Re^7: RFC: Large Floating Point Numbers

... 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.

Comment on Re^7: RFC: Large Floating Point Numbers - Rounding Errors
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Re^8: RFC: Large Floating Point Numbers - Rounding Errors by GAVollink (Novice) on Sep 08, 2011 at 19:52 UTC
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]
Re^9: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 08, 2011 at 22:12 UTC
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, $_ ) for 0.000005, 0.000015, 0.000025, 0.000035, 0.000045, 0.000055, 0.000065, 0.000075, 0.000085, 0.000095;; 5e-006 : 0.00001 1.5e-005 : 0.00002 2.5e-005 : 0.00003 3.5e-005 : 0.00004 4.5e-005 : 0.00005 5.5e-005 : 0.00006 6.5e-005 : 0.00007 7.5e-005 : 0.00008 8.5e-005 : 0.00009 9.5e-005 : 0.00010` [download] Even if it isn't faster than your code -- which instinct tells me it should be -- then it is at least a darn sight clearer :) Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error. "Science is about questioning the status quo. Questioning authority". In the absence of evidence, opinion is indistinguishable from prejudice.	[reply] [d/l]
Re^10: RFC: Large Floating Point Numbers - Rounding Errors by GAVollink (Novice) on Sep 09, 2011 at 23:04 UTC
It's clear enough to plainly see that you are adding something to the number, then rounding it, which means that in any thing close to 0.49e-${p}, you'll force a round-up, so often wrong, in the other direction. Being 9.0e-5 + 0.5e-5 is 9.5e-5 -- So, you are forcing it to always add "up". Just adding a single 0.00009 at the end of your code, shows how bad this can be. However, the same problem also happens (with a smaller error area) if you try a higher exponent -- it simply intentionally inserts an error, which is a really dangerous way to try to correct a problem. `sub rnd{ my( $p, $n ) = @_; return sprintf "%.${p}f", $n + "0.5e-$p" };; print $_, ': ', rnd( 5, $_ ), qq{\n} for 0.000005, 0.000015, 0.000025, 0.000035, 0.000045, 0.000055, 0.000065, 0.000075, 0.000085, 0.000095, 0.00009;; __DATA__ 5e-06: 0.00001 1.5e-05: 0.00002 2.5e-05: 0.00003 3.5e-05: 0.00004 4.5e-05: 0.00005 5.5e-05: 0.00006 6.5e-05: 0.00007 7.5e-05: 0.00008 8.5e-05: 0.00009 9.5e-05: 0.00010 9e-05: 0.00010` [download]	[reply] [d/l]
Re^11: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 10, 2011 at 17:49 UTC
Re^11: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 10, 2011 at 01:30 UTC
Re^8: RFC: Large Floating Point Numbers - Rounding Errors by salva (Canon) on Sep 08, 2011 at 16:48 UTC
You are cheating! can't you see it?	[reply]
Re^9: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 08, 2011 at 16:52 UTC
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]
Re^10: RFC: Large Floating Point Numbers - Rounding Errors by salva (Canon) on Sep 08, 2011 at 20:59 UTC
This is for GCC/Linux: #include <stdio.h> #include <stdlib.h> #include <fenv.h> double n[] = { 0.000005, 0.000015, 0.000025, 0.000035, 0.000045, 0.000 +055, 0.000065 }; char str[] = { "0.000005", "0.000015", "0.000025", "0.000035", "0.000 +045", "0.000055", "0.000065" }; int main(int argc, char argv[]) { int i, j; for (j = 0; j < 4; j++) { fesetround(j); printf("rounding: %d\n", j); double m = n[0]; for (i = 0; i < sizeof(n)/sizeof(*n); i++) { printf(" compiler: %40.30a => %40.30f\n", n[i], n[i]); printf(" atof: %40.30a => %40.30f\n", atof(str[i]), a +tof(str[i])); printf(" calc: %40.30a => %40.30f\n", m, m); m += 0.00001; } } return 0; } [download] rounding: 0 compiler: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 atof: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 calc: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 compiler: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 atof: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 calc: 0x1.f75104d551d6a00000000000000000p-17 => 0.0000 +15000000000000002074078756 compiler: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 atof: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 calc: 0x1.a36e2eb1c432e00000000000000000p-16 => 0.0000 +25000000000000004586175190 compiler: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 atof: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 calc: 0x1.2599ed7c6fbd300000000000000000p-15 => 0.0000 +35000000000000003710139834 compiler: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 atof: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 calc: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 compiler: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 atof: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 calc: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 compiler: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 atof: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 calc: 0x1.10a137f38c54400000000000000000p-14 => 0.0000 +65000000000000007858297346 rounding: 1 compiler: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 atof: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 calc: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 compiler: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 atof: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 calc: 0x1.f75104d551d6a00000000000000000p-17 => 0.0000 +15000000000000002074078756 compiler: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 atof: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 calc: 0x1.a36e2eb1c432e00000000000000000p-16 => 0.0000 +25000000000000004586175190 compiler: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 atof: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 calc: 0x1.2599ed7c6fbd300000000000000000p-15 => 0.0000 +35000000000000003710139834 compiler: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 atof: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 calc: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 compiler: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 atof: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 calc: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 compiler: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 atof: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 calc: 0x1.10a137f38c54400000000000000000p-14 => 0.0000 +65000000000000007858297346 rounding: 2 compiler: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 atof: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 calc: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 compiler: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 atof: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 calc: 0x1.f75104d551d6a00000000000000000p-17 => 0.0000 +15000000000000002074078756 compiler: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 atof: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 calc: 0x1.a36e2eb1c432e00000000000000000p-16 => 0.0000 +25000000000000004586175190 compiler: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 atof: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 calc: 0x1.2599ed7c6fbd300000000000000000p-15 => 0.0000 +35000000000000003710139834 compiler: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 atof: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 calc: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 compiler: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 atof: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 calc: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 compiler: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 atof: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 calc: 0x1.10a137f38c54400000000000000000p-14 => 0.0000 +65000000000000007858297346 rounding: 3 compiler: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 atof: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 calc: 0x1.4f8b588e368f100000000000000000p-18 => 0.0000 +05000000000000000409015270 compiler: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 atof: 0x1.f75104d551d6900000000000000000p-17 => 0.0000 +15000000000000000380012861 calc: 0x1.f75104d551d6a00000000000000000p-17 => 0.0000 +15000000000000002074078756 compiler: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 atof: 0x1.a36e2eb1c432d00000000000000000p-16 => 0.0000 +25000000000000001198043401 calc: 0x1.a36e2eb1c432e00000000000000000p-16 => 0.0000 +25000000000000004586175190 compiler: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 atof: 0x1.2599ed7c6fbd200000000000000000p-15 => 0.0000 +34999999999999996933876256 calc: 0x1.2599ed7c6fbd300000000000000000p-15 => 0.0000 +35000000000000003710139834 compiler: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 atof: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 calc: 0x1.797cc39ffd60f00000000000000000p-15 => 0.0000 +45000000000000002834104479 compiler: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 atof: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 calc: 0x1.cd5f99c38b04b00000000000000000p-15 => 0.0000 +55000000000000001958069124 compiler: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 atof: 0x1.10a137f38c54300000000000000000p-14 => 0.0000 +64999999999999994305770190 calc: 0x1.10a137f38c54400000000000000000p-14 => 0.0000 +65000000000000007858297346 [download] And rounding is as follows: 0 - Rounding is towards 0. 1 - Rounding is towards nearest number. 2 - Rounding is towards positive infinity. 3 - Rounding is towards negative infinity.	[reply] [d/l] [select]
Re^10: RFC: Large Floating Point Numbers - Rounding Errors by salva (Canon) on Sep 08, 2011 at 17:24 UTC
Cheating? By having the compiler produce the correct, required values? By using the FP processor the way it was designed? No, obviusly that's not the reason why you are cheating!	[reply]