{
    "mode": "perldoc",
    "parameter": "Math::BigInt",
    "section": "",
    "url": "https://www.chedong.com/phpMan.php/perldoc/Math%3A%3ABigInt/json",
    "generated": "2026-06-09T21:08:52Z",
    "synopsis": "use Math::BigInt;\n# or make it faster with huge numbers: install (optional)\n# Math::BigInt::GMP and always use (it falls back to\n# pure Perl if the GMP library is not installed):\n# (See also the L<MATH LIBRARY> section!)\n# to warn if Math::BigInt::GMP cannot be found, use\nuse Math::BigInt lib => 'GMP';\n# to suppress the warning if Math::BigInt::GMP cannot be found, use\n# use Math::BigInt try => 'GMP';\n# to die if Math::BigInt::GMP cannot be found, use\n# use Math::BigInt only => 'GMP';\nmy $str = '1234567890';\nmy @values = (64, 74, 18);\nmy $n = 1; my $sign = '-';\n# Configuration methods (may be used as class methods and instance methods)\nMath::BigInt->accuracy();     # get class accuracy\nMath::BigInt->accuracy($n);   # set class accuracy\nMath::BigInt->precision();    # get class precision\nMath::BigInt->precision($n);  # set class precision\nMath::BigInt->roundmode();   # get class rounding mode\nMath::BigInt->roundmode($m); # set global round mode, must be one of\n# 'even', 'odd', '+inf', '-inf', 'zero',\n# 'trunc', or 'common'\nMath::BigInt->config();       # return hash with configuration\n# Constructor methods (when the class methods below are used as instance\n# methods, the value is assigned the invocand)\n$x = Math::BigInt->new($str);             # defaults to 0\n$x = Math::BigInt->new('0x123');          # from hexadecimal\n$x = Math::BigInt->new('0b101');          # from binary\n$x = Math::BigInt->fromhex('cafe');      # from hexadecimal\n$x = Math::BigInt->fromoct('377');       # from octal\n$x = Math::BigInt->frombin('1101');      # from binary\n$x = Math::BigInt->frombase('why', 36);  # from any base\n$x = Math::BigInt->frombasenum([1, 0], 2);  # from any base\n$x = Math::BigInt->bzero();               # create a +0\n$x = Math::BigInt->bone();                # create a +1\n$x = Math::BigInt->bone('-');             # create a -1\n$x = Math::BigInt->binf();                # create a +inf\n$x = Math::BigInt->binf('-');             # create a -inf\n$x = Math::BigInt->bnan();                # create a Not-A-Number\n$x = Math::BigInt->bpi();                 # returns pi\n$y = $x->copy();         # make a copy (unlike $y = $x)\n$y = $x->asint();       # return as a Math::BigInt\n# Boolean methods (these don't modify the invocand)\n$x->iszero();          # if $x is 0\n$x->isone();           # if $x is +1\n$x->isone(\"+\");        # ditto\n$x->isone(\"-\");        # if $x is -1\n$x->isinf();           # if $x is +inf or -inf\n$x->isinf(\"+\");        # if $x is +inf\n$x->isinf(\"-\");        # if $x is -inf\n$x->isnan();           # if $x is NaN\n$x->ispositive();      # if $x > 0\n$x->ispos();           # ditto\n$x->isnegative();      # if $x < 0\n$x->isneg();           # ditto\n$x->isodd();           # if $x is odd\n$x->iseven();          # if $x is even\n$x->isint();           # if $x is an integer\n# Comparison methods\n$x->bcmp($y);           # compare numbers (undef, < 0, == 0, > 0)\n$x->bacmp($y);          # compare absolutely (undef, < 0, == 0, > 0)\n$x->beq($y);            # true if and only if $x == $y\n$x->bne($y);            # true if and only if $x != $y\n$x->blt($y);            # true if and only if $x < $y\n$x->ble($y);            # true if and only if $x <= $y\n$x->bgt($y);            # true if and only if $x > $y\n$x->bge($y);            # true if and only if $x >= $y\n# Arithmetic methods\n$x->bneg();             # negation\n$x->babs();             # absolute value\n$x->bsgn();             # sign function (-1, 0, 1, or NaN)\n$x->bnorm();            # normalize (no-op)\n$x->binc();             # increment $x by 1\n$x->bdec();             # decrement $x by 1\n$x->badd($y);           # addition (add $y to $x)\n$x->bsub($y);           # subtraction (subtract $y from $x)\n$x->bmul($y);           # multiplication (multiply $x by $y)\n$x->bmuladd($y,$z);     # $x = $x * $y + $z\n$x->bdiv($y);           # division (floored), set $x to quotient\n# return (quo,rem) or quo if scalar\n$x->btdiv($y);          # division (truncated), set $x to quotient\n# return (quo,rem) or quo if scalar\n$x->bmod($y);           # modulus (x % y)\n$x->btmod($y);          # modulus (truncated)\n$x->bmodinv($mod);      # modular multiplicative inverse\n$x->bmodpow($y,$mod);   # modular exponentiation (($x  $y) % $mod)\n$x->bpow($y);           # power of arguments (x  y)\n$x->blog();             # logarithm of $x to base e (Euler's number)\n$x->blog($base);        # logarithm of $x to base $base (e.g., base 2)\n$x->bexp();             # calculate e  $x where e is Euler's number\n$x->bnok($y);           # x over y (binomial coefficient n over k)\n$x->buparrow($n, $y);   # Knuth's up-arrow notation\n$x->backermann($y);     # the Ackermann function\n$x->bsin();             # sine\n$x->bcos();             # cosine\n$x->batan();            # inverse tangent\n$x->batan2($y);         # two-argument inverse tangent\n$x->bsqrt();            # calculate square root\n$x->broot($y);          # $y'th root of $x (e.g. $y == 3 => cubic root)\n$x->bfac();             # factorial of $x (1*2*3*4*..$x)\n$x->bdfac();            # double factorial of $x ($x*($x-2)*($x-4)*...)\n$x->btfac();            # triple factorial of $x ($x*($x-3)*($x-6)*...)\n$x->bmfac($k);          # $k'th multi-factorial of $x ($x*($x-$k)*...)\n$x->blsft($n);          # left shift $n places in base 2\n$x->blsft($n,$b);       # left shift $n places in base $b\n# returns (quo,rem) or quo (scalar context)\n$x->brsft($n);          # right shift $n places in base 2\n$x->brsft($n,$b);       # right shift $n places in base $b\n# returns (quo,rem) or quo (scalar context)\n# Bitwise methods\n$x->band($y);           # bitwise and\n$x->bior($y);           # bitwise inclusive or\n$x->bxor($y);           # bitwise exclusive or\n$x->bnot();             # bitwise not (two's complement)\n# Rounding methods\n$x->round($A,$P,$mode); # round to accuracy or precision using\n# rounding mode $mode\n$x->bround($n);         # accuracy: preserve $n digits\n$x->bfround($n);        # $n > 0: round to $nth digit left of dec. point\n# $n < 0: round to $nth digit right of dec. point\n$x->bfloor();           # round towards minus infinity\n$x->bceil();            # round towards plus infinity\n$x->bint();             # round towards zero\n# Other mathematical methods\n$x->bgcd($y);            # greatest common divisor\n$x->blcm($y);            # least common multiple\n# Object property methods (do not modify the invocand)\n$x->sign();              # the sign, either +, - or NaN\n$x->digit($n);           # the nth digit, counting from the right\n$x->digit(-$n);          # the nth digit, counting from the left\n$x->length();            # return number of digits in number\n($xl,$f) = $x->length(); # length of number and length of fraction\n# part, latter is always 0 digits long\n# for Math::BigInt objects\n$x->mantissa();          # return (signed) mantissa as a Math::BigInt\n$x->exponent();          # return exponent as a Math::BigInt\n$x->parts();             # return (mantissa,exponent) as a Math::BigInt\n$x->sparts();            # mantissa and exponent (as integers)\n$x->nparts();            # mantissa and exponent (normalised)\n$x->eparts();            # mantissa and exponent (engineering notation)\n$x->dparts();            # integer and fraction part\n$x->fparts();            # numerator and denominator\n$x->numerator();         # numerator\n$x->denominator();       # denominator\n# Conversion methods (do not modify the invocand)\n$x->bstr();         # decimal notation, possibly zero padded\n$x->bsstr();        # string in scientific notation with integers\n$x->bnstr();        # string in normalized notation\n$x->bestr();        # string in engineering notation\n$x->bdstr();        # string in decimal notation\n$x->tohex();       # as signed hexadecimal string\n$x->tobin();       # as signed binary string\n$x->tooct();       # as signed octal string\n$x->tobytes();     # as byte string\n$x->tobase($b);    # as string in any base\n$x->tobasenum($b);   # as array of integers in any base\n$x->ashex();       # as signed hexadecimal string with prefixed 0x\n$x->asbin();       # as signed binary string with prefixed 0b\n$x->asoct();       # as signed octal string with prefixed 0\n# Other conversion methods\n$x->numify();           # return as scalar (might overflow or underflow)",
    "sections": {
        "NAME": {
            "content": "Math::BigInt - Arbitrary size integer/float math package\n",
            "subsections": []
        },
        "SYNOPSIS": {
            "content": "use Math::BigInt;\n\n# or make it faster with huge numbers: install (optional)\n# Math::BigInt::GMP and always use (it falls back to\n# pure Perl if the GMP library is not installed):\n# (See also the L<MATH LIBRARY> section!)\n\n# to warn if Math::BigInt::GMP cannot be found, use\nuse Math::BigInt lib => 'GMP';\n\n# to suppress the warning if Math::BigInt::GMP cannot be found, use\n# use Math::BigInt try => 'GMP';\n\n# to die if Math::BigInt::GMP cannot be found, use\n# use Math::BigInt only => 'GMP';\n\nmy $str = '1234567890';\nmy @values = (64, 74, 18);\nmy $n = 1; my $sign = '-';\n\n# Configuration methods (may be used as class methods and instance methods)\n\nMath::BigInt->accuracy();     # get class accuracy\nMath::BigInt->accuracy($n);   # set class accuracy\nMath::BigInt->precision();    # get class precision\nMath::BigInt->precision($n);  # set class precision\nMath::BigInt->roundmode();   # get class rounding mode\nMath::BigInt->roundmode($m); # set global round mode, must be one of\n# 'even', 'odd', '+inf', '-inf', 'zero',\n# 'trunc', or 'common'\nMath::BigInt->config();       # return hash with configuration\n\n# Constructor methods (when the class methods below are used as instance\n# methods, the value is assigned the invocand)\n\n$x = Math::BigInt->new($str);             # defaults to 0\n$x = Math::BigInt->new('0x123');          # from hexadecimal\n$x = Math::BigInt->new('0b101');          # from binary\n$x = Math::BigInt->fromhex('cafe');      # from hexadecimal\n$x = Math::BigInt->fromoct('377');       # from octal\n$x = Math::BigInt->frombin('1101');      # from binary\n$x = Math::BigInt->frombase('why', 36);  # from any base\n$x = Math::BigInt->frombasenum([1, 0], 2);  # from any base\n$x = Math::BigInt->bzero();               # create a +0\n$x = Math::BigInt->bone();                # create a +1\n$x = Math::BigInt->bone('-');             # create a -1\n$x = Math::BigInt->binf();                # create a +inf\n$x = Math::BigInt->binf('-');             # create a -inf\n$x = Math::BigInt->bnan();                # create a Not-A-Number\n$x = Math::BigInt->bpi();                 # returns pi\n\n$y = $x->copy();         # make a copy (unlike $y = $x)\n$y = $x->asint();       # return as a Math::BigInt\n\n# Boolean methods (these don't modify the invocand)\n\n$x->iszero();          # if $x is 0\n$x->isone();           # if $x is +1\n$x->isone(\"+\");        # ditto\n$x->isone(\"-\");        # if $x is -1\n$x->isinf();           # if $x is +inf or -inf\n$x->isinf(\"+\");        # if $x is +inf\n$x->isinf(\"-\");        # if $x is -inf\n$x->isnan();           # if $x is NaN\n\n$x->ispositive();      # if $x > 0\n$x->ispos();           # ditto\n$x->isnegative();      # if $x < 0\n$x->isneg();           # ditto\n\n$x->isodd();           # if $x is odd\n$x->iseven();          # if $x is even\n$x->isint();           # if $x is an integer\n\n# Comparison methods\n\n$x->bcmp($y);           # compare numbers (undef, < 0, == 0, > 0)\n$x->bacmp($y);          # compare absolutely (undef, < 0, == 0, > 0)\n$x->beq($y);            # true if and only if $x == $y\n$x->bne($y);            # true if and only if $x != $y\n$x->blt($y);            # true if and only if $x < $y\n$x->ble($y);            # true if and only if $x <= $y\n$x->bgt($y);            # true if and only if $x > $y\n$x->bge($y);            # true if and only if $x >= $y\n\n# Arithmetic methods\n\n$x->bneg();             # negation\n$x->babs();             # absolute value\n$x->bsgn();             # sign function (-1, 0, 1, or NaN)\n$x->bnorm();            # normalize (no-op)\n$x->binc();             # increment $x by 1\n$x->bdec();             # decrement $x by 1\n$x->badd($y);           # addition (add $y to $x)\n$x->bsub($y);           # subtraction (subtract $y from $x)\n$x->bmul($y);           # multiplication (multiply $x by $y)\n$x->bmuladd($y,$z);     # $x = $x * $y + $z\n$x->bdiv($y);           # division (floored), set $x to quotient\n# return (quo,rem) or quo if scalar\n$x->btdiv($y);          # division (truncated), set $x to quotient\n# return (quo,rem) or quo if scalar\n$x->bmod($y);           # modulus (x % y)\n$x->btmod($y);          # modulus (truncated)\n$x->bmodinv($mod);      # modular multiplicative inverse\n$x->bmodpow($y,$mod);   # modular exponentiation (($x  $y) % $mod)\n$x->bpow($y);           # power of arguments (x  y)\n$x->blog();             # logarithm of $x to base e (Euler's number)\n$x->blog($base);        # logarithm of $x to base $base (e.g., base 2)\n$x->bexp();             # calculate e  $x where e is Euler's number\n$x->bnok($y);           # x over y (binomial coefficient n over k)\n$x->buparrow($n, $y);   # Knuth's up-arrow notation\n$x->backermann($y);     # the Ackermann function\n$x->bsin();             # sine\n$x->bcos();             # cosine\n$x->batan();            # inverse tangent\n$x->batan2($y);         # two-argument inverse tangent\n$x->bsqrt();            # calculate square root\n$x->broot($y);          # $y'th root of $x (e.g. $y == 3 => cubic root)\n$x->bfac();             # factorial of $x (1*2*3*4*..$x)\n$x->bdfac();            # double factorial of $x ($x*($x-2)*($x-4)*...)\n$x->btfac();            # triple factorial of $x ($x*($x-3)*($x-6)*...)\n$x->bmfac($k);          # $k'th multi-factorial of $x ($x*($x-$k)*...)