fIbround()\fP/\fIround()\fP/\fIbfround()\fP"
297	.IX Subsection "bround()/round()/bfround()"
298	Are not yet implemented.
299	.Sh "\fIbmod()\fP"
300	.IX Subsection "bmod()"
301	.Vb 4
302	\& use Math::BigRat;
303	\& my $x = Math::BigRat->new('7/4');
304	\& my $y = Math::BigRat->new('4/3');
305	\& print $x->bmod($y);
306	.Ve
307	.PP
308	Set \f(CW$x\fR to the remainder of the division of \f(CW$x\fR by \f(CW$y\fR.
309	.Sh "\fIis_one()\fP"
310	.IX Subsection "is_one()"
311	.Vb 1
312	\& print "$x is 1\en" if $x->is_one();
313	.Ve
314	.PP
315	Return true if \f(CW$x\fR is exactly one, otherwise false.
316	.Sh "\fIis_zero()\fP"
317	.IX Subsection "is_zero()"
318	.Vb 1
319	\& print "$x is 0\en" if $x->is_zero();
320	.Ve
321	.PP
322	Return true if \f(CW$x\fR is exactly zero, otherwise false.
323	.Sh "\fIis_pos()\fP"
324	.IX Subsection "is_pos()"
325	.Vb 1
326	\& print "$x is >= 0\en" if $x->is_positive();
327	.Ve
328	.PP
329	Return true if \f(CW$x\fR is positive (greater than or equal to zero), otherwise
330	false. Please note that '+inf' is also positive, while 'NaN' and '\-inf' aren't.
331	.PP
332	\&\f(CW\(C`is_positive()\(C'\fR is an alias for \f(CW\(C`is_pos()\(C'\fR.
333	.Sh "\fIis_neg()\fP"
334	.IX Subsection "is_neg()"
335	.Vb 1
336	\& print "$x is < 0\en" if $x->is_negative();
337	.Ve
338	.PP
339	Return true if \f(CW$x\fR is negative (smaller than zero), otherwise false. Please
340	note that '\-inf' is also negative, while 'NaN' and '+inf' aren't.
341	.PP
342	\&\f(CW\(C`is_negative()\(C'\fR is an alias for \f(CW\(C`is_neg()\(C'\fR.
343	.Sh "\fIis_int()\fP"
344	.IX Subsection "is_int()"
345	.Vb 1
346	\& print "$x is an integer\en" if $x->is_int();
347	.Ve
348	.PP
349	Return true if \f(CW$x\fR has a denominator of 1 (e.g. no fraction parts), otherwise
350	false. Please note that '\-inf', 'inf' and 'NaN' aren't integer.
351	.Sh "\fIis_odd()\fP"
352	.IX Subsection "is_odd()"
353	.Vb 1
354	\& print "$x is odd\en" if $x->is_odd();
355	.Ve
356	.PP
357	Return true if \f(CW$x\fR is odd, otherwise false.
358	.Sh "\fIis_even()\fP"
359	.IX Subsection "is_even()"
360	.Vb 1
361	\& print "$x is even\en" if $x->is_even();
362	.Ve
363	.PP
364	Return true if \f(CW$x\fR is even, otherwise false.
365	.Sh "\fIbceil()\fP"
366	.IX Subsection "bceil()"
367	.Vb 1
368	\& $x->bceil();
369	.Ve
370	.PP
371	Set \f(CW$x\fR to the next bigger integer value (e.g. truncate the number to integer
372	and then increment it by one).
373	.Sh "\fIbfloor()\fP"
374	.IX Subsection "bfloor()"
375	.Vb 1
376	\& $x->bfloor();
377	.Ve
378	.PP
379	Truncate \f(CW$x\fR to an integer value.
380	.Sh "\fIbsqrt()\fP"
381	.IX Subsection "bsqrt()"
382	.Vb 1
383	\& $x->bsqrt();
384	.Ve
385	.PP
386	Calculate the square root of \f(CW$x\fR.
387	.Sh "config"
388	.IX Subsection "config"
389	.Vb 1
390	\& use Data::Dumper;
391	.Ve
392	.PP
393	.Vb 2
394	\& print Dumper ( Math::BigRat->config() );
395	\& print Math::BigRat->config()->{lib},"\en";
396	.Ve
397	.PP
398	Returns a hash containing the configuration, e.g. the version number, lib
399	loaded etc. The following hash keys are currently filled in with the
400	appropriate information.
401	.PP
402	.Vb 27
403	\& key RO/RW Description
404	\& Example
405	\& ============================================================
406	\& lib RO Name of the Math library
407	\& Math::BigInt::Calc
408	\& lib_version RO Version of 'lib'
409	\& 0.30
410	\& class RO The class of config you just called
411	\& Math::BigRat
412	\& version RO version number of the class you used
413	\& 0.10
414	\& upgrade RW To which class numbers are upgraded
415	\& undef
416	\& downgrade RW To which class numbers are downgraded
417	\& undef
418	\& precision RW Global precision
419	\& undef
420	\& accuracy RW Global accuracy
421	\& undef
422	\& round_mode RW Global round mode
423	\& even
424	\& div_scale RW Fallback acccuracy for div
425	\& 40
426	\& trap_nan RW Trap creation of NaN (undef = no)
427	\& undef
428	\& trap_inf RW Trap creation of +inf/-inf (undef = no)
429	\& undef
430	.Ve
431	.PP
432	By passing a reference to a hash you may set the configuration values. This
433	works only for values that a marked with a \f(CW\(C`RW\(C'\fR above, anything else is
434	read\-only.
435	.SH "BUGS"
436	.IX Header "BUGS"
437	Some things are not yet implemented, or only implemented half\-way:
438	.IP "inf handling (partial)" 2
439	.IX Item "inf handling (partial)"
440	.PD 0
441	.IP "NaN handling (partial)" 2
442	.IX Item "NaN handling (partial)"
443	.IP "rounding (not implemented except for bceil/bfloor)" 2
444	.IX Item "rounding (not implemented except for bceil/bfloor)"
445	.ie n .IP "$x ** $y\fR where \f(CW$y is not an integer" 2
446	.el .IP "$x ** \f(CW$y\fR where \f(CW$y\fR is not an integer" 2
447	.IX Item "$x ** $y where $y is not an integer"
448	.IP "\fIbmod()\fR, \fIblog()\fR, \fIbmodinv()\fR and \fIbmodpow()\fR (partial)" 2
449	.IX Item "bmod(), blog(), bmodinv() and bmodpow() (partial)"
450	.PD
451	.SH "LICENSE"
452	.IX Header "LICENSE"
453	This program is free software; you may redistribute it and/or modify it under
454	the same terms as Perl itself.
455	.SH "SEE ALSO"
456	.IX Header "SEE ALSO"
457	Math::BigFloat and Math::Big as well as Math::BigInt::BitVect,
458	Math::BigInt::Pari and Math::BigInt::GMP.
459	.PP
460	See <http://search.cpan.org/search?dist=bignum> for a way to use
461	Math::BigRat.
462	.PP
463	The package at <http://search.cpan.org/search?dist=Math%3A%3ABigRat>
464	may contain more documentation and examples as well as testcases.
465	.SH "AUTHORS"
466	.IX Header "AUTHORS"
467	(C) by Tels <http://bloodgate.com/> 2001 \- 2005.