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Some more findings:

M.Drochner@fz-juelich.de said:
> -Use of "long double" is just a waste of memory, and memory
>  bandwidth. 

Almost, but not quite: while the exponent is effectively
limited to 53 bits, the mantissa has still 15 bits which
is 4 more than double. So there is no gain in accuracy
but a little more dynamic range.

> +It is almost as easy to implement expl(), logl() and all the other
>  "long double" variants

So, in the light of this, it is not _that_ easy because the numeric
ranges are different. The algorithms can still be reused I think.

Another fact is that the LDBL_* macros of <float.h> don't
reflect reality. Eg LDBL_MAX is already infinity. The long double
support in gdtoa also suffers from this.
See the appended program. On an i386/current box, it gives:
1.189731495357231765021264e+4932
inf
1.189731495357231765021264e+4932
inf
1.189731495357231599977347e+4932
1.189731495357231632999029e+4932
1.189731495357231599977347e+4932
1.189731495357231632999029e+4932

which shows that both the compiler and gdtoa don't know about the
53-bit mantissa -- LDBL_MAX gets converted to a number which will
cause an overflow, and the other number has some excess bits in
the mantissa which will get lost if touched by the FPU later.

If I set the TARGET_96_ROUND_53_LONG_DOUBLE as said in my previous mail,
it gives:
inf
inf
1.189731495357231765021264e+4932
inf
1.189731495357231632999029e+4932
1.189731495357231632999029e+4932
1.189731495357231599977347e+4932
1.189731495357231632999029e+4932

which shows that the constants generated at compile time are
consistent with reality now, but gdtoa still assumes mantissa
bits not usable for further calculations.

Adapting the LDBL_ constants to the 53-bit mantissa should fix
this, but some review is needed because at some points just
mantissa lengths are compared to decide whether a "long double"
is different from a "double".

best regards
Matthias





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

#define TRUE_LDBL_MAX 1.1897314953572316E+4932L
long double null;

void
pr(long double d)
{

	printf("%.25Lg\n", d);
	d += null;
	printf("%.25Lg\n", d);
}

#define pr2(x) pr(x);pr(strtold(#x, 0))
#define pr3(x) pr2(x)

int
main()
{

	pr3(LDBL_MAX);
	pr3(TRUE_LDBL_MAX);

	return 0;
}

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