Class: Bignum

Inherits:

Defined in:: bignum.c

Overview

Bignum objects hold integers outside the range of Fixnum. Bignum objects are created automatically when integer calculations would otherwise overflow a Fixnum. When a calculation involving Bignum objects returns a result that will fit in a Fixnum, the result is automatically converted.

For the purposes of the bitwise operations and [], a Bignum is treated as if it were an infinite-length bitstring with 2's complement representation.

While Fixnum values are immediate, Bignum objects are not---assignment and parameter passing work with references to objects, not the objects themselves.

Instance Method Summary collapse

#% ⇒ Object

Returns big modulo other.
#&(numeric) ⇒ Integer

Performs bitwise and between big and numeric.
#*(other) ⇒ Numeric

Multiplies big and other, returning the result.
#**(exponent) ⇒ Numeric

Raises big to the exponent power (which may be an integer, float, or anything that will coerce to a number).
#+(other) ⇒ Numeric

Adds big and other, returning the result.
#-(other) ⇒ Numeric

Subtracts other from big, returning the result.
#- ⇒ Integer

Unary minus (returns an integer whose value is 0-big).
#/(other) ⇒ Numeric

Performs division: the class of the resulting object depends on the class of numeric and on the magnitude of the result.
#<(real) ⇒ Boolean

Returns true if the value of big is less than that of real.
#<<(numeric) ⇒ Integer

Shifts big left numeric positions (right if numeric is negative).
#<=(real) ⇒ Boolean

Returns true if the value of big is less than or equal to that of real.
#<=>(numeric) ⇒ -1, ...

Comparison---Returns -1, 0, or +1 depending on whether big is less than, equal to, or greater than numeric.
#==(obj) ⇒ Boolean

Returns true only if obj has the same value as big.
#==(obj) ⇒ Boolean

Returns true only if obj has the same value as big.
#>(real) ⇒ Boolean

Returns true if the value of big is greater than that of real.
#>=(real) ⇒ Boolean

Returns true if the value of big is greater than or equal to that of real.
#>>(numeric) ⇒ Integer

Shifts big right numeric positions (left if numeric is negative).
#[](n) ⇒ 0, 1

Bit Reference---Returns the nth bit in the (assumed) binary representation of big, where big[0] is the least significant bit.
#^(numeric) ⇒ Integer

Performs bitwise exclusive or between big and numeric.
#abs ⇒ Bignum

Returns the absolute value of big.
#coerce ⇒ Object

MISSING: documentation.
#div(other) ⇒ Integer

Performs integer division: returns integer value.
#divmod(numeric) ⇒ Array

See Numeric#divmod.
#eql?(obj) ⇒ Boolean

Returns true only if obj is a Bignum with the same value as big.
#even? ⇒ Boolean

Returns true if big is an even number.
#fdiv(numeric) ⇒ Float

Returns the floating point result of dividing big by numeric.
#hash ⇒ Fixnum

Compute a hash based on the value of big.
#abs ⇒ Bignum

Returns the absolute value of big.
#modulo ⇒ Object

Returns big modulo other.
#odd? ⇒ Boolean

Returns true if big is an odd number.
#remainder(numeric) ⇒ Numeric

Returns the remainder after dividing big by numeric.
#size ⇒ Integer

Returns the number of bytes in the machine representation of big.
#to_f ⇒ Float

Converts big to a Float.
#to_s(base = 10) ⇒ String

Returns a string containing the representation of big radix base (2 through 36).
#|(numeric) ⇒ Integer

Performs bitwise or between big and numeric.
#~ ⇒ Integer

Inverts the bits in big.

Instance Method Details

#%(other) ⇒ `Numeric` #modulo(other) ⇒ `Numeric`

Returns big modulo other. See Numeric.divmod for more information.

Overloads:

#%(other) ⇒ Numeric
Returns:
- (Numeric)
#modulo(other) ⇒ Numeric
Returns:
- (Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big % other         -> Numeric
 *     big.modulo(other)   -> Numeric
 *
 *  Returns big modulo other. See Numeric.divmod for more
 *  information.
 */

VALUE
rb_big_modulo(VALUE x, VALUE y)
{
    VALUE z;

    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;

      case T_BIGNUM:
    break;

      default:
    return rb_num_coerce_bin(x, y, '%');
    }
    bigdivmod(x, y, 0, &z);

    return bignorm(z);
}

#&(numeric) ⇒ `Integer`

Performs bitwise and between big and numeric.

Returns:

(Integer)

# File 'bignum.c'

/*
 * call-seq:
 *     big & numeric   ->  integer
 *
 * Performs bitwise +and+ between _big_ and _numeric_.
 */

