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## This file generated by InlineX::C2XS (version 0.22) using Inline::C (version 0.5002)
package Math::Decimal64;
use 5.006;
use warnings;
use strict;
require Exporter;
*import = \&Exporter::import;
require DynaLoader;
our $VERSION = '0.08';
#$VERSION = eval $VERSION;
use subs qw(DEC64_MAX DEC64_MIN);
DynaLoader::bootstrap Math::Decimal64 $Math::Decimal64::VERSION;
@Math::Decimal64::EXPORT = ();
@Math::Decimal64::EXPORT_OK = qw(
    MEtoD64 UVtoD64 IVtoD64 NVtoD64 PVtoD64 STRtoD64 D64toME D64toNV
    FR64toME pFR
    InfD64 NaND64 UnityD64 ZeroD64 is_InfD64 is_NaND64 is_ZeroD64
    D64toLD LDtoD64 DEC64_MAX DEC64_MIN
    assignME assignInf assignNaN assignPV Exp10 have_strtod64
    decode_d64 decode_bid decode_dpd d64_bytes hex2bin d64_fmt
    get_sign get_exp PVtoME MEtoPV assignDPD DPDtoD64
    );
%Math::Decimal64::EXPORT_TAGS = (all => [qw(
    MEtoD64 UVtoD64 IVtoD64 NVtoD64 PVtoD64 STRtoD64 D64toME D64toNV
    FR64toME pFR
    InfD64 NaND64 UnityD64 ZeroD64 is_InfD64 is_NaND64 is_ZeroD64
    D64toLD LDtoD64 DEC64_MAX DEC64_MIN
    assignME assignInf assignNaN assignPV Exp10 have_strtod64
    decode_d64 decode_bid decode_dpd d64_bytes hex2bin d64_fmt
    get_sign get_exp PVtoME MEtoPV assignDPD DPDtoD64
    )]);
use overload
  '+'     => \&_overload_add,
  '*'     => \&_overload_mul,
  '-'     => \&_overload_sub,
  '/'     => \&_overload_div,
  '+='    => \&_overload_add_eq,
  '*='    => \&_overload_mul_eq,
  '-='    => \&_overload_sub_eq,
  '/='    => \&_overload_div_eq,
  '""'    => \&_overload_string,
  '=='    => \&_overload_equiv,
  '!='    => \&_overload_not_equiv,
  '<'     => \&_overload_lt,
  '>'     => \&_overload_gt,
  '<='    => \&_overload_lte,
  '>='    => \&_overload_gte,
  '<=>'   => \&_overload_spaceship,
  '='     => \&_overload_copy,
  '!'     => \&_overload_not,
  'bool'  => \&_overload_true,
  'abs'   => \&_overload_abs,
  '++'    => \&_overload_inc,
  '--'    => \&_overload_dec,
  'int'   => \&_overload_int,
;
%Math::Decimal64::dpd_encode = d64_fmt() eq 'DPD' ? (
     '0000000000' => '000', '0000000001' => '001', '0000000010' => '002', '0000000011' => '003',
     '0000000100' => '004', '0000000101' => '005', '0000000110' => '006', '0000000111' => '007',
     '0000001000' => '008', '0000001001' => '009', '0000010000' => '010', '0000010001' => '011',
     '0000010010' => '012', '0000010011' => '013', '0000010100' => '014', '0000010101' => '015',
     '0000010110' => '016', '0000010111' => '017', '0000011000' => '018', '0000011001' => '019',
     '0000100000' => '020', '0000100001' => '021', '0000100010' => '022', '0000100011' => '023',
     '0000100100' => '024', '0000100101' => '025', '0000100110' => '026', '0000100111' => '027',
     '0000101000' => '028', '0000101001' => '029', '0000110000' => '030', '0000110001' => '031',
     '0000110010' => '032', '0000110011' => '033', '0000110100' => '034', '0000110101' => '035',
     '0000110110' => '036', '0000110111' => '037', '0000111000' => '038', '0000111001' => '039',
     '0001000000' => '040', '0001000001' => '041', '0001000010' => '042', '0001000011' => '043',
     '0001000100' => '044', '0001000101' => '045', '0001000110' => '046', '0001000111' => '047',
     '0001001000' => '048', '0001001001' => '049', '0001010000' => '050', '0001010001' => '051',
     '0001010010' => '052', '0001010011' => '053', '0001010100' => '054', '0001010101' => '055',
     '0001010110' => '056', '0001010111' => '057', '0001011000' => '058', '0001011001' => '059',
     '0001100000' => '060', '0001100001' => '061', '0001100010' => '062', '0001100011' => '063',
     '0001100100' => '064', '0001100101' => '065', '0001100110' => '066', '0001100111' => '067',
     '0001101000' => '068', '0001101001' => '069', '0001110000' => '070', '0001110001' => '071',
     '0001110010' => '072', '0001110011' => '073', '0001110100' => '074', '0001110101' => '075',
     '0001110110' => '076', '0001110111' => '077', '0001111000' => '078', '0001111001' => '079',
     '0000001010' => '080', '0000001011' => '081', '0000101010' => '082', '0000101011' => '083',
     '0001001010' => '084', '0001001011' => '085', '0001101010' => '086', '0001101011' => '087',
     '0001001110' => '088', '0001001111' => '089', '0000011010' => '090', '0000011011' => '091',
     '0000111010' => '092', '0000111011' => '093', '0001011010' => '094', '0001011011' => '095',
     '0001111010' => '096', '0001111011' => '097', '0001011110' => '098', '0001011111' => '099',
     '0010000000' => '100', '0010000001' => '101', '0010000010' => '102', '0010000011' => '103',
     '0010000100' => '104', '0010000101' => '105', '0010000110' => '106', '0010000111' => '107',
     '0010001000' => '108', '0010001001' => '109', '0010010000' => '110', '0010010001' => '111',
     '0010010010' => '112', '0010010011' => '113', '0010010100' => '114', '0010010101' => '115',
     '0010010110' => '116', '0010010111' => '117', '0010011000' => '118', '0010011001' => '119',
     '0010100000' => '120', '0010100001' => '121', '0010100010' => '122', '0010100011' => '123',
     '0010100100' => '124', '0010100101' => '125', '0010100110' => '126', '0010100111' => '127',
     '0010101000' => '128', '0010101001' => '129', '0010110000' => '130', '0010110001' => '131',
     '0010110010' => '132', '0010110011' => '133', '0010110100' => '134', '0010110101' => '135',
     '0010110110' => '136', '0010110111' => '137', '0010111000' => '138', '0010111001' => '139',
     '0011000000' => '140', '0011000001' => '141', '0011000010' => '142', '0011000011' => '143',
     '0011000100' => '144', '0011000101' => '145', '0011000110' => '146', '0011000111' => '147',
     '0011001000' => '148', '0011001001' => '149', '0011010000' => '150', '0011010001' => '151',
     '0011010010' => '152', '0011010011' => '153', '0011010100' => '154', '0011010101' => '155',
     '0011010110' => '156', '0011010111' => '157', '0011011000' => '158', '0011011001' => '159',
     '0011100000' => '160', '0011100001' => '161', '0011100010' => '162', '0011100011' => '163',
     '0011100100' => '164', '0011100101' => '165', '0011100110' => '166', '0011100111' => '167',
     '0011101000' => '168', '0011101001' => '169', '0011110000' => '170', '0011110001' => '171',
     '0011110010' => '172', '0011110011' => '173', '0011110100' => '174', '0011110101' => '175',
     '0011110110' => '176', '0011110111' => '177', '0011111000' => '178', '0011111001' => '179',
     '0010001010' => '180', '0010001011' => '181', '0010101010' => '182', '0010101011' => '183',
     '0011001010' => '184', '0011001011' => '185', '0011101010' => '186', '0011101011' => '187',
     '0011001110' => '188', '0011001111' => '189', '0010011010' => '190', '0010011011' => '191',
     '0010111010' => '192', '0010111011' => '193', '0011011010' => '194', '0011011011' => '195',
     '0011111010' => '196', '0011111011' => '197', '0011011110' => '198', '0011011111' => '199',
     '0100000000' => '200', '0100000001' => '201', '0100000010' => '202', '0100000011' => '203',
     '0100000100' => '204', '0100000101' => '205', '0100000110' => '206', '0100000111' => '207',
     '0100001000' => '208', '0100001001' => '209', '0100010000' => '210', '0100010001' => '211',
     '0100010010' => '212', '0100010011' => '213', '0100010100' => '214', '0100010101' => '215',
     '0100010110' => '216', '0100010111' => '217', '0100011000' => '218', '0100011001' => '219',
     '0100100000' => '220', '0100100001' => '221', '0100100010' => '222', '0100100011' => '223',
     '0100100100' => '224', '0100100101' => '225', '0100100110' => '226', '0100100111' => '227',
     '0100101000' => '228', '0100101001' => '229', '0100110000' => '230', '0100110001' => '231',
     '0100110010' => '232', '0100110011' => '233', '0100110100' => '234', '0100110101' => '235',
     '0100110110' => '236', '0100110111' => '237', '0100111000' => '238', '0100111001' => '239',
     '0101000000' => '240', '0101000001' => '241', '0101000010' => '242', '0101000011' => '243',
     '0101000100' => '244', '0101000101' => '245', '0101000110' => '246', '0101000111' => '247',
     '0101001000' => '248', '0101001001' => '249', '0101010000' => '250', '0101010001' => '251',
     '0101010010' => '252', '0101010011' => '253', '0101010100' => '254', '0101010101' => '255',
     '0101010110' => '256', '0101010111' => '257', '0101011000' => '258', '0101011001' => '259',
     '0101100000' => '260', '0101100001' => '261', '0101100010' => '262', '0101100011' => '263',
     '0101100100' => '264', '0101100101' => '265', '0101100110' => '266', '0101100111' => '267',
     '0101101000' => '268', '0101101001' => '269', '0101110000' => '270', '0101110001' => '271',
     '0101110010' => '272', '0101110011' => '273', '0101110100' => '274', '0101110101' => '275',
     '0101110110' => '276', '0101110111' => '277', '0101111000' => '278', '0101111001' => '279',
     '0100001010' => '280', '0100001011' => '281', '0100101010' => '282', '0100101011' => '283',
     '0101001010' => '284', '0101001011' => '285', '0101101010' => '286', '0101101011' => '287',
     '0101001110' => '288', '0101001111' => '289', '0100011010' => '290', '0100011011' => '291',
     '0100111010' => '292', '0100111011' => '293', '0101011010' => '294', '0101011011' => '295',
     '0101111010' => '296', '0101111011' => '297', '0101011110' => '298', '0101011111' => '299',
     '0110000000' => '300', '0110000001' => '301', '0110000010' => '302', '0110000011' => '303',
     '0110000100' => '304', '0110000101' => '305', '0110000110' => '306', '0110000111' => '307',
     '0110001000' => '308', '0110001001' => '309', '0110010000' => '310', '0110010001' => '311',
     '0110010010' => '312', '0110010011' => '313', '0110010100' => '314', '0110010101' => '315',
     '0110010110' => '316', '0110010111' => '317', '0110011000' => '318', '0110011001' => '319',
     '0110100000' => '320', '0110100001' => '321', '0110100010' => '322', '0110100011' => '323',
     '0110100100' => '324', '0110100101' => '325', '0110100110' => '326', '0110100111' => '327',
     '0110101000' => '328', '0110101001' => '329', '0110110000' => '330', '0110110001' => '331',
     '0110110010' => '332', '0110110011' => '333', '0110110100' => '334', '0110110101' => '335',
     '0110110110' => '336', '0110110111' => '337', '0110111000' => '338', '0110111001' => '339',
     '0111000000' => '340', '0111000001' => '341', '0111000010' => '342', '0111000011' => '343',
     '0111000100' => '344', '0111000101' => '345', '0111000110' => '346', '0111000111' => '347',
     '0111001000' => '348', '0111001001' => '349', '0111010000' => '350', '0111010001' => '351',
     '0111010010' => '352', '0111010011' => '353', '0111010100' => '354', '0111010101' => '355',
     '0111010110' => '356', '0111010111' => '357', '0111011000' => '358', '0111011001' => '359',
     '0111100000' => '360', '0111100001' => '361', '0111100010' => '362', '0111100011' => '363',
     '0111100100' => '364', '0111100101' => '365', '0111100110' => '366', '0111100111' => '367',
     '0111101000' => '368', '0111101001' => '369', '0111110000' => '370', '0111110001' => '371',
     '0111110010' => '372', '0111110011' => '373', '0111110100' => '374', '0111110101' => '375',
     '0111110110' => '376', '0111110111' => '377', '0111111000' => '378', '0111111001' => '379',
     '0110001010' => '380', '0110001011' => '381', '0110101010' => '382', '0110101011' => '383',
     '0111001010' => '384', '0111001011' => '385', '0111101010' => '386', '0111101011' => '387',
     '0111001110' => '388', '0111001111' => '389', '0110011010' => '390', '0110011011' => '391',
     '0110111010' => '392', '0110111011' => '393', '0111011010' => '394', '0111011011' => '395',
     '0111111010' => '396', '0111111011' => '397', '0111011110' => '398', '0111011111' => '399',
     '1000000000' => '400', '1000000001' => '401', '1000000010' => '402', '1000000011' => '403',
     '1000000100' => '404', '1000000101' => '405', '1000000110' => '406', '1000000111' => '407',
     '1000001000' => '408', '1000001001' => '409', '1000010000' => '410', '1000010001' => '411',
     '1000010010' => '412', '1000010011' => '413', '1000010100' => '414', '1000010101' => '415',
     '1000010110' => '416', '1000010111' => '417', '1000011000' => '418', '1000011001' => '419',
     '1000100000' => '420', '1000100001' => '421', '1000100010' => '422', '1000100011' => '423',
     '1000100100' => '424', '1000100101' => '425', '1000100110' => '426', '1000100111' => '427',
     '1000101000' => '428', '1000101001' => '429', '1000110000' => '430', '1000110001' => '431',
     '1000110010' => '432', '1000110011' => '433', '1000110100' => '434', '1000110101' => '435',
     '1000110110' => '436', '1000110111' => '437', '1000111000' => '438', '1000111001' => '439',
     '1001000000' => '440', '1001000001' => '441', '1001000010' => '442', '1001000011' => '443',
     '1001000100' => '444', '1001000101' => '445', '1001000110' => '446', '1001000111' => '447',
     '1001001000' => '448', '1001001001' => '449', '1001010000' => '450', '1001010001' => '451',
     '1001010010' => '452', '1001010011' => '453', '1001010100' => '454', '1001010101' => '455',
     '1001010110' => '456', '1001010111' => '457', '1001011000' => '458', '1001011001' => '459',
     '1001100000' => '460', '1001100001' => '461', '1001100010' => '462', '1001100011' => '463',
     '1001100100' => '464', '1001100101' => '465', '1001100110' => '466', '1001100111' => '467',
     '1001101000' => '468', '1001101001' => '469', '1001110000' => '470', '1001110001' => '471',
     '1001110010' => '472', '1001110011' => '473', '1001110100' => '474', '1001110101' => '475',
     '1001110110' => '476', '1001110111' => '477', '1001111000' => '478', '1001111001' => '479',
     '1000001010' => '480', '1000001011' => '481', '1000101010' => '482', '1000101011' => '483',
     '1001001010' => '484', '1001001011' => '485', '1001101010' => '486', '1001101011' => '487',
     '1001001110' => '488', '1001001111' => '489', '1000011010' => '490', '1000011011' => '491',
     '1000111010' => '492', '1000111011' => '493', '1001011010' => '494', '1001011011' => '495',
     '1001111010' => '496', '1001111011' => '497', '1001011110' => '498', '1001011111' => '499',
     '1010000000' => '500', '1010000001' => '501', '1010000010' => '502', '1010000011' => '503',
     '1010000100' => '504', '1010000101' => '505', '1010000110' => '506', '1010000111' => '507',
     '1010001000' => '508', '1010001001' => '509', '1010010000' => '510', '1010010001' => '511',
     '1010010010' => '512', '1010010011' => '513', '1010010100' => '514', '1010010101' => '515',
     '1010010110' => '516', '1010010111' => '517', '1010011000' => '518', '1010011001' => '519',
     '1010100000' => '520', '1010100001' => '521', '1010100010' => '522', '1010100011' => '523',
     '1010100100' => '524', '1010100101' => '525', '1010100110' => '526', '1010100111' => '527',
     '1010101000' => '528', '1010101001' => '529', '1010110000' => '530', '1010110001' => '531',
     '1010110010' => '532', '1010110011' => '533', '1010110100' => '534', '1010110101' => '535',
     '1010110110' => '536', '1010110111' => '537', '1010111000' => '538', '1010111001' => '539',
     '1011000000' => '540', '1011000001' => '541', '1011000010' => '542', '1011000011' => '543',
     '1011000100' => '544', '1011000101' => '545', '1011000110' => '546', '1011000111' => '547',
     '1011001000' => '548', '1011001001' => '549', '1011010000' => '550', '1011010001' => '551',
     '1011010010' => '552', '1011010011' => '553', '1011010100' => '554', '1011010101' => '555',
     '1011010110' => '556', '1011010111' => '557', '1011011000' => '558', '1011011001' => '559',
     '1011100000' => '560', '1011100001' => '561', '1011100010' => '562', '1011100011' => '563',
     '1011100100' => '564', '1011100101' => '565', '1011100110' => '566', '1011100111' => '567',
     '1011101000' => '568', '1011101001' => '569', '1011110000' => '570', '1011110001' => '571',
     '1011110010' => '572', '1011110011' => '573', '1011110100' => '574', '1011110101' => '575',
     '1011110110' => '576', '1011110111' => '577', '1011111000' => '578', '1011111001' => '579',
     '1010001010' => '580', '1010001011' => '581', '1010101010' => '582', '1010101011' => '583',
     '1011001010' => '584', '1011001011' => '585', '1011101010' => '586', '1011101011' => '587',
     '1011001110' => '588', '1011001111' => '589', '1010011010' => '590', '1010011011' => '591',
     '1010111010' => '592', '1010111011' => '593', '1011011010' => '594', '1011011011' => '595',
     '1011111010' => '596', '1011111011' => '597', '1011011110' => '598', '1011011111' => '599',
     '1100000000' => '600', '1100000001' => '601', '1100000010' => '602', '1100000011' => '603',
     '1100000100' => '604', '1100000101' => '605', '1100000110' => '606', '1100000111' => '607',
     '1100001000' => '608', '1100001001' => '609', '1100010000' => '610', '1100010001' => '611',
     '1100010010' => '612', '1100010011' => '613', '1100010100' => '614', '1100010101' => '615',
     '1100010110' => '616', '1100010111' => '617', '1100011000' => '618', '1100011001' => '619',
     '1100100000' => '620', '1100100001' => '621', '1100100010' => '622', '1100100011' => '623',
     '1100100100' => '624', '1100100101' => '625', '1100100110' => '626', '1100100111' => '627',
     '1100101000' => '628', '1100101001' => '629', '1100110000' => '630', '1100110001' => '631',
     '1100110010' => '632', '1100110011' => '633', '1100110100' => '634', '1100110101' => '635',
     '1100110110' => '636', '1100110111' => '637', '1100111000' => '638', '1100111001' => '639',
     '1101000000' => '640', '1101000001' => '641', '1101000010' => '642', '1101000011' => '643',
     '1101000100' => '644', '1101000101' => '645', '1101000110' => '646', '1101000111' => '647',
     '1101001000' => '648', '1101001001' => '649', '1101010000' => '650', '1101010001' => '651',
     '1101010010' => '652', '1101010011' => '653', '1101010100' => '654', '1101010101' => '655',
     '1101010110' => '656', '1101010111' => '657', '1101011000' => '658', '1101011001' => '659',
     '1101100000' => '660', '1101100001' => '661', '1101100010' => '662', '1101100011' => '663',
     '1101100100' => '664', '1101100101' => '665', '1101100110' => '666', '1101100111' => '667',
     '1101101000' => '668', '1101101001' => '669', '1101110000' => '670', '1101110001' => '671',
     '1101110010' => '672', '1101110011' => '673', '1101110100' => '674', '1101110101' => '675',
     '1101110110' => '676', '1101110111' => '677', '1101111000' => '678', '1101111001' => '679',
     '1100001010' => '680', '1100001011' => '681', '1100101010' => '682', '1100101011' => '683',
     '1101001010' => '684', '1101001011' => '685', '1101101010' => '686', '1101101011' => '687',
     '1101001110' => '688', '1101001111' => '689', '1100011010' => '690', '1100011011' => '691',
     '1100111010' => '692', '1100111011' => '693', '1101011010' => '694', '1101011011' => '695',
     '1101111010' => '696', '1101111011' => '697', '1101011110' => '698', '1101011111' => '699',
     '1110000000' => '700', '1110000001' => '701', '1110000010' => '702', '1110000011' => '703',
     '1110000100' => '704', '1110000101' => '705', '1110000110' => '706', '1110000111' => '707',
     '1110001000' => '708', '1110001001' => '709', '1110010000' => '710', '1110010001' => '711',
     '1110010010' => '712', '1110010011' => '713', '1110010100' => '714', '1110010101' => '715',
     '1110010110' => '716', '1110010111' => '717', '1110011000' => '718', '1110011001' => '719',
     '1110100000' => '720', '1110100001' => '721', '1110100010' => '722', '1110100011' => '723',
     '1110100100' => '724', '1110100101' => '725', '1110100110' => '726', '1110100111' => '727',
     '1110101000' => '728', '1110101001' => '729', '1110110000' => '730', '1110110001' => '731',
     '1110110010' => '732', '1110110011' => '733', '1110110100' => '734', '1110110101' => '735',
     '1110110110' => '736', '1110110111' => '737', '1110111000' => '738', '1110111001' => '739',
     '1111000000' => '740', '1111000001' => '741', '1111000010' => '742', '1111000011' => '743',
     '1111000100' => '744', '1111000101' => '745', '1111000110' => '746', '1111000111' => '747',
     '1111001000' => '748', '1111001001' => '749', '1111010000' => '750', '1111010001' => '751',
     '1111010010' => '752', '1111010011' => '753', '1111010100' => '754', '1111010101' => '755',
     '1111010110' => '756', '1111010111' => '757', '1111011000' => '758', '1111011001' => '759',
     '1111100000' => '760', '1111100001' => '761', '1111100010' => '762', '1111100011' => '763',
     '1111100100' => '764', '1111100101' => '765', '1111100110' => '766', '1111100111' => '767',
     '1111101000' => '768', '1111101001' => '769', '1111110000' => '770', '1111110001' => '771',
     '1111110010' => '772', '1111110011' => '773', '1111110100' => '774', '1111110101' => '775',
     '1111110110' => '776', '1111110111' => '777', '1111111000' => '778', '1111111001' => '779',
     '1110001010' => '780', '1110001011' => '781', '1110101010' => '782', '1110101011' => '783',
     '1111001010' => '784', '1111001011' => '785', '1111101010' => '786', '1111101011' => '787',
     '1111001110' => '788', '1111001111' => '789', '1110011010' => '790', '1110011011' => '791',
     '1110111010' => '792', '1110111011' => '793', '1111011010' => '794', '1111011011' => '795',
     '1111111010' => '796', '1111111011' => '797', '1111011110' => '798', '1111011111' => '799',
     '0000001100' => '800', '0000001101' => '801', '0100001100' => '802', '0100001101' => '803',
     '1000001100' => '804', '1000001101' => '805', '1100001100' => '806', '1100001101' => '807',
     '0000101110' => '808', '0000101111' => '809', '0000011100' => '810', '0000011101' => '811',
     '0100011100' => '812', '0100011101' => '813', '1000011100' => '814', '1000011101' => '815',
     '1100011100' => '816', '1100011101' => '817', '0000111110' => '818', '0000111111' => '819',
     '0000101100' => '820', '0000101101' => '821', '0100101100' => '822', '0100101101' => '823',
     '1000101100' => '824', '1000101101' => '825', '1100101100' => '826', '1100101101' => '827',
     '0100101110' => '828', '0100101111' => '829', '0000111100' => '830', '0000111101' => '831',
     '0100111100' => '832', '0100111101' => '833', '1000111100' => '834', '1000111101' => '835',
     '1100111100' => '836', '1100111101' => '837', '0100111110' => '838', '0100111111' => '839',
     '0001001100' => '840', '0001001101' => '841', '0101001100' => '842', '0101001101' => '843',
     '1001001100' => '844', '1001001101' => '845', '1101001100' => '846', '1101001101' => '847',
     '1000101110' => '848', '1000101111' => '849', '0001011100' => '850', '0001011101' => '851',
     '0101011100' => '852', '0101011101' => '853', '1001011100' => '854', '1001011101' => '855',
     '1101011100' => '856', '1101011101' => '857', '1000111110' => '858', '1000111111' => '859',
     '0001101100' => '860', '0001101101' => '861', '0101101100' => '862', '0101101101' => '863',
     '1001101100' => '864', '1001101101' => '865', '1101101100' => '866', '1101101101' => '867',
     '1100101110' => '868', '1100101111' => '869', '0001111100' => '870', '0001111101' => '871',
     '0101111100' => '872', '0101111101' => '873', '1001111100' => '874', '1001111101' => '875',
     '1101111100' => '876', '1101111101' => '877', '1100111110' => '878', '1100111111' => '879',
     '0000001110' => '880', '0000001111' => '881', '0100001110' => '882', '0100001111' => '883',
     '1000001110' => '884', '1000001111' => '885', '1100001110' => '886', '1100001111' => '887',
     '0001101110' => '888', '0001101111' => '889', '0000011110' => '890', '0000011111' => '891',
     '0100011110' => '892', '0100011111' => '893', '1000011110' => '894', '1000011111' => '895',
     '1100011110' => '896', '1100011111' => '897', '0001111110' => '898', '0001111111' => '899',
     '0010001100' => '900', '0010001101' => '901', '0110001100' => '902', '0110001101' => '903',
     '1010001100' => '904', '1010001101' => '905', '1110001100' => '906', '1110001101' => '907',
     '0010101110' => '908', '0010101111' => '909', '0010011100' => '910', '0010011101' => '911',
     '0110011100' => '912', '0110011101' => '913', '1010011100' => '914', '1010011101' => '915',
     '1110011100' => '916', '1110011101' => '917', '0010111110' => '918', '0010111111' => '919',
     '0010101100' => '920', '0010101101' => '921', '0110101100' => '922', '0110101101' => '923',
     '1010101100' => '924', '1010101101' => '925', '1110101100' => '926', '1110101101' => '927',
     '0110101110' => '928', '0110101111' => '929', '0010111100' => '930', '0010111101' => '931',
     '0110111100' => '932', '0110111101' => '933', '1010111100' => '934', '1010111101' => '935',
     '1110111100' => '936', '1110111101' => '937', '0110111110' => '938', '0110111111' => '939',
     '0011001100' => '940', '0011001101' => '941', '0111001100' => '942', '0111001101' => '943',
     '1011001100' => '944', '1011001101' => '945', '1111001100' => '946', '1111001101' => '947',
     '1010101110' => '948', '1010101111' => '949', '0011011100' => '950', '0011011101' => '951',
     '0111011100' => '952', '0111011101' => '953', '1011011100' => '954', '1011011101' => '955',
     '1111011100' => '956', '1111011101' => '957', '1010111110' => '958', '1010111111' => '959',
     '0011101100' => '960', '0011101101' => '961', '0111101100' => '962', '0111101101' => '963',
     '1011101100' => '964', '1011101101' => '965', '1111101100' => '966', '1111101101' => '967',
     '1110101110' => '968', '1110101111' => '969', '0011111100' => '970', '0011111101' => '971',
     '0111111100' => '972', '0111111101' => '973', '1011111100' => '974', '1011111101' => '975',
     '1111111100' => '976', '1111111101' => '977', '1110111110' => '978', '1110111111' => '979',
     '0010001110' => '980', '0010001111' => '981', '0110001110' => '982', '0110001111' => '983',
     '1010001110' => '984', '1010001111' => '985', '1110001110' => '986', '1110001111' => '987',
     '0011101110' => '988', '0011101111' => '989', '0010011110' => '990', '0010011111' => '991',
     '0110011110' => '992', '0110011111' => '993', '1010011110' => '994', '1010011111' => '995',
     '1110011110' => '996', '1110011111' => '997', '0011111110' => '998', '0011111111' => '999',
) : ();
#######################################################################
#######################################################################
# %Math::Decimal64::dpd_decode is simply %Math::Decimal64::dpd_encode
# with the keys and values interchanged.
for my $key(keys(%Math::Decimal64::dpd_encode)) {
  $Math::Decimal64::dpd_decode{$Math::Decimal64::dpd_encode{$key}} = $key;
}
#######################################################################
#######################################################################
%Math::Decimal64::bid_decode = d64_fmt() eq 'BID' ? (
 0 => MEtoD64('1' . ('0' x 15), 0), 1 => MEtoD64('1' . ('0' x 14), 0),
 2 => MEtoD64('1' . ('0' x 13), 0), 3 => MEtoD64('1' . ('0' x 12), 0),
 4 => MEtoD64('1' . ('0' x 11), 0), 5 => MEtoD64('1' . ('0' x 10), 0),
 6 => MEtoD64('1' . ('0' x 9), 0), 7 => MEtoD64('1' . ('0' x 8), 0),
 8 => MEtoD64('1' . ('0' x 7), 0), 9 => MEtoD64('1' . ('0' x 6), 0),
 10 => MEtoD64('1' . ('0' x 5), 0), 11 => MEtoD64('1' . ('0' x 4), 0),
 12 => MEtoD64('1' . ('0' x 3), 0), 13 => MEtoD64('1' . ('0' x 2), 0),
 14 => MEtoD64('1' . ('0' x 1), 0), 15 => MEtoD64('1', 0)
) : ();
#######################################################################
#######################################################################
$Math::Decimal64::nan_str  = unpack("a*", pack( "B*", '011111' . ('0' x 58)));
$Math::Decimal64::ninf_str = unpack("a*", pack( "B*", '11111'  . ('0' x 59)));
$Math::Decimal64::pinf_str = unpack("a*", pack( "B*", '01111'  . ('0' x 59)));
$Math::Decimal64::fmt = d64_fmt();
#######################################################################
#######################################################################
sub _decode_mant {
  my $val = shift;
  my $ret = '';
  for my $i(0 .. 15) {
    my $count = 0;
    if($val > 0) {
      while($val >= $Math::Decimal64::bid_decode{$i}) {
        $val -= $Math::Decimal64::bid_decode{$i};
        $count++;
      }
    }
    $ret .= $count;
  }
  return $ret;
}
#######################################################################
#######################################################################
sub dl_load_flags {0} # Prevent DynaLoader from complaining and croaking
#######################################################################
#######################################################################
sub _overload_string {
    my @ret = D64toME($_[0]);
    if(is_InfD64($_[0]) || !$_[0]) {return $ret[0]}
    return $ret[0] . 'e' . $ret[1];
}
#######################################################################
#######################################################################
sub pFR {
    my @ret = FR64toME($_[0]);
    if(is_InfD64($_[0]) || !$_[0]) {print $ret[0]}
    else {print $ret[0] . "e" . $ret[1]}
}
#######################################################################
#######################################################################
sub _overload_int {
    if(is_NaND64($_[0]) || is_InfD64($_[0]) || is_ZeroD64($_[0])) {return $_[0]}
    my($man, $exp) = D64toME($_[0]);
    if($exp >= 0) {return $_[0]}
    my $man_length = length($man);
    $man_length-- if $man =~ /^\-/;
    if(-$exp >= $man_length) {              # -1 <= $_[0] <= 1
       my $z = ZeroD64(1);
       if($_[0] < $z) {return ZeroD64(-1)}  # return -0
       return $z;                           # return  0
    }
    substr($man, $exp, -$exp, '');
    return MEtoD64($man, 0);
}
#######################################################################
#######################################################################
sub new {
    # This function caters for 2 possibilities:
    # 1) that 'new' has been called OOP style - in which
    #    case there will be a maximum of 2 args
    # 2) that 'new' has been called as a function - in
    #    which case there will be a maximum of 1 arg.
    # If there are no args, then we just want to return a
    # Math::Decimal64 object that's a NaN.
    if(!@_) {return NaND64()}
    if(@_ > 3) {die "More than 3 arguments supplied to new()"}
    # If 'new' has been called OOP style, the first arg is the string
    # "Math::Decimal64" which we don't need - so let's remove it. However,
    # if the first arg is a Math::Decimal64 object (which is a possibility),
    # then we'll get a fatal error when we check it for equivalence to
    # the string "Math::Decimal64". So we first need to check that it's not
    # an object - which we'll do by using the ref() function:
    if(!ref($_[0]) && $_[0] eq "Math::Decimal64") {
      shift;
      if(!@_) {return NaND64()}
      }
    # @_ can now contain max of 2 vals - the mantissa and exponent.
    # If @_ == 1 then it contains the value.
    if(@_ > 2) {die "Too many arguments supplied to new() - expected no more than 2"}
    if(@_ == 2) {return MEtoD64(shift, shift)}
    my $arg = shift;
    my $type = _itsa($arg);
    if($type == 1) { # UV
      return UVtoD64($arg);
    }
    if($type == 2) { # IV
      return IVtoD64($arg);
    }
    if($type == 3) { # NV
      return NVtoD64($arg);
    }
    if($type == 4) { # PV
      return STRtoD64($arg) if have_strtod64();
      return PVtoD64($arg);
    }
    if($type == 64) { # Math::Decimal64 object
      return D64toD64($arg);
    }
    die "Bad argument given to new";
}
#######################################################################
#######################################################################
sub D64toME {
    return ('-0', '0') if (is_ZeroD64($_[0]) == -1); # Negative Zero.
    my @ret = _D64toME($_[0]);
    if(!defined($ret[1])) {
      @ret = _sci2me($ret[0], $ret[2]);
    }
    return @ret;
}
#######################################################################
#######################################################################
sub FR64toME {
  my $fr = Math::MPFR::Rmpfr_init2(55);
  Math::MPFR::Rmpfr_set_decimal64($fr, $_[0], 0); #MPFR_RNDN
  if(Math::MPFR::Rmpfr_zero_p($fr) ||
     Math::MPFR::Rmpfr_inf_p($fr)  ||
     Math::MPFR::Rmpfr_nan_p($fr)) {
    return D64toME($_[0]);
  }
  my($man, $exp) = Math::MPFR::Rmpfr_deref2($fr, 10, 16, 0); #MPFR_RNDN
  chop $man while(length($man) > 1 && $man =~ /0$/);
  $exp -= length($man);
  $exp++ if $man =~/^\-/;
  return ($man, $exp);
}
#######################################################################
#######################################################################
sub MEtoD64 {
  # Check that 2 args are supplied
  die "MEtoD64 takes 2 args" if @_ != 2;
  my $arg1 = shift;
  my $arg2 = shift;
  die "Invalid 1st arg ($arg1) to MEtoD64" if $arg1 =~ /[^0-9\-]/;
  die "Invalid 2nd arg ($arg2) to MEtoD64" if $arg2 =~ /[^0-9\-]/;
  my $len_1 = length $arg1;
  $len_1-- if $arg1 =~ /^\-/;
  if($len_1 > 16 || $arg2 < -398) {
    die "$arg1 exceeds _Decimal64 precision. It needs to be shortened to no more than 16 decimal digits"
      if $len_1 > 16;
    ($arg1, $arg2) = _round_as_needed($arg1, $arg2);
  }
  return _MEtoD64($arg1, $arg2);
}
#######################################################################
#######################################################################
# Values such as (d, -400), (dd, -401), (ddd, -402), etc evaluate to zero.
# But values such as (dddd, -400), (ddd, -401), (dddddddd, -402), etc may be non-zero.
# In such cases we'll remove the ignored (trailing) digits, rounding the leading
# digits to nearest - tied to even for midway cases.
sub _round_as_needed {
   my($sign, $man, $exp) = ('', shift, shift);
   if($man =~ /^\-/) {
     $man =~ s/^\-//;
     $sign = '-';
   }
   my $length = length $man;
   my $maxlen = -398 - $exp;
   if($length >= $maxlen) {
     my $rounder = substr($man, $length - $maxlen); # The trailing (ignored) digits
     $man = $length > $maxlen ? substr($man, 0, $length - $maxlen)
                               : '0';
     my $roundup = 0;
     $roundup = 1 if substr($rounder, 0, 1) > 5;
     $roundup = 1 if ((substr($rounder, 0, 1) == 5) &&
                      ((substr($rounder, 1) =~ /[1-9]/) || (substr($man, -1, 1) %2 == 1)));
     $man++ if $roundup;
     $exp += $maxlen; # Removal of trailing digits moved the implied
                       # decimal point $maxlen places to the left
   }
   return ($sign . $man, $exp);
}
#######################################################################
#######################################################################
sub assignME {
  # Check that 3 args are supplied
  die "assignME takes 3 args" if @_ != 3;
  my $arg1 = shift;
  my $arg2 = shift;
  my $arg3 = shift;
  die "Invalid 1st arg ($arg1) to assignME" if _itsa($arg1) != 64;
  die "Invalid 2nd arg ($arg2) to assignME" if $arg2 =~ /[^0-9\-]/;
  die "Invalid 3rd arg ($arg3) to assignME" if $arg3 =~ /[^0-9\-]/;
  my $len_2 = length($arg2);
  $len_2-- if $arg2 =~ /^\-/;
  if($len_2 > 16 || $arg3 < -398) {
    die "$arg2 exceeds _Decimal64 precision. It needs to be shortened to no more than 16 decimal digits"
      if $len_2 > 16;
    ($arg2, $arg3) = _round_as_needed($arg2, $arg3);
  }
  return _assignME($arg1, $arg2, $arg3);
}
#######################################################################
#######################################################################
sub _sci2me {
    my @ret = split /e/i, $_[0];
    chop $ret[0] while $ret[0] =~ /0\b/;
    my @adj = split /\./, $ret[0];
    my $adj = defined $adj[1] ? length($adj[1])
                              : 0;
    $ret[0] =~ s/\.//;
    $ret[1] += $_[1] - $adj;
    return @ret;
}
#######################################################################
#######################################################################
sub d64_bytes {
  my @ret = _d64_bytes($_[0]);
  return join '', @ret;
}
#######################################################################
#######################################################################
sub hex2bin {
    my $ret = unpack("B*", (pack "H*", $_[0]));
    my $len = length $ret;
    die "hex2bin() yielded $len bits" if $len != 64;
    return $ret;
}
#######################################################################
#######################################################################
sub d64_fmt {
  my $d64 = MEtoD64('1234567890123456', 0);
  # BID: 31C462D53C8ABAC0
  # DPD: 263934B9C1E28E56
  return 'DPD' if d64_bytes($d64) =~ /E56$/i;
  return 'BID' if d64_bytes($d64) =~ /AC0$/i;
  return 'Unknown';
}
#######################################################################
#######################################################################
sub decode_dpd {
  # Takes the Math::Decimal64 object as its arg.
  # Decodes Densely Packed Decimal formatting of the Decimal64 value.
  my $binstring = hex2bin(d64_bytes($_[0]));
  my @first = decode_dpd_1st($binstring);
  return ($first[0] . $first[1]) if ($first[1] =~ /inf/i || $first[1] =~ /nan/i);
  my $mantissa = $first[1] . decode_dpd_2nd($binstring);
  # Remove leading zeroes from the mantissa
  $mantissa =~ s/^0+//;
  if($mantissa eq '') {$mantissa = '0'}
  else {
    # Remove trailing zeroes
    while($mantissa =~ /0$/) {
      $mantissa =~ s/0$//;
      $first[2]++;
    }
  }
  my $ret = $first[0] . $mantissa . 'e' . $first[2];
}
#######################################################################
#######################################################################
sub decode_dpd_1st{
  # Takes the entire binary string as its arg.
  die "Argument to decode_dpd_1st is wrong size (", length($_[0]), ")"
    if length($_[0]) != 64;
  my $leading_bits = 14;
  my $trailing_bits = 50;
  my $msd;                  # significand's most siginificant digit
  my $exp;                  # exponent
  my $keep = substr($_[0], 0, $leading_bits);
  my $sign = substr($keep, 0, 1) ? '-' : '';
  return ('','nan') if substr($keep, 1, 5) eq '11111';
  if(substr($keep, 1 ,5) eq '11110') {return ($sign, 'inf')}
  my $pre = substr($keep, 1, 2);
  if($pre eq '00' || $pre eq '01' || $pre eq '10') {
    $msd = oct('0b0' . substr($keep, 3, 3));
    $exp = oct('0b' . $pre . substr($keep, 6, 8)) - 398;
    return ($sign, $msd, $exp);
  }
  $pre = substr($keep, 1, 4);
  if($pre eq '1100' || $pre eq '1101' || $pre eq '1110') {
    $exp = oct('0b' . substr($pre, 2, 2) . substr($keep, 6, 8)) - 398;
    $msd = oct('0b' .  '100' . substr($keep, 5, 1));
    return ($sign, $msd, $exp);
  }
  die "decode_dpd_1st function failed to parse its argument ($_[0])";
}
#######################################################################
#######################################################################
sub decode_dpd_2nd {
  # Takes the entire binary string as its arg.
  die "Argument to decode_dpd_2nd is wrong size (", length($_[0]), ")"
    if length($_[0]) != 64; # 64 for Decimal64
  my $leading_bits = 14;    # 18 for Decimal28
  my $trailing_bits = 50;   # 110 for Decimal28
  my $keep = substr($_[0], $leading_bits, $trailing_bits);
  my $ret = '';
  for my $i(0, 10, 20, 30, 40) {
    my $key = substr($keep, $i, 10);
    $ret .= $Math::Decimal64::dpd_encode{$key};
  }
  return $ret;
}
#######################################################################
#######################################################################
sub decode_bid {
  # Takes a Math::Decimal64 object as its arg.
  # Decodes Binary Integer Decimal formatting of the _Decimal64 value.
  my $keep = hex2bin(d64_bytes($_[0]));
  die "Base 2 representation is wrong size (", length($keep), ")"
    if length($keep) != 64; # 64 for Decimal64
  my $leading_bits =  13;
  my $trailing_bits = 51;
  my @mantissa;
  my $exp;                  # exponent
  my $sign = substr($keep, 0, 1) ? '-' : '';
  return 'nan' if substr($keep, 1, 5) eq '11111';
  if(substr($keep, 1 ,5) eq '11110') {return $sign . 'inf'}
  my $pre = substr($keep, 1, 2);
  if($pre eq '00' || $pre eq '01' || $pre eq '10') {
    $exp = oct('0b' . substr($keep, 1, 10)) - 398;
    @mantissa =  reverse(split(//, '0' . substr($keep, 11, 53)));
    my $mantissa = _bid_mant(\@mantissa);
    if($mantissa !~ /[1-9]/) { $mantissa = '0'}
    else {
      while($mantissa =~ /0$/) {
        $mantissa =~ s/0$//;
        $exp++;
      }
    }
    return $sign . $mantissa . 'e' . $exp;
  }
  $pre = substr($keep, 1, 4);
  if($pre eq '1100' || $pre eq '1101' || $pre eq '1110') {
    $exp = oct('0b' . substr($keep, 3, 10)) - 398;
    @mantissa = reverse(split(//,'100' . substr($keep, 13, 51)));
    my $mantissa = _bid_mant(\@mantissa);
    if($mantissa !~ /[1-9]/) { $mantissa = '0'}
    else {
      while($mantissa =~ /0$/) {
        $mantissa =~ s/0$//;
        $exp++;
      }
    }
    return $sign . $mantissa . 'e' . $exp;
  }
  die "decode_bid function failed to parse its argument ($_[0])";
}
#######################################################################
#######################################################################
sub PVtoD64 {
  my($arg1, $arg2) = PVtoME($_[0]);
  if($arg1 =~ /inf|nan/i) {
    $arg1 =~ /nan/i ? return NaND64()
                    : $arg1 =~ /^\-/ ? return InfD64(-1)
                                     : return InfD64(1);
  }
  return MEtoD64($arg1, $arg2);
}
#######################################################################
#######################################################################
sub assignPV {
  my($arg1, $arg2) = PVtoME($_[1]);
  if($arg1 =~ /inf|nan/i) {
    $arg1 =~ /nan/i ? assignNaN($_[0])
                    : $arg1 =~ /^\-/ ? assignInf($_[0], -1)
                                     : assignInf($_[0], 1);
  }
  else {
    assignME($_[0], $arg1, $arg2);
  }
}
#######################################################################
#######################################################################
sub DEC64_MAX {return _DEC64_MAX()}
sub DEC64_MIN {return _DEC64_MIN()}
#######################################################################
#######################################################################
sub get_exp {
  my $keep = hex2bin(d64_bytes($_[0]));
  my $pre = substr($keep, 1, 2);
  if(d64_fmt() eq 'DPD') {
    if($pre eq '00' || $pre eq '01' || $pre eq '10') {
      return oct('0b' . $pre . substr($keep, 6, 8)) - 398;
    }
    else {
      return oct('0b' . substr($pre, 2, 2) . substr($keep, 6, 8)) - 398;
    }
  }
  else {
    if($pre eq '00' || $pre eq '01' || $pre eq '10') {
      return oct('0b' . substr($keep, 1, 10)) - 398;
    }
    else {
      return oct('0b' . substr($keep, 3, 10)) - 398;
    }
  }
}
#######################################################################
#######################################################################
sub get_sign {
  return '-' if hex(substr(d64_bytes($_[0]), 0, 1)) >= 8;
  return '+';
}
#######################################################################
#######################################################################
sub DPDtoD64 {
  # Usable only where DPD format is in use.
  # Converts the 64-bit string returned by _MEtoBINSTR into
  # a Math::Decimal64 object set to the value encoded by the
  # the 64-bit string. This is all done without having to calculate
  # the actual value - and is typically ~25 times quicker than
  # MEtoD64.
  my($man, $exp) = (shift, shift);
  my $arg = _MEtoBINSTR($man, $exp);
  return _DPDtoD64(unpack("a*", pack( "B*", $arg)));
}
#######################################################################
#######################################################################
sub PVtoME {
  my($arg1, $arg2) = split /e/i, $_[0];
  if($arg1 =~ /^(\-|\+)?inf|^(\-|\+)?nan/i) {
    return ($arg1, 0);
  }
  _sanitise_args($arg1, $arg2);
  return ($arg1, $arg2);
}
sub MEtoPV {
  my $arg1 = shift;
  if($arg1 =~ /^(\-|\+)?inf|^(\-|\+)?nan/i) {
    $arg1 =~ s/\+//;
    return $arg1;
  }
  my $arg2 = shift;
  return $arg1 . 'e' . $arg2;
}
#######################################################################
#######################################################################
sub _sanitise_args {
    $_[1] = 0 unless defined $_[1];
    $_[0] =~ s/\.0+$//;
    my @split = split /\./, $_[0];
    $split[1] = '' unless defined $split[1];
    $_[1] -= length($split[1]);
    $_[0] =~ s/\.//;
    $_[0] =~ s/^0+//;
}
#######################################################################
#######################################################################
sub assignDPD {
  _assignDPD($_[0], unpack("a*", pack("B*", _MEtoBINSTR($_[1], $_[2]))));
}
#######################################################################
#######################################################################
sub _MEtoBINSTR {
  # Converts (mantissa, exponent) strings to DPD encoded 64-bit string - without
  # the need to actually calculate the value.
  my $man = shift;
  if($man =~ /^(\-|\+)?inf|^(\-|\+)?nan/i) {
     $man =~ /\-inf/i ? return '11111' . ('0' x 59)
                      : $man =~ /^(\-|\+)?nan/i ? return '011111' . ('0' x 58)
                                                : return '01111'  . ('0' x 59);
  }
  my $exp = shift;
  # Determine the sign, and remove it.
  my $sign = $man =~ /^\-/ ? '1' : '0';
  $man =~ s/[\+\-]//;
  die "_MEtoBINSTR has been passed (probably from DPDtoBINSTR) an illegal mantissa"
    if $man =~ /[^0-9]/;
  # Remove leading zeroes, and return zero (of appropriate sign)
  # if we're left with the empty string.
  $man =~ s/^0+//;
  return $sign . '0100001101101' . ('0' x 50) unless $man;
  # Fill the mantissa with 16 digits - by zero padding the end.
  my $add_zeroes = 16 - length($man);
  $man .= '0' x $add_zeroes;
  $exp -= $add_zeroes;
  if(length($man) > 16 || $exp < -398) {
    die "$man exceeds _Decimal64 precision. It needs to be shortened to no more than 16 decimal digits"
      if length($man) > 16;
    ($man, $exp) = _round_as_needed($man, $exp);
  }
  # Return 0 if $exp is still less that -398.
  return $sign . '0100001101101' . ('0' x 50) if $exp < -398;
  # Return -inf/inf if value is infinite
  if($exp > 369) {
    return $sign . '1111'  . ('0' x 59) if (length($man) + $exp) > 385;
  }
  $man = '0' . $man while length($man) < 16;
  # The last 50 bits encode the last 15 digits.
  my $last_15_dig = substr($man, 1, 15);
  my $last_50_bits;
  for(my $i = 0; $i < 13; $i += 3) {
    $last_50_bits .= $Math::Decimal64::dpd_decode{substr($last_15_dig, $i, 3)}
  }
  my $len = length($last_50_bits);
  die "Wrong bitsize ($len != 50) in _MEtoBINSTR()" if $len != 50;
  my $leading_digit = substr($man, 0, 1); # ie the msd (most siginificant digit).
  my $exp_base_2 = sprintf "%010b", $exp + 398;
  # The encoding of the exponent and msd depends upon the value of the msd.
  # If it's 0..7, it's done one way; if it's 8 or 9 it's done th'other way.
  if($leading_digit < 8) {
    my $leading_digit_bits = sprintf "%03b", $leading_digit;
    substr($exp_base_2, 2, 0, $leading_digit_bits);
  }
  else {
    my $leading_digit_bit = $leading_digit == 8 ? '0' : '1';
    $exp_base_2 = '11' . substr($exp_base_2, 0, 2) . $leading_digit_bit . substr($exp_base_2, 2, 8);
  }
  $len = length($exp_base_2);
  die "Exponent (= $exp) component length is wrong ($len != 13) in _MEtoBINSTR()" if $len != 13;
  return $sign . $exp_base_2 . $last_50_bits;
}
#######################################################################
#######################################################################
*decode_d64 = $Math::Decimal64::fmt eq 'DPD' ? \&decode_dpd : \&decode_bid;
#######################################################################
#######################################################################
1;
__END__
HideShow 422 lines of Pod
=head1 NAME
Math::Decimal64 - perl interface to C's _Decimal64 operations.
=head1 DEPENDENCIES
   In order to compile this module, a C compiler that provides
   the _Decimal64 type is needed.
=head1 DESCRIPTION
   Math::Decimal64 supports up to 16 decimal digits of significand
   (mantissa) and an exponent range of -383 to +384.
   The smallest expressable value is -9.999999999999999e384 (which
   is also equivalent to -9999999999999999e369).
   The largest expressable value is 9.999999999999999e384 (which
   also equivalent to 9999999999999999e369).
   The closest we can get to zero is (plus or minus) 1e-384
   (which is also equivalent to 1000000000000000e-399).
   This module allows decimal floating point arithmetic via
   operator overloading - see "OVERLOADING".
   In the documentation that follows, "$mantissa" is a perl scalar
   holding a string of up to 16 decimal digits:
    $mantissa = '1234';
    $mantissa = '1234567890123456';
=head1 SYNOPSIS
   use Math::Decimal64 qw(:all);
   my $d64_1 = MEtoD64('9927', -2); # the decimal 99.27
   my $d64_2 = MEtoD64('3', 0);     # the decimal 3.0
   $d64_1 /= $d64_2;
   print $d64_1; # prints 3309e-2 (33.09)
=head1 OVERLOADING
   The following operations are overloaded:
    + - * /
    += -= *= /=
    != == <= >= <=> < >
    ++ --
    =
    abs bool int print
    Arguments to the overloaded operations must be Math::Decimal64
    objects or integer (IV/UV) values.
     $d64_2 = $d64_1 + 3.1; # Error. Best to either:
     $d64_2 = $d64_1 + MEtoD64('31',-1); # or (equivalentally):
     $d64_2 = $d64_1 + Math::Decimal64->new('31',-1);
=head1 CREATION & ASSIGNMENT FUNCTIONS
    The following create and assign a new Math::Decimal64 object.
     ###################################
     # Assign from mantissa and exponent
     $d64 = MEtoD64($mantissa, $exponent);
      eg: $d64 = MEtoD64('12345', -3); # 12.345
      It's a little kludgy, but this is the safest and surest way
      of creating the Math::Decimal64 object with the intended
      value.
      Checks are conducted to ensure that the arguments are suitable.
      The mantissa string must represent an integer. (There's an
      implicit '.0' at the end of the string.)
      Only known caveat is that, since this function does a strtold()
      on the mantissa, the 'long double' needs to have at least 55
      bits of precision.
      Doing Math::Decimal64->new($mantissa, $exponent) will also
      create and assign using MEtoD64(), and is equally acceptable.
     ######################################
     $d64 = DPDtoD64($mantissa, $exponent);
      eg: $d64 = DPDtoD64('12345', -3); # 12.345
      This perhaps a quicker way of creating the Math::Decimal128
      object with the intended value - but works only for DPD format
      - ie only if d128_fmt() returns 'DPD'.
      The mantissa string can be 'inf' or 'nan', optionally prefixed
      with '-' or '+'. Otherwise, the mantissa string must
      represent an integer value (with implied '.0' at the end) - ie
      cannot contain a decimal point.
     ######################
     # Assign from a string
     $d64 = PVtoD64($string);
      eg: $d64 = PVtoD64('-9427199254740993');
          $d64 = PVtoD64('-9307199254740993e-15');
          $d64 = Math::Decimal64->new('-9787199254740993');
          $d64 = Math::Decimal64->new('-9307199254740993e-23');
          $d64 = Math::Decimal64->new('-inf');
          $d64 = Math::Decimal64->new('nan');
      Does no checks on its arg. The arg can be in either integer
      format or scientific notation, float format or (+-)inf/nan.
      Doing Math::Decimal64->new($string) will also create and
      assign using PVtoD64().
      This assigns using the C standard library function strtold(),
      and then casting to a _Decimal64.
     #####################################
     # Assign from a UV (unsigned integer)
     $d64 = UVtoD64($uv);
      eg: $d64 = UVtoD64(~0);
      Doing Math::Decimal64->new($uv) will also create and assign
      using UVtoD64().
      Assigns the designated UV value to the Math::Decimal64 object
      (but only to the extent that the _Decimal64 can accommodate
      the value of the UV).
     ####################################
     # Assign from an IV (signed integer)
     $d64 = IVtoD64($iv);
      eg: $d64 = IVtoD64(-15); # -15.0
      Doing Math::Decimal64->new($iv) will also create and assign
      using IVtoD64().
      Assigns the designated IV value to the Math::Decimal64 object
      (but only to the extent that the _Decimal64 can accommodate
      the value of the IV).
     ################################################
     # Assign from an existing Math::Decimal64 object
     $d64 = D64toD64($d64_0);
     Also:
      $d64 = Math::Decimal64->new($d64_0);
      $d64 = $d64_0; # uses overloaded '='
     ###########################
     # Assign from an NV (real))
     $d64 = NVtoD64($nv);
      eg: $d64 = NVtoD64(-3.25);
      Doing Math::Decimal64->new($nv) will also create and assign
      using NVtoD64().
      Might not always assign the value you think it does. (Eg,
      see test 5 in t/overload_cmp.t.)
     ####################
     # Assign using new()
     $d64 = Math::Decimal64->new([$arg1, [$arg2]]);
      This function calls one of the above functions. It
      determines the appropriate function to call by examining
      the argument(s) provided.
      If no argument is provided, a Math::Decimal64 object
      with a value of NaN is returned.
      If 2 arguments are supplied it uses MEtoD64().
      If one argument is provided, that arg's internal flags are
      used to determine the appropriate function to call.
     #######################
     # Assign using STRtoD64
     $d64 = STRtoD64($string);
      If your C compiler provides the strtod64 function, and
      you configured the Makefile.PL to enable access to that
      function then you can use this function.
      Usage is is as for PVtoD64().
     ##############################
=head1 ASSIGN A NEW VALUE TO AN EXISTING OBJECT
     #####################################
     assignME($d64, $mantissa, $exponent);
      Assigns the value represented by ($mantissa, $exponent)
      to the Math::Decimal64 object, $d64.
      Performs same argument checking as MEtoD64.
      eg: assignME($d64, '123459', -6); # 0.123459
     ######################################
     assignDPD($d64, $mantissa, $exponent);
      Assigns the value represented by ($mantissa, $exponent)
      to the Math::Decimal128 object, $d128. This might work
      more efficiently than assignME(), but works only when the
      _Decimal128 type is DPD-formatted. (The d128_fmt function
      will tell you whether the _Decimal128 is DPD-formatted or
      BID-formatted.)
      eg: assignDPD($d64, '123459', -6); # 0.123459
     ########################
     assignPV($d64, $string);
      Assigns the value represented by $string to the
      Math::Decimal64 object, $d64.
      eg: assignPV($d64, '123459e-6'); # 0.123459
     ################
     assignNaN($d64);
      Assigns a NaN to the Math::Decimal64 object, $d64.
     #######################
     assignInf($d64, $sign);
      Assigns an Inf to the Math::Decimal64 object, $d64.
      If $sign is negative, assigns -Inf; otherwise +Inf.
     #######################
=head1 INF, NAN and ZERO OBJECTS
     #####################
     $d64 = InfD64($sign);
      If $sign < 0, creates a new Math::Decimal64 object set to
      negative infinity; else creates a Math::Decimal64 object set
      to positive infinity.
     ################
     $d64 = NaND64();
      Creates a new Math::Decimal64 object set to NaN.
      Same as "$d64 = Math::Decimal64->new();"
     ######################
     $d64 = ZeroD64($sign);
      If $sign < 0, creates a new Math::Decimal64 object set to
      negative zero; else creates a Math::Decimal64 object set to
      zero.
    #######################
=head1 RETRIEVAL FUNCTIONS
    The following functions provide ways of seeing the value of
    Math::Decimal64 objects.
     ###########################
     $string = decode_d64($d64);
      This function calls either decode_dpd() or decode_bid(),
      depending upon the formatting used to encode the
      _Decimal64 value (as determined by the d64_fmt() sub).
      It returns the value as a string of the form (-)ME, where:
        "M" is the mantissa, containing up to 16 base 10 digits;
        "E" is the letter "e" followed by the exponent;
      A minus sign is prefixed to any -ve number (incl -0), but no
      sign at all is prefixed for +ve numbers (incl +0).
      Returns the strings '+inf', '-inf', 'nan' for (respectively)
      +infinity, -infinity, NaN.
      The value will be decoded correctly.
     ##################################
     $string = decode_dpd($d64_binary);
     $string = decode_bid($d64_binary);
      As for decode_d64(), except it takes the 64-bit binary
      representation of the _Decimal64 value as its argument. This
      argument is derived from the Math::Decimal64 object ($d64)
      by doing:
        $binary = hex2bin(d64_bytes($d64));
      DPD and BID formats will return different strings - so you
      need to know which encoding (DPD or BID) was used, and then
      call the appropriate decode_*() function for that encoding.
      The d64_fmt() sub will tell you which encoding is in use.
     #######################################
     ($mantissa, $exponent) = D64toME($d64);
      Returns the value of the Math::Decimal object as a
      mantissa (string of up to 16 decimal digits) and exponent.
      You can then manipulate those values to output the
      value in your preferred format. Afaik, the value will be
      decoded accurately.
     ########################################
     ($mantissa, $exponent) = FR64toME($d64);
      Requires that Math::MPFR version 3.18 or later has been
      loaded. It also requires that Math:MPFR has been built with
      support for the mpfr library's Decimal64 conversion
      functions - in which case Math::MPFR::_WANT_DECIMAL_FLOATS()
      will return true. (Otherwise it returns false.)
      Afaik, the value will be decoded accurately.
     ####################
     $nv = D64toNV($d64);
      This function returns the value of the Math::Decimal64
      object to a perl scalar (NV). Under certain conditions
      it may not translate the value accurately.
     ###########
     print $d64;
      Will print the value in the format (eg) -12345e-2, which
      equates to the decimal -123.45. Uses D64toME().
     #########
     pFR $d64;
      Will print the value in the format (eg) -12345e-2, which
      equates to the decimal -123.45. Uses FR64toME() - which
      should always print the value accurately, but requires
      that Math::MPFR:
       1) has been loaded;
       2) supports the Decimal64 mpfr conversion functions.
     #########
=head1 OTHER FUNCTIONS
     ################################
     ($man, $exp) = PVtoME($string);
      $string is a string representing a floating-point value - eg
      'inf', '+nan', '123.456', '-1234.56e-1', or '12345.6E-2'.
      The function returns an array of (mantissa, exponent), where
      the mantissa is a string of base 10 digits (prefixed with a
      '-' for -ve values) with an implied decimal point at the
      end of the string. For strings such as 'inf' and 'nan', the
      mantissa will be set to $string, and the exponent to 0.
      For the example strings given above, the returned arrays
      would be ('inf', 0), ('+nan', 0), ('123456', -3), ('-123456',
      -3) and ('123456', -3) respectively.
     #######################################
     $string = MEtoPV($mantissa, $exponent);
      If $mantissa =~ /inf|nan/i returns $mantissa.
      Else returns $mantissa . 'e' . $exponent.
     #################
     $fmt = d64_fmt();
      Returns either 'DPD' or 'BID', depending upon whether the
      (internal) _Decimal64 values are encoded using the 'Densely
      Packed Decimal' format or the 'Binary Integer Decimal'
      format.
     #######################
     $hex = d64_bytes($d64);
      Returns the hex representation of the _Decimal64 value
      as a string of 16 hex characters.
     ############################
     $binary = hex2bin($d64_hex);
      Takes the string returned by d64_bytes (above) and
      rewrites it in binary form - ie as a string of 64 base 2
      digits.
     #################
     $d64 = DEC64_MAX; # 9999999999999999e369
     $d64 = DEC64_MIN; # 1e-398
      DEC64_MAX is the largest positive finite representable
      _Decimal64 value.
      DEC64_MIN is the smallest positive non-zero representable
      _Decimal64 value.
      Multiply these by -1 to get their negative counterparts.
     ###################
     $d64 = Exp10($pow);
      Returns a Math::Decimal64 object with a value of
      10 ** $pow, for $pow in the range (-398 .. 384). Croaks
      with appropriate message if $pow is not within that range.
     ########################
     $bool = have_strtod64();
      Returns true if, when building Math::Decimal64,
      the Makefile.PL was configured to make the STRtoD64()
      function available for your build of Math::Decimal64. Else
      returns false.
      (No use making this function available if your compiler's
      C library doesn't provide the strtod64 function.)
     #########################
     $test = is_ZeroD64($d64);
      Returns:
       -1 if $d64 is negative zero;
        1 if $d64 is zero, but not negative zero;
        0 if $d64 is not zero.
     ########################
     $test = is_InfD64($d64);
      Returns:
       -1 if $d64 is negative infinity;
        1 if $d64 is positive infinity;
        0 if $d64 is not infinity.
     ########################
     $bool = is_NaND64($d64);
      Returns:
        1 if $d64 is a NaN;
        0 if $d64 is not a NaN.
     ###################
     LDtoD64($d64, $ld); # $ld is a Math::LongDouble object
     D64toLD($ld, $d64); # $ld is a Math::LongDouble object
     Conversions between Math::LongDouble and Math::Decimal64
     objects - done by simply casting the long double value to a
     _Decimal64 value, or (resp.) vice-versa.
     Requires that Math::LongDouble has been loaded.
     #######################
     $sign = get_sign($d64);
      Returns the sign ('+' or '-') of $d64.
     #####################
     $exp = get_exp($d64);
      Returns the exponent of $d64. This is the exponent value
      that's stored internally within the encapsulated _Decimal64
      value; it may differ from the value that you assigned.
      For example, if you've assigned the value MEtoD64('100', 0)
      it will probably be held internally as '1e2', not '100e0',
      in which case get_exp() would return 2, not 0.
     ####################
=head1 LICENSE
    This program is free software; you may redistribute it and/or
    modify it under the same terms as Perl itself.
    Copyright 2012-14 Sisyphus
=head1 AUTHOR
    Sisyphus <sisyphus at(@) cpan dot (.) org>
=cut