By my reckoning, this produces a correct doubledouble for 3.1415926535897932384626433832795 - and it uses only Math::BIgFloat.
It relies on %a printf formatting, so requires perl 5.22.0. 
use strict;
use warnings;
use Math::BigFloat;
use 5.22.0;

my %bits_table = (
 1 => '0001',
 2 => '0010',
 3 => '0011',
 4 => '0100',
 5 => '0101',
 6 => '0110',
 7 => '0111',
 8 => '1000',
 9 => '1001',
 a => '1010',
 A => '1010',
 b => '1011',
 B => '1011',
 c => '1100',
 C => '1100',
 d => '1101',
 D => '1101',
 e => '1110',
 E => '1110',
 f => '1111',
 F => '1111',
);

my %vals_table = (
0 => '1',
1 => '0.5',
2 => '0.25',
3 => '0.125',
4 => '0.0625',
5 => '0.03125',
6 => '0.015625',
7 => '0.0078125',
8 => '0.00390625',
9 => '0.001953125',
10 => '0.0009765625',
11 => '0.00048828125',
12 => '0.000244140625',
13 => '0.0001220703125',
14 => '0.00006103515625',
15 => '0.000030517578125',
16 => '0.0000152587890625',
17 => '0.00000762939453125',
18 => '0.000003814697265625',
19 => '0.0000019073486328125',
20 => '0.00000095367431640625',
21 => '0.000000476837158203125',
22 => '0.0000002384185791015625',
23 => '0.00000011920928955078125',
24 => '0.000000059604644775390625',
25 => '0.0000000298023223876953125',
26 => '0.00000001490116119384765625',
27 => '0.000000007450580596923828125',
28 => '0.0000000037252902984619140625',
29 => '0.00000000186264514923095703125',
30 => '0.000000000931322574615478515625',
31 => '0.0000000004656612873077392578125',
32 => '0.00000000023283064365386962890625',
33 => '0.000000000116415321826934814453125',
34 => '0.0000000000582076609134674072265625',
35 => '0.00000000002910383045673370361328125',
36 => '0.000000000014551915228366851806640625',
37 => '0.0000000000072759576141834259033203125',
38 => '0.00000000000363797880709171295166015625',
39 => '0.000000000001818989403545856475830078125',
40 => '0.0000000000009094947017729282379150390625',
41 => '0.00000000000045474735088646411895751953125',
42 => '0.000000000000227373675443232059478759765625',
43 => '0.0000000000001136868377216160297393798828125',
44 => '0.00000000000005684341886080801486968994140625',
45 => '0.000000000000028421709430404007434844970703125',
46 => '0.0000000000000142108547152020037174224853515625',
47 => '0.00000000000000710542735760100185871124267578125',
48 => '0.000000000000003552713678800500929355621337890625',
49 => '0.0000000000000017763568394002504646778106689453125',
50 => '0.00000000000000088817841970012523233890533447265625',
51 => '0.000000000000000444089209850062616169452667236328125',
52 => '0.0000000000000002220446049250313080847263336181640625',
53 => '0.00000000000000011102230246251565404236316680908203125',
54 => '0.000000000000000055511151231257827021181583404541015625',
55 => '0.0000000000000000277555756156289135105907917022705078125',
56 => '0.00000000000000001387778780781445675529539585113525390625',
57 => '0.000000000000000006938893903907228377647697925567626953125',
58 => '0.0000000000000000034694469519536141888238489627838134765625',
59 => '0.00000000000000000173472347597680709441192448139190673828125',
60 => '0.000000000000000000867361737988403547205962240695953369140625'
+,
61 => '0.0000000000000000004336808689942017736029811203479766845703125
+',
62 => '0.0000000000000000002168404344971008868014905601739883422851562
+5',
63 => '0.0000000000000000001084202172485504434007452800869941711425781
+25',
64 => '0.0000000000000000000542101086242752217003726400434970855712890
+625',
65 => '0.0000000000000000000271050543121376108501863200217485427856445
+3125',
66 => '0.0000000000000000000135525271560688054250931600108742713928222
+65625',
67 => '0.0000000000000000000067762635780344027125465800054371356964111
+328125',
68 => '0.0000000000000000000033881317890172013562732900027185678482055
+6640625',
69 => '0.0000000000000000000016940658945086006781366450013592839241027
+83203125',
70 => '0.0000000000000000000008470329472543003390683225006796419620513
+916015625',
71 => '0.0000000000000000000004235164736271501695341612503398209810256
+9580078125',
72 => '0.0000000000000000000002117582368135750847670806251699104905128
+4790039062',
73 => '0.0000000000000000000001058791184067875423835403125849552452564
+2395019531',
74 => '0.0000000000000000000000529395592033937711917701562924776226282
+11975097656',
75 => '0.0000000000000000000000264697796016968855958850781462388113141
+05987548828',
76 => '0.0000000000000000000000132348898008484427979425390731194056570
+52993774414',
77 => '0.0000000000000000000000066174449004242213989712695365597028285
+26496887207',
78 => '0.0000000000000000000000033087224502121106994856347682798514142
+632484436035',
79 => '0.0000000000000000000000016543612251060553497428173841399257071
+316242218018',
80 => '0.0000000000000000000000008271806125530276748714086920699628535
+6581211090088',
81 => '0.0000000000000000000000004135903062765138374357043460349814267
+8290605545044',
82 => '0.0000000000000000000000002067951531382569187178521730174907133
+9145302772522',
83 => '0.0000000000000000000000001033975765691284593589260865087453566
+9572651386261',
84 => '0.0000000000000000000000000516987882845642296794630432543726783
+47863256931305',
85 => '0.0000000000000000000000000258493941422821148397315216271863391
+73931628465652',
86 => '0.0000000000000000000000000129246970711410574198657608135931695
+86965814232826',
87 => '0.0000000000000000000000000064623485355705287099328804067965847
+934829071164131',
88 => '0.0000000000000000000000000032311742677852643549664402033982923
+967414535582066',
89 => '0.0000000000000000000000000016155871338926321774832201016991461
+983707267791033',
90 => '0.0000000000000000000000000008077935669463160887416100508495730
+9918536338955164',
91 => '0.0000000000000000000000000004038967834731580443708050254247865
+4959268169477582',
92 => '0.0000000000000000000000000002019483917365790221854025127123932
+7479634084738791',
93 => '0.0000000000000000000000000001009741958682895110927012563561966
+3739817042369395',
94 => '0.0000000000000000000000000000504870979341447555463506281780983
+18699085211846977',
95 => '0.0000000000000000000000000000252435489670723777731753140890491
+59349542605923489',
96 => '0.0000000000000000000000000000126217744835361888865876570445245
+79674771302961744',
97 => '0.0000000000000000000000000000063108872417680944432938285222622
+898373856514808722',