VALUE
rb_big_and(VALUE xx, VALUE yy)
{
    volatile VALUE x, y, z;
    BDIGIT *ds1, *ds2, *zds;
    long i, l1, l2;
    char sign;

    x = xx;
    y = bit_coerce(yy);
    if (!RBIGNUM_SIGN(x)) {
    x = rb_big_clone(x);
    get2comp(x);
    }
    if (FIXNUM_P(y)) {
    return bigand_int(x, FIX2LONG(y));
    }
    if (!RBIGNUM_SIGN(y)) {
    y = rb_big_clone(y);
    get2comp(y);
    }
    if (RBIGNUM_LEN(x) > RBIGNUM_LEN(y)) {
    l1 = RBIGNUM_LEN(y);
    l2 = RBIGNUM_LEN(x);
    ds1 = BDIGITS(y);
    ds2 = BDIGITS(x);
    sign = RBIGNUM_SIGN(y);
    }
    else {
    l1 = RBIGNUM_LEN(x);
    l2 = RBIGNUM_LEN(y);
    ds1 = BDIGITS(x);
    ds2 = BDIGITS(y);
    sign = RBIGNUM_SIGN(x);
    }
    z = bignew(l2, RBIGNUM_SIGN(x) || RBIGNUM_SIGN(y));
    zds = BDIGITS(z);

    for (i=0; i<l1; i++) {
    zds[i] = ds1[i] & ds2[i];
    }
    for (; i<l2; i++) {
    zds[i] = sign?0:ds2[i];
    }
    if (!RBIGNUM_SIGN(z)) get2comp(z);
    return bignorm(z);
}

#*(other) ⇒ `Numeric`

Multiplies big and other, returning the result.

Returns:

(Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big * other  -> Numeric
 *
 *  Multiplies big and other, returning the result.
 */

VALUE
rb_big_mul(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;

      case T_BIGNUM:
    break;

      case T_FLOAT:
    return DBL2NUM(rb_big2dbl(x) * RFLOAT_VALUE(y));

      default:
    return rb_num_coerce_bin(x, y, '*');
    }

    return bignorm(bigmul0(x, y));
}

#**(exponent) ⇒ `Numeric`

Raises big to the exponent power (which may be an integer, float, or anything that will coerce to a number). The result may be a Fixnum, Bignum, or Float

123456789 ** 2      #=> 15241578750190521
123456789 ** 1.2    #=> 5126464716.09932
123456789 ** -2     #=> 6.5610001194102e-17

Returns:

(Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big ** exponent   -> numeric
 *
 *  Raises _big_ to the _exponent_ power (which may be an integer, float,
 *  or anything that will coerce to a number). The result may be
 *  a Fixnum, Bignum, or Float
 *
 *    123456789 ** 2      #=> 15241578750190521
 *    123456789 ** 1.2    #=> 5126464716.09932
 *    123456789 ** -2     #=> 6.5610001194102e-17
 */

VALUE
rb_big_pow(VALUE x, VALUE y)
{
    double d;
    SIGNED_VALUE yy;

    if (y == INT2FIX(0)) return INT2FIX(1);
    switch (TYPE(y)) {
      case T_FLOAT:
    d = RFLOAT_VALUE(y);
    if ((!RBIGNUM_SIGN(x) && !BIGZEROP(x)) && d != round(d))
        return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y);
    break;

      case T_BIGNUM:
    rb_warn("in a**b, b may be too big");
    d = rb_big2dbl(y);
    break;

      case T_FIXNUM:
    yy = FIX2LONG(y);

    if (yy < 0)
        return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, y);
    else {
        VALUE z = 0;
        SIGNED_VALUE mask;
        const long BIGLEN_LIMIT = 1024*1024 / SIZEOF_BDIGITS;

        if ((RBIGNUM_LEN(x) > BIGLEN_LIMIT) ||
        (RBIGNUM_LEN(x) > BIGLEN_LIMIT / yy)) {
        rb_warn("in a**b, b may be too big");
        d = (double)yy;
        break;
        }
        for (mask = FIXNUM_MAX + 1; mask; mask >>= 1) {
        if (z) z = bigsqr(z);
        if (yy & mask) {
            z = z ? bigtrunc(bigmul0(z, x)) : x;
        }
        }
        return bignorm(z);
    }
    /* NOTREACHED */
    break;

      default:
    return rb_num_coerce_bin(x, y, rb_intern("**"));
    }
    return DBL2NUM(pow(rb_big2dbl(x), d));
}

#+(other) ⇒ `Numeric`

Adds big and other, returning the result.

Returns:

(Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big + other  -> Numeric
 *
 *  Adds big and other, returning the result.
 */

VALUE
rb_big_plus(VALUE x, VALUE y)
{
    long n;

    switch (TYPE(y)) {
      case T_FIXNUM:
    n = FIX2LONG(y);
    if ((n > 0) != RBIGNUM_SIGN(x)) {
        if (n < 0) {
        n = -n;
        }
        return bigsub_int(x, n);
    }
    if (n < 0) {
        n = -n;
    }
    return bigadd_int(x, n);

      case T_BIGNUM:
    return bignorm(bigadd(x, y, 1));

      case T_FLOAT:
    return DBL2NUM(rb_big2dbl(x) + RFLOAT_VALUE(y));

      default:
    return rb_num_coerce_bin(x, y, '+');
    }
}

#-(other) ⇒ `Numeric`

Subtracts other from big, returning the result.

