Re^2: Integers sometimes turn into Reals after substraction (error correction ?)

Well Perl's error correction (or that of the underlying C lib) is better than it's reputation

   
DB<186> $x1= 1000*(4/25)
 => 160

  DB<187> $x2= 4000/25
 => 160

  DB<188> $x1 == $x2
 => 1
[download]

What's puzzling me is this behaviour:

  DB<205>  for (254..263) {$x = 1000 * ( $_ + 4/25 ); printf "%.20f\n"
+, $x} 

254160.00000000000000000000
255160.00000000000000000000
256160.00000000002910383046
257160.00000000002910383046
258160.00000000002910383046
259160.00000000002910383046
260160.00000000002910383046
261160.00000000002910383046
262160.00000000000000000000
263160.00000000000000000000
[download]

Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)

Je suis Charlie!}

update

interestingly this only seems to happen near some powers of 2

  DB<220>  for (0..20) {$e=2**$_; $x = 1000 * ( $e + 4/25 ); printf "$
+_:$e => %.20f\n", $x if ($x-int($x))} 
5:32 => 32159.99999999999636202119
8:256 => 256160.00000000002910383046
9:512 => 512159.99999999994179233909
10:1024 => 1024160.00000000011641532183
11:2048 => 2048159.99999999976716935635
15:32768 => 32768160.00000000372529029846
18:262144 => 262144159.99999997019767761230
19:524288 => 524288160.00000005960464477539
20:1048576 => 1048576159.99999988079071044922
[download]

update

in hindsight this may be an effect of precision and correction of the underlying processor and usage of arithmetic units, hence machine dependent.

Comment on Re^2: Integers sometimes turn into Reals after substraction (error correction ?) Select or Download Code

