mathfunc 
Mathematical functions for Tcl expressions
package require Tcl 8.5
::tcl::mathfunc::abs arg
::tcl::mathfunc::acos arg
::tcl::mathfunc::asin arg
::tcl::mathfunc::atan arg
::tcl::mathfunc::atan2 y x
::tcl::mathfunc::bool arg
::tcl::mathfunc::ceil arg
::tcl::mathfunc::cos arg
::tcl::mathfunc::cosh arg
::tcl::mathfunc::double arg
::tcl::mathfunc::entier arg
::tcl::mathfunc::exp arg
::tcl::mathfunc::floor arg
::tcl::mathfunc::fmod x y
::tcl::mathfunc::hypot x y
::tcl::mathfunc::int arg
::tcl::mathfunc::isqrt arg
::tcl::mathfunc::log arg
::tcl::mathfunc::log10 arg
::tcl::mathfunc::max arg ?arg ...?
::tcl::mathfunc::min arg ?arg ...?
::tcl::mathfunc::pow x y
::tcl::mathfunc::rand
::tcl::mathfunc::round arg
::tcl::mathfunc::sin arg
::tcl::mathfunc::sinh arg
::tcl::mathfunc::sqrt arg
::tcl::mathfunc::srand arg
::tcl::mathfunc::tan arg
::tcl::mathfunc::tanh arg
::tcl::mathfunc::wide arg
The expr command handles mathematical functions of the form
sin($x) or atan2($y,$x) by converting them to calls of the
form [tcl::mathfunc::sin [expr {$x}]] or
[tcl::mathfunc::atan2 [expr {$y}] [expr {$x}]].
A number of math functions are available by default within the
namespace ::tcl::mathfunc; these functions are also available
for code apart from expr, by invoking the given commands
directly.
Tcl supports the following mathematical functions in expressions, all
of which work solely with floatingpoint numbers unless otherwise noted:
In addition to these predefined functions, applications may
define additional functions by using proc (or any other method,
such as interp alias or Tcl_CreateObjCommand) to define
new commands in the tcl::mathfunc namespace. In addition, an
obsolete interface named Tcl_CreateMathFunc() is available to
extensions that are written in C. The latter interface is not recommended
for new implementations.

abs arg
 Returns the absolute value of arg. Arg may be either
integer or floatingpoint, and the result is returned in the same form.

acos arg
 Returns the arc cosine of arg, in the range [0,pi]
radians. Arg should be in the range [1,1].

asin arg
 Returns the arc sine of arg, in the range [pi/2,pi/2]
radians. Arg should be in the range [1,1].

atan arg
 Returns the arc tangent of arg, in the range [pi/2,pi/2]
radians.

atan2 y x
 Returns the arc tangent of y/x, in the range [pi,pi]
radians. x and y cannot both be 0. If x is greater
than 0, this is equivalent to
"atan [expr {y/x}]".

bool arg
 Accepts any numeric value, or any string acceptable to
string is boolean, and returns the corresponding
boolean value 0 or 1. Nonzero numbers are true.
Other numbers are false. Nonnumeric strings produce boolean value in
agreement with string is true and string is false.

ceil arg
 Returns the smallest integral floatingpoint value (i.e. with a zero
fractional part) not less than arg. The argument may be any
numeric value.

cos arg
 Returns the cosine of arg, measured in radians.

cosh arg
 Returns the hyperbolic cosine of arg. If the result would cause
an overflow, an error is returned.

double arg
 The argument may be any numeric value,
If arg is a floatingpoint value, returns arg, otherwise converts
arg to floatingpoint and returns the converted value. May return
Inf or Inf when the argument is a numeric value that exceeds
the floatingpoint range.

entier arg
 The argument may be any numeric value. The integer part of arg
is determined and returned. The integer range returned by this function
is unlimited, unlike int and wide which
truncate their range to fit in particular storage widths.

exp arg
 Returns the exponential of arg, defined as e**arg.
If the result would cause an overflow, an error is returned.

floor arg
 Returns the largest integral floatingpoint value (i.e. with a zero
fractional part) not greater than arg. The argument may be
any numeric value.

fmod x y
 Returns the floatingpoint remainder of the division of x by
y. If y is 0, an error is returned.

hypot x y
 Computes the length of the hypotenuse of a rightangled triangle,
approximately
"sqrt [expr {x*x+y*y}]" except for being more numerically stable when the two arguments have
substantially different magnitudes.

int arg
 The argument may be any numeric value. The integer part of arg
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 wordSize
element of the tcl_platform array.

isqrt arg
 Computes the integer part of the square root of arg. Arg must be
a positive value, either an integer or a floating point number.
Unlike sqrt, which is limited to the precision of a floating point
number, isqrt will return a result of arbitrary precision.

log arg
 Returns the natural logarithm of arg. Arg must be a
positive value.

log10 arg
 Returns the base 10 logarithm of arg. Arg must be a
positive value.

max arg ...
 Accepts one or more numeric arguments. Returns the one argument
with the greatest value.

min arg ...
 Accepts one or more numeric arguments. Returns the one argument
with the least value.

pow x y
 Computes the value of x raised to the power y. If x
is negative, y must be an integer value.
 rand
 Returns a pseudorandom floatingpoint value in the range (0,1).
The generator algorithm is a simple linear congruential generator that
is not cryptographically secure. Each result from rand completely
determines all future results from subsequent calls to rand, so
rand should not be used to generate a sequence of secrets, such as
onetime passwords. The seed of the generator is initialized from the
internal clock of the machine or may be set with the srand function.

round arg
 If arg is an integer value, returns arg, otherwise converts
arg to integer by rounding and returns the converted value.

sin arg
 Returns the sine of arg, measured in radians.

sinh arg
 Returns the hyperbolic sine of arg. If the result would cause
an overflow, an error is returned.

sqrt arg
 The argument may be any nonnegative numeric value. Returns a floatingpoint
value that is the square root of arg. May return Inf when the
argument is a numeric value that exceeds the square of the maximum value of
the floatingpoint range.

srand arg
 The arg, which must be an integer, is used to reset the seed for
the random number generator of rand. Returns the first random
number (see rand) from that seed. Each interpreter has its own seed.

tan arg
 Returns the tangent of arg, measured in radians.

tanh arg
 Returns the hyperbolic tangent of arg.

wide arg
 The argument may be any numeric value. The integer part of arg
is determined, and then the low order 64 bits of that integer value
are returned as an integer value.
expr(n), mathop(n), namespace(n)
Copyright (c) 1993 The Regents of the University of California.
Copyright (c) 19942000 Sun Microsystems Incorporated.
Copyright (c) 2005, 2006 by Kevin B. Kenny <kennykb@acm.org>.