Returns:

(Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big - other  -> Numeric
 *
 *  Subtracts other from big, returning the result.
 */

VALUE
rb_big_minus(VALUE x, VALUE y)
{
    long n;

    switch (TYPE(y)) {
      case T_FIXNUM:
    n = FIX2LONG(y);
    if ((n > 0) != RBIGNUM_SIGN(x)) {
        if (n < 0) {
        n = -n;
        }
        return bigadd_int(x, n);
    }
    if (n < 0) {
        n = -n;
    }
    return bigsub_int(x, n);

      case T_BIGNUM:
    return bignorm(bigadd(x, y, 0));

      case T_FLOAT:
    return DBL2NUM(rb_big2dbl(x) - RFLOAT_VALUE(y));

      default:
    return rb_num_coerce_bin(x, y, '-');
    }
}

#- ⇒ `Integer`

Unary minus (returns an integer whose value is 0-big)

Returns:

(Integer)

# File 'bignum.c'

/*
 * call-seq:
 *    -big   ->  integer
 *
 * Unary minus (returns an integer whose value is 0-big)
 */

static VALUE
rb_big_uminus(VALUE x)
{
    VALUE z = rb_big_clone(x);

    RBIGNUM_SET_SIGN(z, !RBIGNUM_SIGN(x));

    return bignorm(z);
}

#/(other) ⇒ `Numeric`

Performs division: the class of the resulting object depends on the class of numeric and on the magnitude of the result.

Returns:

(Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big / other     -> Numeric
 *
 * Performs division: the class of the resulting object depends on
 * the class of <code>numeric</code> and on the magnitude of the
 * result.
 */

VALUE
rb_big_div(VALUE x, VALUE y)
{
    return rb_big_divide(x, y, '/');
}

#<(real) ⇒ `Boolean`

Returns true if the value of big is less than that of real.

Returns:

(Boolean)

# File 'bignum.c'

/*
 * call-seq:
 *   big < real  ->  true or false
 *
 * Returns <code>true</code> if the value of <code>big</code> is
 * less than that of <code>real</code>.
 */

static VALUE
big_lt(VALUE x, VALUE y)
{
    return big_op(x, y, 2);
}

#<<(numeric) ⇒ `Integer`

Shifts big left numeric positions (right if numeric is negative).

Returns:

(Integer)

# File 'bignum.c'

/*
 * call-seq:
 *     big << numeric   ->  integer
 *
 * Shifts big left _numeric_ positions (right if _numeric_ is negative).
 */

VALUE
rb_big_lshift(VALUE x, VALUE y)
{
    long shift;
    int neg = 0;

    for (;;) {
    if (FIXNUM_P(y)) {
        shift = FIX2LONG(y);
        if (shift < 0) {
        neg = 1;
        shift = -shift;
        }
        break;
    }
    else if (TYPE(y) == T_BIGNUM) {
        if (!RBIGNUM_SIGN(y)) {
        VALUE t = check_shiftdown(y, x);
        if (!NIL_P(t)) return t;
        neg = 1;
        }
        shift = big2ulong(y, "long", TRUE);
        break;
    }
    y = rb_to_int(y);
    }

    x = neg ? big_rshift(x, shift) : big_lshift(x, shift);
    return bignorm(x);
}

#<=(real) ⇒ `Boolean`

Returns true if the value of big is less than or equal to that of real.

Returns:

(Boolean)

# File 'bignum.c'

/*
 * call-seq:
 *   big <= real  ->  true or false
 *
 * Returns <code>true</code> if the value of <code>big</code> is
 * less than or equal to that of <code>real</code>.
 */

static VALUE
big_le(VALUE x, VALUE y)
{
    return big_op(x, y, 3);
}

#<=>(numeric) ⇒ `-1`, ...

Comparison---Returns -1, 0, or +1 depending on whether big is less than, equal to, or greater than numeric. This is the basis for the tests in Comparable.

Returns:

(-1, 0, +1, nil)

# File 'bignum.c'

/*
 *  call-seq:
 *     big <=> numeric   -> -1, 0, +1 or nil
 *
 *  Comparison---Returns -1, 0, or +1 depending on whether <i>big</i> is
 *  less than, equal to, or greater than <i>numeric</i>. This is the
 *  basis for the tests in <code>Comparable</code>.
 *
 */

VALUE
rb_big_cmp(VALUE x, VALUE y)
{
    long xlen = RBIGNUM_LEN(x);
    BDIGIT *xds, *yds;

    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;

      case T_BIGNUM:
    break;

      case T_FLOAT:
    {
        double a = RFLOAT_VALUE(y);

        if (isinf(a)) {
        if (a > 0.0) return INT2FIX(-1);
        else return INT2FIX(1);
        }
        return rb_dbl_cmp(rb_big2dbl(x), a);
    }

      default:
    return rb_num_coerce_cmp(x, y, rb_intern("<=>"));
    }

    if (RBIGNUM_SIGN(x) > RBIGNUM_SIGN(y)) return INT2FIX(1);
    if (RBIGNUM_SIGN(x) < RBIGNUM_SIGN(y)) return INT2FIX(-1);
    if (xlen < RBIGNUM_LEN(y))
    return (RBIGNUM_SIGN(x)) ? INT2FIX(-1) : INT2FIX(1);
    if (xlen > RBIGNUM_LEN(y))
    return (RBIGNUM_SIGN(x)) ? INT2FIX(1) : INT2FIX(-1);

    xds = BDIGITS(x);
    yds = BDIGITS(y);

    while(xlen-- && (xds[xlen]==yds[xlen]));
    if (-1 == xlen) return INT2FIX(0);
    return (xds[xlen] > yds[xlen]) ?
    (RBIGNUM_SIGN(x) ? INT2FIX(1) : INT2FIX(-1)) :
        (RBIGNUM_SIGN(x) ? INT2FIX(-1) : INT2FIX(1));
}

#==(obj) ⇒ `Boolean`

Returns true only if obj has the same value as big. Contrast this with Bignum#eql?, which requires obj to be a Bignum.

