'\"
'\" Copyright (c) 1993 The Regents of the University of California.
'\" Copyright (c) 1994-2000 Sun Microsystems, Inc.
'\" Copyright (c) 2005 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
.nf
\fBpackage require Tcl 8.5-\fR

\fB::tcl::mathfunc::abs\fI arg\fR
\fB::tcl::mathfunc::acos\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::acosh\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::asin\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::asin\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::atan\fI arg\fR
\fB::tcl::mathfunc::atan2\fI y x\fR
.VS TIP745
\fB::tcl::mathfunc::atan\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::bool\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::cbrt\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::ceil\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::copysign\fI x y\fR
.VE TIP745
\fB::tcl::mathfunc::cos\fI arg\fR
\fB::tcl::mathfunc::cosh\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::dim\fI x y\fR
.VE TIP745
\fB::tcl::mathfunc::double\fI arg\fR
\fB::tcl::mathfunc::entier\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::erf\fI arg\fR
\fB::tcl::mathfunc::erfc\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::exp\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::exp2\fI arg\fR
\fB::tcl::mathfunc::expm1\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::floor\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::fma\fI x y z\fR
.VE TIP745
\fB::tcl::mathfunc::fmod\fI x y\fR
\fB::tcl::mathfunc::hypot\fI x y\fR
\fB::tcl::mathfunc::int\fI arg\fR
.VS TIP521
\fB::tcl::mathfunc::isfinite\fI arg\fR
\fB::tcl::mathfunc::isinf\fI arg\fR
\fB::tcl::mathfunc::isnan\fI arg\fR
\fB::tcl::mathfunc::isnormal\fI arg\fR
.VE TIP521
\fB::tcl::mathfunc::isqrt\fI arg\fR
.VS TIP521
\fB::tcl::mathfunc::issubnormal\fI arg\fR
\fB::tcl::mathfunc::isunordered\fI x y\fR
.VE TIP521
.VS TIP745
\fB::tcl::mathfunc::lgamma\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::log\fI arg\fR
\fB::tcl::mathfunc::log10\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::log1p\fI arg\fR
\fB::tcl::mathfunc::log2\fI arg\fR
\fB::tcl::mathfunc::logb\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::max\fI arg\fR ?\fIarg ...\fR?
\fB::tcl::mathfunc::min\fI arg\fR ?\fIarg ...\fR?
.VS TIP745
\fB::tcl::mathfunc::nextafter\fI x y\fR
.VE TIP745
\fB::tcl::mathfunc::pow\fI x y\fR
\fB::tcl::mathfunc::rand\fR
.VS TIP745
\fB::tcl::mathfunc::remainder\fI x y\fR
.VE TIP745
\fB::tcl::mathfunc::round\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::signbit\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::sin\fI arg\fR
\fB::tcl::mathfunc::sinh\fI arg\fR
\fB::tcl::mathfunc::sqrt\fI arg\fR
\fB::tcl::mathfunc::srand\fI arg\fR
\fB::tcl::mathfunc::tan\fI arg\fR
\fB::tcl::mathfunc::tanh\fI arg\fR
.VS TIP745
\fB::tcl::mathfunc::gamma\fI arg\fR
\fB::tcl::mathfunc::trunc\fI arg\fR
.VE TIP745
\fB::tcl::mathfunc::wide\fI arg\fR
.fi
.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 3.2c 6.4c 9.6c
\fBabs\fR	\fBacos\fR	\fBacosh\fR	\fBasin\fR
\fBasinh\fR	\fBatan\fR	\fBatan2\fR	\fBatanh\fR
\fBbool\fR	\fBcbrt\fR	\fBcopysign\fR	\fBceil\fR
\fBcos\fR	\fBcosh\fR	\fBdim\fR	\fBdouble\fR
\fBentier\fR	\fBerf\fR	\fBerfc\fR	\fBexp\fR
\fBexp2\fR	\fBexpm1\fR	\fBfloor\fR	\fBfma\fR
\fBfmod\fR	\fBgamma\fR	\fBhypot\fR	\fBint\fR
\fBisfinite\fR	\fBisinf\fR	\fBisnan\fR	\fBisnormal\fR
\fBisqrt\fR	\fBissubnormal\fR	\fBisunordered\fR	\fBldexp\fR
\fBlgamma\fR	\fBlog\fR	\fBlog10\fR	\fBlog1p\fR
\fBlog2\fR	\fBlogb\fR	\fBmax\fR	\fBmin\fR
\fBnextafter\fR	\fBpow\fR	\fBrand\fR	\fBremainder\fR
\fBround\fR	\fBsin\fR	\fBsinh\fR	\fBsqrt\fR
\fBsrand\fR	\fBtan\fR	\fBtanh\fR	\fBtrunc\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.
.SS "DETAILED DEFINITIONS"
.\" COMMAND: abs
.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.
.\" COMMAND: acos
.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].
.\" COMMAND: acosh
.TP
\fBacosh \fIarg\fR
.VS TIP745
Returns the arc hyperbolic cosine of \fIarg\fR, in the range [\fI0\fR,\fIinf\fR]
radians. \fIArg\fR should be in the range [\fI1\fR,\fIinf\fR].
