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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 [_,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 _, 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 cor-responding corresponding
              responding  boolean  value 0 or 1.  Non-zero numbers are true.  Other numbers are false.  Non-numeric Nonnumeric
              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,  other-wise otherwise
              wise  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_plat-form(wordSize). tcl_platform(wordSize).
              form(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 (_,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(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)