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(a <= 0.5) and (a > 0.5) both fail with intervening output



When compiled -O, on a pentium the following produces no output whatsoever,
i.e. both (at0 <=0.5)  and (at0 > 0.5) test false.
The problem is that norm(u0) evaluates to 0.5 + 5.14996e-17
(in a register), so the first test fails. But then because of the 
possible intervening output, at0 is written to memory and truncated
to 64 bits, so that it becomes exactly 0.5, and so the second test
fails as well.
If at0 is declared as volatile double at0, then at0 is written to memory
and read back again before the first test, so then (a <= 0.5) tests true.

I don't know whether this classifies as a bug or as 'the usual trouble
with floating point numbers'; in any case, it was a nasty surprise to me.

=========================================================================
// testfwhm.h -- triggers optimizing bug

#include <math.h>
#include <iostream>
#include <complex>

int main() {

  // generate a number whose norm is _exactly_ 0.5:
  double T1 = 5 / sqrt(2 * log(2));
  double z = 2.5 / T1;
  complex<double> u0 = exp(complex<double>(-z*z, 7)); // norm(u0) == 0.5 !!

#ifdef VOLATILE
  volatile double at0;
#else
   double at0;
#endif
   at0 = norm(u0);
   if (at0 <= 0.5) cout << "smaller or equal" <<endl;
   if (at0 > 0.5) cout << "larger" <<endl;
  return 0;
}

The difference in the generated assembler code (between
volatile -- volatile double at0 and nonvolatile -- double at0) is:

=========================================================================
--- volatile/testfwhm.s	Thu May  6 22:25:55 1999
+++ nonvolatile/testfwhm.s	Thu May  6 22:21:26 1999
@@ -63,33 +63,31 @@
 	call exp__H1Zd_RCt7complex1ZX01_t7complex1ZX01
 	addl $4,%esp
 	fldl -16(%ebp)
 	fmul %st(0),%st
 	fldl -8(%ebp)
 	fmul %st(0),%st
 	faddp %st,%st(1)
-	fstpl -40(%ebp)
-	fldl -40(%ebp)
+	fstl -40(%ebp)
 	fldl .LC18
 	fcompp
 	fnstsw %ax
 	andb $5,%ah
 	jne .L1091
 	pushl $.LC19
 	pushl $cout
 	call __ls__7ostreamPCc
 	addl $8,%esp
 	pushl %eax
 .LCFI4:
 	call endl__FR7ostream
 	addl $4,%esp
 .L1091:
-	fldl -40(%ebp)
 	fldl .LC18
-	fcompp
+	fcompl -40(%ebp)
 	fnstsw %ax
 	andb $69,%ah
 	cmpb $1,%ah
 	jne .L1093
 	pushl $.LC20
 	pushl $cout
 .LCFI5:
=========================================================================

I've appended testfwhm.ii.gz and  testfwhm.s.gz (base64 encoded) below.

Yours,

Jeroen Nijhof

=========================================================================
Content-Type: application/octet-stream; name="testfwhm.ii.gz"
Content-Transfer-Encoding: base64
Content-Disposition: inline; filename="testfwhm.ii.gz"
Content-MD5: OJaylKW3Wk9PbmxapUZAxw==

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