path: root/usr/man/mann/mathfunc.n

'\"
'\" Copyright (c) 1993 The Regents of the University of California.
'\" Copyright (c) 1994-2000 Sun Microsystems, Inc.
'\" Copyright (c) 2005 by Kevin B. Kenny <kennykb@acm.org>. All rights reserved
'\"
'\" See the file "license.terms" for information on usage and redistribution
'\" of this file, and for a DISCLAIMER OF ALL WARRANTIES.
'\" 
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,
.\"	and indent is equivalent to second arg of .IP (shouldn't ever be
.\"	needed;  use .AS below instead)
.\"
.\" .AS ?type? ?name?
.\"	Give maximum sizes of arguments for setting tab stops.  Type and
.\"	name are examples of largest possible arguments that will be passed
.\"	to .AP later.  If args are omitted, default tab stops are used.
.\"
.\" .BS
.\"	Start box enclosure.  From here until next .BE, everything will be
.\"	enclosed in one large box.
.\"
.\" .BE
.\"	End of box enclosure.
.\"
.\" .CS
.\"	Begin code excerpt.
.\"
.\" .CE
.\"	End code excerpt.
.\"
.\" .VS ?version? ?br?
.\"	Begin vertical sidebar, for use in marking newly-changed parts
.\"	of man pages.  The first argument is ignored and used for recording
.\"	the version when the .VS was added, so that the sidebars can be
.\"	found and removed when they reach a certain age.  If another argument
.\"	is present, then a line break is forced before starting the sidebar.
.\"
.\" .VE
.\"	End of vertical sidebar.
.\"
.\" .DS
.\"	Begin an indented unfilled display.
.\"
.\" .DE
.\"	End of indented unfilled display.
.\"
.\" .SO ?manpage?
.\"	Start of list of standard options for a Tk widget. The manpage
.\"	argument defines where to look up the standard options; if
.\"	omitted, defaults to "options". The options follow on successive
.\"	lines, in three columns separated by tabs.
.\"
.\" .SE
.\"	End of list of standard options for a Tk widget.
.\"
.\" .OP cmdName dbName dbClass
.\"	Start of description of a specific option.  cmdName gives the
.\"	option's name as specified in the class command, dbName gives
.\"	the option's name in the option database, and dbClass gives
.\"	the option's class in the option database.
.\"
.\" .UL arg1 arg2
.\"	Print arg1 underlined, then print arg2 normally.
.\"
.\" .QW arg1 ?arg2?
.\"	Print arg1 in quotes, then arg2 normally (for trailing punctuation).
.\"
.\" .PQ arg1 ?arg2?
.\"	Print an open parenthesis, arg1 in quotes, then arg2 normally
.\"	(for trailing punctuation) and then a closing parenthesis.
.\"
.\"	# Set up traps and other miscellaneous stuff for Tcl/Tk man pages.
.if t .wh -1.3i ^B
.nr ^l \n(.l
.ad b
.\"	# Start an argument description
.de AP
.ie !"\\$4"" .TP \\$4
.el \{\
.   ie !"\\$2"" .TP \\n()Cu
.   el          .TP 15
.\}
.ta \\n()Au \\n()Bu
.ie !"\\$3"" \{\
\&\\$1 \\fI\\$2\\fP (\\$3)
.\".b
.\}
.el \{\
.br
.ie !"\\$2"" \{\
\&\\$1	\\fI\\$2\\fP
.\}
.el \{\
\&\\fI\\$1\\fP
.\}
.\}
..
.\"	# define tabbing values for .AP
.de AS
.nr )A 10n
.if !"\\$1"" .nr )A \\w'\\$1'u+3n
.nr )B \\n()Au+15n
.\"
.if !"\\$2"" .nr )B \\w'\\$2'u+\\n()Au+3n
.nr )C \\n()Bu+\\w'(in/out)'u+2n
..