98 => '0.0000000000000000000000000000031554436208840472216469142611311
+449186928257404361',
99 => '0.0000000000000000000000000000015777218104420236108234571305655
+72459346412870218',
100 => '0.000000000000000000000000000000788860905221011805411728565282
+78622967320643510902',
101 => '0.000000000000000000000000000000394430452610505902705864282641
+39311483660321755451',
102 => '0.000000000000000000000000000000197215226305252951352932141320
+69655741830160877726',
103 => '0.000000000000000000000000000000098607613152626475676466070660
+348278709150804388628',
104 => '0.000000000000000000000000000000049303806576313237838233035330
+174139354575402194314',
105 => '0.000000000000000000000000000000024651903288156618919116517665
+087069677287701097157',
106 => '0.000000000000000000000000000000012325951644078309459558258832
+543534838643850548578',
107 => '0.000000000000000000000000000000006162975822039154729779129416
+2717674193219252742892',
108 => '0.000000000000000000000000000000003081487911019577364889564708
+1358837096609626371446',
109 => '0.000000000000000000000000000000001540743955509788682444782354
+0679418548304813185723',
110 => '0.000000000000000000000000000000000770371977754894341222391177
+03397092741524065928616',
111 => '0.000000000000000000000000000000000385185988877447170611195588
+51698546370762032964308',
112 => '0.000000000000000000000000000000000192592994438723585305597794
+25849273185381016482154',
113 => '0.000000000000000000000000000000000096296497219361792652798897
+129246365926905082410769',
114 => '0.000000000000000000000000000000000048148248609680896326399448
+564623182963452541205385',
115 => '0.000000000000000000000000000000000024074124304840448163199724
+282311591481726270602692',
116 => '0.000000000000000000000000000000000012037062152420224081599862
+141155795740863135301346',
117 => '0.000000000000000000000000000000000006018531076210112040799931
+0705778978704315676506731',
118 => '0.000000000000000000000000000000000003009265538105056020399965
+5352889489352157838253365',
119 => '0.000000000000000000000000000000000001504632769052528010199982
+7676444744676078919126683',
120 => '0.000000000000000000000000000000000000752316384526264005099991
+38382223723380394595633414',
121 => '0.000000000000000000000000000000000000376158192263132002549995
+69191111861690197297816707',
122 => '0.000000000000000000000000000000000000188079096131566001274997
+84595555930845098648908353',
123 => '0.000000000000000000000000000000000000094039548065783000637498
+922977779654225493244541767',
124 => '0.000000000000000000000000000000000000047019774032891500318749
+461488889827112746622270884',
125 => '0.000000000000000000000000000000000000023509887016445750159374
+730744444913556373311135442',
126 => '0.000000000000000000000000000000000000011754943508222875079687
+365372222456778186655567721',
127 => '0.000000000000000000000000000000000000005877471754111437539843
+6826861112283890933277838604',
128 => '0.000000000000000000000000000000000000002938735877055718769921
+8413430556141945466638919302',
129 => '0.000000000000000000000000000000000000001469367938527859384960
+9206715278070972733319459651',
130 => '0.000000000000000000000000000000000000000734683969263929692480
+46033576390354863666597298255',
131 => '0.000000000000000000000000000000000000000367341984631964846240
+23016788195177431833298649128',
132 => '0.000000000000000000000000000000000000000183670992315982423120
+11508394097588715916649324564',
133 => '0.000000000000000000000000000000000000000091835496157991211560
+057541970487943579583246622819',
134 => '0.000000000000000000000000000000000000000045917748078995605780
+02877098524397178979162331141',
135 => '0.000000000000000000000000000000000000000022958874039497802890
+014385492621985894895811655705',
136 => '0.000000000000000000000000000000000000000011479437019748901445
+007192746310992947447905827852',
137 => '0.000000000000000000000000000000000000000005739718509874450722
+5035963731554964737239529139262',
138 => '0.000000000000000000000000000000000000000002869859254937225361
+2517981865777482368619764569631',
139 => '0.000000000000000000000000000000000000000001434929627468612680
+6258990932888741184309882284816',
140 => '0.000000000000000000000000000000000000000000717464813734306340
+31294954664443705921549411424078',
141 => '0.000000000000000000000000000000000000000000358732406867153170
+15647477332221852960774705712039',
142 => '0.000000000000000000000000000000000000000000179366203433576585
+07823738666110926480387352856019',
143 => '0.000000000000000000000000000000000000000000089683101716788292
+539118693330554632401936764280097',
144 => '0.000000000000000000000000000000000000000000044841550858394146
+269559346665277316200968382140049',
145 => '0.000000000000000000000000000000000000000000022420775429197073
+134779673332638658100484191070024',
146 => '0.000000000000000000000000000000000000000000011210387714598536
+567389836666319329050242095535012',
147 => '0.000000000000000000000000000000000000000000005605193857299268
+2836949183331596645251210477675061',
148 => '0.000000000000000000000000000000000000000000002802596928649634
+141847459166579832262560523883753',
149 => '0.000000000000000000000000000000000000000000001401298464324817
+0709237295832899161312802619418765',
150 => '0.000000000000000000000000000000000000000000000700649232162408
+53546186479164495806564013097093826',
151 => '0.000000000000000000000000000000000000000000000350324616081204
+26773093239582247903282006548546913',
152 => '0.000000000000000000000000000000000000000000000175162308040602
+13386546619791123951641003274273456',
153 => '0.000000000000000000000000000000000000000000000087581154020301
+066932733098955619758205016371367282',
154 => '0.000000000000000000000000000000000000000000000043790577010150
+533466366549477809879102508185683641',
155 => '0.000000000000000000000000000000000000000000000021895288505075
+266733183274738904939551254092841821',
156 => '0.000000000000000000000000000000000000000000000010947644252537
+63336659163736945246977562704642091',
157 => '0.000000000000000000000000000000000000000000000005473822126268
+8166832958186847262348878135232104551',
158 => '0.000000000000000000000000000000000000000000000002736911063134
+4083416479093423631174439067616052276',
159 => '0.000000000000000000000000000000000000000000000001368455531567
+2041708239546711815587219533808026138',
);

