Re: Sines and Cosines

On Sat, 22 Mar 2008 08:58:59 -0400, Eric Sosman wrote:


The thing is that in this case the real problem is at the hardware level.
I suspect that our two compilers are producing essentially identical code
for the sin and cos, and that our libraries are dutifully translating
these calls to a single assembly language instruction in the Intel
floating point processor.

The thing is that our Java implementations are making different choices
about whether that strategy is accurate enough, with Java on my machine
the JVM is running under the assumption that the answer my floating
processor gives simply isn't accurate enough. Whereas on your machine a
choice is being made to use the floating point processor.

At least, that's what I guess is going on. So, is your machine's floating
point processor more accurate than mine? Is the implementation of Java on
my hardware making the wrong choice? These are the questions I have.

Ok, I found an example of the problem on the web in the initial report of
the problem as reported to Sun in Java. I implemented the first example
of the problem in C and, sure enough, my Intel box still displays the
problem. So my JVM is doing the right thing to work around the inaccuracy.

Try running this on your computer:

kt@lovelace:/tmp$ ./cos
Expected: 3ee4f8b588dd0ce3
Actual: 3ee4f8b588dd0ce1

Notice that the difference isn't in the last bit.

#include <math.h>
#include <stdlib.h>
#include <stdio.h>

int main(int argc, char* argv[]) {
        unsigned long long *ivalp, eval;
        unsigned long long ival;
        sscanf("0x3ff921f0d7e968a9", "%llx", &ival); // input
        sscanf("0x3ee4f8b588dd0ce3", "%llx", &eval); // expected
        ivalp = &ival;
        double *val;
        val = (double*) ivalp;
        double nval = cos(*val);
        unsigned long long *oval;
        oval = (unsigned long long*) &nval;
        printf("Expected: %llx\n", eval);
        printf("Actual: %llx\n", *oval);
}

What result do you get?

--
Kenneth P. Turvey <kt-usenet@squeakydolphin.com>