On Sat, Apr 22, 2023 at 4:34 PM Ben Pfaff <b...@cs.stanford.edu> wrote:
> Before this afternoon, I thought that a check like this for a double 'd':
> d == floor (d) && d >= LONG_MIN && d <= LONG_MAX
> was sufficient to determine whether converting 'd' to 'long' would
> yield a 'long' with the same value as 'd'.
>
> Now I realize that this is wrong. In particular, take a look at the
> following program:
>
> #include <limits.h>
> #include <stdio.h>
>
> int main (void)
> {
> long i = LONG_MAX;
> double d = i;
> long j = d;
> printf ("%ld, %f, %ld\n", i, d, j);
> return 0;
> }
>
> On my system, this prints:
>
> 9223372036854775807, 9223372036854775808.000000, -9223372036854775808
>
> In other words, LONG_MAX gets rounded up to 2**63 when it's converted to
> 'double', which makes sense because 'double' only has 53 bits of precision,
> but this also means that 'd <= LONG_MAX' and still doesn't fit in 'long', as
> one
> can see from it getting converted to a wrong answer (-2**63 instead of
> 2**63) when converted back to 'long'. And of course any answer is OK there,
> since this out-of-range conversion yields undefined behavior.
>
> Can anyone suggest a correct way to check whether a 'double' is in the
> range of 'long'?
I figured out a solution to the problem I wanted to solve. After
thinking about it for
a while longer, I realized that what I really wanted was the range of
integers that
'double' represents without loss of precision, that is, most
commonly,-2**53...2**53.
And then I wanted the intersection of this range with the range of
'long'. Typically
that's going to be -2**53...2**53 also, of course.
I came up with the following. Feedback welcomed!
#include <limits.h>
#include <stdio.h>
#include <float.h>
#include <math.h>
/* Maximum positive integer 'double' represented with no loss of precision
(that is, with unit precision).
The maximum negative integer with this property is -DBL_UNIT_MAX. */
#if DBL_MANT_DIG == 53 /* 64-bit double */
#define DBL_UNIT_MAX 9007199254740992.0
#elif DBL_MANT_DIG == 64 /* 80-bit double */
#define DBL_UNIT_MAX 18446744073709551616.0
#elif DBL_MANT_DIG == 113 /* 128-bit double */
#define DBL_UNIT_MAX 10384593717069655257060992658440192.0
#else
#error "Please define DBL_UNIT_MAX for your system (as 2**DBL_MANT_DIG)."
#endif
/* Intersection of ranges [LONG_MIN,LONG_MAX] and [-DBL_UNIT_MAX,DBL_UNIT_MAX],
as a range of 'long's. This range is the (largest contiguous) set of
integer values that can be safely converted between 'long' and 'double'
without loss of precision. */
#if DBL_MANT_DIG < LONG_WIDTH - 1
#define DBL_UNIT_LONG_MIN ((long) -DBL_UNIT_MAX)
#define DBL_UNIT_LONG_MAX ((long) DBL_UNIT_MAX)
#else
#define DBL_UNIT_LONG_MIN LONG_MIN
#define DBL_UNIT_LONG_MAX LONG_MAX
#endif
int main (void)
{
long i = DBL_UNIT_LONG_MAX;
double d = i;
long j = d;
printf ("%ld, %f, %ld\n", i, d, j);
printf ("%f\n", DBL_UNIT_MAX);
printf ("%d, %d\n", DBL_MANT_DIG, LONG_WIDTH);
printf ("%ld, %ld\n", DBL_UNIT_LONG_MIN, DBL_UNIT_LONG_MAX);
printf ("%ld, %ld\n", LONG_MIN, LONG_MAX);
return 0;
}
