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