my $pi = '3.1415926535897932384626433832795';
my ($msd, $lsd) = i2dd($pi, \%bits_table, \%vals_table);
print "$msd $lsd\n";
printf "%a %a\n", $msd, $lsd ;


sub i2dd {
  my $str = $_[0];
  my $sign = $str =~ s/^\-// ? -1 : 1;
  my $val = Math::BigFloat->new($str);
  my $msd = 0 + $val->bstr;
  my ($bin, $exp) = d2bin($msd, $_[1]);
  my $to_subtract = bin2val($bin, $_[2]) * (2 ** $exp);
  $val -= $to_subtract;
  my $lsd = 0 + $val->bstr;
  return ($msd * $sign, $lsd * $sign);
}


sub d2bin {
  my ($mant, $exp) = split /p/, sprintf("%a", $_[0]);
  my %bits = %{$_[1]};
  $mant =~ s/-?0x//i;
  my $bin = $mant =~ /^1/ ? 1 : 0;
  $mant =~ s/.+\.//;
  for(1 .. length($mant)) {
    $bin .= $bits{substr($mant, $_ - 1, 1)};
  }
  return ($bin, $exp);
}

sub bin2val {
  my $bin = $_[0];
  my %vals = %{$_[1]};
  my $val = Math::BigFloat->new(0);

  for(1 .. length($bin)) {
    $val += Math::BigFloat->new($vals{$_ - 1}) if substr($bin, $_ - 1,
+ 1);  
  }
  return $val;
}

__END__

Outputs:
3.14159265358979 1.22464679914735e-016
0x1.921fb54442d18p+1 0x1.1a62633145c07p-53

[download]
The values in %vals_tab have been calculated to 160 bits of precision. 160 is an arbitrarily chosen value, == 1 + (3 * 53).
I make no claims about this approach. (I'll scrutinise it and test it over the next week or so.)

Cheers,
Rob

In reply to Re^13: Math::BigFloat to native double? by syphilis
in thread Math::BigFloat to native double? by BrowserUk

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