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# -*- mode: perl; -*-
use strict;
use warnings;
use Test::More tests => 11;
use Math::BigInt;
use Math::BigFloat;
my $b = 2; # base
my $p = 64; # precision in bits
my $w = 15; # width of exponent
$b = Math::BigInt -> new($b);
$p = Math::BigInt -> new($p);
my $emax = 2 ** ($w - 1) - 1;
my $emin = 1 - $emax;
my $format = 'fp80';
#my $binv = Math::BigFloat -> new("0.5");
my $data =
[
{
dsc => "positive zero",
bin => "0"
. ("0" x $w)
. ("0" x $p),
asc => "+0",
obj => Math::BigInt -> new("0"),
},
{
dsc => "one",
bin => "0"
. "0" . ("1" x ($w - 1))
. "1" . "0" x ($p - 1),
asc => "1",
obj => Math::BigInt -> new("1"),
},
{
dsc => "largest normal number",
bin => "0"
. ("1" x ($w - 1)) . "0"
. "1" x $p,
asc => "$b ** $emax * ($b - $b ** (" . (1 - $p) . "))",
#obj => $b ** $emax * ($b - $binv ** ($p - 1)),
obj => $b ** ($emax + 1) - $b ** ($emax + 1 - $p),
},
{
dsc => "minus one",
bin => "1"
. "0" . ("1" x ($w - 1))
. "1" . "0" x ($p - 1),
asc => "-1",
obj => Math::BigInt -> new("-1"),
},
{
dsc => "two",
bin => "0"
. "1" . ("0" x ($w - 1))
. "1" . ("0" x ($p - 1)),
asc => "2",
obj => Math::BigInt -> new("2"),
},
{
dsc => "minus two",
bin => "1"
. "1" . ("0" x ($w - 1))
. "1" . ("0" x ($p - 1)),
asc => "-2",
obj => Math::BigInt -> new("-2"),
},
{
dsc => "positive infinity",
bin => "0"
. ("1" x $w)
. ("0" x $p),
asc => "+inf",
obj => Math::BigInt -> new("inf"),
},
{
dsc => "negative infinity",
bin => "1"
. ("1" x $w)
. ("0" x $p),
asc => "-inf",
obj => Math::BigInt -> new("-inf"),
},
{
dsc => "NaN",
bin => "1"
. ("1" x $w)
. ("1" x $p),
asc => "NaN",
obj => Math::BigInt -> new("NaN"),
},
];
for my $entry (@$data) {
my $bin = $entry -> {bin};
my $bytes = pack "B*", $bin;
my $hex = unpack "H*", $bytes;
my $str = join "", map "\\x$_", unpack "(a2)*", $hex;
note("\n",
" format : ", $format, "\n",
"description : ", $entry -> {dsc}, "\n",
" value : ", $entry -> {asc}, "\n",
" binary : ", join(" ", unpack "(a8)*", $bin), "\n",
"hexadecimal : ", join(" ", unpack "(a2)*", $hex), "\n",
" bytes : ", $str, "\n",
"\n");
my $x = $entry -> {obj};
my $test = qq|Math::BigInt -> new("$x") -> to_fp80()|;
my $got_bytes = $x -> to_fp80();
my $got_hex = unpack "H*", $got_bytes;
$got_hex =~ s/(..)/\\x$1/g;
my $expected_hex = $hex;
$expected_hex =~ s/(..)/\\x$1/g;
is($got_hex, $expected_hex);
}
note("\nRounding close to the largest normal number.\n\n");
{
# largest normal number: 2 ** 16383 * (2 - 2 ** (-63))
my $lo = Math::BigFloat -> from_fp80("7ffeffffffffffffffff");
# 2 ** 16383 * 2 = 2 ** 16384
my $hi = Math::BigFloat -> new("2") -> bpow("16384");
# compute an average weighted towards the smaller of the two
my $x1 = 0.75 * $lo + 0.25 * $hi;
note "";
note "lo ≈ ", $lo -> bnstr(40);
note "hi ≈ ", $hi -> bnstr(40);
note "x1 ≈ ", $x1 -> bnstr(40);
note "";
# this must round down to the largest normal number
my $got1 = unpack "H*", $x1 -> to_fp80();
is($got1, "7ffeffffffffffffffff");
# compute an average weighted towards the larger of the two
my $x3 = 0.25 * $lo + 0.75 * $hi;
note "";
note "lo ≈ ", $lo -> bnstr(40);
note "hi ≈ ", $hi -> bnstr(40);
note "x3 ≈ ", $x3 -> bnstr(40);
note "";
# this must round up to infinity
my $got3 = unpack "H*", $x3 -> to_fp80();
is($got3, "7fff0000000000000000");
}
|