68719476736 == 68719476736.0   #=> true

Returns:

(Boolean)

# File 'bignum.c'

/*
 *  call-seq:
 *     big == obj  -> true or false
 *
 *  Returns <code>true</code> only if <i>obj</i> has the same value
 *  as <i>big</i>. Contrast this with <code>Bignum#eql?</code>, which
 *  requires <i>obj</i> to be a <code>Bignum</code>.
 *
 *     68719476736 == 68719476736.0   #=> true
 */

VALUE
rb_big_eq(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;
      case T_BIGNUM:
    break;
      case T_FLOAT:
    {
        volatile double a, b;

        a = RFLOAT_VALUE(y);
        if (isnan(a)) return Qfalse;
        b = rb_big2dbl(x);
        return (a == b)?Qtrue:Qfalse;
    }
      default:
    return rb_equal(y, x);
    }
    if (RBIGNUM_SIGN(x) != RBIGNUM_SIGN(y)) return Qfalse;
    if (RBIGNUM_LEN(x) != RBIGNUM_LEN(y)) return Qfalse;
    if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM_LEN(y)) != 0) return Qfalse;
    return Qtrue;
}

#==(obj) ⇒ `Boolean`

Returns true only if obj has the same value as big. Contrast this with Bignum#eql?, which requires obj to be a Bignum.

68719476736 == 68719476736.0   #=> true

Returns:

(Boolean)

# File 'bignum.c'

/*
 *  call-seq:
 *     big == obj  -> true or false
 *
 *  Returns <code>true</code> only if <i>obj</i> has the same value
 *  as <i>big</i>. Contrast this with <code>Bignum#eql?</code>, which
 *  requires <i>obj</i> to be a <code>Bignum</code>.
 *
 *     68719476736 == 68719476736.0   #=> true
 */

VALUE
rb_big_eq(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;
      case T_BIGNUM:
    break;
      case T_FLOAT:
    {
        volatile double a, b;

        a = RFLOAT_VALUE(y);
        if (isnan(a)) return Qfalse;
        b = rb_big2dbl(x);
        return (a == b)?Qtrue:Qfalse;
    }
      default:
    return rb_equal(y, x);
    }
    if (RBIGNUM_SIGN(x) != RBIGNUM_SIGN(y)) return Qfalse;
    if (RBIGNUM_LEN(x) != RBIGNUM_LEN(y)) return Qfalse;
    if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM_LEN(y)) != 0) return Qfalse;
    return Qtrue;
}

#>(real) ⇒ `Boolean`

Returns true if the value of big is greater than that of real.

Returns:

(Boolean)

# File 'bignum.c'

/*
 * call-seq:
 *   big > real  ->  true or false
 *
 * Returns <code>true</code> if the value of <code>big</code> is
 * greater than that of <code>real</code>.
 */

static VALUE
big_gt(VALUE x, VALUE y)
{
    return big_op(x, y, 0);
}

#>=(real) ⇒ `Boolean`

Returns true if the value of big is greater than or equal to that of real.

Returns:

(Boolean)

# File 'bignum.c'

/*
 * call-seq:
 *   big >= real  ->  true or false
 *
 * Returns <code>true</code> if the value of <code>big</code> is
 * greater than or equal to that of <code>real</code>.
 */

static VALUE
big_ge(VALUE x, VALUE y)
{
    return big_op(x, y, 1);
}

#>>(numeric) ⇒ `Integer`

Shifts big right numeric positions (left if numeric is negative).

Returns:

(Integer)

# File 'bignum.c'

/*
 * call-seq:
 *     big >> numeric   ->  integer
 *
 * Shifts big right _numeric_ positions (left if _numeric_ is negative).
 */

VALUE
rb_big_rshift(VALUE x, VALUE y)
{
    long shift;
    int neg = 0;

    for (;;) {
    if (FIXNUM_P(y)) {
        shift = FIX2LONG(y);
        if (shift < 0) {
        neg = 1;
        shift = -shift;
        }
        break;
    }
    else if (TYPE(y) == T_BIGNUM) {
        if (RBIGNUM_SIGN(y)) {
        VALUE t = check_shiftdown(y, x);
        if (!NIL_P(t)) return t;
        }
        else {
        neg = 1;
        }
        shift = big2ulong(y, "long", TRUE);
        break;
    }
    y = rb_to_int(y);
    }

    x = neg ? big_lshift(x, shift) : big_rshift(x, shift);
    return bignorm(x);
}

#[](n) ⇒ `0`, `1`

Bit Reference---Returns the nth bit in the (assumed) binary representation of big, where big[0] is the least significant bit.

a = 9**15
50.downto(0) do |n|
  print a[n]
end

produces:

000101110110100000111000011110010100111100010111001

Returns:

(0, 1)