.AS Tcl_Interp Tcl_CreateInterp in/out
.\"	# BS - start boxed text
.\"	# ^y = starting y location
.\"	# ^b = 1
.de BS
.br
.mk ^y
.nr ^b 1u
.if n .nf
.if n .ti 0
.if n \l'\\n(.lu\(ul'
.if n .fi
..
.\"	# BE - end boxed text (draw box now)
.de BE
.nf
.ti 0
.mk ^t
.ie n \l'\\n(^lu\(ul'
.el \{\
.\"	Draw four-sided box normally, but don't draw top of
.\"	box if the box started on an earlier page.
.ie !\\n(^b-1 \{\
\h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
.\}
.el \}\
\h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\l'|0u-1.5n\(ul'
.\}
.\}
.fi
.br
.nr ^b 0
..
.\"	# VS - start vertical sidebar
.\"	# ^Y = starting y location
.\"	# ^v = 1 (for troff;  for nroff this doesn't matter)
.de VS
.if !"\\$2"" .br
.mk ^Y
.ie n 'mc \s12\(br\s0
.el .nr ^v 1u
..
.\"	# VE - end of vertical sidebar
.de VE
.ie n 'mc
.el \{\
.ev 2
.nf
.ti 0
.mk ^t
\h'|\\n(^lu+3n'\L'|\\n(^Yu-1v\(bv'\v'\\n(^tu+1v-\\n(^Yu'\h'-|\\n(^lu+3n'
.sp -1
.fi
.ev
.\}
.nr ^v 0
..
.\"	# Special macro to handle page bottom:  finish off current
.\"	# box/sidebar if in box/sidebar mode, then invoked standard
.\"	# page bottom macro.
.de ^B
.ev 2
'ti 0
'nf
.mk ^t
.if \\n(^b \{\
.\"	Draw three-sided box if this is the box's first page,
.\"	draw two sides but no top otherwise.
.ie !\\n(^b-1 \h'-1.5n'\L'|\\n(^yu-1v'\l'\\n(^lu+3n\(ul'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c
.el \h'-1.5n'\L'|\\n(^yu-1v'\h'\\n(^lu+3n'\L'\\n(^tu+1v-\\n(^yu'\h'|0u'\c
.\}
.if \\n(^v \{\
.nr ^x \\n(^tu+1v-\\n(^Yu
\kx\h'-\\nxu'\h'|\\n(^lu+3n'\ky\L'-\\n(^xu'\v'\\n(^xu'\h'|0u'\c
.\}
.bp
'fi
.ev
.if \\n(^b \{\
.mk ^y
.nr ^b 2
.\}
.if \\n(^v \{\
.mk ^Y
.\}
..
.\"	# DS - begin display
.de DS
.RS
.nf
.sp
..
.\"	# DE - end display
.de DE
.fi
.RE
.sp
..
.\"	# SO - start of list of standard options
.de SO
'ie '\\$1'' .ds So \\fBoptions\\fR
'el .ds So \\fB\\$1\\fR
.SH "STANDARD OPTIONS"
.LP
.nf
.ta 5.5c 11c
.ft B
..
.\"	# SE - end of list of standard options
.de SE
.fi
.ft R
.LP
See the \\*(So manual entry for details on the standard options.
..
.\"	# OP - start of full description for a single option
.de OP
.LP
.nf
.ta 4c
Command-Line Name:	\\fB\\$1\\fR
Database Name:	\\fB\\$2\\fR
Database Class:	\\fB\\$3\\fR
.fi
.IP
..
.\"	# CS - begin code excerpt
.de CS
.RS
.nf
.ta .25i .5i .75i 1i
..
.\"	# CE - end code excerpt
.de CE
.fi
.RE
..
.\"	# UL - underline word
.de UL
\\$1\l'|0\(ul'\\$2
..
.\"	# QW - apply quotation marks to word
.de QW
.ie '\\*(lq'"' ``\\$1''\\$2
.\"" fix emacs highlighting
.el \\*(lq\\$1\\*(rq\\$2
..
.\"	# PQ - apply parens and quotation marks to word
.de PQ
.ie '\\*(lq'"' (``\\$1''\\$2)\\$3
.\"" fix emacs highlighting
.el (\\*(lq\\$1\\*(rq\\$2)\\$3
..
