# Numerical functions
#FIXME: these need to be cleaned up!
#Indeed, some of these should probably be built-in

#just for somewhat of "source compatibility"
SetHelp ("AbsoluteValue", "numeric", "Absolute value");
function AbsoluteValue (x) = |x|
protect ("AbsoluteValue")
SetHelpAlias ("AbsoluteValue", "abs")
abs = AbsoluteValue
protect ("abs")

SetHelp("Sign","numeric","Return the sign (-1,0,1)");
function Sign (x) = (
	if IsMatrix (x) then
		return ApplyOverMatrix (x, Sign)
	else if not IsValue (x) then
		(error("Sign: argument not a value");bailout);
	if IsComplex (x) then (
		x / |x|
	) else if x > 0 then (
		1
	) else if x < 0 then (
		-1
	) else 0
);
protect("Sign")
SetHelpAlias ("Sign", "sign")
sign = Sign
protect("sign")

#-----

SetHelp ("FractionalPart", "numeric", "Return the fractional part of a number")
function FractionalPart(x) =
(
	if not IsValue(x) then
		(error("FractionalPart: argument not a value");bailout)
	else
		x - IntegerPart (x)
)
protect ("FractionalPart")

# Chop replaces very small number with zero
parameter ChopTolerance = 10.0^(-10);
SetHelp ("ChopTolerance", "parameters", "Tolerance of the Chop function")

SetHelp ("Chop", "numeric", "Replace very small number with zero")
function Chop(x) =
(
	if not IsValue(x) then
		(error("Chop: argument not a value");bailout)
	else if |x| < ChopTolerance then
		0
	else
		x
)
protect ("Chop")

#-----
# Mod (built-in)
# FIXME: Mod with offset (m mod n offset d = something in [d,d+n-1])

# Division w/o remainder
SetHelp ("IntegerQuotient", "numeric", "Division w/o remainder")
function IntegerQuotient(m,n) = floor(m/n)
protect ("IntegerQuotient")
# IntergerQuotient w/offset (such that d <= m-r*n < d+n
# IntegerDigits = (convert interger to its list of digits, base b, of length len)
# IntegerExponent = (number of trailing zeros in base b expansion = heighest power
#		of b that divides n)