.VE TIP745
.\" COMMAND: asin
.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].
.\" COMMAND: asinh
.TP
\fBasinh \fIarg\fR
.VS TIP745
Returns the arc hyperbolic sine of \fIarg\fR, in the range [\fI\-inf\fR,\fIinf\fR].
.VE TIP745
.\" COMMAND: atan
.TP
\fBatan \fIarg\fR
.
Returns the arc tangent of \fIarg\fR, in the range [\fI\-pi/2\fR,\fIpi/2\fR]
radians.
.\" COMMAND: atan2
.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}]" .
.\" COMMAND: atanh
.TP
\fBatanh \fIarg\fR
.VS TIP745
Returns the arc hyperbolic tangent of \fIarg\fR, in the range [\fI\-inf\fR,\fIinf\fR].
\fIArg\fR should be in the range [\fI\-1\fR,\fI1\fR].
.VE TIP745
.\" COMMAND: bool
.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.
.\" COMMAND: cbrt
.TP
\fBcbrt \fIarg\fR
.VS TIP745
The argument may be any numeric value.  Returns a floating-point
value that is the cube root of \fIarg\fR.  May return \fBInf\fR when the
argument is a numeric value that exceeds the cube of the maximum value of
the floating-point range.
.VE TIP745
.\" COMMAND: ceil
.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.
.\" COMMAND: copysign
.TP
\fBcopysign \fIx y\fR
.VS TIP745
Returns the floating-point value with the magnitude of \fIx\fR and sign of \fIy\fR.
.VE TIP745
.\" COMMAND: cos
.TP
\fBcos \fIarg\fR
.
Returns the cosine of \fIarg\fR, measured in radians.
.\" COMMAND: cosh
.TP
\fBcosh \fIarg\fR
.
Returns the hyperbolic cosine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.\" COMMAND: dim
.TP
\fBdim \fIx y\fR
.VS TIP745
Returns the floating-point value that is the maximum of 0 and \fIx\fR\-\fIy\fR.
.VE TIP745
.\" COMMAND: double
.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.
.\" COMMAND: entier
.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.
.\" COMMAND: erf
.TP
\fBerf \fIarg\fR
.VS TIP745
Computes the Gauss error function of the numeric value \fIarg\fR.
.VE TIP745
.\" COMMAND: erfc
.TP
\fBerfc \fIarg\fR
.VS TIP745
Computes the complementary error function of the numeric value \fIarg\fR.
.VE TIP745
.\" COMMAND: exp
.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.
.\" COMMAND: exp2
.TP
\fBexp2 \fIarg\fR
.VS TIP745
Returns the 2 to the power of \fIarg\fR, defined as \fB2\fR**\fIarg\fR.
The result is always a floating point number except if it would cause an
overflow, when an error is returned.
.VE TIP745
.\" COMMAND: expm1
.TP
\fBexpm1 \fIarg\fR
.VS TIP745
Returns the exponential of \fIarg\fR, minus 1, defined as \fIe\fR**\fIarg\fR\-\fB1\fR.
If the result would cause an overflow, an error is returned.
Use of this function can be numerically preferable to of \fBexp\fR for values
close to 1, and is matched with \fBlog1p\fR.
.VE TIP745
.\" COMMAND: floor
.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.
.\" COMMAND: fma
.TP
\fBfma \fIx y z\fR
.VS TIP745
Returns the floating-point value that is the sum of the product of \fIx\fR and
\fIy\fR, and \fIz\fR, without unnecessarily losing intermediate accuracy.
.VE TIP745
.\" COMMAND: fmod
.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.
.\" COMMAND: gamma
.TP
\fBgamma \fIarg\fR
.VS TIP745
Returns the absolute value of the gamma function of \fIarg\fR (a generalized factorial).
If the result would cause an overflow, an error is returned.
.VE TIP745
.\" COMMAND: hypot
.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.
.\" COMMAND: int
.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.
.\" COMMAND: isfinite
.TP
\fBisfinite \fIarg\fR
.VS TIP521
Returns 1 if the floating-point number \fIarg\fR is finite. That is, if it is
zero, subnormal, or normal. Returns 0 if the number is infinite or NaN. Throws
an error if \fIarg\fR cannot be promoted to a floating-point value.
.VE TIP521
.\" COMMAND: isinf
.TP
\fBisinf \fIarg\fR
.VS TIP521
Returns 1 if the floating-point number \fIarg\fR is infinite. Returns 0 if the
number is finite or NaN. Throws an error if \fIarg\fR cannot be promoted to a
floating-point value.
.VE TIP521
.\" COMMAND: isnan
.TP
\fBisnan \fIarg\fR
.VS TIP521
Returns 1 if the floating-point number \fIarg\fR is Not-a-Number. Returns 0 if
the number is finite or infinite. Throws an error if \fIarg\fR cannot be
promoted to a floating-point value.
.VE TIP521
.\" COMMAND: isnormal
.TP
\fBisnormal \fIarg\fR
.VS TIP521
Returns 1 if the floating-point number \fIarg\fR is normal. Returns 0 if the
number is zero, subnormal, infinite or NaN. Throws an error if \fIarg\fR
cannot be promoted to a floating-point value.
