Re: compile-time conversion of floating-point expressions to long longs

["Nelson H. F. Beebe" <beebe@math.utah.edu>]

Jim Cromie <jim.cromie@gmail.com> asks on Wed, 03 May 2006 12:17:38 -0400:

>> ...
>> Are there any macros that can tear into a floating point number and
>> pull out the exponent and mantissa ?
>> ...

Yes, the C89 and C99 ISO C Standards include ldexp(x,n), which forms x
* 2**n, and "f = frexp(x,&n);", which returns the fraction as a value
in [1/2,1) (or 0 if x is zero) and the exponent of 2 in n.  Both are
exact, and can be implemented reasonably efficiently.

Two related, and useful, functions are

(1) modf(x,*y), which splits x into an integral part stored in y as an
    exactly-representable floating-point number, and returns the
    fractional part as the function value.  Both have the same sign as x.

(2) fmod(x,y), which returns the remainder of x divided by y.

All four of these functions are EXACT; no rounding errors whatsoever
are possible.  Note that for fmod(), the computation involves finding
the integer close to x/y, and that can be very large: in IEEE 754
128-bit arithmetic, it is a number of nearly 9900 decimal digits.
Fortunately, it is possible to implement fmod() iteratively, without
access to high-precision floating-point.

ldexp() and frexp() were in C in Unix Version 7 in the late 1970s; the
other two are more recent.  You can safely use all four of them on
modern systems.  Pre-C99 implementations may lack the float and long
double counterparts.  However, glibc on GNU/Linux offers all twelve
variants.

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