\n\n$x->blsft($n);          # left shift $n places in base 2\n$x->blsft($n,$b);       # left shift $n places in base $b\n# returns (quo,rem) or quo (scalar context)\n$x->brsft($n);          # right shift $n places in base 2\n$x->brsft($n,$b);       # right shift $n places in base $b\n# returns (quo,rem) or quo (scalar context)\n\n# Bitwise methods\n\n$x->band($y);           # bitwise and\n$x->bior($y);           # bitwise inclusive or\n$x->bxor($y);           # bitwise exclusive or\n$x->bnot();             # bitwise not (two's complement)\n\n# Rounding methods\n$x->round($A,$P,$mode); # round to accuracy or precision using\n# rounding mode $mode\n$x->bround($n);         # accuracy: preserve $n digits\n$x->bfround($n);        # $n > 0: round to $nth digit left of dec. point\n# $n < 0: round to $nth digit right of dec. point\n$x->bfloor();           # round towards minus infinity\n$x->bceil();            # round towards plus infinity\n$x->bint();             # round towards zero\n\n# Other mathematical methods\n\n$x->bgcd($y);            # greatest common divisor\n$x->blcm($y);            # least common multiple\n\n# Object property methods (do not modify the invocand)\n\n$x->sign();              # the sign, either +, - or NaN\n$x->digit($n);           # the nth digit, counting from the right\n$x->digit(-$n);          # the nth digit, counting from the left\n$x->length();            # return number of digits in number\n($xl,$f) = $x->length(); # length of number and length of fraction\n# part, latter is always 0 digits long\n# for Math::BigInt objects\n$x->mantissa();          # return (signed) mantissa as a Math::BigInt\n$x->exponent();          # return exponent as a Math::BigInt\n$x->parts();             # return (mantissa,exponent) as a Math::BigInt\n$x->sparts();            # mantissa and exponent (as integers)\n$x->nparts();            # mantissa and exponent (normalised)\n$x->eparts();            # mantissa and exponent (engineering notation)\n$x->dparts();            # integer and fraction part\n$x->fparts();            # numerator and denominator\n$x->numerator();         # numerator\n$x->denominator();       # denominator\n\n# Conversion methods (do not modify the invocand)\n\n$x->bstr();         # decimal notation, possibly zero padded\n$x->bsstr();        # string in scientific notation with integers\n$x->bnstr();        # string in normalized notation\n$x->bestr();        # string in engineering notation\n$x->bdstr();        # string in decimal notation\n\n$x->tohex();       # as signed hexadecimal string\n$x->tobin();       # as signed binary string\n$x->tooct();       # as signed octal string\n$x->tobytes();     # as byte string\n$x->tobase($b);    # as string in any base\n$x->tobasenum($b);   # as array of integers in any base\n\n$x->ashex();       # as signed hexadecimal string with prefixed 0x\n$x->asbin();       # as signed binary string with prefixed 0b\n$x->asoct();       # as signed octal string with prefixed 0\n\n# Other conversion methods\n\n$x->numify();           # return as scalar (might overflow or underflow)\n",
            "subsections": []
        },
        "DESCRIPTION": {
            "content": "Math::BigInt provides support for arbitrary precision integers. Overloading is also provided for\nPerl operators.\n",
            "subsections": [
                {
                    "name": "Input",
                    "content": "Input values to these routines may be any scalar number or string that looks like a number and\nrepresents an integer. Anything that is accepted by Perl as a literal numeric constant should be\naccepted by this module, except that finite non-integers return NaN.\n\n*   Leading and trailing whitespace is ignored.\n\n*   Leading zeros are ignored, except for floating point numbers with a binary exponent, in\nwhich case the number is interpreted as an octal floating point number. For example,\n\"01.4p+0\" gives 1.5, \"00.4p+0\" gives 0.5, but \"0.4p+0\" gives a NaN. And while \"0377\" gives\n255, \"0377p0\" gives 255.\n\n*   If the string has a \"0x\" or \"0X\" prefix, it is interpreted as a hexadecimal number.\n\n*   If the string has a \"0o\" or \"0O\" prefix, it is interpreted as an octal number. A floating\npoint literal with a \"0\" prefix is also interpreted as an octal number.\n\n*   If the string has a \"0b\" or \"0B\" prefix, it is interpreted as a binary number.\n\n*   Underline characters are allowed in the same way as they are allowed in literal numerical\nconstants.\n\n*   If the string can not be interpreted, or does not represent a finite integer, NaN is\nreturned.\n\n*   For hexadecimal, octal, and binary floating point numbers, the exponent must be separated\nfrom the significand (mantissa) by the letter \"p\" or \"P\", not \"e\" or \"E\" as with decimal\nnumbers.\n\nSome examples of valid string input\n\nInput string                Resulting value\n\n123                         123\n1.23e2                      123\n12300e-2                    123\n\n67538754                  67538754\n-456.789e+010         -4567890000000\n\n0x13a                       314\n0x13ap0                     314\n0x1.3ap+8                   314\n0x0.00013ap+24              314\n0x13a000p-12                314\n\n0o472                       314\n0o1.164p+8                  314\n0o0.0001164p+20             314\n0o1164000p-10               314\n\n0472                        472     Note!\n01.164p+8                   314\n00.0001164p+20              314\n01164000p-10                314\n\n0b100111010                 314\n0b1.0011101p+8              314\n0b0.00010011101p+12         314\n0b100111010000p-3           314\n\nInput given as scalar numbers might lose precision. Quote your input to ensure that no digits\nare lost:\n\n$x = Math::BigInt->new( 56789012345678901234 );   # bad\n$x = Math::BigInt->new('56789012345678901234');   # good\n\nCurrently, \"Math::BigInt-\"new()> (no input argument) and \"Math::BigInt-\"new(\"\")> return 0. This\nmight change in the future, so always use the following explicit forms to get a zero:\n\n$zero = Math::BigInt->bzero();\n"
                },
                {
                    "name": "Output",
                    "content": "Output values are usually Math::BigInt objects.\n\nBoolean operators \"iszero()\", \"isone()\", \"isinf()\", etc. return true or false.\n\nComparison operators \"bcmp()\" and \"bacmp()\") return -1, 0, 1, or undef.\n"
                }
            ]
        },
        "METHODS": {
            "content": "",
            "subsections": [
                {
                    "name": "Configuration methods",
                    "content": "Each of the methods below (except config(), accuracy() and precision()) accepts three additional\nparameters. These arguments $A, $P and $R are \"accuracy\", \"precision\" and \"roundmode\". Please\nsee the section about \"ACCURACY and PRECISION\" for more information.\n\nSetting a class variable effects all object instance that are created afterwards.\n"
                },
                {
                    "name": "accuracy",
                    "content": "Math::BigInt->accuracy(5);      # set class accuracy\n$x->accuracy(5);                # set instance accuracy\n\n$A = Math::BigInt->accuracy();  # get class accuracy\n$A = $x->accuracy();            # get instance accuracy\n\nSet or get the accuracy, i.e., the number of significant digits. The accuracy must be an\ninteger. If the accuracy is set to \"undef\", no rounding is done.\n\nAlternatively, one can round the results explicitly using one of \"round()\", \"bround()\" or\n\"bfround()\" or by passing the desired accuracy to the method as an additional parameter:\n\nmy $x = Math::BigInt->new(30000);\nmy $y = Math::BigInt->new(7);\nprint scalar $x->copy()->bdiv($y, 2);               # prints 4300\nprint scalar $x->copy()->bdiv($y)->bround(2);       # prints 4300\n\nPlease see the section about \"ACCURACY and PRECISION\" for further details.\n\n$y = Math::BigInt->new(1234567);    # $y is not rounded\nMath::BigInt->accuracy(4);          # set class accuracy to 4\n$x = Math::BigInt->new(1234567);    # $x is rounded automatically\nprint \"$x $y\";                      # prints \"1235000 1234567\"\n\nprint $x->accuracy();       # prints \"4\"\nprint $y->accuracy();       # also prints \"4\", since\n#   class accuracy is 4\n\nMath::BigInt->accuracy(5);  # set class accuracy to 5\nprint $x->accuracy();       # prints \"4\", since instance\n#   accuracy is 4\nprint $y->accuracy();       # prints \"5\", since no instance\n#   accuracy, and class accuracy is 5\n\nNote: Each class has it's own globals separated from Math::BigInt, but it is possible to\nsubclass Math::BigInt and make the globals of the subclass aliases to the ones from\nMath::BigInt.\n"
                },
                {
                    "name": "precision",
                    "content": "Math::BigInt->precision(-2);     # set class precision\n$x->precision(-2);               # set instance precision\n\n$P = Math::BigInt->precision();  # get class precision\n$P = $x->precision();            # get instance precision\n\nSet or get the precision, i.e., the place to round relative to the decimal point. The\nprecision must be a integer. Setting the precision to $P means that each number is rounded\nup or down, depending on the rounding mode, to the nearest multiple of 10$P. If the\nprecision is set to \"undef\", no rounding is done.\n\nYou might want to use \"accuracy()\" instead. With \"accuracy()\" you set the number of digits\neach result should have, with \"precision()\" you set the place where to round.\n\nPlease see the section about \"ACCURACY and PRECISION\" for further details.\n\n$y = Math::BigInt->new(1234567);    # $y is not rounded\nMath::BigInt->precision(4);         # set class precision to 4\n$x = Math::BigInt->new(1234567);    # $x is rounded automatically\nprint $x;                           # prints \"1230000\"\n\nNote: Each class has its own globals separated from Math::BigInt, but it is possible to\nsubclass Math::BigInt and make the globals of the subclass aliases to the ones from\nMath::BigInt.\n"
                },
                {
                    "name": "div_scale",
                    "content": "Set/get the fallback accuracy. This is the accuracy used when neither accuracy nor precision\nis set explicitly. It is used when a computation might otherwise attempt to return an\ninfinite number of digits.\n"
                },
                {
                    "name": "round_mode",
                    "content": "Set/get the rounding mode.\n"
                },
                {
                    "name": "upgrade",
                    "content": "Set/get the class for upgrading. When a computation might result in a non-integer, the\noperands are upgraded to this class. This is used for instance by bignum. The default is\n\"undef\", thus the following operation creates a Math::BigInt, not a Math::BigFloat:\n\nmy $i = Math::BigInt->new(123);\nmy $f = Math::BigFloat->new('123.1');\n\nprint $i + $f, \"\\n\";                # prints 246\n"
                },
                {
                    "name": "downgrade",
                    "content": "Set/get the class for downgrading. The default is \"undef\". Downgrading is not done by\nMath::BigInt.\n"
                },
                {
                    "name": "modify",
                    "content": "$x->modify('bpowd');\n\nThis method returns 0 if the object can be modified with the given operation, or 1 if not.\n\nThis is used for instance by Math::BigInt::Constant.\n"
                },
                {
                    "name": "config",
                    "content": "Math::BigInt->config(\"trapnan\" => 1);      # set\n$accu = Math::BigInt->config(\"accuracy\");   # get\n\nSet or get class variables. Read-only parameters are marked as RO. Read-write parameters are\nmarked as RW. The following parameters are supported.\n\nParameter       RO/RW   Description\nExample\n============================================================\nlib             RO      Name of the math backend library\nMath::BigInt::Calc\nlibversion     RO      Version of the math backend library\n0.30\nclass           RO      The class of config you just called\nMath::BigRat\nversion         RO      version number of the class you used\n0.10\nupgrade         RW      To which class numbers are upgraded\nundef\ndowngrade       RW      To which class numbers are downgraded\nundef\nprecision       RW      Global precision\nundef\naccuracy        RW      Global accuracy\nundef\nroundmode      RW      Global round mode\neven\ndivscale       RW      Fallback accuracy for division etc.\n40\ntrapnan        RW      Trap NaNs\nundef\ntrapinf        RW      Trap +inf/-inf\nundef\n"
                },
                {
                    "name": "Constructor methods",
                    "content": ""
                },
                {
                    "name": "new",
                    "content": "$x = Math::BigInt->new($str,$A,$P,$R);\n\nCreates a new Math::BigInt object from a scalar or another Math::BigInt object. The input is\naccepted as decimal, hexadecimal (with leading '0x') or binary (with leading '0b').\n\nSee \"Input\" for more info on accepted input formats.\n"
                },
                {
                    "name": "from_dec",
                    "content": "$x = Math::BigInt->fromdec(\"314159\");    # input is decimal\n\nInterpret input as a decimal. It is equivalent to new(), but does not accept anything but\nstrings representing finite, decimal numbers.\n"
                },
                {
                    "name": "from_hex",
                    "content": "$x = Math::BigInt->fromhex(\"0xcafe\");    # input is hexadecimal\n\nInterpret input as a hexadecimal string. A \"0x\" or \"x\" prefix is optional. A single\nunderscore character may be placed right after the prefix, if present, or between any two\ndigits. If the input is invalid, a NaN is returned.\n"
                },
                {
                    "name": "from_oct",
                    "content": "$x = Math::BigInt->fromoct(\"0775\");      # input is octal\n\nInterpret the input as an octal string and return the corresponding value. A \"0\" (zero)\nprefix is optional. A single underscore character may be placed right after the prefix, if\npresent, or between any two digits. If the input is invalid, a NaN is returned.\n"
                },
                {
                    "name": "from_bin",
                    "content": "$x = Math::BigInt->frombin(\"0b10011\");   # input is binary\n\nInterpret the input as a binary string. A \"0b\" or \"b\" prefix is optional. A single\nunderscore character may be placed right after the prefix, if present, or between any two\ndigits. If the input is invalid, a NaN is returned.\n"
