mathfunc - Mathematical functions for Tcl expressions

       Copyright © 1993 The Regents of the University of California.
       Copyright © 1994-2000 Sun Microsystems Incorporated.
       Copyright © 2005-2006 Kevin B. Kenny <kennykb@acm.org>.

Tcl                                                    8.5                                        mathfunc(3tcl)

       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:

              absacosasinatanatan2boolceilcoscoshdoubleentierexpfloorfmodhypotintisfiniteisinfisnanisnormalisqrtissubnormalisunorderedloglog10maxminpowrandroundsinsinhsqrtsrandtantanhwide

       In addition to these predefined functions, applications may define additional functions by using proc (or
       any  other  method,  such  as  interpalias  or  Tcl_CreateObjCommand)  to  define  new  commands in the
       tcl::mathfunc namespace.

   DETAILEDDEFINITIONSabsarg
              Returns the absolute value of arg.  Arg may be either integer or floating-point, and the result is
              returned in the same form.

       acosarg
              Returns the arc cosine of arg, in the range [0,pi] radians. Arg should be in the range [-1,1].

       asinarg
              Returns the arc sine of arg, in the range [-pi/2,pi/2]  radians.   Arg  should  be  in  the  range
              [-1,1].

       atanarg
              Returns the arc tangent of arg, in the range [-pi/2,pi/2] radians.

       atan2yx
              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}]”.

       boolarg
              Accepts  any  numeric  value,  or  any  string  acceptable  to  stringisboolean, 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 stringistrue and stringisfalse.

       ceilarg
              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.

       cosarg
              Returns the cosine of arg, measured in radians.

       cosharg
              Returns the hyperbolic cosine of arg.  If  the  result  would  cause  an  overflow,  an  error  is
              returned.

       doublearg
              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.

       entierarg
              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.

       exparg
              Returns  the  exponential  of  arg,  defined as e**arg.  If the result would cause an overflow, an
              error is returned.

       floorarg
              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.

       fmodxy
              Returns the floating-point remainder of the division of x by y.  If y is 0, an error is returned.

       hypotxy
              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.

       intarg
              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.

       isfinitearg
              Returns 1 if the floating-point number arg is finite. That  is,  if  it  is  zero,  subnormal,  or 2
              normal. Returns 0 if the number is infinite or NaN. Throws an error if arg cannot be promoted to a 2
              floating-point value.

       isinfarg
              Returns  1 if the floating-point number arg is infinite. Returns 0 if the number is finite or NaN. 2
              Throws an error if arg cannot be promoted to a floating-point value.

       isnanarg
              Returns 1 if the floating-point number arg is Not-a-Number. Returns 0 if the number is  finite  or 2
              infinite. Throws an error if arg cannot be promoted to a floating-point value.

       isnormalarg
              Returns  1 if the floating-point number arg is normal. Returns 0 if the number is zero, subnormal, 2
              infinite or NaN. Throws an error if arg cannot be promoted to a floating-point value.

       isqrtarg
              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.

       issubnormalarg
              Returns 1 if the floating-point number arg is subnormal, i.e., the result  of  gradual  underflow. 2
              Returns  0  if  the  number  is  zero,  normal,  infinite or NaN. Throws an error if arg cannot be 2
              promoted to a floating-point value.

       isunorderedxy
              Returns 1 if x and y cannot be compared for ordering, that is, if either one is NaN. Returns 0  if 2
              both  values  can  be  ordered,  that  is,  if  they  are  both chosen from among the set of zero, 2
              subnormal, normal and infinite values. Throws an error if either x or y cannot be  promoted  to  a 2
              floating-point value.

       logarg
              Returns the natural logarithm of arg.  Arg must be a positive value.

       log10arg
              Returns the base 10 logarithm of arg.  Arg must be a positive value.

       maxarg...
              Accepts one or more numeric arguments.  Returns the one argument with the greatest value.

       minarg...
              Accepts one or more numeric arguments.  Returns the one argument with the least value.

       powxy
              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.

       roundarg
              If arg is an integer value, returns arg, otherwise converts arg to integer by rounding and returns
              the converted value.

       sinarg
              Returns the sine of arg, measured in radians.

       sinharg
              Returns the hyperbolic sine of arg.  If the result would cause an overflow, an error is returned.

       sqrtarg
              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.

       srandarg
              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.

       tanarg
              Returns the tangent of arg, measured in radians.

       tanharg
              Returns the hyperbolic tangent of arg.

       widearg
              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.

       mathfunc - Mathematical functions for Tcl expressions

expr(3tcl), fpclassify(3tcl), mathop(3tcl), namespace(3tcl)

       package require Tcl8.5-::tcl::mathfunc::absarg::tcl::mathfunc::acosarg::tcl::mathfunc::asinarg::tcl::mathfunc::atanarg::tcl::mathfunc::atan2yx::tcl::mathfunc::boolarg::tcl::mathfunc::ceilarg::tcl::mathfunc::cosarg::tcl::mathfunc::cosharg::tcl::mathfunc::doublearg::tcl::mathfunc::entierarg::tcl::mathfunc::exparg::tcl::mathfunc::floorarg::tcl::mathfunc::fmodxy::tcl::mathfunc::hypotxy::tcl::mathfunc::intarg::tcl::mathfunc::isfinitearg                                                                             2
       ::tcl::mathfunc::isinfarg                                                                                2
       ::tcl::mathfunc::isnanarg                                                                                2
       ::tcl::mathfunc::isnormalarg                                                                             2
       ::tcl::mathfunc::isqrtarg::tcl::mathfunc::issubnormalarg                                                                          2
       ::tcl::mathfunc::isunorderedxy                                                                          2
       ::tcl::mathfunc::logarg::tcl::mathfunc::log10arg::tcl::mathfunc::maxarg ?arg ...?
       ::tcl::mathfunc::minarg ?arg ...?
       ::tcl::mathfunc::powxy::tcl::mathfunc::rand::tcl::mathfunc::roundarg::tcl::mathfunc::sinarg::tcl::mathfunc::sinharg::tcl::mathfunc::sqrtarg::tcl::mathfunc::srandarg::tcl::mathfunc::tanarg::tcl::mathfunc::tanharg::tcl::mathfunc::widearg
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