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mathfunc(n)		  Tcl Mathematical Functions		   mathfunc(n)

______________________________________________________________________________

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,$x) by converting  them	 to  calls  of	the  form  [tcl::math‐
       func::sin  [expr	 {$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	  dou‐
       ble	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::math‐
       func 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] radi‐
	      ans.

       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	trian‐
	      gle, 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  num‐
	      ber.  Unlike sqrt, which is limited to the precision of a float‐
	      ing point number, isqrt will return a result of arbitrary preci‐
	      sion.

       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 nega‐
	      tive, 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 genera‐
	      tor 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(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)
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