in reply to Re^5: RFC: Large Floating Point Numbers - Rounding Errors
in thread RFC: Large Floating Point Numbers - Rounding Errors

No, they are not, this is a borderline case.

Try the following C program and see how the periodic part of the base 2 representation of those rational numbers is truncated and how it converts back to base 10: 

#include <stdio.h>

double n[] = { 0.000005, 0.000015, 0.000025, 0.000035, 0.000045, 0.000
+055, 0.000065 };

int main(int argc, char *argv[]) {
    int i;
    for (i = 0; i < sizeof(n)/sizeof(*n); i++) {
        printf("%40.30a => %40.30f\n", n[i], n[i]);
    }
    return 0;
}

[download]
On my amd64 linux box it outputs: 
  0x1.4f8b588e368f100000000000000000p-18 =>         0.0000050000000000
+00000409015270
  0x1.f75104d551d6900000000000000000p-17 =>         0.0000150000000000
+00000380012861
  0x1.a36e2eb1c432d00000000000000000p-16 =>         0.0000250000000000
+00001198043401
  0x1.2599ed7c6fbd200000000000000000p-15 =>         0.0000349999999999
+99996933876256
  0x1.797cc39ffd60f00000000000000000p-15 =>         0.0000450000000000
+00002834104479
  0x1.cd5f99c38b04b00000000000000000p-15 =>         0.0000550000000000
+00001958069124
  0x1.10a137f38c54300000000000000000p-14 =>         0.0000649999999999
+99994305770190

[download]

Replies are listed 'Best First'.
Re^7: RFC: Large Floating Point Numbers - Rounding Errors
by BrowserUk (Patriarch) on Sep 08, 2011 at 16:40 UTC
    ... this is a borderline case.

    Because YOU haven't set the rounding mode:

    #include <stdio.h>
#include <float.h>

int main( int argc, char **argv ) {
    double n;

    printf( "Setting mode CHOP; controlFP returned: %u\n", 
            _controlfp( _RC_CHOP, _MCW_RC ) 
         );
    for( n = 0.000005; n < 0.0001; n += 0.00001 ) {
        printf( "%.15f %.5f\n", n, n );
    }

    printf( "Setting mode UP; controlFP returned: %u\n", 
             _controlfp( _RC_UP, _MCW_RC ) 
         );
    for( n = 0.000005; n < 0.0001; n += 0.00001 ) {
        printf( "%.15f %.5f\n", n, n );
    }

    printf( "Setting mode DOWN; controlFP returned: %u\n", 
             _controlfp( _RC_DOWN, _MCW_RC ) 
         );
    for( n = 0.000005; n < 0.0001; n += 0.00001 ) {
        printf( "%.15f %.5f\n", n, n );
    }

    printf( "Setting mode NEAR; controlFP returned: %u\n", 
            _controlfp( _RC_NEAR, _MCW_RC ) 
         );
    for( n = 0.000005; n < 0.0001; n += 0.00001 ) {
        printf( "%.15f %.5f\n", n, n );
    }
    return 1;
}

    [download]
    C:\test>ieeeroundingmode.exe
Setting mode CHOP; controlFP returned: 525087
0.000005000000000 0.00001
0.000015000000000 0.00002
0.000025000000000 0.00003
0.000035000000000 0.00003
0.000045000000000 0.00004
0.000055000000000 0.00005
0.000065000000000 0.00006
0.000075000000000 0.00007
0.000085000000000 0.00008
0.000095000000000 0.00009
Setting mode UP; controlFP returned: 524831
0.000005000000000 0.00001
0.000015000000000 0.00002
0.000025000000000 0.00003
0.000035000000000 0.00004
0.000045000000000 0.00005
0.000055000000000 0.00006
0.000065000000000 0.00007
0.000075000000000 0.00008
0.000085000000000 0.00009
0.000095000000000 0.00010
Setting mode DOWN; controlFP returned: 524575
0.000005000000000 0.00001
0.000015000000000 0.00002
0.000025000000000 0.00003
0.000035000000000 0.00003
0.000045000000000 0.00004
0.000055000000000 0.00005
0.000065000000000 0.00006
0.000075000000000 0.00007
0.000085000000000 0.00008
0.000095000000000 0.00009
Setting mode NEAR; controlFP returned: 524319
0.000005000000000 0.00001
0.000015000000000 0.00002
0.000025000000000 0.00003
0.000035000000000 0.00004
0.000045000000000 0.00005
0.000055000000000 0.00006
0.000065000000000 0.00007
0.000075000000000 0.00008
0.000085000000000 0.00009
0.000095000000000 0.00010

    [download]
    Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
    "Science is about questioning the status quo. Questioning authority".
    In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
[d/l]
[select]
      Sadly, Solaris doesn't implement _controlFP (nor does Inline exist in this environment). There is a Solaris method by which I can ask what the rounding method is on this system, just no way to set it.

      Like I said, something bigger is wrong here, and no, I shouldn't have to use a string manipulation program to deal with this, but ... I'm pretty stuck otherwise.
[reply]
        Sadly, Solaris doesn't implement _controlFP()

        In that case, maybe something like this would work for you? 

        sub rnd{ 
    my( $p, $n ) = @_; 
    return sprintf "%.${p}f", $n + "0.5e-$p" 
};;

print $_, ': ', rnd( 5, $_ ) for 
    0.000005, 0.000015, 0.000025, 0.000035, 0.000045, 
    0.000055, 0.000065, 0.000075, 0.000085, 0.000095;;

5e-006 :  0.00001
1.5e-005 :  0.00002
2.5e-005 :  0.00003
3.5e-005 :  0.00004
4.5e-005 :  0.00005
5.5e-005 :  0.00006
6.5e-005 :  0.00007
7.5e-005 :  0.00008
8.5e-005 :  0.00009
9.5e-005 :  0.00010

        [download]

        Even if it isn't faster than your code -- which instinct tells me it should be -- then it is at least a darn sight clearer :)

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
[d/l]
      You are cheating! can't you see it?
[reply]
        You are cheating!

        Cheating? By having the compiler produce the correct, required values? By using the FP processor the way it was designed?

        Now I heard all the excuses for not understanding the oft-cited but little understood paper http://docs.sun.com/source/806-3568/ncg_goldberg.html

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]

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