.\"	# QR - quoted range
.de QR
.ie '\\*(lq'"' ``\\$1''\\-``\\$2''\\$3
.\"" fix emacs highlighting
.el \\*(lq\\$1\\*(rq\\-\\*(lq\\$2\\*(rq\\$3
..
.\"	# MT - "empty" string
.de MT
.QW ""
..
.TH mathfunc n 8.5 Tcl "Tcl Mathematical Functions"
.BS
'\" Note:  do not modify the .SH NAME line immediately below!
.SH NAME
mathfunc \- Mathematical functions for Tcl expressions
.SH SYNOPSIS
package require \fBTcl 8.5\fR
.sp
\fB::tcl::mathfunc::abs\fR \fIarg\fR
.br
\fB::tcl::mathfunc::acos\fR \fIarg\fR
.br
\fB::tcl::mathfunc::asin\fR \fIarg\fR
.br
\fB::tcl::mathfunc::atan\fR \fIarg\fR
.br
\fB::tcl::mathfunc::atan2\fR \fIy\fR \fIx\fR
.br
\fB::tcl::mathfunc::bool\fR \fIarg\fR
.br
\fB::tcl::mathfunc::ceil\fR \fIarg\fR
.br
\fB::tcl::mathfunc::cos\fR \fIarg\fR
.br
\fB::tcl::mathfunc::cosh\fR \fIarg\fR
.br
\fB::tcl::mathfunc::double\fR \fIarg\fR
.br
.VS 8.5
\fB::tcl::mathfunc::entier\fR \fIarg\fR
.br
.VE 8.5
\fB::tcl::mathfunc::exp\fR \fIarg\fR
.br
\fB::tcl::mathfunc::floor\fR \fIarg\fR
.br
\fB::tcl::mathfunc::fmod\fR \fIx\fR \fIy\fR
.br
\fB::tcl::mathfunc::hypot\fR \fIx\fR \fIy\fR
.br
\fB::tcl::mathfunc::int\fR \fIarg\fR
.br
\fB::tcl::mathfunc::isqrt\fR \fIarg\fR
.br
\fB::tcl::mathfunc::log\fR \fIarg\fR
.br
\fB::tcl::mathfunc::log10\fR \fIarg\fR
.br
\fB::tcl::mathfunc::max\fR \fIarg\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathfunc::min\fR \fIarg\fR ?\fIarg\fR ...?
.br
\fB::tcl::mathfunc::pow\fR \fIx\fR \fIy\fR
.br
\fB::tcl::mathfunc::rand\fR
.br
\fB::tcl::mathfunc::round\fR \fIarg\fR
.br
\fB::tcl::mathfunc::sin\fR \fIarg\fR
.br
\fB::tcl::mathfunc::sinh\fR \fIarg\fR
.br
\fB::tcl::mathfunc::sqrt\fR \fIarg\fR
.br
\fB::tcl::mathfunc::srand\fR \fIarg\fR
.br
\fB::tcl::mathfunc::tan\fR \fIarg\fR
.br
\fB::tcl::mathfunc::tanh\fR \fIarg\fR
.br
\fB::tcl::mathfunc::wide\fR \fIarg\fR
.sp
.BE
.SH "DESCRIPTION"
.PP
The \fBexpr\fR command handles mathematical functions of the form
\fBsin($x)\fR or \fBatan2($y,$x)\fR by converting them to calls of the
form \fB[tcl::mathfunc::sin [expr {$x}]]\fR or
\fB[tcl::mathfunc::atan2 [expr {$y}] [expr {$x}]]\fR.
A number of math functions are available by default within the
namespace \fB::tcl::mathfunc\fR; these functions are also available
for code apart from \fBexpr\fR, by invoking the given commands
directly.