.VE TIP521
.\" COMMAND: isqrt
.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.
.\" COMMAND: issubnormal
.TP
\fBissubnormal \fIarg\fR
.VS TIP521
Returns 1 if the floating-point number \fIarg\fR is subnormal, i.e., the
result of gradual underflow. Returns 0 if the number is zero, normal, infinite
or NaN. Throws an error if \fIarg\fR cannot be promoted to a floating-point
value.
.VE TIP521
.\" COMMAND: isunordered
.TP
\fBisunordered \fIx y\fR
.VS TIP521
Returns 1 if \fIx\fR and \fIy\fR cannot be compared for ordering, that is, if
either one is NaN. Returns 0 if both values can be ordered, that is, if they
are both chosen from among the set of zero, subnormal, normal and infinite
values. Throws an error if either \fIx\fR or \fIy\fR cannot be promoted to a
floating-point value.
.VE TIP521
.\" COMMAND: ldexp
.TP
\fBldexp \fIx y\fR
.VS TIP745
Multiplies a floating-point value \fIx\fR by the number 2 raised to the \fIy\fR power.
.VE TIP745
.\" COMMAND: lgamma
.TP
\fBlgamma \fIarg\fR
.VS TIP745
Returns the natural logarithm of the absolute value of the gamma function of \fIarg\fR.
If the result would cause an overflow, an error is returned.
.VE TIP745
.\" COMMAND: log
.TP
\fBlog \fIarg\fR
.
Returns the natural logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.\" COMMAND: log10
.TP
\fBlog10 \fIarg\fR
.
Returns the base 10 logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.\" COMMAND: log1p
.TP
\fBlog1p \fIarg\fR
.VS TIP745
Returns the natural logarithm of \fIarg\fR+\fB1\fR.  \fIArg\fR must be a
value greater than \-1. This function is numerically preferable to \fBlog\fR
for values very close to 1, and is matched with \fBexpm1\fR.
.VE TIP745
.\" COMMAND: log2
.TP
\fBlog2 \fIarg\fR
.VS TIP745
Returns the base 2 logarithm of \fIarg\fR.  \fIArg\fR must be a
positive value.
.VE TIP745
.\" COMMAND: logb
.TP
\fBlogb \fIarg\fR
.VS TIP745
Returns the value of the unbiased radix-independent exponent from the
floating-point argument \fIarg\fR.
.VE TIP745
.\" COMMAND: max
.TP
\fBmax \fIarg\fB \fR...
.
Accepts one or more numeric arguments.  Returns the one argument
with the greatest value.
.\" COMMAND: min
.TP
\fBmin \fIarg\fB \fR...
.
Accepts one or more numeric arguments.  Returns the one argument
with the least value.
.\" COMMAND: nextafter
.TP
\fBnextafter \fIx y\fR
.VS TIP745
Returns the next floating-point value after (or before) \fIx\fR in the
direction of \fIy\fR. If \fIx\fR and \fIy\fR are equal, returns \fIy\fR.
.VE TIP745
.\" COMMAND: pow
.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.
.\" COMMAND: rand
.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.
.\" COMMAND: remainder
.TP
\fBremainder \fIx y\fR
.VS TIP745
Computes the IEEE remainder of the floating point division operation \fIx\fR/\fIy\fR.
.VE TIP745
.\" COMMAND: round
.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.
.\" COMMAND: signbit
.TP
\fBsignbit \fIarg\fR
.VS TIP745
Get the sign bit of the numeric value, \fIarg\fR, as 0 (positive) or 1 (negative).
.VE TIP745
.\" COMMAND: sin
.TP
\fBsin \fIarg\fR
.
Returns the sine of \fIarg\fR, measured in radians.
.\" COMMAND: sinh
.TP
\fBsinh \fIarg\fR
.
Returns the hyperbolic sine of \fIarg\fR.  If the result would cause
an overflow, an error is returned.
.\" COMMAND: sqrt
.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.
.\" COMMAND: srand
.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.
.\" COMMAND: tan
.TP
\fBtan \fIarg\fR
.
Returns the tangent of \fIarg\fR, measured in radians.
.\" COMMAND: tanh
.TP
\fBtanh \fIarg\fR
.
Returns the hyperbolic tangent of \fIarg\fR.
.\" COMMAND: trunc
.TP
\fBtrunc \fIarg\fR
.VS TIP745
Returns the nearest integer not greater in magnitude than \fIarg\fR.
.VE TIP745
.\" COMMAND: wide
.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"
divmod(n), expr(n), fpclassify(n), frexp(n),
mathop(n), modf(n), namespace(n), remquo(n)
.SH "COPYRIGHT"
.nf
Copyright \(co 1993 The Regents of the University of California.
Copyright \(co 1994-2000 Sun Microsystems Incorporated.
Copyright \(co 2005-2006 Kevin B. Kenny <kennykb@acm.org>.
.fi
'\" Local Variables:
'\" mode: nroff
'\" fill-column: 78
'\" End:
