floating point in 2.0

[Edward Jason Riedy]

And Tim Peters writes:
 - 
 - Note that this is platform-dependent, and even across platforms 
 - that conform fully to IEEE-754:  they're allowed to display only 
 - zeroes after the 17th significant decimal digit.

I've forgotten the exact language, but we're going to strongly 
recommend using Steele and White's algorithm by default:

  http://www.acm.org/pubs/citations/proceedings/pldi/93542/p112-steele/

Given 0.1 converted to binary, this will print 0.1.  It's a
complicated algorithm, but worth it.  And it's not a lie.
It returns the shortest decimal string which will reproduce
the given binary number after a decimal->binary conversion.

Of course, you may worry about 0.1 + 0.1 + ... != 1.0.  We're
also going to be giving a good deal of advice (and some
requirements) on handling arithmetic.  I'm working on a paper 
with greater detail, but try the following C program for a
taste of some intended advice:
========
#include <stdio.h>

/*
  Accumulating in more precision than the data `deserves'
  AND rounding the output gives the right answer for more 
  cases.
*/

int
main (void)
{
  int i;
  float x = 0.1;
  double accum = 0.0;
  float accumf = 0.0;
  float y;

  for (i = 0; i < 100; ++i) {
    accum += x;  /* accumulate in double... */
    accumf += x;
  }

  y = (float) accum;  /* round back to float... */
  printf ("%.36g\n%.36g\n%.36g\n", accumf, accum, y);
}
========

Next meeting for 754r is on the 20th somewhere around San Jose.  
There's a mostly inactive mailing list about it; people honestly 
interested in participating can mail me for more info.

Jason
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