                },
                {
                    "name": "from_bytes",
                    "content": "$x = Math::BigInt->frombytes(\"\\xf3\\x6b\");  # $x = 62315\n\nInterpret the input as a byte string, assuming big endian byte order. The output is always a\nnon-negative, finite integer.\n\nIn some special cases, frombytes() matches the conversion done by unpack():\n\n$b = \"\\x4e\";                             # one char byte string\n$x = Math::BigInt->frombytes($b);       # = 78\n$y = unpack \"C\", $b;                     # ditto, but scalar\n\n$b = \"\\xf3\\x6b\";                         # two char byte string\n$x = Math::BigInt->frombytes($b);       # = 62315\n$y = unpack \"S>\", $b;                    # ditto, but scalar\n\n$b = \"\\x2d\\xe0\\x49\\xad\";                 # four char byte string\n$x = Math::BigInt->frombytes($b);       # = 769673645\n$y = unpack \"L>\", $b;                    # ditto, but scalar\n\n$b = \"\\x2d\\xe0\\x49\\xad\\x2d\\xe0\\x49\\xad\"; # eight char byte string\n$x = Math::BigInt->frombytes($b);       # = 3305723134637787565\n$y = unpack \"Q>\", $b;                    # ditto, but scalar\n"
                },
                {
                    "name": "from_base",
                    "content": "Given a string, a base, and an optional collation sequence, interpret the string as a number\nin the given base. The collation sequence describes the value of each character in the\nstring.\n\nIf a collation sequence is not given, a default collation sequence is used. If the base is\nless than or equal to 36, the collation sequence is the string consisting of the 36\ncharacters \"0\" to \"9\" and \"A\" to \"Z\". In this case, the letter case in the input is ignored.\nIf the base is greater than 36, and smaller than or equal to 62, the collation sequence is\nthe string consisting of the 62 characters \"0\" to \"9\", \"A\" to \"Z\", and \"a\" to \"z\". A base\nlarger than 62 requires the collation sequence to be specified explicitly.\n\nThese examples show standard binary, octal, and hexadecimal conversion. All cases return\n250.\n\n$x = Math::BigInt->frombase(\"11111010\", 2);\n$x = Math::BigInt->frombase(\"372\", 8);\n$x = Math::BigInt->frombase(\"fa\", 16);\n\nWhen the base is less than or equal to 36, and no collation sequence is given, the letter\ncase is ignored, so both of these also return 250:\n\n$x = Math::BigInt->frombase(\"6Y\", 16);\n$x = Math::BigInt->frombase(\"6y\", 16);\n\nWhen the base greater than 36, and no collation sequence is given, the default collation\nsequence contains both uppercase and lowercase letters, so the letter case in the input is\nnot ignored:\n\n$x = Math::BigInt->frombase(\"6S\", 37);         # $x is 250\n$x = Math::BigInt->frombase(\"6s\", 37);         # $x is 276\n$x = Math::BigInt->frombase(\"121\", 3);         # $x is 16\n$x = Math::BigInt->frombase(\"XYZ\", 36);        # $x is 44027\n$x = Math::BigInt->frombase(\"Why\", 42);        # $x is 58314\n\nThe collation sequence can be any set of unique characters. These two cases are equivalent\n\n$x = Math::BigInt->frombase(\"100\", 2, \"01\");   # $x is 4\n$x = Math::BigInt->frombase(\"|--\", 2, \"-|\");   # $x is 4\n"
                },
                {
                    "name": "from_base_num",
                    "content": "Returns a new Math::BigInt object given an array of values and a base. This method is\nequivalent to \"frombase()\", but works on numbers in an array rather than characters in a\nstring. Unlike \"frombase()\", all input values may be arbitrarily large.\n\n$x = Math::BigInt->frombasenum([1, 1, 0, 1], 2)     # $x is 13\n$x = Math::BigInt->frombasenum([3, 125, 39], 128)   # $x is 65191\n"
                },
                {
                    "name": "bzero",
                    "content": "$x = Math::BigInt->bzero();\n$x->bzero();\n\nReturns a new Math::BigInt object representing zero. If used as an instance method, assigns\nthe value to the invocand.\n"
                },
                {
                    "name": "bone",
                    "content": "$x = Math::BigInt->bone();          # +1\n$x = Math::BigInt->bone(\"+\");       # +1\n$x = Math::BigInt->bone(\"-\");       # -1\n$x->bone();                         # +1\n$x->bone(\"+\");                      # +1\n$x->bone('-');                      # -1\n\nCreates a new Math::BigInt object representing one. The optional argument is either '-' or\n'+', indicating whether you want plus one or minus one. If used as an instance method,\nassigns the value to the invocand.\n"
                },
                {
                    "name": "binf",
                    "content": "$x = Math::BigInt->binf($sign);\n\nCreates a new Math::BigInt object representing infinity. The optional argument is either '-'\nor '+', indicating whether you want infinity or minus infinity. If used as an instance\nmethod, assigns the value to the invocand.\n\n$x->binf();\n$x->binf('-');\n"
                },
                {
                    "name": "bnan",
                    "content": "$x = Math::BigInt->bnan();\n\nCreates a new Math::BigInt object representing NaN (Not A Number). If used as an instance\nmethod, assigns the value to the invocand.\n\n$x->bnan();\n"
                },
                {
                    "name": "bpi",
                    "content": "$x = Math::BigInt->bpi(100);        # 3\n$x->bpi(100);                       # 3\n\nCreates a new Math::BigInt object representing PI. If used as an instance method, assigns\nthe value to the invocand. With Math::BigInt this always returns 3.\n\nIf upgrading is in effect, returns PI, rounded to N digits with the current rounding mode:\n\nuse Math::BigFloat;\nuse Math::BigInt upgrade => \"Math::BigFloat\";\nprint Math::BigInt->bpi(3), \"\\n\";           # 3.14\nprint Math::BigInt->bpi(100), \"\\n\";         # 3.1415....\n"
                },
                {
                    "name": "copy",
                    "content": "$x->copy();         # make a true copy of $x (unlike $y = $x)\n"
                },
                {
                    "name": "as_int",
                    "content": ""
                },
                {
                    "name": "as_number",
                    "content": "These methods are called when Math::BigInt encounters an object it doesn't know how to\nhandle. For instance, assume $x is a Math::BigInt, or subclass thereof, and $y is defined,\nbut not a Math::BigInt, or subclass thereof. If you do\n\n$x -> badd($y);\n\n$y needs to be converted into an object that $x can deal with. This is done by first\nchecking if $y is something that $x might be upgraded to. If that is the case, no further\nattempts are made. The next is to see if $y supports the method \"asint()\". If it does,\n\"asint()\" is called, but if it doesn't, the next thing is to see if $y supports the method\n\"asnumber()\". If it does, \"asnumber()\" is called. The method \"asint()\" (and\n\"asnumber()\") is expected to return either an object that has the same class as $x, a\nsubclass thereof, or a string that \"ref($x)->new()\" can parse to create an object.\n\n\"asnumber()\" is an alias to \"asint()\". \"asnumber\" was introduced in v1.22, while\n\"asint()\" was introduced in v1.68.\n\nIn Math::BigInt, \"asint()\" has the same effect as \"copy()\".\n"
                },
                {
                    "name": "Boolean methods",
                    "content": "None of these methods modify the invocand object.\n"
                },
                {
                    "name": "is_zero",
                    "content": "$x->iszero();              # true if $x is 0\n\nReturns true if the invocand is zero and false otherwise.\n"
                },
                {
                    "name": "is_one",
                    "content": "$x->isone();               # true if $x is +1\n$x->isone(\"+\");            # ditto\n$x->isone(\"-\");            # true if $x is -1\n\nReturns true if the invocand is one and false otherwise.\n"
                },
                {
                    "name": "is_finite",
                    "content": "$x->isfinite();    # true if $x is not +inf, -inf or NaN\n\nReturns true if the invocand is a finite number, i.e., it is neither +inf, -inf, nor NaN.\n"
                },
                {
                    "name": "is_inf",
                    "content": "$x->isinf();               # true if $x is +inf\n$x->isinf(\"+\");            # ditto\n$x->isinf(\"-\");            # true if $x is -inf\n\nReturns true if the invocand is infinite and false otherwise.\n"
                },
                {
                    "name": "is_nan",
                    "content": "$x->isnan();               # true if $x is NaN\n"
                },
                {
                    "name": "is_positive",
                    "content": ""
                },
                {
                    "name": "is_pos",
                    "content": "$x->ispositive();          # true if > 0\n$x->ispos();               # ditto\n\nReturns true if the invocand is positive and false otherwise. A \"NaN\" is neither positive\nnor negative.\n"
                },
                {
                    "name": "is_negative",
                    "content": ""
                },
                {
                    "name": "is_neg",
                    "content": "$x->isnegative();          # true if < 0\n$x->isneg();               # ditto\n\nReturns true if the invocand is negative and false otherwise. A \"NaN\" is neither positive\nnor negative.\n"
                },
                {
                    "name": "is_non_positive",
                    "content": "$x->isnonpositive();      # true if <= 0\n\nReturns true if the invocand is negative or zero.\n"
                },
                {
                    "name": "is_non_negative",
                    "content": "$x->isnonnegative();      # true if >= 0\n\nReturns true if the invocand is positive or zero.\n"
                },
                {
                    "name": "is_odd",
                    "content": "$x->isodd();               # true if odd, false for even\n\nReturns true if the invocand is odd and false otherwise. \"NaN\", \"+inf\", and \"-inf\" are\nneither odd nor even.\n"
                },
                {
                    "name": "is_even",
                    "content": "$x->iseven();              # true if $x is even\n\nReturns true if the invocand is even and false otherwise. \"NaN\", \"+inf\", \"-inf\" are not\nintegers and are neither odd nor even.\n"
                },
                {
                    "name": "is_int",
                    "content": "$x->isint();               # true if $x is an integer\n\nReturns true if the invocand is an integer and false otherwise. \"NaN\", \"+inf\", \"-inf\" are\nnot integers.\n"
                },
                {
                    "name": "Comparison methods",
                    "content": "None of these methods modify the invocand object. Note that a \"NaN\" is neither less than,\ngreater than, or equal to anything else, even a \"NaN\".\n"
                },
                {
                    "name": "bcmp",
                    "content": "$x->bcmp($y);\n\nReturns -1, 0, 1 depending on whether $x is less than, equal to, or grater than $y. Returns\nundef if any operand is a NaN.\n"
                },
                {
                    "name": "bacmp",
                    "content": "$x->bacmp($y);\n\nReturns -1, 0, 1 depending on whether the absolute value of $x is less than, equal to, or\ngrater than the absolute value of $y. Returns undef if any operand is a NaN.\n"
                },
                {
                    "name": "beq",
                    "content": "$x -> beq($y);\n\nReturns true if and only if $x is equal to $y, and false otherwise.\n"
                },
                {
                    "name": "bne",
                    "content": "$x -> bne($y);\n\nReturns true if and only if $x is not equal to $y, and false otherwise.\n"
                },
                {
                    "name": "blt",
                    "content": "$x -> blt($y);\n\nReturns true if and only if $x is equal to $y, and false otherwise.\n"
                },
                {
                    "name": "ble",
                    "content": "$x -> ble($y);\n\nReturns true if and only if $x is less than or equal to $y, and false otherwise.\n"
                },
                {
                    "name": "bgt",
                    "content": "$x -> bgt($y);\n\nReturns true if and only if $x is greater than $y, and false otherwise.\n"
                },
                {
                    "name": "bge",
                    "content": "$x -> bge($y);\n\nReturns true if and only if $x is greater than or equal to $y, and false otherwise.\n"
                },
                {
                    "name": "Arithmetic methods",
                    "content": "These methods modify the invocand object and returns it.\n"
                },
                {
                    "name": "bneg",
                    "content": "$x->bneg();\n\nNegate the number, e.g. change the sign between '+' and '-', or between '+inf' and '-inf',\nrespectively. Does nothing for NaN or zero.\n"
                },
                {
                    "name": "babs",
                    "content": "$x->babs();\n\nSet the number to its absolute value, e.g. change the sign from '-' to '+' and from '-inf'\nto '+inf', respectively. Does nothing for NaN or positive numbers.\n"
                },
                {
                    "name": "bsgn",
                    "content": "$x->bsgn();\n\nSignum function. Set the number to -1, 0, or 1, depending on whether the number is negative,\nzero, or positive, respectively. Does not modify NaNs.\n"
                },
                {
                    "name": "bnorm",
                    "content": "$x->bnorm();                        # normalize (no-op)\n\nNormalize the number. This is a no-op and is provided only for backwards compatibility.\n"
                },
                {
                    "name": "binc",
                    "content": "$x->binc();                 # increment x by 1\n"
