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```mathfunc(n)               Tcl Mathematical Functions               mathfunc(n)

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NAME
mathfunc - Mathematical functions for Tcl expressions

SYNOPSIS
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

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DESCRIPTION
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 floating-point numbers unless otherwise
noted:

abs         acos        asin       atan
atan2       bool        ceil       cos
cosh        double      entier     exp
floor       fmod        hypot      int
isqrt       log         log10      max
min         pow         rand       round
sin         sinh        sqrt       srand
tan         tanh        wide

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.

DETAILED DEFINITIONS
abs arg
Returns the absolute value of arg.  Arg may be either integer or
floating-point, 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]

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.
Non-zero numbers are true.  Other numbers are false.  Non-
numeric strings produce boolean value in agreement with string
is true and string is false.

ceil arg
Returns the smallest integral floating-point 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 floating-
point value, returns arg, otherwise converts arg to floating-
point and returns the converted value.  May return Inf or -Inf
when the argument is a numeric value that exceeds the floating-
point 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 floating-point value (i.e. with a
zero fractional part) not greater than arg.  The argument may be
any numeric value.

fmod x y
Returns the floating-point 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 right-angled
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 pseudo-random floating-point 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 one-time 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 non-negative numeric value.  Returns a
floating-point 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 floating-point 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.