# File 'bignum.c'

/*
 *  call-seq:
 *     big[n] -> 0, 1
 *
 *  Bit Reference---Returns the <em>n</em>th bit in the (assumed) binary
 *  representation of <i>big</i>, where <i>big</i>[0] is the least
 *  significant bit.
 *
 *     a = 9**15
 *     50.downto(0) do |n|
 *       print a[n]
 *     end
 *
 *  <em>produces:</em>
 *
 *     000101110110100000111000011110010100111100010111001
 *
 */

static VALUE
rb_big_aref(VALUE x, VALUE y)
{
    BDIGIT *xds;
    BDIGIT_DBL num;
    VALUE shift;
    long i, s1, s2;

    if (TYPE(y) == T_BIGNUM) {
    if (!RBIGNUM_SIGN(y))
        return INT2FIX(0);
    bigtrunc(y);
    if (RBIGNUM_LEN(y) > DIGSPERLONG) {
      out_of_range:
        return RBIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
    }
    shift = big2ulong(y, "long", FALSE);
    }
    else {
    i = NUM2LONG(y);
    if (i < 0) return INT2FIX(0);
    shift = (VALUE)i;
    }
    s1 = shift/BITSPERDIG;
    s2 = shift%BITSPERDIG;

    if (s1 >= RBIGNUM_LEN(x)) goto out_of_range;
    if (!RBIGNUM_SIGN(x)) {
    xds = BDIGITS(x);
    i = 0; num = 1;
    while (num += ~xds[i], ++i <= s1) {
        num = BIGDN(num);
    }
    }
    else {
    num = BDIGITS(x)[s1];
    }
    if (num & ((BDIGIT_DBL)1<<s2))
    return INT2FIX(1);
    return INT2FIX(0);
}

#^(numeric) ⇒ `Integer`

Performs bitwise exclusive or between big and numeric.

Returns:

(Integer)

# File 'bignum.c'

/*
 * call-seq:
 *     big ^ numeric   ->  integer
 *
 * Performs bitwise +exclusive or+ between _big_ and _numeric_.
 */

VALUE
rb_big_xor(VALUE xx, VALUE yy)
{
    volatile VALUE x, y;
    VALUE z;
    BDIGIT *ds1, *ds2, *zds;
    long i, l1, l2;
    char sign;

    x = xx;
    y = bit_coerce(yy);

    if (!RBIGNUM_SIGN(x)) {
    x = rb_big_clone(x);
    get2comp(x);
    }
    if (FIXNUM_P(y)) {
    return bigxor_int(x, FIX2LONG(y));
    }
    if (!RBIGNUM_SIGN(y)) {
    y = rb_big_clone(y);
    get2comp(y);
    }
    if (RBIGNUM_LEN(x) > RBIGNUM_LEN(y)) {
    l1 = RBIGNUM_LEN(y);
    l2 = RBIGNUM_LEN(x);
    ds1 = BDIGITS(y);
    ds2 = BDIGITS(x);
    sign = RBIGNUM_SIGN(y);
    }
    else {
    l1 = RBIGNUM_LEN(x);
    l2 = RBIGNUM_LEN(y);
    ds1 = BDIGITS(x);
    ds2 = BDIGITS(y);
    sign = RBIGNUM_SIGN(x);
    }
    RBIGNUM_SET_SIGN(x, RBIGNUM_SIGN(x)?1:0);
    RBIGNUM_SET_SIGN(y, RBIGNUM_SIGN(y)?1:0);
    z = bignew(l2, !(RBIGNUM_SIGN(x) ^ RBIGNUM_SIGN(y)));
    zds = BDIGITS(z);

    for (i=0; i<l1; i++) {
    zds[i] = ds1[i] ^ ds2[i];
    }
    for (; i<l2; i++) {
    zds[i] = sign?ds2[i]:~ds2[i];
    }
    if (!RBIGNUM_SIGN(z)) get2comp(z);

    return bignorm(z);
}

#abs ⇒ `Bignum`

Returns the absolute value of big.

-1234567890987654321.abs   #=> 1234567890987654321

Returns:

(Bignum)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.abs -> aBignum
 *
 *  Returns the absolute value of <i>big</i>.
 *
 *     -1234567890987654321.abs   #=> 1234567890987654321
 */

static VALUE
rb_big_abs(VALUE x)
{
    if (!RBIGNUM_SIGN(x)) {
    x = rb_big_clone(x);
    RBIGNUM_SET_SIGN(x, 1);
    }
    return x;
}

#coerce ⇒ `Object`

MISSING: documentation

# File 'bignum.c'

/*
 * MISSING: documentation
 */

static VALUE
rb_big_coerce(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
    return rb_assoc_new(rb_int2big(FIX2LONG(y)), x);
    }
    else if (TYPE(y) == T_BIGNUM) {
       return rb_assoc_new(y, x);
    }
    else {
    rb_raise(rb_eTypeError, "can't coerce %s to Bignum",
         rb_obj_classname(y));
    }
    /* not reached */
    return Qnil;
}

#div(other) ⇒ `Integer`

Performs integer division: returns integer value.

Returns:

(Integer)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.div(other)  -> integer
 *
 * Performs integer division: returns integer value.
 */

VALUE
rb_big_idiv(VALUE x, VALUE y)
{
    return rb_big_divide(x, y, rb_intern("div"));
}

#divmod(numeric) ⇒ `Array`

See Numeric#divmod.