.PP
Tcl supports the following mathematical functions in expressions, all
of which work solely with floating-point numbers unless otherwise noted:
.DS
.ta 3c 6c 9c
\fBabs\fR	\fBacos\fR	\fBasin\fR	\fBatan\fR
\fBatan2\fR	\fBbool\fR	\fBceil\fR	\fBcos\fR
\fBcosh\fR	\fBdouble\fR	\fBentier\fR	\fBexp\fR
\fBfloor\fR	\fBfmod\fR	\fBhypot\fR	\fBint\fR
\fBisqrt\fR	\fBlog\fR	\fBlog10\fR	\fBmax\fR
\fBmin\fR	\fBpow\fR	\fBrand\fR	\fBround\fR
\fBsin\fR	\fBsinh\fR	\fBsqrt\fR	\fBsrand\fR
\fBtan\fR	\fBtanh\fR	\fBwide\fR
.DE
.PP
In addition to these predefined functions, applications may
define additional functions by using \fBproc\fR (or any other method,
such as \fBinterp alias\fR or \fBTcl_CreateObjCommand\fR) to define
new commands in the \fBtcl::mathfunc\fR namespace.  In addition, an
obsolete interface named \fBTcl_CreateMathFunc\fR() is available to
extensions that are written in C. The latter interface is not recommended
for new implementations.
.SS "DETAILED DEFINITIONS"
.TP
\fBabs \fIarg\fR
Returns the absolute value of \fIarg\fR.  \fIArg\fR may be either
integer or floating-point, and the result is returned in the same form.
.TP
\fBacos \fIarg\fR
Returns the arc cosine of \fIarg\fR, in the range [\fI0\fR,\fIpi\fR]
radians. \fIArg\fR should be in the range [\fI\-1\fR,\fI1\fR].
.TP
\fBasin \fIarg\fR
Returns the arc sine of \fIarg\fR, in the range [\fI\-pi/2\fR,\fIpi/2\fR]
radians.  \fIArg\fR should be in the range [\fI\-1\fR,\fI1\fR].
.TP
\fBatan \fIarg\fR
Returns the arc tangent of \fIarg\fR, in the range [\fI\-pi/2\fR,\fIpi/2\fR]
radians.
.TP
\fBatan2 \fIy x\fR
Returns the arc tangent of \fIy\fR/\fIx\fR, in the range [\fI\-pi\fR,\fIpi\fR]
radians.  \fIx\fR and \fIy\fR cannot both be 0.  If \fIx\fR is greater
than \fI0\fR, this is equivalent to
.QW "\fBatan \fR[\fBexpr\fR {\fIy\fB/\fIx\fR}]" .
.TP
\fBbool \fIarg\fR
Accepts any numeric value, or any string acceptable to
\fBstring is boolean\fR, and returns the corresponding 
boolean value \fB0\fR or \fB1\fR.  Non-zero numbers are true.
Other numbers are false.  Non-numeric strings produce boolean value in
agreement with \fBstring is true\fR and \fBstring is false\fR.
.TP
\fBceil \fIarg\fR
Returns the smallest integral floating-point value (i.e. with a zero
fractional part) not less than \fIarg\fR.  The argument may be any
numeric value.
.TP
\fBcos \fIarg\fR
Returns the cosine of \fIarg\fR, measured in radians.
.TP
\fBcosh \fIarg\fR
Returns the hyperbolic cosine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.TP
\fBdouble \fIarg\fR
The argument may be any numeric value,
If \fIarg\fR is a floating-point value, returns \fIarg\fR, otherwise converts
\fIarg\fR to floating-point and returns the converted value.  May return
\fBInf\fR or \fB\-Inf\fR when the argument is a numeric value that exceeds
the floating-point range.
.TP
\fBentier \fIarg\fR
.VS 8.5
The argument may be any numeric value.  The integer part of \fIarg\fR
is determined and returned.  The integer range returned by this function
is unlimited, unlike \fBint\fR and \fBwide\fR which
truncate their range to fit in particular storage widths.
.VE 8.5
.TP
\fBexp \fIarg\fR
Returns the exponential of \fIarg\fR, defined as \fIe\fR**\fIarg\fR.
