## Tcl8.6.0/Tk8.6.0 Documentation > Tcl Commands, version 8.6.0 > mathfunc

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  NAME
    mathfunc — Mathematical functions for Tcl expressions
  SYNOPSIS
  DESCRIPTION
  DETAILED DEFINITIONS
    abs arg
    acos arg
    asin arg
    atan arg
    atan2 y x
    bool arg
    ceil arg
    cos arg
    cosh arg
    double arg
    entier arg
    exp arg
    floor arg
    fmod x y
    hypot x y
    int arg
    isqrt arg
    log arg
    log10 arg
    max arg ...
    min arg ...
    pow x y
    rand
    round arg
    sin arg
    sinh arg
    sqrt arg
    srand arg
    tan arg
    tanh arg
    wide arg
  SEE ALSO
  COPYRIGHT

### 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

### 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] 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. 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.

### SEE ALSO

expr, mathop, namespace

### COPYRIGHT

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>.
Copyright © 1993 The Regents of the University of California. Copyright © 1994-2000 Sun Microsystems, Inc. Copyright © 2005 by Kevin B. Kenny <kennykb(at)acm.org>. All rights reserved