Tcl 9.1/Tk9.1 Documentation > Tcl Commands, version 9.1b0 > mathfunc

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NAME

mathfunc — Mathematical functions for Tcl expressions

SYNOPSIS

DESCRIPTION

DETAILED DEFINITIONS

abs arg

acos arg

acosh arg

asin arg

asinh arg

atan arg

atan2 y x

atanh arg

bool arg

cbrt arg

ceil arg

copysign x y

cos arg

cosh arg

dim x y

double arg

entier arg

erf arg

erfc arg

exp arg

exp2 arg

expm1 arg

floor arg

fma x y z

fmod x y

gamma arg

hypot x y

int arg

isfinite arg

isinf arg

isnan arg

isnormal arg

isqrt arg

issubnormal arg

isunordered x y

ldexp x y

lgamma arg

log arg

log10 arg

log1p arg

log2 arg

logb arg

max arg ...

min arg ...

nextafter x y

pow x y

rand

remainder x y

round arg

signbit arg

sin arg

sinh arg

sqrt arg

srand arg

tan arg

tanh arg

trunc arg

wide arg

SEE ALSO

COPYRIGHT

NAME

SYNOPSIS

DESCRIPTION

Tcl supports the following mathematical functions in expressions, all of which work solely with floating-point numbers unless otherwise noted:

abs	acos	acosh	asin
asinh	atan	atan2	atanh
bool	cbrt	copysign	ceil
cos	cosh	dim	double
entier	erf	erfc	exp
exp2	expm1	floor	fma
fmod	gamma	hypot	int
isfinite	isinf	isnan	isnormal
isqrt	issubnormal	isunordered	ldexp
lgamma	log	log10	log1p
log2	logb	max	min
nextafter	pow	rand	remainder
round	sin	sinh	sqrt
srand	tan	tanh	trunc
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.

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].

acosh arg

Returns the arc hyperbolic cosine of arg, in the range [0,inf] radians. Arg should be in the range [1,inf].

asin arg

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

asinh arg

Returns the arc hyperbolic sine of arg, in the range [-inf,inf].

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}]”.

atanh arg

Returns the arc hyperbolic tangent of arg, in the range [-inf,inf]. Arg should be in the range [-1,1].

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.

cbrt arg

The argument may be any numeric value. Returns a floating-point value that is the cube root of arg. May return Inf when the argument is a numeric value that exceeds the cube of the maximum value of the floating-point range.

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.

copysign x y

Returns the floating-point value with the magnitude of x and sign of y.

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.

dim x y

Returns the floating-point value that is the maximum of 0 and x-y.

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.

erf arg

Computes the Gauss error function of the numeric value arg.

erfc arg

Computes the complementary error function of the numeric value arg.

exp arg

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

exp2 arg

Returns the 2 to the power of arg, defined as 2**arg. The result is always a floating point number except if it would cause an overflow, when an error is returned.

expm1 arg

Returns the exponential of arg, minus 1, defined as e**arg-1. If the result would cause an overflow, an error is returned. Use of this function can be numerically preferable to of exp for values close to 1, and is matched with log1p.

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.

fma x y z

Returns the floating-point value that is the sum of the product of x and y, and z, without unnecessarily losing intermediate accuracy.

fmod x y

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

gamma arg

Returns the absolute value of the gamma function of arg (a generalized factorial). If the result would cause an overflow, 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.

isfinite arg

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

isinf arg

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

isnan arg

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

isnormal arg

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

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.

issubnormal arg

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

isunordered x y

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

ldexp x y

Multiplies a floating-point value x by the number 2 raised to the y power.

lgamma arg

Returns the natural logarithm of the absolute value of the gamma function of arg. If the result would cause an overflow, an error is returned.

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.

log1p arg

Returns the natural logarithm of arg+1. Arg must be a value greater than -1. This function is numerically preferable to log for values very close to 1, and is matched with expm1.

log2 arg

Returns the base 2 logarithm of arg. Arg must be a positive value.

logb arg

Returns the value of the unbiased radix-independent exponent from the floating-point argument arg.

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.

nextafter x y

Returns the next floating-point value after (or before) x in the direction of y. If x and y are equal, returns y.

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.

remainder x y

Computes the IEEE remainder of the floating point division operation x/y.

round arg

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

signbit arg

Get the sign bit of the numeric value, arg, as 0 (positive) or 1 (negative).

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.

trunc arg

Returns the nearest integer not greater in magnitude than 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

COPYRIGHT