gcc rounding difference between versions

Question

I'm looking into why a test case is failing

The problematic test can be reduced to doing (4.0/9.0) ** (1.0/2.6), rounding this to 6 digits and checking against a known value (as a string):

#include<stdio.h>
#include<math.h>
int main(){
    printf("%.06f\n", powf(4.0/9.0, (1.0/2.6)));
}

If I compile and run this in gcc 4.1.2 on Linux, I get:

0.732057

Python agrees, as does Wolfram|Alpha:

$ python2.7 -c 'print "%.06f" % (4.0/9.0)**(1/2.6)'
0.732057

However I get the following result on gcc 4.4.0 on Linux, and 4.2.1 on OS X:

0.732058

A double acts identically (although I didn't test this extensively)

I'm not sure how to narrow this down any further.. Is this a gcc regression? A change in rounding algorithm? Me doing something silly?

Edit: Printing the result to 12 digits, the digit at the 7th place is 4 vs 5, which explains the rounding difference, but not the value difference:

gcc 4.1.2:

0.732057452202

gcc 4.4.0:

0.732057511806

Here's the gcc -S output from both versions: https://gist.github.com/1588729

Answer 1

Recent gcc version are able to use mfpr to do compile time floating point computation. My guess is that your recent gcc does that and use an higher precision for the compile time version. This is allowed by the at least the C99 standard (I've not looked in other one if it was modified)

6.3.1.8/2 in C99

The values of floating operands and of the results of floating expressions may be represented in greater precision and range than that required by the type; the types are not changed thereby.

Edit: your gcc -S results confirm that. I haven't checked the computations, but the old one has (after substituting memory for its constant content)

movss 1053092943, %xmm1
movss 1055100473, %xmm0
call powf

calling powf with the precomputed values for 4/9.0 and 1/2.6 and then printing the result after promotion to double, while the new one just print the float 0x3f3b681f promoted to double.