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,$x) by converting them to calls of the form [tcl::math-
       func::sin [expr {$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_Cre-
       ateMathFunc() 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  equiva-
	      lent 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 "sqrt [expr {x*x+y*y}]".

       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
	      tcl_platform(wordSize).

       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 num-
	      ber (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(n), mathop(n), namespace(n)

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>.

Tcl									8.5							       mathfunc(n)