                },
                {
                    "name": "bdec",
                    "content": "$x->bdec();                 # decrement x by 1\n"
                },
                {
                    "name": "badd",
                    "content": "$x->badd($y);               # addition (add $y to $x)\n"
                },
                {
                    "name": "bsub",
                    "content": "$x->bsub($y);               # subtraction (subtract $y from $x)\n"
                },
                {
                    "name": "bmul",
                    "content": "$x->bmul($y);               # multiplication (multiply $x by $y)\n"
                },
                {
                    "name": "bmuladd",
                    "content": "$x->bmuladd($y,$z);\n\nMultiply $x by $y, and then add $z to the result,\n\nThis method was added in v1.87 of Math::BigInt (June 2007).\n"
                },
                {
                    "name": "bdiv",
                    "content": "$x->bdiv($y);               # divide, set $x to quotient\n\nDivides $x by $y by doing floored division (F-division), where the quotient is the floored\n(rounded towards negative infinity) quotient of the two operands. In list context, returns\nthe quotient and the remainder. The remainder is either zero or has the same sign as the\nsecond operand. In scalar context, only the quotient is returned.\n\nThe quotient is always the greatest integer less than or equal to the real-valued quotient\nof the two operands, and the remainder (when it is non-zero) always has the same sign as the\nsecond operand; so, for example,\n\n1 /  4  => ( 0,  1)\n1 / -4  => (-1, -3)\n-3 /  4  => (-1,  1)\n-3 / -4  => ( 0, -3)\n-11 /  2  => (-5,  1)\n11 / -2  => (-5, -1)\n\nThe behavior of the overloaded operator % agrees with the behavior of Perl's built-in %\noperator (as documented in the perlop manpage), and the equation\n\n$x == ($x / $y) * $y + ($x % $y)\n\nholds true for any finite $x and finite, non-zero $y.\n\nPerl's \"use integer\" might change the behaviour of % and / for scalars. This is because\nunder 'use integer' Perl does what the underlying C library thinks is right, and this\nvaries. However, \"use integer\" does not change the way things are done with Math::BigInt\nobjects.\n"
                },
                {
                    "name": "btdiv",
                    "content": "$x->btdiv($y);              # divide, set $x to quotient\n\nDivides $x by $y by doing truncated division (T-division), where quotient is the truncated\n(rouneded towards zero) quotient of the two operands. In list context, returns the quotient\nand the remainder. The remainder is either zero or has the same sign as the first operand.\nIn scalar context, only the quotient is returned.\n"
                },
                {
                    "name": "bmod",
                    "content": "$x->bmod($y);               # modulus (x % y)\n\nReturns $x modulo $y, i.e., the remainder after floored division (F-division). This method\nis like Perl's % operator. See \"bdiv()\".\n"
                },
                {
                    "name": "btmod",
                    "content": "$x->btmod($y);              # modulus\n\nReturns the remainer after truncated division (T-division). See \"btdiv()\".\n"
                },
                {
                    "name": "bmodinv",
                    "content": "$x->bmodinv($mod);          # modular multiplicative inverse\n\nReturns the multiplicative inverse of $x modulo $mod. If\n\n$y = $x -> copy() -> bmodinv($mod)\n\nthen $y is the number closest to zero, and with the same sign as $mod, satisfying\n\n($x * $y) % $mod = 1 % $mod\n\nIf $x and $y are non-zero, they must be relative primes, i.e., \"bgcd($y, $mod)==1\". '\"NaN\"'\nis returned when no modular multiplicative inverse exists.\n"
                },
                {
                    "name": "bmodpow",
                    "content": "$num->bmodpow($exp,$mod);           # modular exponentiation\n# ($num$exp % $mod)\n\nReturns the value of $num taken to the power $exp in the modulus $mod using binary\nexponentiation. \"bmodpow\" is far superior to writing\n\n$num  $exp % $mod\n\nbecause it is much faster - it reduces internal variables into the modulus whenever\npossible, so it operates on smaller numbers.\n\n\"bmodpow\" also supports negative exponents.\n\nbmodpow($num, -1, $mod)\n\nis exactly equivalent to\n\nbmodinv($num, $mod)\n"
                },
                {
                    "name": "bpow",
                    "content": "$x->bpow($y);               # power of arguments (x  y)\n\n\"bpow()\" (and the rounding functions) now modifies the first argument and returns it, unlike\nthe old code which left it alone and only returned the result. This is to be consistent with\n\"badd()\" etc. The first three modifies $x, the last one won't:\n\nprint bpow($x,$i),\"\\n\";         # modify $x\nprint $x->bpow($i),\"\\n\";        # ditto\nprint $x = $i,\"\\n\";           # the same\nprint $x  $i,\"\\n\";            # leave $x alone\n\nThe form \"$x = $y\" is faster than \"$x = $x  $y;\", though.\n"
                },
                {
                    "name": "blog",
                    "content": "$x->blog($base, $accuracy);         # logarithm of x to the base $base\n\nIf $base is not defined, Euler's number (e) is used:\n\nprint $x->blog(undef, 100);         # log(x) to 100 digits\n"
                },
                {
                    "name": "bexp",
                    "content": "$x->bexp($accuracy);                # calculate e  X\n\nCalculates the expression \"e  $x\" where \"e\" is Euler's number.\n\nThis method was added in v1.82 of Math::BigInt (April 2007).\n\nSee also \"blog()\".\n"
                },
                {
                    "name": "bnok",
                    "content": "$x->bnok($y);               # x over y (binomial coefficient n over k)\n\nCalculates the binomial coefficient n over k, also called the \"choose\" function, which is\n\n( n )       n!\n|   |  = --------\n( k )    k!(n-k)!\n\nwhen n and k are non-negative. This method implements the full Kronenburg extension\n(Kronenburg, M.J. \"The Binomial Coefficient for Negative Arguments.\" 18 May 2011.\nhttp://arxiv.org/abs/1105.3689/) illustrated by the following pseudo-code:\n\nif n >= 0 and k >= 0:\nreturn binomial(n, k)\nif k >= 0:\nreturn (-1)^k*binomial(-n+k-1, k)\nif k <= n:\nreturn (-1)^(n-k)*binomial(-k-1, n-k)\nelse\nreturn 0\n\nThe behaviour is identical to the behaviour of the Maple and Mathematica function for\nnegative integers n, k.\n"
                },
                {
                    "name": "buparrow",
                    "content": ""
                },
                {
                    "name": "uparrow",
                    "content": "$a -> buparrow($n, $b);         # modifies $a\n$x = $a -> uparrow($n, $b);     # does not modify $a\n\nThis method implements Knuth's up-arrow notation, where $n is a non-negative integer\nrepresenting the number of up-arrows. $n = 0 gives multiplication, $n = 1 gives\nexponentiation, $n = 2 gives tetration, $n = 3 gives hexation etc. The following illustrates\nthe relation between the first values of $n.\n\nSee <https://en.wikipedia.org/wiki/Knuth%27sup-arrownotation>.\n"
                },
                {
                    "name": "backermann",
                    "content": ""
                },
                {
                    "name": "ackermann",
                    "content": "$m -> backermann($n);           # modifies $a\n$x = $m -> ackermann($n);       # does not modify $a\n\nThis method implements the Ackermann function:\n\n/ n + 1              if m = 0\nA(m, n) = | A(m-1, 1)          if m > 0 and n = 0\n\\ A(m-1, A(m, n-1))  if m > 0 and n > 0\n\nIts value grows rapidly, even for small inputs. For example, A(4, 2) is an integer of 19729\ndecimal digits.\n\nSee https://en.wikipedia.org/wiki/Ackermannfunction\n"
                },
                {
                    "name": "bsin",
                    "content": "my $x = Math::BigInt->new(1);\nprint $x->bsin(100), \"\\n\";\n\nCalculate the sine of $x, modifying $x in place.\n\nIn Math::BigInt, unless upgrading is in effect, the result is truncated to an integer.\n\nThis method was added in v1.87 of Math::BigInt (June 2007).\n"
                },
                {
                    "name": "bcos",
                    "content": "my $x = Math::BigInt->new(1);\nprint $x->bcos(100), \"\\n\";\n\nCalculate the cosine of $x, modifying $x in place.\n\nIn Math::BigInt, unless upgrading is in effect, the result is truncated to an integer.\n\nThis method was added in v1.87 of Math::BigInt (June 2007).\n"
                },
                {
                    "name": "batan",
                    "content": "my $x = Math::BigFloat->new(0.5);\nprint $x->batan(100), \"\\n\";\n\nCalculate the arcus tangens of $x, modifying $x in place.\n\nIn Math::BigInt, unless upgrading is in effect, the result is truncated to an integer.\n\nThis method was added in v1.87 of Math::BigInt (June 2007).\n"
                },
                {
                    "name": "batan2",
                    "content": "my $x = Math::BigInt->new(1);\nmy $y = Math::BigInt->new(1);\nprint $y->batan2($x), \"\\n\";\n\nCalculate the arcus tangens of $y divided by $x, modifying $y in place.\n\nIn Math::BigInt, unless upgrading is in effect, the result is truncated to an integer.\n\nThis method was added in v1.87 of Math::BigInt (June 2007).\n"
                },
                {
                    "name": "bsqrt",
                    "content": "$x->bsqrt();                # calculate square root\n\n\"bsqrt()\" returns the square root truncated to an integer.\n\nIf you want a better approximation of the square root, then use:\n\n$x = Math::BigFloat->new(12);\nMath::BigFloat->precision(0);\nMath::BigFloat->roundmode('even');\nprint $x->copy->bsqrt(),\"\\n\";           # 4\n\nMath::BigFloat->precision(2);\nprint $x->bsqrt(),\"\\n\";                 # 3.46\nprint $x->bsqrt(3),\"\\n\";                # 3.464\n"
                },
                {
                    "name": "broot",
                    "content": "$x->broot($N);\n\nCalculates the N'th root of $x.\n"
                },
                {
                    "name": "bfac",
                    "content": "$x->bfac();             # factorial of $x\n\nReturns the factorial of $x, i.e., $x*($x-1)*($x-2)*...*2*1, the product of all positive\nintegers up to and including $x. $x must be > -1. The factorial of N is commonly written as\nN!, or N!1, when using the multifactorial notation.\n"
                },
                {
                    "name": "bdfac",
                    "content": "$x->bdfac();                # double factorial of $x\n\nReturns the double factorial of $x, i.e., $x*($x-2)*($x-4)*... $x must be > -2. The double\nfactorial of N is commonly written as N!!, or N!2, when using the multifactorial notation.\n"
                },
                {
                    "name": "btfac",
                    "content": "$x->btfac();            # triple factorial of $x\n\nReturns the triple factorial of $x, i.e., $x*($x-3)*($x-6)*... $x must be > -3. The triple\nfactorial of N is commonly written as N!!!, or N!3, when using the multifactorial notation.\n"
                },
                {
                    "name": "bmfac",
                    "content": "$x->bmfac($k);          # $k'th multifactorial of $x\n\nReturns the multi-factorial of $x, i.e., $x*($x-$k)*($x-2*$k)*... $x must be > -$k. The\nmulti-factorial of N is commonly written as N!K.\n"
                },
                {
                    "name": "bfib",
                    "content": "$F = $n->bfib();            # a single Fibonacci number\n@F = $n->bfib();            # a list of Fibonacci numbers\n\nIn scalar context, returns a single Fibonacci number. In list context, returns a list of\nFibonacci numbers. The invocand is the last element in the output.\n\nThe Fibonacci sequence is defined by\n\nF(0) = 0\nF(1) = 1\nF(n) = F(n-1) + F(n-2)\n\nIn list context, F(0) and F(n) is the first and last number in the output, respectively. For\nexample, if $n is 12, then \"@F = $n->bfib()\" returns the following values, F(0) to F(12):\n\n0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144\n\nThe sequence can also be extended to negative index n using the re-arranged recurrence\nrelation\n\nF(n-2) = F(n) - F(n-1)\n\ngiving the bidirectional sequence\n\nn  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7\nF(n)  13  -8   5  -3   2  -1   1   0   1   1   2   3   5   8  13\n\nIf $n is -12, the following values, F(0) to F(12), are returned:\n\n0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144\n"
                },
                {
                    "name": "blucas",
                    "content": "$F = $n->blucas();          # a single Lucas number\n@F = $n->blucas();          # a list of Lucas numbers\n\nIn scalar context, returns a single Lucas number. In list context, returns a list of Lucas\nnumbers. The invocand is the last element in the output.\n\nThe Lucas sequence is defined by\n\nL(0) = 2\nL(1) = 1\nL(n) = L(n-1) + L(n-2)\n\nIn list context, L(0) and L(n) is the first and last number in the output, respectively. For\nexample, if $n is 12, then \"@L = $n->blucas()\" returns the following values, L(0) to L(12):\n\n2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322\n\nThe sequence can also be extended to negative index n using the re-arranged recurrence\nrelation\n\nL(n-2) = L(n) - L(n-1)\n\ngiving the bidirectional sequence\n\nn  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7\nL(n)  29 -18  11  -7   4  -3   1   2   1   3   4   7  11  18  29\n\nIf $n is -12, the following values, L(0) to L(-12), are returned:\n\n2, 1, -3, 4, -7, 11, -18, 29, -47, 76, -123, 199, -322\n"
                },
                {
                    "name": "brsft",
                    "content": "$x->brsft($n);              # right shift $n places in base 2\n$x->brsft($n, $b);          # right shift $n places in base $b\n\nThe latter is equivalent to\n\n$x -> bdiv($b -> copy() -> bpow($n))\n"
                },
                {
                    "name": "blsft",
                    "content": "$x->blsft($n);              # left shift $n places in base 2\n$x->blsft($n, $b);          # left shift $n places in base $b\n\nThe latter is equivalent to\n\n$x -> bmul($b -> copy() -> bpow($n))\n"
                },
                {
                    "name": "Bitwise methods",
                    "content": ""
                },
                {
                    "name": "band",
                    "content": "$x->band($y);               # bitwise and\n"
                },
                {
                    "name": "bior",
                    "content": "$x->bior($y);               # bitwise inclusive or\n"
                },
                {
                    "name": "bxor",
                    "content": "$x->bxor($y);               # bitwise exclusive or\n"
                },
                {
                    "name": "bnot",
                    "content": "$x->bnot();                 # bitwise not (two's complement)\n\nTwo's complement (bitwise not). This is equivalent to, but faster than,\n\n$x->binc()->bneg();\n"
                },
                {
                    "name": "Rounding methods",
                    "content": ""
                },
                {
                    "name": "round",
                    "content": "$x->round($A,$P,$roundmode);\n\nRound $x to accuracy $A or precision $P using the round mode $roundmode.\n"
                },
                {
                    "name": "bround",
                    "content": "$x->bround($N);               # accuracy: preserve $N digits\n\nRounds $x to an accuracy of $N digits.\n"
                },
                {
                    "name": "bfround",
                    "content": "$x->bfround($N);\n\nRounds to a multiple of 10$N. Examples:\n\nInput            N          Result\n\n123456.123456    3          123500\n123456.123456    2          123450\n123456.123456   -2          123456.12\n123456.123456   -3          123456.123\n"
                },
                {
                    "name": "bfloor",
                    "content": "$x->bfloor();\n\nRound $x towards minus infinity, i.e., set $x to the largest integer less than or equal to\n$x.\n"
                },
                {
                    "name": "bceil",
                    "content": "$x->bceil();\n\nRound $x towards plus infinity, i.e., set $x to the smallest integer greater than or equal\nto $x).\n"
                },
                {
                    "name": "bint",
                    "content": "$x->bint();\n\nRound $x towards zero.\n"
                },
                {
                    "name": "Other mathematical methods",
                    "content": ""
                },
                {
                    "name": "bgcd",
                    "content": "$x -> bgcd($y);             # GCD of $x and $y\n$x -> bgcd($y, $z, ...);    # GCD of $x, $y, $z, ...\n\nReturns the greatest common divisor (GCD).\n"
                },
                {
                    "name": "blcm",
                    "content": "$x -> blcm($y);             # LCM of $x and $y\n$x -> blcm($y, $z, ...);    # LCM of $x, $y, $z, ...\n\nReturns the least common multiple (LCM).\n"
                },
                {
                    "name": "Object property methods",
                    "content": ""
                },
                {
                    "name": "sign",
                    "content": "$x->sign();\n\nReturn the sign, of $x, meaning either \"+\", \"-\", \"-inf\", \"+inf\" or NaN.\n\nIf you want $x to have a certain sign, use one of the following methods:\n\n$x->babs();                 # '+'\n$x->babs()->bneg();         # '-'\n$x->bnan();                 # 'NaN'\n$x->binf();                 # '+inf'\n$x->binf('-');              # '-inf'\n"
                },
                {
                    "name": "digit",
                    "content": "$x->digit($n);       # return the nth digit, counting from right\n\nIf $n is negative, returns the digit counting from left.\n"
                },
                {
                    "name": "digitsum",
                    "content": "$x->digitsum();\n\nComputes the sum of the base 10 digits and returns it.\n"
                },
                {
                    "name": "bdigitsum",
                    "content": "$x->bdigitsum();\n\nComputes the sum of the base 10 digits and assigns the result to the invocand.\n"
                },
                {
                    "name": "length",
                    "content": "$x->length();\n($xl, $fl) = $x->length();\n\nReturns the number of digits in the decimal representation of the number. In list context,\nreturns the length of the integer and fraction part. For Math::BigInt objects, the length of\nthe fraction part is always 0.\n\nThe following probably doesn't do what you expect:\n\n$c = Math::BigInt->new(123);\nprint $c->length(),\"\\n\";                # prints 30\n\nIt prints both the number of digits in the number and in the fraction part since print calls\n\"length()\" in list context. Use something like:\n\nprint scalar $c->length(),\"\\n\";         # prints 3\n"
                },
                {
                    "name": "mantissa",
                    "content": "$x->mantissa();\n\nReturn the signed mantissa of $x as a Math::BigInt.\n"
                },
                {
                    "name": "exponent",
                    "content": "$x->exponent();\n\nReturn the exponent of $x as a Math::BigInt.\n"
                },
                {
                    "name": "parts",
                    "content": "$x->parts();\n\nReturns the significand (mantissa) and the exponent as integers. In Math::BigFloat, both are\nreturned as Math::BigInt objects.\n"
                },
                {
                    "name": "sparts",
                    "content": "Returns the significand (mantissa) and the exponent as integers. In scalar context, only the\nsignificand is returned. The significand is the integer with the smallest absolute value.\nThe output of \"sparts()\" corresponds to the output from \"bsstr()\".\n\nIn Math::BigInt, this method is identical to \"parts()\".\n"
                },
                {
                    "name": "nparts",
                    "content": "Returns the significand (mantissa) and exponent corresponding to normalized notation. In\nscalar context, only the significand is returned. For finite non-zero numbers, the\nsignificand's absolute value is greater than or equal to 1 and less than 10. The output of\n\"nparts()\" corresponds to the output from \"bnstr()\". In Math::BigInt, if the significand can\nnot be represented as an integer, upgrading is performed or NaN is returned.\n"
                },
                {
                    "name": "eparts",
                    "content": "Returns the significand (mantissa) and exponent corresponding to engineering notation. In\nscalar context, only the significand is returned. For finite non-zero numbers, the\nsignificand's absolute value is greater than or equal to 1 and less than 1000, and the\nexponent is a multiple of 3. The output of \"eparts()\" corresponds to the output from\n\"bestr()\". In Math::BigInt, if the significand can not be represented as an integer,\nupgrading is performed or NaN is returned.\n"
                },
                {
                    "name": "dparts",
                    "content": "Returns the integer part and the fraction part. If the fraction part can not be represented\nas an integer, upgrading is performed or NaN is returned. The output of \"dparts()\"\ncorresponds to the output from \"bdstr()\".\n"
                },
                {
                    "name": "fparts",
                    "content": "Returns the smallest possible numerator and denominator so that the numerator divided by the\ndenominator gives back the original value. For finite numbers, both values are integers.\nMnemonic: fraction.\n"
                },
                {
                    "name": "numerator",
                    "content": "Together with \"denominator()\", returns the smallest integers so that the numerator divided\nby the denominator reproduces the original value. With Math::BigInt, numerator() simply\nreturns a copy of the invocand.\n"
                },
                {
                    "name": "denominator",
                    "content": "Together with \"numerator()\", returns the smallest integers so that the numerator divided by\nthe denominator reproduces the original value. With Math::BigInt, denominator() always\nreturns either a 1 or a NaN.\n"
                },
                {
                    "name": "String conversion methods",
                    "content": ""
                },
                {
                    "name": "bstr",
                    "content": "Returns a string representing the number using decimal notation. In Math::BigFloat, the\noutput is zero padded according to the current accuracy or precision, if any of those are\ndefined.\n"
                },
                {
                    "name": "bsstr",
                    "content": "Returns a string representing the number using scientific notation where both the\nsignificand (mantissa) and the exponent are integers. The output corresponds to the output\nfrom \"sparts()\".\n\n123 is returned as \"123e+0\"\n1230 is returned as \"123e+1\"\n12300 is returned as \"123e+2\"\n12000 is returned as \"12e+3\"\n10000 is returned as \"1e+4\"\n"
                },
                {
                    "name": "bnstr",
                    "content": "Returns a string representing the number using normalized notation, the most common variant\nof scientific notation. For finite non-zero numbers, the absolute value of the significand\nis greater than or equal to 1 and less than 10. The output corresponds to the output from\n\"nparts()\".\n\n123 is returned as \"1.23e+2\"\n1230 is returned as \"1.23e+3\"\n12300 is returned as \"1.23e+4\"\n12000 is returned as \"1.2e+4\"\n10000 is returned as \"1e+4\"\n"
                },
                {
                    "name": "bestr",
                    "content": "Returns a string representing the number using engineering notation. For finite non-zero\nnumbers, the absolute value of the significand is greater than or equal to 1 and less than\n1000, and the exponent is a multiple of 3. The output corresponds to the output from\n\"eparts()\".\n\n123 is returned as \"123e+0\"\n1230 is returned as \"1.23e+3\"\n12300 is returned as \"12.3e+3\"\n12000 is returned as \"12e+3\"\n10000 is returned as \"10e+3\"\n"
                },
                {
                    "name": "bdstr",
                    "content": "Returns a string representing the number using decimal notation. The output corresponds to\nthe output from \"dparts()\".\n\n123 is returned as \"123\"\n1230 is returned as \"1230\"\n12300 is returned as \"12300\"\n12000 is returned as \"12000\"\n10000 is returned as \"10000\"\n"
                },
                {
                    "name": "to_hex",
                    "content": "$x->tohex();\n\nReturns a hexadecimal string representation of the number. See also fromhex().\n"
                },
                {
                    "name": "to_bin",
                    "content": "$x->tobin();\n\nReturns a binary string representation of the number. See also frombin().\n"
                },
                {
                    "name": "to_oct",
                    "content": "$x->tooct();\n\nReturns an octal string representation of the number. See also fromoct().\n"
                },
                {
                    "name": "to_bytes",
                    "content": "$x = Math::BigInt->new(\"1667327589\");\n$s = $x->tobytes();                    # $s = \"cafe\"\n\nReturns a byte string representation of the number using big endian byte order. The invocand\nmust be a non-negative, finite integer. See also frombytes().\n"
                },
                {
                    "name": "to_base",
                    "content": "$x = Math::BigInt->new(\"250\");\n$x->tobase(2);     # returns \"11111010\"\n$x->tobase(8);     # returns \"372\"\n$x->tobase(16);    # returns \"fa\"\n\nReturns a string representation of the number in the given base. If a collation sequence is\ngiven, the collation sequence determines which characters are used in the output.\n\nHere are some more examples\n\n$x = Math::BigInt->new(\"16\")->tobase(3);       # returns \"121\"\n$x = Math::BigInt->new(\"44027\")->tobase(36);   # returns \"XYZ\"\n$x = Math::BigInt->new(\"58314\")->tobase(42);   # returns \"Why\"\n$x = Math::BigInt->new(\"4\")->tobase(2, \"-|\");  # returns \"|--\"\n\nSee frombase() for information and examples.\n"
                },
                {
                    "name": "to_base_num",
                    "content": "Converts the given number to the given base. This method is equivalent to \"tobase()\", but\nreturns numbers in an array rather than characters in a string. In the output, the first\nelement is the most significant. Unlike \"tobase()\", all input values may be arbitrarily\nlarge.\n\n$x = Math::BigInt->new(13);\n$x->tobasenum(2);                         # returns [1, 1, 0, 1]\n\n$x = Math::BigInt->new(65191);\n$x->tobasenum(128);                       # returns [3, 125, 39]\n"
                },
                {
                    "name": "as_hex",
                    "content": "$x->ashex();\n\nAs, \"tohex()\", but with a \"0x\" prefix.\n"
                },
                {
                    "name": "as_bin",
                    "content": "$x->asbin();\n\nAs, \"tobin()\", but with a \"0b\" prefix.\n"
                },
                {
                    "name": "as_oct",
                    "content": "$x->asoct();\n\nAs, \"tooct()\", but with a \"0\" prefix.\n"
                },
                {
                    "name": "as_bytes",
                    "content": "This is just an alias for \"tobytes()\".\n"
                },
                {
                    "name": "Other conversion methods",
                    "content": ""
                },
                {
                    "name": "numify",
                    "content": "print $x->numify();\n\nReturns a Perl scalar from $x. It is used automatically whenever a scalar is needed, for\ninstance in array index operations.\n"
                },
                {
                    "name": "Utility methods",
                    "content": "These utility methods are made public\n"
                },
                {
                    "name": "dec_str_to_dec_flt_str",
                    "content": "Takes a string representing any valid number using decimal notation and converts it to a\nstring representing the same number using decimal floating point notation. The output\nconsists of five parts joined together: the sign of the significand, the absolute value of\nthe significand as the smallest possible integer, the letter \"e\", the sign of the exponent,\nand the absolute value of the exponent. If the input is invalid, nothing is returned.\n\n$str2 = $class -> decstrtodecfltstr($str1);\n\nSome examples\n\nInput           Output\n31400.00e-4     +314e-2\n-0.00012300e8   -123e+2\n0               +0e+0\n"
                },
                {
                    "name": "hex_str_to_dec_flt_str",
                    "content": "Takes a string representing any valid number using hexadecimal notation and converts it to a\nstring representing the same number using decimal floating point notation. The output has\nthe same format as that of \"decstrtodecfltstr()\".\n\n$str2 = $class -> hexstrtodecfltstr($str1);\n\nSome examples\n\nInput           Output\n0xff            +255e+0\n\nSome examples\n"
                },
                {
                    "name": "oct_str_to_dec_flt_str",
                    "content": "Takes a string representing any valid number using octal notation and converts it to a\nstring representing the same number using decimal floating point notation. The output has\nthe same format as that of \"decstrtodecfltstr()\".\n\n$str2 = $class -> octstrtodecfltstr($str1);\n"
                },
                {
                    "name": "bin_str_to_dec_flt_str",
                    "content": "Takes a string representing any valid number using binary notation and converts it to a\nstring representing the same number using decimal floating point notation. The output has\nthe same format as that of \"decstrtodecfltstr()\".\n\n$str2 = $class -> binstrtodecfltstr($str1);\n"
                },
                {
                    "name": "dec_str_to_dec_str",
                    "content": "Takes a string representing any valid number using decimal notation and converts it to a\nstring representing the same number using decimal notation. If the number represents an\ninteger, the output consists of a sign and the absolute value. If the number represents a\nnon-integer, the output consists of a sign, the integer part of the number, the decimal\npoint \".\", and the fraction part of the number without any trailing zeros. If the input is\ninvalid, nothing is returned.\n"
                },
                {
                    "name": "hex_str_to_dec_str",
                    "content": "Takes a string representing any valid number using hexadecimal notation and converts it to a\nstring representing the same number using decimal notation. The output has the same format\nas that of \"decstrtodecstr()\".\n"
                },
                {
                    "name": "oct_str_to_dec_str",
                    "content": "Takes a string representing any valid number using octal notation and converts it to a\nstring representing the same number using decimal notation. The output has the same format\nas that of \"decstrtodecstr()\".\n"
                },
                {
                    "name": "bin_str_to_dec_str",
                    "content": "Takes a string representing any valid number using binary notation and converts it to a\nstring representing the same number using decimal notation. The output has the same format\nas that of \"decstrtodecstr()\".\n\nACCURACY and PRECISION\nMath::BigInt and Math::BigFloat have full support for accuracy and precision based rounding,\nboth automatically after every operation, as well as manually.\n\nThis section describes the accuracy/precision handling in Math::BigInt and Math::BigFloat as it\nused to be and as it is now, complete with an explanation of all terms and abbreviations.\n\nNot yet implemented things (but with correct description) are marked with '!', things that need\nto be answered are marked with '?'.\n\nIn the next paragraph follows a short description of terms used here (because these may differ\nfrom terms used by others people or documentation).\n\nDuring the rest of this document, the shortcuts A (for accuracy), P (for precision), F\n(fallback) and R (rounding mode) are be used.\n"
                },
                {
                    "name": "Precision P",
                    "content": "Precision is a fixed number of digits before (positive) or after (negative) the decimal point.\nFor example, 123.45 has a precision of -2. 0 means an integer like 123 (or 120). A precision of\n2 means at least two digits to the left of the decimal point are zero, so 123 with P = 1 becomes\n120. Note that numbers with zeros before the decimal point may have different precisions,\nbecause 1200 can have P = 0, 1 or 2 (depending on what the initial value was). It could also\nhave p < 0, when the digits after the decimal point are zero.\n\nThe string output (of floating point numbers) is padded with zeros:\n\nInitial value    P      A       Result          String\n------------------------------------------------------------\n1234.01         -3              1000            1000\n1234            -2              1200            1200\n1234.5          -1              1230            1230\n1234.001         1              1234            1234.0\n1234.01          0              1234            1234\n1234.01          2              1234.01         1234.01\n1234.01          5              1234.01         1234.01000\n\nFor Math::BigInt objects, no padding occurs.\n"
                },
                {
                    "name": "Accuracy A",
                    "content": "Number of significant digits. Leading zeros are not counted. A number may have an accuracy\ngreater than the non-zero digits when there are zeros in it or trailing zeros. For example,\n123.456 has A of 6, 10203 has 5, 123.0506 has 7, 123.45000 has 8 and 0.000123 has 3.\n\nThe string output (of floating point numbers) is padded with zeros:\n\nInitial value    P      A       Result          String\n------------------------------------------------------------\n1234.01                 3       1230            1230\n1234.01                 6       1234.01         1234.01\n1234.1                  8       1234.1          1234.1000\n\nFor Math::BigInt objects, no padding occurs.\n"
                },
                {
                    "name": "Fallback F",
                    "content": "When both A and P are undefined, this is used as a fallback accuracy when dividing numbers.\n"
                },
                {
                    "name": "Rounding mode R",
                    "content": "When rounding a number, different 'styles' or 'kinds' of rounding are possible. (Note that\nrandom rounding, as in Math::Round, is not implemented.)\n\nDirected rounding\nThese round modes always round in the same direction.\n\n'trunc'\nRound towards zero. Remove all digits following the rounding place, i.e., replace them with\nzeros. Thus, 987.65 rounded to tens (P=1) becomes 980, and rounded to the fourth significant\ndigit becomes 987.6 (A=4). 123.456 rounded to the second place after the decimal point\n(P=-2) becomes 123.46. This corresponds to the IEEE 754 rounding mode 'roundTowardZero'.\n\nRounding to nearest\nThese rounding modes round to the nearest digit. They differ in how they determine which way to\nround in the ambiguous case when there is a tie.\n\n'even'\nRound towards the nearest even digit, e.g., when rounding to nearest integer, -5.5 becomes\n-6, 4.5 becomes 4, but 4.501 becomes 5. This corresponds to the IEEE 754 rounding mode\n'roundTiesToEven'.\n\n'odd'\nRound towards the nearest odd digit, e.g., when rounding to nearest integer, 4.5 becomes 5,\n-5.5 becomes -5, but 5.501 becomes 6. This corresponds to the IEEE 754 rounding mode\n'roundTiesToOdd'.\n\n'+inf'\nRound towards plus infinity, i.e., always round up. E.g., when rounding to the nearest\ninteger, 4.5 becomes 5, -5.5 becomes -5, and 4.501 also becomes 5. This corresponds to the\nIEEE 754 rounding mode 'roundTiesToPositive'.\n\n'-inf'\nRound towards minus infinity, i.e., always round down. E.g., when rounding to the nearest\ninteger, 4.5 becomes 4, -5.5 becomes -6, but 4.501 becomes 5. This corresponds to the IEEE\n754 rounding mode 'roundTiesToNegative'.\n\n'zero'\nRound towards zero, i.e., round positive numbers down and negative numbers up. E.g., when\nrounding to the nearest integer, 4.5 becomes 4, -5.5 becomes -5, but 4.501 becomes 5. This\ncorresponds to the IEEE 754 rounding mode 'roundTiesToZero'.\n\n'common'\nRound away from zero, i.e., round to the number with the largest absolute value. E.g., when\nrounding to the nearest integer, -1.5 becomes -2, 1.5 becomes 2 and 1.49 becomes 1. This\ncorresponds to the IEEE 754 rounding mode 'roundTiesToAway'.\n\nThe handling of A & P in MBI/MBF (the old core code shipped with Perl versions <= 5.7.2) is like\nthis:\n\nPrecision\n* bfround($p) is able to round to $p number of digits after the decimal\npoint\n* otherwise P is unused\n\nAccuracy (significant digits)\n* bround($a) rounds to $a significant digits\n* only bdiv() and bsqrt() take A as (optional) parameter\n+ other operations simply create the same number (bneg etc), or\nmore (bmul) of digits\n+ rounding/truncating is only done when explicitly calling one\nof bround or bfround, and never for Math::BigInt (not implemented)\n* bsqrt() simply hands its accuracy argument over to bdiv.\n* the documentation and the comment in the code indicate two\ndifferent ways on how bdiv() determines the maximum number\nof digits it should calculate, and the actual code does yet\nanother thing\nPOD:\nmax($Math::BigFloat::divscale,length(dividend)+length(divisor))\nComment:\nresult has at most max(scale, length(dividend), length(divisor)) digits\nActual code:\nscale = max(scale, length(dividend)-1,length(divisor)-1);\nscale += length(divisor) - length(dividend);\nSo for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10\nSo for lx = 3, ly = 9, scale = 10, scale will actually be 16\n(10+9-3). Actually, the 'difference' added to the scale is cal-\nculated from the number of \"significant digits\" in dividend and\ndivisor, which is derived by looking at the length of the man-\ntissa. Which is wrong, since it includes the + sign (oops) and\nactually gets 2 for '+100' and 4 for '+101'. Oops again. Thus\n124/3 with divscale=1 will get you '41.3' based on the strange\nassumption that 124 has 3 significant digits, while 120/7 will\nget you '17', not '17.1' since 120 is thought to have 2 signif-\nicant digits. The rounding after the division then uses the\nremainder and $y to determine whether it must round up or down.\n?  I have no idea which is the right way. That's why I used a slightly more\n?  simple scheme and tweaked the few failing testcases to match it.\n\nThis is how it works now:\n\nSetting/Accessing\n* You can set the A global via Math::BigInt->accuracy() or\nMath::BigFloat->accuracy() or whatever class you are using.\n* You can also set P globally by using Math::SomeClass->precision()\nlikewise.\n* Globals are classwide, and not inherited by subclasses.\n* to undefine A, use Math::SomeClass->accuracy(undef);\n* to undefine P, use Math::SomeClass->precision(undef);\n* Setting Math::SomeClass->accuracy() clears automatically\nMath::SomeClass->precision(), and vice versa.\n* To be valid, A must be > 0, P can have any value.\n* If P is negative, this means round to the P'th place to the right of the\ndecimal point; positive values mean to the left of the decimal point.\nP of 0 means round to integer.\n* to find out the current global A, use Math::SomeClass->accuracy()\n* to find out the current global P, use Math::SomeClass->precision()\n* use $x->accuracy() respective $x->precision() for the local\nsetting of $x.\n* Please note that $x->accuracy() respective $x->precision()\nreturn eventually defined global A or P, when $x's A or P is not\nset.\n\nCreating numbers\n* When you create a number, you can give the desired A or P via:\n$x = Math::BigInt->new($number,$A,$P);\n* Only one of A or P can be defined, otherwise the result is NaN\n* If no A or P is give ($x = Math::BigInt->new($number) form), then the\nglobals (if set) will be used. Thus changing the global defaults later on\nwill not change the A or P of previously created numbers (i.e., A and P of\n$x will be what was in effect when $x was created)\n* If given undef for A and P, NO rounding will occur, and the globals will\nNOT be used. This is used by subclasses to create numbers without\nsuffering rounding in the parent. Thus a subclass is able to have its own\nglobals enforced upon creation of a number by using\n$x = Math::BigInt->new($number,undef,undef):\n\nuse Math::BigInt::SomeSubclass;\nuse Math::BigInt;\n\nMath::BigInt->accuracy(2);\nMath::BigInt::SomeSubclass->accuracy(3);\n$x = Math::BigInt::SomeSubclass->new(1234);\n\n$x is now 1230, and not 1200. A subclass might choose to implement\nthis otherwise, e.g. falling back to the parent's A and P.\n\nUsage\n* If A or P are enabled/defined, they are used to round the result of each\noperation according to the rules below\n* Negative P is ignored in Math::BigInt, since Math::BigInt objects never\nhave digits after the decimal point\n* Math::BigFloat uses Math::BigInt internally, but setting A or P inside\nMath::BigInt as globals does not tamper with the parts of a Math::BigFloat.\nA flag is used to mark all Math::BigFloat numbers as 'never round'.\n\nPrecedence\n* It only makes sense that a number has only one of A or P at a time.\nIf you set either A or P on one object, or globally, the other one will\nbe automatically cleared.\n* If two objects are involved in an operation, and one of them has A in\neffect, and the other P, this results in an error (NaN).\n* A takes precedence over P (Hint: A comes before P).\nIf neither of them is defined, nothing is used, i.e. the result will have\nas many digits as it can (with an exception for bdiv/bsqrt) and will not\nbe rounded.\n* There is another setting for bdiv() (and thus for bsqrt()). If neither of\nA or P is defined, bdiv() will use a fallback (F) of $divscale digits.