.\"
'\" 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.
'\" 
'\" RCS: @(#) $Id: mathfunc.n,v 1.5 2005/05/26 08:08:49 dkf Exp $
'\" 
.so man.macros
.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
\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::log\fR \fIarg\fR
.br
\fB::tcl::mathfunc::log10\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,$x)\fR by converting them to calls of the
form \fB[tcl::math::sin [expr {$x}]]\fR or
\fB[tcl::math::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	\fBcos\fR	\fBint\fR	\fBsinh\fR
\fBacos\fR	\fBcosh\fR	\fBlog\fR	\fBsqrt\fR
\fBasin\fR	\fBdouble\fR	\fBlog10\fR	\fBsrand\fR
\fBatan\fR	\fBexp\fR	\fBpow\fR	\fBtan\fR
\fBatan2\fR	\fBfloor\fR	\fBrand\fR	\fBtanh\fR
\fBbool\fR	\fBfmod\fR	\fBround\fR	\fBwide\fR
\fBceil\fR	\fBhypot\fR	\fBsin\fR
.DE
.PP
.TP
\fBabs(\fIarg\fB)\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\fB)\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\fB)\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\fB)\fR
Returns the arc tangent of \fIarg\fR, in the range [\fI-pi/2\fR,\fIpi/2\fR]
radians.
.TP
\fBatan2(\fIy, x\fB)\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 \fBatan(\fIy/x\fB)\fR.
.TP
\fBbool(\fIarg\fB)\fR
Accepts any numerical 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\fB)\fR
Returns the smallest integral floating-point value (i.e. with a zero
fractional part) not less than \fIarg\fR.
.TP
\fBcos(\fIarg\fB)\fR
Returns the cosine of \fIarg\fR, measured in radians.
.TP
\fBcosh(\fIarg\fB)\fR
Returns the hyperbolic cosine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.TP
\fBdouble(\fIarg\fB)\fR
If \fIarg\fR is a floating-point value, returns \fIarg\fR, otherwise converts
\fIarg\fR to floating-point and returns the converted value.
.TP
\fBexp(\fIarg\fB)\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\fB)\fR
Returns the largest integral floating-point value (i.e. with a zero
fractional part) not greater than \fIarg\fR.
.TP
\fBfmod(\fIx, y\fB)\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\fB)\fR
Computes the length of the hypotenuse of a right-angled triangle
\fBsqrt(\fIx\fR*\fIx\fR+\fIy\fR*\fIy\fB)\fR.
.TP
\fBint(\fIarg\fB)\fR
If \fIarg\fR is an integer value of the same width as the machine
word, returns \fIarg\fR, otherwise
converts \fIarg\fR to an integer (of the same size as a machine word,
i.e. 32-bits on 32-bit systems, and 64-bits on 64-bit systems) by
truncation and returns the converted value.
.TP
\fBlog(\fIarg\fB)\fR
Returns the natural logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.TP
\fBlog10(\fIarg\fB)\fR
Returns the base 10 logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.TP
\fBpow(\fIx, y\fB)\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\fB)\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\fB)\fR
Returns the sine of \fIarg\fR, measured in radians.
.TP
\fBsinh(\fIarg\fB)\fR
Returns the hyperbolic sine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.TP
\fBsqrt(\fIarg\fB)\fR
Returns the square root of \fIarg\fR.  \fIArg\fR must be non-negative.
.TP
\fBsrand(\fIarg\fB)\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\fB)\fR
Returns the tangent of \fIarg\fR, measured in radians.
.TP
\fBtanh(\fIarg\fB)\fR
Returns the hyperbolic tangent of \fIarg\fR.
.TP
\fBwide(\fIarg\fB)\fR
Converts \fIarg\fR to an integer value at least 64-bits wide (by sign-extension
if \fIarg\fR is a 32-bit number) if it is not one already.
.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..
.SH "SEE ALSO"
expr(n), namespace(n)
.SH "COPYRIGHT"
Copyright (c) 1993 The Regents of the University of California.
.br
Copyright (c) 1994-2000 Sun Microsystems Incorporated.
.br
Copyright (c) 2005 by Kevin B. Kenny <kennykb@acm.org>. All rights reserved.
