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-'\"
-'\" 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.
-'\"
-.TH mathfunc n 8.5 Tcl "Tcl Mathematical Functions"
-.so man.macros
-.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::entier\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::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
-.
-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.
-.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,
-approximately
-.QW "\fBsqrt\fR [\fBexpr\fR {\fIx\fB*\fIx\fB+\fIy\fB*\fIy\fR}]"
-except for being more numerically stable when the two arguments have
-substantially different magnitudes.
-.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 the \fBwordSize\fR
-element of the \fBtcl_platform\fR array.
-.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
-'\" Local Variables:
-'\" mode: nroff
-'\" fill-column: 78
-'\" End: