use warnings;
use strict;
use Data::IEEE754::Tools 0.016 qw/:all/;
use Math::MPFR qw/:mpfr/;
use POSIX qw/floor ceil log10 log2/;

Rmpfr_set_default_prec(1000);

# easy to come up with one that takes many digits to express:
my $x = nextUp( POS_NORM_SMALLEST() );
print "POS_NORM_SMALLEST = 2**-1022\n";
print "POS_NORM_SMALLEST+1ULP = (1 + 2**-52)*(2**-1022)\n";
print "\n";
print "(      1  )           \n";
print "(1 + -----)*(2**-1022)\n";
print "(    2**52)           \n";
print "\n";
printf "IEEE754 Hex String: '%s'\n", hexstr754_from_double($x);
printf "%-30a %-30s %-30s\n", $x, to_hex_floatingpoint($x), to_dec_floatingpoint($x);
my $s=Math::MPFR->new($x);
printf "[%d digits long]: %s\n", length($s)-6, $s;

my $d = ceil(-log10($x));   # start digit
printf "For _FIXED POINT_ notation,\n";
printf "\tstarts %d digits after the decimal point\n", $d;
my $ulp = ulp($x);          # value of last bit (whether or not it is set)
printf "long version of ulp: %s\n", Math::MPFR->new($ulp);
my $l2 = log2($ulp);
printf "log2(ulp) = %d, so I expect it to fit within %d digits of the fixed decimal point\n", $l2, -$l2;

##</code><code>##

__OUTPUT__
POS_NORM_SMALLEST = 2**-1022
POS_NORM_SMALLEST+1ULP = (1 + 2**-52)*(2**-1022)

(      1  )
(1 + -----)*(2**-1022)
(    2**52)

IEEE754 Hex String: '0010000000000001'
0x1.0000000000001p-1022        +0x1.0000000000001p-1022       +0d1.0000000000000002p-1022
[303 digits long]: 2.22507385850720187715587855857894824078800884868370419561313003121196886039960069652979042922126288586390370136702819080171712960727119103551272274131751521990557400431388045678032333775398816391773873289592460742292701130780538133970816533612964474495297895212189790907838525833659018517896187998851504e-308
For _FIXED POINT_ notation,
        starts 308 digits after the decimal point