Returns:

(Array)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.divmod(numeric)   -> array
 *
 *  See <code>Numeric#divmod</code>.
 *
 */
VALUE
rb_big_divmod(VALUE x, VALUE y)
{
    VALUE div, mod;

    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;

      case T_BIGNUM:
    break;

      default:
    return rb_num_coerce_bin(x, y, rb_intern("divmod"));
    }
    bigdivmod(x, y, &div, &mod);

    return rb_assoc_new(bignorm(div), bignorm(mod));
}

#eql?(obj) ⇒ `Boolean`

Returns true only if obj is a Bignum with the same value as big. Contrast this with Bignum#==, which performs type conversions.

68719476736.eql?(68719476736.0)   #=> false

Returns:

(Boolean)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.eql?(obj)   -> true or false
 *
 *  Returns <code>true</code> only if <i>obj</i> is a
 *  <code>Bignum</code> with the same value as <i>big</i>. Contrast this
 *  with <code>Bignum#==</code>, which performs type conversions.
 *
 *     68719476736.eql?(68719476736.0)   #=> false
 */

static VALUE
rb_big_eql(VALUE x, VALUE y)
{
    if (TYPE(y) != T_BIGNUM) return Qfalse;
    if (RBIGNUM_SIGN(x) != RBIGNUM_SIGN(y)) return Qfalse;
    if (RBIGNUM_LEN(x) != RBIGNUM_LEN(y)) return Qfalse;
    if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM_LEN(y)) != 0) return Qfalse;
    return Qtrue;
}

#even? ⇒ `Boolean`

Returns true if big is an even number.

Returns:

(Boolean)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.even? -> true or false
 *
 *  Returns <code>true</code> if <i>big</i> is an even number.
 */

static VALUE
rb_big_even_p(VALUE num)
{
    if (BDIGITS(num)[0] & 1) {
    return Qfalse;
    }
    return Qtrue;
}

#fdiv(numeric) ⇒ `Float`

Returns the floating point result of dividing big by numeric.

-1234567890987654321.fdiv(13731)      #=> -89910996357705.5
-1234567890987654321.fdiv(13731.24)   #=> -89909424858035.7

Returns:

(Float)

# File 'bignum.c'

/*
 *  call-seq:
  *     big.fdiv(numeric) -> float
 *
 *  Returns the floating point result of dividing <i>big</i> by
 *  <i>numeric</i>.
 *
 *     -1234567890987654321.fdiv(13731)      #=> -89910996357705.5
 *     -1234567890987654321.fdiv(13731.24)   #=> -89909424858035.7
 *
 */


VALUE
rb_big_fdiv(VALUE x, VALUE y)
{
    double dx, dy;

    dx = big2dbl(x);
    switch (TYPE(y)) {
      case T_FIXNUM:
    dy = (double)FIX2LONG(y);
    if (isinf(dx))
        return big_fdiv(x, y);
    break;

      case T_BIGNUM:
    dy = rb_big2dbl(y);
    if (isinf(dx) || isinf(dy))
        return big_fdiv(x, y);
    break;

      case T_FLOAT:
    dy = RFLOAT_VALUE(y);
    if (isnan(dy))
        return y;
    if (isinf(dx))
        return big_fdiv(x, y);
    break;

      default:
    return rb_num_coerce_bin(x, y, rb_intern("fdiv"));
    }
    return DBL2NUM(dx / dy);
}

#hash ⇒ `Fixnum`

Compute a hash based on the value of big.

Returns:

(Fixnum)

# File 'bignum.c'

/*
 * call-seq:
 *   big.hash   -> fixnum
 *
 * Compute a hash based on the value of _big_.
 */

static VALUE
rb_big_hash(VALUE x)
{
    st_index_t hash;

    hash = rb_memhash(BDIGITS(x), sizeof(BDIGIT)*RBIGNUM_LEN(x)) ^ RBIGNUM_SIGN(x);
    return INT2FIX(hash);
}

#abs ⇒ `Bignum`

Returns the absolute value of big.

-1234567890987654321.abs   #=> 1234567890987654321

Returns:

(Bignum)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.abs -> aBignum
 *
 *  Returns the absolute value of <i>big</i>.
 *
 *     -1234567890987654321.abs   #=> 1234567890987654321
 */

static VALUE
rb_big_abs(VALUE x)
{
    if (!RBIGNUM_SIGN(x)) {
    x = rb_big_clone(x);
    RBIGNUM_SET_SIGN(x, 1);
    }
    return x;
}

#%(other) ⇒ `Numeric` #modulo(other) ⇒ `Numeric`

Returns big modulo other. See Numeric.divmod for more information.

Overloads:

#%(other) ⇒ Numeric
Returns:
- (Numeric)
#modulo(other) ⇒ Numeric
Returns:
- (Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big % other         -> Numeric
 *     big.modulo(other)   -> Numeric
 *
 *  Returns big modulo other. See Numeric.divmod for more
 *  information.
 */

VALUE
rb_big_modulo(VALUE x, VALUE y)
{
    VALUE z;

    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;

      case T_BIGNUM:
    break;

      default:
    return rb_num_coerce_bin(x, y, '%');
    }
    bigdivmod(x, y, 0, &z);

    return bignorm(z);
}

#odd? ⇒ `Boolean`

Returns true if big is an odd number.

