floating point precision on gcc-4 differs using variables or arrays

[Asfand Yar Qazi <email at asfandyar dot cjb dot net>]

Hi,

Consider the following little bunch of code (perpared specially for 
this question:)

-------------CODE---------------
#ifdef __cplusplus
extern "C"
#endif
int printf(const char *format, ...);

/*

Lesson: store stuff either as variables, or in arrays - not both!

*/

float a[4] = {0.123, -0.231, 0.652, 1};
float b[4] = {-0.523, -9.6421, 0.0123, 1};

float a0 = 0.123,  a1 = -0.231, a2 = 0.652, a3 = 1;
float b0 = -0.523, b1 = -9.6421, b2 = 0.0123, b3 = 1;

const int loopcount = 1000000;

void
thefunc1(void)
{
	int i;
	for(i = 0; i < loopcount; ++i) {
		a[0] = (b[0] * 0.9999f) + (b[0] * 0.00001f);
		a[1] = (b[1] * 0.9999f) + (b[1] * 0.00001f);
		a[2] = (b[2] * 0.9999f) + (b[2] * 0.00001f);

		b[0] = a[0];
		b[1] = a[1];
		b[2] = a[2];
	}
}

void
thefunc2(void)
{
	int i;
	for(i = 0; i < loopcount; ++i) {
		a0 = (b0 * 0.9999f) + (b0 * 0.00001f);
		a1 = (b1 * 0.9999f) + (b1 * 0.00001f);
		a2 = (b2 * 0.9999f) + (b2 * 0.00001f);

		b0 = a0;
		b1 = a1;
		b2 = a2;
	}
}

int
main()
{
	thefunc1();
	thefunc2();

	printf("t1: [%.24e, %.24e, %.24e, %.24e]\n", a[0], a[1], a[2], a[3]);
	printf("t2: [%.24e, %.24e, %.24e, %.24e]\n", a0, a1, a2, a3);

	return 0;
}
-------------CODE---------------

Now, consider the output, using gcc 4 cvs and gcc 3.4.3 (compilation 
flags:  -ffast-math -march=pentium3 -msse -mfpmath=387 -O3 
-fno-unroll-loops )

./gcc_error-3.4.3
t1: [-4.255309033630528751103380e-40, -7.845134420060880251139727e-39, 
1.000768933567725568230718e-41, 1.000000000000000000000000e+00]
t2: [-4.255309033630528751103380e-40, -7.845134420060880251139727e-39, 
1.000807363220784352053728e-41, 1.000000000000000000000000e+00]

./gcc_error-4
t1: [-4.255302206601370422491529e-40, -7.845133972967615879964511e-39, 
1.000768933567725568230718e-41, 1.000000000000000000000000e+00]
t2: [-4.255309033630528751103380e-40, -7.845134420060880251139727e-39, 
1.000807363220784352053728e-41, 1.000000000000000000000000e+00]

Note how on gcc 3.4.3, using variables or arrays of floats gives the 
same results.  However, on gcc 4, it seems this is no longer the case 
(using the above flags, anyhow.)

Its not a bug, I assume, but could someone explain it to me why this 
is happening?

Then, observe the following with sse fpmath (flags: -ffast-math 
-march=pentium3 -msse -mfpmath=sse -O3 -fno-unroll-loops)

./gcc_error-3.4.3
t1: [-4.255449163476961232810473e-40, -7.845069960331521309554464e-39, 
9.890364561204558886579683e-42, 1.000000000000000000000000e+00]
t2: [-4.255449163476961232810473e-40, -7.845069960331521309554464e-39, 
9.890364561204558886579683e-42, 1.000000000000000000000000e+00]

./gcc_error-4
t1: [-4.255449163476961232810473e-40, -7.845069960331521309554464e-39, 
9.890364561204558886579683e-42, 1.000000000000000000000000e+00]
t2: [-4.255449163476961232810473e-40, -7.845069960331521309554464e-39, 
9.890364561204558886579683e-42, 1.000000000000000000000000e+00]

Using SSE seems to give the sames answers using variables or arrays. 
Wha?!?!?!  Now I'm even more confused.

Could someone explain the above to me?  Why is there a difference 
using arrays or variables in 387 maths, and not in SSE maths?

Also, is it better (i.e. more efficient, faster, etc.) to use 
variables or arrays to hold the data in matrix/vector classes in C++?

Thanks,
	Asfand Yar