\nIf either the dividend's or the divisor's mantissa has more digits than\nthe value of F, the higher value will be used instead of F.\nThis is to limit the digits (A) of the result (just consider what would\nhappen with unlimited A and P in the case of 1/3 :-)\n* bdiv will calculate (at least) 4 more digits than required (determined by\nA, P or F), and, if F is not used, round the result\n(this will still fail in the case of a result like 0.12345000000001 with A\nor P of 5, but this can not be helped - or can it?)\n* Thus you can have the math done by on Math::Big* class in two modi:\n+ never round (this is the default):\nThis is done by setting A and P to undef. No math operation\nwill round the result, with bdiv() and bsqrt() as exceptions to guard\nagainst overflows. You must explicitly call bround(), bfround() or\nround() (the latter with parameters).\nNote: Once you have rounded a number, the settings will 'stick' on it\nand 'infect' all other numbers engaged in math operations with it, since\nlocal settings have the highest precedence. So, to get SaferRound[tm],\nuse a copy() before rounding like this:\n\n$x = Math::BigFloat->new(12.34);\n$y = Math::BigFloat->new(98.76);\n$z = $x * $y;                           # 1218.6984\nprint $x->copy()->bround(3);            # 12.3 (but A is now 3!)\n$z = $x * $y;                           # still 1218.6984, without\n# copy would have been 1210!\n\n+ round after each op:\nAfter each single operation (except for testing like iszero()), the\nmethod round() is called and the result is rounded appropriately. By\nsetting proper values for A and P, you can have all-the-same-A or\nall-the-same-P modes. For example, Math::Currency might set A to undef,\nand P to -2, globally.\n\n?Maybe an extra option that forbids local A & P settings would be in order,\n?so that intermediate rounding does not 'poison' further math?\n\nOverriding globals\n* you will be able to give A, P and R as an argument to all the calculation\nroutines; the second parameter is A, the third one is P, and the fourth is\nR (shift right by one for binary operations like badd). P is used only if\nthe first parameter (A) is undefined. These three parameters override the\nglobals in the order detailed as follows, i.e. the first defined value\nwins:\n(local: per object, global: global default, parameter: argument to sub)\n+ parameter A\n+ parameter P\n+ local A (if defined on both of the operands: smaller one is taken)\n+ local P (if defined on both of the operands: bigger one is taken)\n+ global A\n+ global P\n+ global F\n* bsqrt() will hand its arguments to bdiv(), as it used to, only now for two\narguments (A and P) instead of one\n\nLocal settings\n* You can set A or P locally by using $x->accuracy() or\n$x->precision()\nand thus force different A and P for different objects/numbers.\n* Setting A or P this way immediately rounds $x to the new value.\n* $x->accuracy() clears $x->precision(), and vice versa.\n\nRounding\n* the rounding routines will use the respective global or local settings.\nbround() is for accuracy rounding, while bfround() is for precision\n* the two rounding functions take as the second parameter one of the\nfollowing rounding modes (R):\n'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common'\n* you can set/get the global R by using Math::SomeClass->roundmode()\nor by setting $Math::SomeClass::roundmode\n* after each operation, $result->round() is called, and the result may\neventually be rounded (that is, if A or P were set either locally,\nglobally or as parameter to the operation)\n* to manually round a number, call $x->round($A,$P,$roundmode);\nthis will round the number by using the appropriate rounding function\nand then normalize it.\n* rounding modifies the local settings of the number:\n\n$x = Math::BigFloat->new(123.456);\n$x->accuracy(5);\n$x->bround(4);\n\nHere 4 takes precedence over 5, so 123.5 is the result and $x->accuracy()\nwill be 4 from now on.\n\nDefault values\n* R: 'even'\n* F: 40\n* A: undef\n* P: undef\n\nRemarks\n* The defaults are set up so that the new code gives the same results as\nthe old code (except in a few cases on bdiv):\n+ Both A and P are undefined and thus will not be used for rounding\nafter each operation.\n+ round() is thus a no-op, unless given extra parameters A and P\n"
                }
            ]
        },
        "Infinity and Not a Number": {
            "content": "While Math::BigInt has extensive handling of inf and NaN, certain quirks remain.\n",
            "subsections": [
                {
                    "name": "oct",
                    "content": "These perl routines currently (as of Perl v.5.8.6) cannot handle passed inf.\n\nte@linux:~> perl -wle 'print 2  3333'\nInf\nte@linux:~> perl -wle 'print 2  3333 == 2  3333'\n1\nte@linux:~> perl -wle 'print oct(2  3333)'\n0\nte@linux:~> perl -wle 'print hex(2  3333)'\nIllegal hexadecimal digit 'I' ignored at -e line 1.\n0\n\nThe same problems occur if you pass them Math::BigInt->binf() objects. Since overloading\nthese routines is not possible, this cannot be fixed from Math::BigInt.\n"
                }
            ]
        },
        "INTERNALS": {
            "content": "You should neither care about nor depend on the internal representation; it might change without\nnotice. Use ONLY method calls like \"$x->sign();\" instead relying on the internal representation.\n\nMATH LIBRARY\nThe mathematical computations are performed by a backend library. It is not required to specify\nwhich backend library to use, but some backend libraries are much faster than the default\nlibrary.\n\nThe default library\nThe default library is Math::BigInt::Calc, which is implemented in pure Perl and hence does not\nrequire a compiler.\n\nSpecifying a library\nThe simple case\n\nuse Math::BigInt;\n\nis equivalent to saying\n\nuse Math::BigInt try => 'Calc';\n\nYou can use a different backend library with, e.g.,\n\nuse Math::BigInt try => 'GMP';\n\nwhich attempts to load the Math::BigInt::GMP library, and falls back to the default library if\nthe specified library can't be loaded.\n\nMultiple libraries can be specified by separating them by a comma, e.g.,\n\nuse Math::BigInt try => 'GMP,Pari';\n\nIf you request a specific set of libraries and do not allow fallback to the default library,\nspecify them using \"only\",\n\nuse Math::BigInt only => 'GMP,Pari';\n\nIf you prefer a specific set of libraries, but want to see a warning if the fallback library is\nused, specify them using \"lib\",\n\nuse Math::BigInt lib => 'GMP,Pari';\n\nThe following first tries to find Math::BigInt::Foo, then Math::BigInt::Bar, and if this also\nfails, reverts to Math::BigInt::Calc:\n\nuse Math::BigInt try => 'Foo,Math::BigInt::Bar';\n\nWhich library to use?\nNote: General purpose packages should not be explicit about the library to use; let the script\nauthor decide which is best.\n\nMath::BigInt::GMP, Math::BigInt::Pari, and Math::BigInt::GMPz are in cases involving big numbers\nmuch faster than Math::BigInt::Calc. However these libraries are slower when dealing with very\nsmall numbers (less than about 20 digits) and when converting very large numbers to decimal (for\ninstance for printing, rounding, calculating their length in decimal etc.).\n\nSo please select carefully what library you want to use.\n\nDifferent low-level libraries use different formats to store the numbers, so mixing them won't\nwork. You should not depend on the number having a specific internal format.\n\nSee the respective math library module documentation for further details.\n\nLoading multiple libraries\nThe first library that is successfully loaded is the one that will be used. Any further attempts\nat loading a different module will be ignored. This is to avoid the situation where module A\nrequires math library X, and module B requires math library Y, causing modules A and B to be\nincompatible. For example,\n\nuse Math::BigInt;                   # loads default \"Calc\"\nuse Math::BigFloat only => \"GMP\";   # ignores \"GMP\"\n\nSIGN\nThe sign is either '+', '-', 'NaN', '+inf' or '-inf'.\n\nA sign of 'NaN' is used to represent the result when input arguments are not numbers or as a\nresult of 0/0. '+inf' and '-inf' represent plus respectively minus infinity. You get '+inf' when\ndividing a positive number by 0, and '-inf' when dividing any negative number by 0.\n",
            "subsections": []
        },
        "EXAMPLES": {
            "content": "use Math::BigInt;\n\nsub bigint { Math::BigInt->new(shift); }\n\n$x = Math::BigInt->bstr(\"1234\")       # string \"1234\"\n$x = \"$x\";                            # same as bstr()\n$x = Math::BigInt->bneg(\"1234\");      # Math::BigInt \"-1234\"\n$x = Math::BigInt->babs(\"-12345\");    # Math::BigInt \"12345\"\n$x = Math::BigInt->bnorm(\"-0.00\");    # Math::BigInt \"0\"\n$x = bigint(1) + bigint(2);           # Math::BigInt \"3\"\n$x = bigint(1) + \"2\";                 # ditto (\"2\" becomes a Math::BigInt)\n$x = bigint(1);                       # Math::BigInt \"1\"\n$x = $x + 5 / 2;                      # Math::BigInt \"3\"\n$x = $x  3;                         # Math::BigInt \"27\"\n$x *= 2;                              # Math::BigInt \"54\"\n$x = Math::BigInt->new(0);            # Math::BigInt \"0\"\n$x--;                                 # Math::BigInt \"-1\"\n$x = Math::BigInt->badd(4,5)          # Math::BigInt \"9\"\nprint $x->bsstr();                    # 9e+0\n\nExamples for rounding:\n\nuse Math::BigFloat;\nuse Test::More;\n\n$x = Math::BigFloat->new(123.4567);\n$y = Math::BigFloat->new(123.456789);\nMath::BigFloat->accuracy(4);          # no more A than 4\n\nis ($x->copy()->bround(),123.4);      # even rounding\nprint $x->copy()->bround(),\"\\n\";      # 123.4\nMath::BigFloat->roundmode('odd');    # round to odd\nprint $x->copy()->bround(),\"\\n\";      # 123.5\nMath::BigFloat->accuracy(5);          # no more A than 5\nMath::BigFloat->roundmode('odd');    # round to odd\nprint $x->copy()->bround(),\"\\n\";      # 123.46\n$y = $x->copy()->bround(4),\"\\n\";      # A = 4: 123.4\nprint \"$y, \",$y->accuracy(),\"\\n\";     # 123.4, 4\n\nMath::BigFloat->accuracy(undef);      # A not important now\nMath::BigFloat->precision(2);         # P important\nprint $x->copy()->bnorm(),\"\\n\";       # 123.46\nprint $x->copy()->bround(),\"\\n\";      # 123.46\n\nExamples for converting:\n\nmy $x = Math::BigInt->new('0b1'.'01' x 123);\nprint \"bin: \",$x->asbin(),\" hex:\",$x->ashex(),\" dec: \",$x,\"\\n\";\n",
            "subsections": []
        },
        "NUMERIC LITERALS": {
            "content": "After \"use Math::BigInt ':constant'\" all numeric literals in the given scope are converted to\n\"Math::BigInt\" objects. This conversion happens at compile time. Every non-integer is convert to\na NaN.\n\nFor example,\n\nperl -MMath::BigInt=:constant -le 'print 2150'\n\nprints the exact value of \"2150\". Note that without conversion of constants to objects the\nexpression \"2150\" is calculated using Perl scalars, which leads to an inaccurate result.\n\nPlease note that strings are not affected, so that\n\nuse Math::BigInt qw/:constant/;\n\n$x = \"1234567890123456789012345678901234567890\"\n+ \"123456789123456789\";\n\ndoes give you what you expect. You need an explicit Math::BigInt->new() around at least one of\nthe operands. You should also quote large constants to prevent loss of precision:\n\nuse Math::BigInt;\n\n$x = Math::BigInt->new(\"1234567889123456789123456789123456789\");\n\nWithout the quotes Perl first converts the large number to a floating point constant at compile\ntime, and then converts the result to a Math::BigInt object at run time, which results in an\ninaccurate result.\n",
            "subsections": [
                {
                    "name": "Hexadecimal, octal, and binary floating point literals",
                    "content": "Perl (and this module) accepts hexadecimal, octal, and binary floating point literals, but use\nthem with care with Perl versions before v5.32.0, because some versions of Perl silently give\nthe wrong result. Below are some examples of different ways to write the number decimal 314.\n\nHexadecimal floating point literals:\n\n0x1.3ap+8         0X1.3AP+8\n0x1.3ap8          0X1.3AP8\n0x13a0p-4         0X13A0P-4\n\nOctal floating point literals (with \"0\" prefix):\n\n01.164p+8         01.164P+8\n01.164p8          01.164P8\n011640p-4         011640P-4\n\nOctal floating point literals (with \"0o\" prefix) (requires v5.34.0):\n\n0o1.164p+8        0O1.164P+8\n0o1.164p8         0O1.164P8\n0o11640p-4        0O11640P-4\n\nBinary floating point literals:\n\n0b1.0011101p+8    0B1.0011101P+8\n0b1.0011101p8     0B1.0011101P8\n0b10011101000p-2  0B10011101000P-2\n"
                }
            ]
        },
        "PERFORMANCE": {
            "content": "Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x must be made in the\nsecond case. For long numbers, the copy can eat up to 20% of the work (in the case of\naddition/subtraction, less for multiplication/division). If $y is very small compared to $x, the\nform $x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes more time then\nthe actual addition.\n\nWith a technique called copy-on-write, the cost of copying with overload could be minimized or\neven completely avoided. A test implementation of COW did show performance gains for overloaded\nmath, but introduced a performance loss due to a constant overhead for all other operations. So\nMath::BigInt does currently not COW.\n\nThe rewritten version of this module (vs. v0.01) is slower on certain operations, like \"new()\",\n\"bstr()\" and \"numify()\". The reason are that it does now more work and handles much more cases.\nThe time spent in these operations is usually gained in the other math operations so that code\non the average should get (much) faster. If they don't, please contact the author.\n\nSome operations may be slower for small numbers, but are significantly faster for big numbers.\nOther operations are now constant (O(1), like \"bneg()\", \"babs()\" etc), instead of O(N) and thus\nnearly always take much less time. These optimizations were done on purpose.\n\nIf you find the Calc module to slow, try to install any of the replacement modules and see if\nthey help you.\n",
            "subsections": [
                {
                    "name": "Alternative math libraries",
