Re^4: RFC: Large Floating Point Numbers

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Re^5: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 08, 2011 at 16:13 UTC
the result of converting numbers between base 10 and 2. No. It isn't. 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^5: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 08, 2011 at 16:18 UTC
YOU are wrong! Wrong! Wrong! IEEE 64-bit doubles are perfectly capable of representing these values to sufficient accuracy to allow them to be rounded correctly. See Re: RFC: Large Floating Point Numbers - Rounding Errors (Rounding mode) 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^6: RFC: Large Floating Point Numbers - Rounding Errors by salva (Canon) on Sep 08, 2011 at 16:33 UTC
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]	[reply] [d/l] [select]
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]
Re^8: RFC: Large Floating Point Numbers - Rounding Errors by GAVollink (Novice) on Sep 08, 2011 at 19:52 UTC
Re^9: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 08, 2011 at 22:12 UTC
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Re^8: RFC: Large Floating Point Numbers - Rounding Errors by salva (Canon) on Sep 08, 2011 at 16:48 UTC
Re^9: RFC: Large Floating Point Numbers - Rounding Errors by BrowserUk (Patriarch) on Sep 08, 2011 at 16:52 UTC
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Re^4: RFC: Large Floating Point Numbers - Rounding Errors