Import Tcl 8.5.15 (as of svn r89086)
This commit is contained in:
Zachary Ware
271
doc/mathfunc.n
Normal file
271
doc/mathfunc.n
Normal file
@@ -0,0 +1,271 @@
|
||||
'\"
|
||||
'\" 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.
|
||||
'\"
|
||||
.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
|
||||
.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
|
||||
Reference in New Issue
Block a user