                    "content": "You can use an alternative library to drive Math::BigInt. See the section \"MATH LIBRARY\" for\nmore information.\n\nFor more benchmark results see <http://bloodgate.com/perl/benchmarks.html>.\n"
                }
            ]
        },
        "SUBCLASSING": {
            "content": "",
            "subsections": [
                {
                    "name": "Subclassing Math::BigInt",
                    "content": "The basic design of Math::BigInt allows simple subclasses with very little work, as long as a\nfew simple rules are followed:\n\n*   The public API must remain consistent, i.e. if a sub-class is overloading addition, the\nsub-class must use the same name, in this case badd(). The reason for this is that\nMath::BigInt is optimized to call the object methods directly.\n\n*   The private object hash keys like \"$x->{sign}\" may not be changed, but additional keys can\nbe added, like \"$x->{custom}\".\n\n*   Accessor functions are available for all existing object hash keys and should be used\ninstead of directly accessing the internal hash keys. The reason for this is that\nMath::BigInt itself has a pluggable interface which permits it to support different storage\nmethods.\n\nMore complex sub-classes may have to replicate more of the logic internal of Math::BigInt if\nthey need to change more basic behaviors. A subclass that needs to merely change the output only\nneeds to overload \"bstr()\".\n\nAll other object methods and overloaded functions can be directly inherited from the parent\nclass.\n\nAt the very minimum, any subclass needs to provide its own \"new()\" and can store additional hash\nkeys in the object. There are also some package globals that must be defined, e.g.:\n\n# Globals\n$accuracy = undef;\n$precision = -2;       # round to 2 decimal places\n$roundmode = 'even';\n$divscale = 40;\n\nAdditionally, you might want to provide the following two globals to allow auto-upgrading and\nauto-downgrading to work correctly:\n\n$upgrade = undef;\n$downgrade = undef;\n\nThis allows Math::BigInt to correctly retrieve package globals from the subclass, like\n$SubClass::precision. See t/Math/BigInt/Subclass.pm or t/Math/BigFloat/SubClass.pm completely\nfunctional subclass examples.\n\nDon't forget to\n\nuse overload;\n\nin your subclass to automatically inherit the overloading from the parent. If you like, you can\nchange part of the overloading, look at Math::String for an example.\n"
                }
            ]
        },
        "UPGRADING": {
            "content": "When used like this:\n\nuse Math::BigInt upgrade => 'Foo::Bar';\n\ncertain operations 'upgrade' their calculation and thus the result to the class Foo::Bar.\nUsually this is used in conjunction with Math::BigFloat:\n\nuse Math::BigInt upgrade => 'Math::BigFloat';\n\nAs a shortcut, you can use the module bignum:\n\nuse bignum;\n\nAlso good for one-liners:\n\nperl -Mbignum -le 'print 2  255'\n\nThis makes it possible to mix arguments of different classes (as in 2.5 + 2) as well es preserve\naccuracy (as in sqrt(3)).\n\nBeware: This feature is not fully implemented yet.\n",
            "subsections": [
                {
                    "name": "Auto-upgrade",
                    "content": "The following methods upgrade themselves unconditionally; that is if upgrade is in effect, they\nalways hands up their work:\n\ndiv bsqrt blog bexp bpi bsin bcos batan batan2\n\nAll other methods upgrade themselves only when one (or all) of their arguments are of the class\nmentioned in $upgrade.\n"
                }
            ]
        },
        "EXPORTS": {
            "content": "\"Math::BigInt\" exports nothing by default, but can export the following methods:\n\nbgcd\nblcm\n",
            "subsections": []
        },
        "CAVEATS": {
            "content": "Some things might not work as you expect them. Below is documented what is known to be\ntroublesome:\n\nComparing numbers as strings\nBoth \"bstr()\" and \"bsstr()\" as well as stringify via overload drop the leading '+'. This is\nto be consistent with Perl and to make \"cmp\" (especially with overloading) to work as you\nexpect. It also solves problems with \"Test.pm\" and Test::More, which stringify arguments\nbefore comparing them.\n\nMark Biggar said, when asked about to drop the '+' altogether, or make only \"cmp\" work:\n\nI agree (with the first alternative), don't add the '+' on positive\nnumbers.  It's not as important anymore with the new internal form\nfor numbers.  It made doing things like abs and neg easier, but\nthose have to be done differently now anyway.\n\nSo, the following examples now works as expected:\n\nuse Test::More tests => 1;\nuse Math::BigInt;\n\nmy $x = Math::BigInt -> new(3*3);\nmy $y = Math::BigInt -> new(3*3);\n\nis($x,3*3, 'multiplication');\nprint \"$x eq 9\" if $x eq $y;\nprint \"$x eq 9\" if $x eq '9';\nprint \"$x eq 9\" if $x eq 3*3;\n\nAdditionally, the following still works:\n\nprint \"$x == 9\" if $x == $y;\nprint \"$x == 9\" if $x == 9;\nprint \"$x == 9\" if $x == 3*3;\n\nThere is now a \"bsstr()\" method to get the string in scientific notation aka 1e+2 instead of\n100. Be advised that overloaded 'eq' always uses bstr() for comparison, but Perl represents\nsome numbers as 100 and others as 1e+308. If in doubt, convert both arguments to\nMath::BigInt before comparing them as strings:\n\nuse Test::More tests => 3;\nuse Math::BigInt;\n\n$x = Math::BigInt->new('1e56'); $y = 1e56;\nis($x,$y);                     # fails\nis($x->bsstr(),$y);            # okay\n$y = Math::BigInt->new($y);\nis($x,$y);                     # okay\n\nAlternatively, simply use \"<=>\" for comparisons, this always gets it right. There is not yet\na way to get a number automatically represented as a string that matches exactly the way\nPerl represents it.\n\nSee also the section about \"Infinity and Not a Number\" for problems in comparing NaNs.\n",
            "subsections": [
                {
                    "name": "int",
                    "content": "\"int()\" returns (at least for Perl v5.7.1 and up) another Math::BigInt, not a Perl scalar:\n\n$x = Math::BigInt->new(123);\n$y = int($x);                           # 123 as a Math::BigInt\n$x = Math::BigFloat->new(123.45);\n$y = int($x);                           # 123 as a Math::BigFloat\n\nIf you want a real Perl scalar, use \"numify()\":\n\n$y = $x->numify();                      # 123 as a scalar\n\nThis is seldom necessary, though, because this is done automatically, like when you access\nan array:\n\n$z = $array[$x];                        # does work automatically\n\nModifying and =\nBeware of:\n\n$x = Math::BigFloat->new(5);\n$y = $x;\n\nThis makes a second reference to the same object and stores it in $y. Thus anything that\nmodifies $x (except overloaded operators) also modifies $y, and vice versa. Or in other\nwords, \"=\" is only safe if you modify your Math::BigInt objects only via overloaded math. As\nsoon as you use a method call it breaks:\n\n$x->bmul(2);\nprint \"$x, $y\\n\";       # prints '10, 10'\n\nIf you want a true copy of $x, use:\n\n$y = $x->copy();\n\nYou can also chain the calls like this, this first makes a copy and then multiply it by 2:\n\n$y = $x->copy()->bmul(2);\n\nSee also the documentation for overload.pm regarding \"=\".\n\nOverloading -$x\nThe following:\n\n$x = -$x;\n\nis slower than\n\n$x->bneg();\n\nsince overload calls \"sub($x,0,1);\" instead of \"neg($x)\". The first variant needs to\npreserve $x since it does not know that it later gets overwritten. This makes a copy of $x\nand takes O(N), but $x->bneg() is O(1).\n\nMixing different object types\nWith overloaded operators, it is the first (dominating) operand that determines which method\nis called. Here are some examples showing what actually gets called in various cases.\n\nuse Math::BigInt;\nuse Math::BigFloat;\n\n$mbf  = Math::BigFloat->new(5);\n$mbi2 = Math::BigInt->new(5);\n$mbi  = Math::BigInt->new(2);\n# what actually gets called:\n$float = $mbf + $mbi;           # $mbf->badd($mbi)\n$float = $mbf / $mbi;           # $mbf->bdiv($mbi)\n$integer = $mbi + $mbf;         # $mbi->badd($mbf)\n$integer = $mbi2 / $mbi;        # $mbi2->bdiv($mbi)\n$integer = $mbi2 / $mbf;        # $mbi2->bdiv($mbf)\n\nFor instance, Math::BigInt->bdiv() always returns a Math::BigInt, regardless of whether the\nsecond operant is a Math::BigFloat. To get a Math::BigFloat you either need to call the\noperation manually, make sure each operand already is a Math::BigFloat, or cast to that type\nvia Math::BigFloat->new():\n\n$float = Math::BigFloat->new($mbi2) / $mbi;     # = 2.5\n\nBeware of casting the entire expression, as this would cast the result, at which point it is\ntoo late:\n\n$float = Math::BigFloat->new($mbi2 / $mbi);     # = 2\n\nBeware also of the order of more complicated expressions like:\n\n$integer = ($mbi2 + $mbi) / $mbf;               # int / float => int\n$integer = $mbi2 / Math::BigFloat->new($mbi);   # ditto\n\nIf in doubt, break the expression into simpler terms, or cast all operands to the desired\nresulting type.\n\nScalar values are a bit different, since:\n\n$float = 2 + $mbf;\n$float = $mbf + 2;\n\nboth result in the proper type due to the way the overloaded math works.\n\nThis section also applies to other overloaded math packages, like Math::String.\n\nOne solution to you problem might be autoupgrading|upgrading. See the pragmas bignum, bigint\nand bigrat for an easy way to do this.\n"
                }
            ]
        },
        "BUGS": {
            "content": "Please report any bugs or feature requests to \"bug-math-bigint at rt.cpan.org\", or through the\nweb interface at <https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt> (requires login). We\nwill be notified, and then you'll automatically be notified of progress on your bug as I make\nchanges.\n",
            "subsections": []
        },
        "SUPPORT": {
            "content": "You can find documentation for this module with the perldoc command.\n\nperldoc Math::BigInt\n\nYou can also look for information at:\n\n*   GitHub\n\n<https://github.com/pjacklam/p5-Math-BigInt>\n\n*   RT: CPAN's request tracker\n\n<https://rt.cpan.org/Dist/Display.html?Name=Math-BigInt>\n\n*   MetaCPAN\n\n<https://metacpan.org/release/Math-BigInt>\n\n*   CPAN Testers Matrix\n\n<http://matrix.cpantesters.org/?dist=Math-BigInt>\n\n*   CPAN Ratings\n\n<https://cpanratings.perl.org/dist/Math-BigInt>\n\n*   The Bignum mailing list\n\n*   Post to mailing list\n\n\"bignum at lists.scsys.co.uk\"\n\n*   View mailing list\n\n<http://lists.scsys.co.uk/pipermail/bignum/>\n\n*   Subscribe/Unsubscribe\n\n<http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum>\n",
            "subsections": []
        },
        "LICENSE": {
            "content": "This program is free software; you may redistribute it and/or modify it under the same terms as\nPerl itself.\n",
            "subsections": []
        },
        "SEE ALSO": {
            "content": "Math::BigFloat and Math::BigRat as well as the backends Math::BigInt::FastCalc,\nMath::BigInt::GMP, and Math::BigInt::Pari.\n\nThe pragmas bignum, bigint and bigrat also might be of interest because they solve the\nautoupgrading/downgrading issue, at least partly.\n",
            "subsections": []
        },
        "AUTHORS": {
            "content": "*   Mark Biggar, overloaded interface by Ilya Zakharevich, 1996-2001.\n\n*   Completely rewritten by Tels <http://bloodgate.com>, 2001-2008.\n\n*   Florian Ragwitz <flora@cpan.org>, 2010.\n\n*   Peter John Acklam <pjacklam@gmail.com>, 2011-.\n\nMany people contributed in one or more ways to the final beast, see the file CREDITS for an\n(incomplete) list. If you miss your name, please drop me a mail. Thank you!\n",
            "subsections": []
        }
    },
    "summary": "Math::BigInt - Arbitrary size integer/float math package",
    "flags": [],
    "examples": [
        "use Math::BigInt;",
        "sub bigint { Math::BigInt->new(shift); }",
        "$x = Math::BigInt->bstr(\"1234\")       # string \"1234\"",
        "$x = \"$x\";                            # same as bstr()",
        "$x = Math::BigInt->bneg(\"1234\");      # Math::BigInt \"-1234\"",
        "$x = Math::BigInt->babs(\"-12345\");    # Math::BigInt \"12345\"",
        "$x = Math::BigInt->bnorm(\"-0.00\");    # Math::BigInt \"0\"",
        "$x = bigint(1) + bigint(2);           # Math::BigInt \"3\"",
        "$x = bigint(1) + \"2\";                 # ditto (\"2\" becomes a Math::BigInt)",
        "$x = bigint(1);                       # Math::BigInt \"1\"",
        "$x = $x + 5 / 2;                      # Math::BigInt \"3\"",
        "$x = $x  3;                         # Math::BigInt \"27\"",
        "$x *= 2;                              # Math::BigInt \"54\"",
        "$x = Math::BigInt->new(0);            # Math::BigInt \"0\"",
        "$x--;                                 # Math::BigInt \"-1\"",
        "$x = Math::BigInt->badd(4,5)          # Math::BigInt \"9\"",
        "print $x->bsstr();                    # 9e+0",
        "Examples for rounding:",
        "use Math::BigFloat;",
        "use Test::More;",
        "$x = Math::BigFloat->new(123.4567);",
        "$y = Math::BigFloat->new(123.456789);",
        "Math::BigFloat->accuracy(4);          # no more A than 4",
        "is ($x->copy()->bround(),123.4);      # even rounding",
        "print $x->copy()->bround(),\"\\n\";      # 123.4",
        "Math::BigFloat->roundmode('odd');    # round to odd",
        "print $x->copy()->bround(),\"\\n\";      # 123.5",
        "Math::BigFloat->accuracy(5);          # no more A than 5",
        "Math::BigFloat->roundmode('odd');    # round to odd",
        "print $x->copy()->bround(),\"\\n\";      # 123.46",
        "$y = $x->copy()->bround(4),\"\\n\";      # A = 4: 123.4",
        "print \"$y, \",$y->accuracy(),\"\\n\";     # 123.4, 4",
        "Math::BigFloat->accuracy(undef);      # A not important now",
        "Math::BigFloat->precision(2);         # P important",
        "print $x->copy()->bnorm(),\"\\n\";       # 123.46",
        "print $x->copy()->bround(),\"\\n\";      # 123.46",
        "Examples for converting:",
        "my $x = Math::BigInt->new('0b1'.'01' x 123);",
        "print \"bin: \",$x->asbin(),\" hex:\",$x->ashex(),\" dec: \",$x,\"\\n\";"
    ],
    "see_also": []
}