On Wed, Feb 04, 2015 at 04:37:14AM +1100, Bruce Evans wrote:
> On Tue, 3 Feb 2015, Steve Kargl wrote:
>
> > -#include <limits.h>
> > +#include <float.h>
> > #include <math.h>
> >
> > +#define FLT_LARGE FLT_MAX_EXP - FLT_MIN_EXP + FLT_MANT_DIG
> > +#define FLT_SMALL FLT_MIN_EXP - FLT_MAX_EXP
> > +#define DBL_LARGE DBL_MAX_EXP - DBL_MIN_EXP + DBL_MANT_DIG
> > +#define DBL_SMALL DBL_MIN_EXP - DBL_MAX_EXP
> > +#define LDBL_LARGE LDBL_MAX_EXP - LDBL_MIN_EXP + LDBL_MANT_DIG
> > +#define LDBL_SMALL LDBL_MIN_EXP - LDBL_MAX_EXP
> > +
>
> This is a lot of code and bugs (missing parentheses) for negative gain.
My crystal ball isn't function too well lately.
> To work, it depends on all of the above expressions having results that
> can be represented as an int. There is no guarantee of this in general.
On all architecture that FreeBSD currently supports, there is a guarantee
to the extent that src/sys/${MACHINE}/include/_limits.h shows
#define __INT_MAX 0x7fffffff
#define __INT_MIN (-0x7fffffff - 1)
> However, we can show that the above values are within certain fixed
> limits just as easily as we can show that they are within the INT32
> limits, and then hard-code the fixed limits. E,g, +-16384 might work,
> and +-32768 surely works when the exponent field is limited to 8 bits.
> Double a few more times for safety. Hard-coding a limit related to
> an assumed maximum supported width for the exponent field is easier
> to get right that the above expressions. I think the above are quite
> buggy, and so are my +-16384 and +-32768. The full exponent range
> plus more for denormals is needed in both directions. You only have
> it for the LARGE direction. This can be hard-coded for a 15-bit
> exponent field as +-32768 +- extras for denormals, -+ a couple for
> special exponents. This needs strictly larger than 16-bit ints for
> the denormals only. Make it +-65536 to avoid having to count carefully
> to avoid off-by-1 errors. Double a few times for larger exponent fields,
> or just add assertions to detect increases of the maxima, or just hard-
> code the limits as the int32_t extrema.
Given that the widest field width in IEEE754-2008 for
binary128 is 15, which gives a maximum unbiased exponent
of 2**15, then using +-65536 should cover our needs. The
functions scalbn[fl] can then deal with values of n
that may result in exponents that are too small or too
large. Untested diff below.
--
Steve
Index: s_scalbln.c
===================================================================
--- s_scalbln.c (revision 278165)
+++ s_scalbln.c (working copy)
@@ -27,17 +27,17 @@
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
-#include <limits.h>
#include <math.h>
+#define LARGE 65536
+#define SMALL -65536
+
double
scalbln (double x, long n)
{
int in;
- in = (int)n;
- if (in != n)
- in = (n > 0) ? INT_MAX: INT_MIN;
+ in = n > LARGE ? LARGE : n < SMALL ? SMALL : n;
return (scalbn(x, in));
}
@@ -46,9 +46,7 @@
{
int in;
- in = (int)n;
- if (in != n)
- in = (n > 0) ? INT_MAX: INT_MIN;
+ in = n > LARGE ? LARGE : n < SMALL ? SMALL : n;
return (scalbnf(x, in));
}
@@ -57,8 +55,6 @@
{
int in;
- in = (int)n;
- if (in != n)
- in = (n > 0) ? INT_MAX: INT_MIN;
+ in = n > LARGE ? LARGE : n < SMALL ? SMALL : n;
return (scalbnl(x, in));
}
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