in reply to Re^7: RFC: Large Floating Point Numbers - Rounding Errors
in thread RFC: Large Floating Point Numbers - Rounding Errors

You are cheating! can't you see it?
  • Comment on Re^8: RFC: Large Floating Point Numbers - Rounding Errors

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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]
      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:
      1. 0 - Rounding is towards 0.
      2. 1 - Rounding is towards nearest number.
      3. 2 - Rounding is towards positive infinity.
      4. 3 - Rounding is towards negative infinity.
[reply]
[d/l]
[select]
      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]

In Section Meditations