These functions are to help visualize integer and rational numbers in
a more comprehensible format (as a decimal string
). The SigFig
argument is optional; its default value is 5.
ToString(N)
converts N
to a (decimal) string.
FloatStr(N, SigFig)
convert the number N
into a string choosing
between "decimal" format and "scientific" format. The default value for
SigFig
is 5. NOTE: this may throw an exception for large values of N
.
ScientificStr(N, SigFig)
convert the number N
into a string of the
form mantissa times power-of-ten, with SigFig
digits in the mantissa.
Note that trailing zeroes are not removed from the mantissa.
DecimalStr(N, DecPlaces)
convert the number N
into a decimal string
with DecPlaces
digits after the decimal point. The default value for
DecPlaces
is 3.
Note: for values with large numerator or denominator it is quicker to convert
the value to a RingElem
belonging to a RingTwinFloat
and then print
the result. This approach offers less control over the output, and no
guarantee of correct rounding.
The function ScientificStr
gives the clearest guarantees about the
format used, but also produces the least humanly readable result. It
uses MantissaAndExponent10
to do the conversion.
The function FloatStr
is supposed to be the best general choice.
It passes its args to ScientificStr
in two situations: if the
number is so large that padding would be needed before the decimal
point; if the number is so small that the ScientificStr
format
would be shorter (i.e. if the exponent is less than -8).
The function DecimalStr
is Anna's preferred choice. It uses
ToString
to convert to decimal.
These functions cannot be applied directly to a machine integer; to call
them you have to convert explicitly into a BigInt
(or BigRat
).
The switch-over in FloatStr
to scientific notation for "large"
numbers is not ideal; in C the "g" format chooses the shorter between
float and scientific formats. Is it worth the doing the same here?
Anna says an older version of DecimalStr
would suppress trailing zeroes
if the result is exact (e.g. DecimalStr(5/4,9)
would produce 1.25
rather than 1.250000000
. Is this a good idea?
These fns are too slow if N
is a very large integer (or if numerator
and/or denominator are very large). Converting to an mpf_t
and
printing that would be much faster (except in delicate rounding cases).
2014
FloatStr
to ScientificStr
,
added new FloatStr
2011