Returns:

(Boolean)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.odd? -> true or false
 *
 *  Returns <code>true</code> if <i>big</i> is an odd number.
 */

static VALUE
rb_big_odd_p(VALUE num)
{
    if (BDIGITS(num)[0] & 1) {
    return Qtrue;
    }
    return Qfalse;
}

#remainder(numeric) ⇒ `Numeric`

Returns the remainder after dividing big by numeric.

-1234567890987654321.remainder(13731)      #=> -6966
-1234567890987654321.remainder(13731.24)   #=> -9906.22531493148

Returns:

(Numeric)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.remainder(numeric)    -> number
 *
 *  Returns the remainder after dividing <i>big</i> by <i>numeric</i>.
 *
 *     -1234567890987654321.remainder(13731)      #=> -6966
 *     -1234567890987654321.remainder(13731.24)   #=> -9906.22531493148
 */
static VALUE
rb_big_remainder(VALUE x, VALUE y)
{
    VALUE z;

    switch (TYPE(y)) {
      case T_FIXNUM:
    y = rb_int2big(FIX2LONG(y));
    break;

      case T_BIGNUM:
    break;

      default:
    return rb_num_coerce_bin(x, y, rb_intern("remainder"));
    }
    bigdivrem(x, y, 0, &z);

    return bignorm(z);
}

#size ⇒ `Integer`

Returns the number of bytes in the machine representation of big.

(256**10 - 1).size   #=> 12
(256**20 - 1).size   #=> 20
(256**40 - 1).size   #=> 40

Returns:

(Integer)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.size -> integer
 *
 *  Returns the number of bytes in the machine representation of
 *  <i>big</i>.
 *
 *     (256**10 - 1).size   #=> 12
 *     (256**20 - 1).size   #=> 20
 *     (256**40 - 1).size   #=> 40
 */

static VALUE
rb_big_size(VALUE big)
{
    return LONG2FIX(RBIGNUM_LEN(big)*SIZEOF_BDIGITS);
}

#to_f ⇒ `Float`

Converts big to a Float. If big doesn't fit in a Float, the result is infinity.

Returns:

(Float)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.to_f -> float
 *
 *  Converts <i>big</i> to a <code>Float</code>. If <i>big</i> doesn't
 *  fit in a <code>Float</code>, the result is infinity.
 *
 */

static VALUE
rb_big_to_f(VALUE x)
{
    return DBL2NUM(rb_big2dbl(x));
}

#to_s(base = 10) ⇒ `String`

Returns a string containing the representation of big radix base (2 through 36).

12345654321.to_s         #=> "12345654321"
12345654321.to_s(2)      #=> "1011011111110110111011110000110001"
12345654321.to_s(8)      #=> "133766736061"
12345654321.to_s(16)     #=> "2dfdbbc31"
78546939656932.to_s(36)  #=> "rubyrules"

Returns:

(String)

# File 'bignum.c'

/*
 *  call-seq:
 *     big.to_s(base=10)   ->  string
 *
 *  Returns a string containing the representation of <i>big</i> radix
 *  <i>base</i> (2 through 36).
 *
 *     12345654321.to_s         #=> "12345654321"
 *     12345654321.to_s(2)      #=> "1011011111110110111011110000110001"
 *     12345654321.to_s(8)      #=> "133766736061"
 *     12345654321.to_s(16)     #=> "2dfdbbc31"
 *     78546939656932.to_s(36)  #=> "rubyrules"
 */

static VALUE
rb_big_to_s(int argc, VALUE *argv, VALUE x)
{
    int base;

    if (argc == 0) base = 10;
    else {
    VALUE b;

    rb_scan_args(argc, argv, "01", &b);
    base = NUM2INT(b);
    }
    return rb_big2str(x, base);
}

#|(numeric) ⇒ `Integer`

Performs bitwise or between big and numeric.

Returns:

(Integer)

# File 'bignum.c'

/*
 * call-seq:
 *     big | numeric   ->  integer
 *
 * Performs bitwise +or+ between _big_ and _numeric_.
 */

VALUE
rb_big_or(VALUE xx, VALUE yy)
{
    volatile VALUE x, y, z;
    BDIGIT *ds1, *ds2, *zds;
    long i, l1, l2;
    char sign;

    x = xx;
    y = bit_coerce(yy);

    if (!RBIGNUM_SIGN(x)) {
    x = rb_big_clone(x);
    get2comp(x);
    }
    if (FIXNUM_P(y)) {
    return bigor_int(x, FIX2LONG(y));
    }
    if (!RBIGNUM_SIGN(y)) {
    y = rb_big_clone(y);
    get2comp(y);
    }
    if (RBIGNUM_LEN(x) > RBIGNUM_LEN(y)) {
    l1 = RBIGNUM_LEN(y);
    l2 = RBIGNUM_LEN(x);
    ds1 = BDIGITS(y);
    ds2 = BDIGITS(x);
    sign = RBIGNUM_SIGN(y);
    }
    else {
    l1 = RBIGNUM_LEN(x);
    l2 = RBIGNUM_LEN(y);
    ds1 = BDIGITS(x);
    ds2 = BDIGITS(y);
    sign = RBIGNUM_SIGN(x);
    }
    z = bignew(l2, RBIGNUM_SIGN(x) && RBIGNUM_SIGN(y));
    zds = BDIGITS(z);

    for (i=0; i<l1; i++) {
    zds[i] = ds1[i] | ds2[i];
    }
    for (; i<l2; i++) {
    zds[i] = sign?ds2[i]:(BDIGIT)(BIGRAD-1);
    }
    if (!RBIGNUM_SIGN(z)) get2comp(z);
    return bignorm(z);
}