If the result would cause an overflow, an error is returned.
.TP
\fBfloor \fIarg\fR
Returns the largest integral floating-point value (i.e. with a zero
fractional part) not greater than \fIarg\fR.  The argument may be
any numeric value.
.TP
\fBfmod \fIx y\fR
Returns the floating-point remainder of the division of \fIx\fR by
\fIy\fR.  If \fIy\fR is 0, an error is returned.
.TP
\fBhypot \fIx y\fR
Computes the length of the hypotenuse of a right-angled triangle
.QW "\fBsqrt\fR [\fBexpr\fR {\fIx\fB*\fIx\fB+\fIy\fB*\fIy\fR}]".
.TP
\fBint \fIarg\fR
The argument may be any numeric value.  The integer part of \fIarg\fR
is determined, and then the low order bits of that integer value up
to the machine word size are returned as an integer value.  For reference,
the number of bytes in the machine word are stored in
\fBtcl_platform(wordSize)\fR.
.TP
\fBisqrt \fIarg\fR
Computes the integer part of the square root of \fIarg\fR.  \fIArg\fR must be
a positive value, either an integer or a floating point number.
Unlike \fBsqrt\fR, which is limited to the precision of a floating point
number, \fIisqrt\fR will return a result of arbitrary precision.
.TP
\fBlog \fIarg\fR
Returns the natural logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.TP
\fBlog10 \fIarg\fR
Returns the base 10 logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.TP
\fBmax \fIarg\fB \fI...\fR
Accepts one or more numeric arguments.  Returns the one argument
with the greatest value.
.TP
\fBmin \fIarg\fB \fI...\fR
Accepts one or more numeric arguments.  Returns the one argument
with the least value.
.TP
\fBpow \fIx y\fR
Computes the value of \fIx\fR raised to the power \fIy\fR.  If \fIx\fR
is negative, \fIy\fR must be an integer value.
.TP
\fBrand\fR
Returns a pseudo-random floating-point value in the range (\fI0\fR,\fI1\fR).  
The generator algorithm is a simple linear congruential generator that
is not cryptographically secure.  Each result from \fBrand\fR completely
determines all future results from subsequent calls to \fBrand\fR, so
\fBrand\fR should not be used to generate a sequence of secrets, such as
one-time passwords.  The seed of the generator is initialized from the
internal clock of the machine or may be set with the \fBsrand\fR function.
.TP
\fBround \fIarg\fR
If \fIarg\fR is an integer value, returns \fIarg\fR, otherwise converts
\fIarg\fR to integer by rounding and returns the converted value.
.TP
\fBsin \fIarg\fR
Returns the sine of \fIarg\fR, measured in radians.
.TP
\fBsinh \fIarg\fR
Returns the hyperbolic sine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.TP
\fBsqrt \fIarg\fR
The argument may be any non-negative numeric value.  Returns a floating-point
value that is the square root of \fIarg\fR.  May return \fBInf\fR when the
argument is a numeric value that exceeds the square of the maximum value of
the floating-point range.
.TP
\fBsrand \fIarg\fR
The \fIarg\fR, which must be an integer, is used to reset the seed for
the random number generator of \fBrand\fR.  Returns the first random
number (see \fBrand\fR) from that seed.  Each interpreter has its own seed.
.TP
\fBtan \fIarg\fR
Returns the tangent of \fIarg\fR, measured in radians.
.TP
\fBtanh \fIarg\fR
Returns the hyperbolic tangent of \fIarg\fR.
.TP
\fBwide \fIarg\fR
The argument may be any numeric value.  The integer part of \fIarg\fR
is determined, and then the low order 64 bits of that integer value
are returned as an integer value.  
.SH "SEE ALSO"
expr(n), mathop(n), namespace(n)
.SH "COPYRIGHT"
.nf
Copyright (c) 1993 The Regents of the University of California.
Copyright (c) 1994-2000 Sun Microsystems Incorporated.
Copyright (c) 2005, 2006 by Kevin B. Kenny <kennykb@acm.org>.
.fi