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Re^3: Integers sometimes turn into Reals after substraction (error correction ?) by pryrt (Abbot) on May 14, 2016 at 17:02 UTC
IEEE double-precision float is 53 bit float. 0.00000000002910383046 = 2*-35. With the 18 bits for the integral portion of 255160 or 256160, that's the full 53bits. So, apparently, when you take the 53bit fractional representation of 255.16 multiplied by 1000dec, round-off sets the final bit to 0; when you take 256.16 1000, round-off sets the final bit to 1. Now (when I have time) I'm going to have to figure out the formula to figure out which powers of two will have this error and which won't. It all depends on the 53rd bit of the product of 2**N+16/25 times 128 (same as the bits of times 1000, since the factor of 8 is a binary shift). Oh, I'm nearly there... the 125 is 0b111_1101... and that will just interact with the 53rd bit... urgh but I've got to leave now... I guess it's an exercise for later. :-)	[reply]
Re^4: Integers sometimes turn into Reals after substraction (error correction ?) by pryrt (Abbot) on May 14, 2016 at 19:21 UTC
Convert ieee floats into hex notation, for each of 2n - 1 and 2n: cmd.exe> perl -e "use 5.010; for(0..31){$e=2*$_; $f=$e-1; $str = join + '', map { sprintf '%02x ', ord } split(//, pack('dddd', $f+4/25, $e+ +4/25, ($f+4/25)1000, ($e+4/25)1000)); $str =~ s/(.{24})(.{24})(.{24 +})(.{24})/\1\t\2\t\3\t\4/; say qq{$_\t$str};}" 0 7b 14 ae 47 e1 7a c4 3f 8f c2 f5 28 5c 8f f2 3f + 00 00 00 00 00 00 64 40 00 00 00 00 00 20 92 40 1 8f c2 f5 28 5c 8f f2 3f 48 e1 7a 14 ae 47 01 40 + 00 00 00 00 00 20 92 40 00 00 00 00 00 e0 a0 40 2 48 e1 7a 14 ae 47 09 40 a4 70 3d 0a d7 a3 10 40 + 00 00 00 00 00 b0 a8 40 00 00 00 00 00 40 b0 40 3 a4 70 3d 0a d7 a3 1c 40 52 b8 1e 85 eb 51 20 40 + 00 00 00 00 00 f8 bb 40 00 00 00 00 00 e0 bf 40 4 52 b8 1e 85 eb 51 2e 40 29 5c 8f c2 f5 28 30 40 + 00 00 00 00 00 9c cd 40 00 00 00 00 00 90 cf 40 5 29 5c 8f c2 f5 28 3f 40 14 ae 47 e1 7a 14 40 40 + 00 00 00 00 00 6e de 40 ff ff ff ff ff 67 df 40 6 14 ae 47 e1 7a 94 4f 40 0a d7 a3 70 3d 0a 50 40 + 00 00 00 00 00 d7 ee 40 00 00 00 00 00 54 ef 40 7 0a d7 a3 70 3d ca 5f 40 85 eb 51 b8 1e 05 60 40 + 00 00 00 00 80 0b ff 40 00 00 00 00 00 4a ff 40 8 85 eb 51 b8 1e e5 6f 40 c3 f5 28 5c 8f 02 70 40 + 00 00 00 00 c0 25 0f 41 01 00 00 00 00 45 0f 41 9 c3 f5 28 5c 8f f2 7f 40 e1 7a 14 ae 47 01 80 40 + 00 00 00 00 e0 32 1f 41 ff ff ff ff 7f 42 1f 41 10 e1 7a 14 ae 47 f9 8f 40 71 3d 0a d7 a3 00 90 40 + 00 00 00 00 70 39 2f 41 01 00 00 00 40 41 2f 41 11 71 3d 0a d7 a3 fc 9f 40 b8 1e 85 eb 51 00 a0 40 + 00 00 00 00 b8 3c 3f 41 ff ff ff ff 9f 40 3f 41 12 b8 1e 85 eb 51 fe af 40 5c 8f c2 f5 28 00 b0 40 + 00 00 00 00 5c 3e 4f 41 00 00 00 00 50 40 4f 41 13 5c 8f c2 f5 28 ff bf 40 ae 47 e1 7a 14 00 c0 40 + 00 00 00 00 2e 3f 5f 41 00 00 00 00 28 40 5f 41 14 ae 47 e1 7a 94 ff cf 40 d7 a3 70 3d 0a 00 d0 40 + 00 00 00 00 97 3f 6f 41 00 00 00 00 14 40 6f 41 15 d7 a3 70 3d ca ff df 40 ec 51 b8 1e 05 00 e0 40 + 00 00 00 80 cb 3f 7f 41 01 00 00 00 0a 40 7f 41 16 ec 51 b8 1e e5 ff ef 40 f6 28 5c 8f 02 00 f0 40 + 00 00 00 c0 e5 3f 8f 41 00 00 00 00 05 40 8f 41 17 f6 28 5c 8f f2 ff ff 40 7b 14 ae 47 01 00 00 41 + 00 00 00 e0 f2 3f 9f 41 00 00 00 80 02 40 9f 41 18 7b 14 ae 47 f9 ff 0f 41 3d 0a d7 a3 00 00 10 41 + 00 00 00 70 f9 3f af 41 ff ff ff 3f 01 40 af 41 19 3d 0a d7 a3 fc ff 1f 41 1f 85 eb 51 00 00 20 41 + 00 00 00 b8 fc 3f bf 41 01 00 00 a0 00 40 bf 41 20 1f 85 eb 51 fe ff 2f 41 8f c2 f5 28 00 00 30 41 + 00 00 00 5c fe 3f cf 41 ff ff ff 4f 00 40 cf 41 21 8f c2 f5 28 ff ff 3f 41 48 e1 7a 14 00 00 40 41 + 00 00 00 2e ff 3f df 41 01 00 00 28 00 40 df 41 22 48 e1 7a 94 ff ff 4f 41 a4 70 3d 0a 00 00 50 41 + 00 00 00 97 ff 3f ef 41 00 00 00 14 00 40 ef 41 23 a4 70 3d ca ff ff 5f 41 52 b8 1e 05 00 00 60 41 + 00 00 80 cb ff 3f ff 41 00 00 00 0a 00 40 ff 41 24 52 b8 1e e5 ff ff 6f 41 29 5c 8f 02 00 00 70 41 + 00 00 c0 e5 ff 3f 0f 42 00 00 00 05 00 40 0f 42 25 29 5c 8f f2 ff ff 7f 41 14 ae 47 01 00 00 80 41 + 00 00 e0 f2 ff 3f 1f 42 ff ff 7f 02 00 40 1f 42 26 14 ae 47 f9 ff ff 8f 41 0a d7 a3 00 00 00 90 41 + 00 00 70 f9 ff 3f 2f 42 00 00 40 01 00 40 2f 42 27 0a d7 a3 fc ff ff 9f 41 85 eb 51 00 00 00 a0 41 + 00 00 b8 fc ff 3f 3f 42 00 00 a0 00 00 40 3f 42 28 85 eb 51 fe ff ff af 41 c3 f5 28 00 00 00 b0 41 + 00 00 5c fe ff 3f 4f 42 01 00 50 00 00 40 4f 42 29 c3 f5 28 ff ff ff bf 41 e1 7a 14 00 00 00 c0 41 + 00 00 2e ff ff 3f 5f 42 ff ff 27 00 00 40 5f 42 30 e1 7a 94 ff ff ff cf 41 71 3d 0a 00 00 00 d0 41 + 00 00 97 ff ff 3f 6f 42 01 00 14 00 00 40 6f 42 31 71 3d ca ff ff ff df 41 b8 1e 05 00 00 00 e0 41 + 00 80 cb ff ff 3f 7f 42 ff ff 09 00 00 40 7f 42 n 2n - 1 2n + (2n - 1)1000 (2*n) 1000 [download]	[reply] [d/l]