#~ ⇒ `Integer`

Inverts the bits in big. As Bignums are conceptually infinite length, the result acts as if it had an infinite number of one bits to the left. In hex representations, this is displayed as two periods to the left of the digits.

sprintf("%X", ~0x1122334455)    #=> "..FEEDDCCBBAA"

Returns:

(Integer)

# File 'bignum.c'

/*
 * call-seq:
 *     ~big  ->  integer
 *
 * Inverts the bits in big. As Bignums are conceptually infinite
 * length, the result acts as if it had an infinite number of one
 * bits to the left. In hex representations, this is displayed
 * as two periods to the left of the digits.
 *
 *   sprintf("%X", ~0x1122334455)    #=> "..FEEDDCCBBAA"
 */

static VALUE
rb_big_neg(VALUE x)
{
    VALUE z = rb_big_clone(x);
    BDIGIT *ds;
    long i;

    if (!RBIGNUM_SIGN(x)) get2comp(z);
    ds = BDIGITS(z);
    i = RBIGNUM_LEN(x);
    if (!i) return INT2FIX(~(SIGNED_VALUE)0);
    while (i--) {
    ds[i] = ~ds[i];
    }
    RBIGNUM_SET_SIGN(z, !RBIGNUM_SIGN(z));
    if (RBIGNUM_SIGN(x)) get2comp(z);

    return bignorm(z);
}

Class: Bignum

Overview

Instance Method Summary collapse

Methods inherited from Integer

Methods inherited from Numeric

Methods included from Comparable

Instance Method Details

#%(other) ⇒ Numeric #modulo(other) ⇒ Numeric

#&(numeric) ⇒ Integer

#*(other) ⇒ Numeric

#**(exponent) ⇒ Numeric

#+(other) ⇒ Numeric

#-(other) ⇒ Numeric

#- ⇒ Integer

#/(other) ⇒ Numeric

#<(real) ⇒ Boolean

#<<(numeric) ⇒ Integer

#<=(real) ⇒ Boolean

#<=>(numeric) ⇒ -1, ...

#==(obj) ⇒ Boolean

#==(obj) ⇒ Boolean

#>(real) ⇒ Boolean

#>=(real) ⇒ Boolean

#>>(numeric) ⇒ Integer

#[](n) ⇒ 0, 1

#^(numeric) ⇒ Integer

#abs ⇒ Bignum

#coerce ⇒ Object

#div(other) ⇒ Integer

#divmod(numeric) ⇒ Array

#eql?(obj) ⇒ Boolean

#even? ⇒ Boolean

#fdiv(numeric) ⇒ Float

#hash ⇒ Fixnum

#abs ⇒ Bignum

#%(other) ⇒ Numeric #modulo(other) ⇒ Numeric

#odd? ⇒ Boolean

#remainder(numeric) ⇒ Numeric

#size ⇒ Integer

#to_f ⇒ Float

#to_s(base = 10) ⇒ String

#|(numeric) ⇒ Integer

#~ ⇒ Integer

#%(other) ⇒ `Numeric` #modulo(other) ⇒ `Numeric`

#&(numeric) ⇒ `Integer`

#*(other) ⇒ `Numeric`

#**(exponent) ⇒ `Numeric`

#+(other) ⇒ `Numeric`

#-(other) ⇒ `Numeric`

#- ⇒ `Integer`

#/(other) ⇒ `Numeric`

#<(real) ⇒ `Boolean`

#<<(numeric) ⇒ `Integer`

#<=(real) ⇒ `Boolean`

#<=>(numeric) ⇒ `-1`, ...

#==(obj) ⇒ `Boolean`

#==(obj) ⇒ `Boolean`

#>(real) ⇒ `Boolean`

#>=(real) ⇒ `Boolean`

#>>(numeric) ⇒ `Integer`

#[](n) ⇒ `0`, `1`

#^(numeric) ⇒ `Integer`

#abs ⇒ `Bignum`

#coerce ⇒ `Object`

#div(other) ⇒ `Integer`

#divmod(numeric) ⇒ `Array`

#eql?(obj) ⇒ `Boolean`

#even? ⇒ `Boolean`

#fdiv(numeric) ⇒ `Float`

#hash ⇒ `Fixnum`

#abs ⇒ `Bignum`

#%(other) ⇒ `Numeric` #modulo(other) ⇒ `Numeric`

#odd? ⇒ `Boolean`

#remainder(numeric) ⇒ `Numeric`

#size ⇒ `Integer`

#to_f ⇒ `Float`

#to_s(base = 10) ⇒ `String`

#|(numeric) ⇒ `Integer`

#~ ⇒ `Integer`