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Re: Converting Floats to Strings yields erratic results

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[ Re-posting through E-S, as aioe seems heavily filtered ]
OT: How many see this post, and not the one through aioe?

BartC wrote:

> Clearly 1e40 can't be stored exactly (can it?
> I thought it would need over 120 bits of precision)

1e40 = 10^40
     =  5^40 * 2^40
     = 0x1D6329F1C35CA4BFABB9F561 * 2^40

5^40 requires 93 bits to store precisely.

Thus, a double-precision IEEE 754 floating-point number
cannot store 1e40 exactly, as the mantissa is expressed
over (only) 52 bits.

http://en.wikipedia.org/wiki/Double_precision_floating-point_format

0x1.D6329F1C35CA4 * 2^132 < 1e40 < 0x1.D6329F1C35CA5 * 2^132

i.e. respectively
 9999999999999999094860208812374492184576
10000000000000000000000000000000000000000
10000000000000000303786028427003666890752

The exponent (132) is stored as 132+1023 = 1155 = 0x483

And, in fact, the following program prints 483d6329f1c35ca3
(Note the rounding error).

#include <stdio.h>
#include <string.h>
int main(void)
{
  int i;
  double d = 1.0;
  for (i=0; i < 40; ++i) d *= 10.0;
  unsigned char buf[8];
  memcpy(buf, &d, sizeof buf);
  for (i=0; i < 8; ++i) printf("%02x", buf[7-i]);
  putchar('\n');
  return 0;
}

cf. also
What Every Computer Scientist Should Know About Floating-Point Arithmetic
http://download.oracle.com/docs/cd/E19957-01/806-3568/ncg_goldberg.html

Regards.

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Converting Floats to Strings yields erratic results "Dirk T. Shelley" <nospam@nospam.com> - 2011-06-07 21:10 +0000
  Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 14:25 -0700
    Re: Converting Floats to Strings yields erratic results Peter Nilsson <airia@acay.com.au> - 2011-06-07 20:13 -0700
      Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 20:27 -0700
    Re: Converting Floats to Strings yields erratic results "Dirk T. Shelley" <nospam@nospam.com> - 2011-06-08 16:34 +0000
      Re: Converting Floats to Strings yields erratic results Ian Collins <ian-news@hotmail.com> - 2011-06-09 07:53 +1200
        Re: Converting Floats to Strings yields erratic results "Dirk T. Shelley" <nospam@nospam.com> - 2011-06-08 20:46 +0000
      Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-08 22:40 +0100
        Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 11:03 +0100
          Re: Converting Floats to Strings yields erratic results James Kuyper <jameskuyper@verizon.net> - 2011-06-09 08:06 -0400
            Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 16:57 +0100
          Re: Converting Floats to Strings yields erratic results Noob <root@127.0.0.1> - 2011-06-09 14:13 +0200
          Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-09 09:26 -0700
            Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 19:07 +0100
              Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-09 11:52 -0700
                Re: Converting Floats to Strings yields erratic results "BartC" <bc@freeuk.com> - 2011-06-09 20:30 +0100
            Re: Converting Floats to Strings yields erratic results "io_x" <a@b.c.invalid> - 2011-06-13 12:21 +0200
            Re: Converting Floats to Strings yields erratic results "io_x" <a@b.c.invalid> - 2011-06-13 22:31 +0200
          Re: Converting Floats to Strings yields erratic results Noob <root@127.0.0.1> - 2011-06-10 10:58 +0200
            Re: Converting Floats to Strings yields erratic results Seebs <usenet-nospam@seebs.net> - 2011-06-10 22:49 +0000
      Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-08 21:51 -0400
      Re: Converting Floats to Strings yields erratic results Mark Bluemel <mark_bluemel@pobox.com> - 2011-06-09 08:50 +0100
  Re: Converting Floats to Strings yields erratic results gordonb.9ycz5@burditt.org (Gordon Burditt) - 2011-06-07 18:13 -0500
  Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-07 20:47 -0400
    Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 20:08 -0700
      Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-07 23:38 -0400
    Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-07 23:49 -0400
      Re: Converting Floats to Strings yields erratic results Shao Miller <sha0.miller@gmail.com> - 2011-06-08 00:54 -0500
  Re: Converting Floats to Strings yields erratic results Thad Smith <ThadSmith@acm.org> - 2011-06-07 20:38 -0700
    Re: Converting Floats to Strings yields erratic results Keith Thompson <kst-u@mib.org> - 2011-06-07 20:30 -0700
  Re: Converting Floats to Strings yields erratic results falk@rahul.net (Edward A. Falk) - 2011-06-08 20:54 +0000
    Re: Converting Floats to Strings yields erratic results Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-06-08 21:56 -0400

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