Class: Bignum (Ruby 1.9.1)

big % other => Numeric click to toggle source

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);
}

big & numeric => integer click to toggle source

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 (FIXNUM_P(y)) {
        y = rb_int2big(FIX2LONG(y));
    }
    if (!RBIGNUM_SIGN(y)) {
        y = rb_big_clone(y);
        get2comp(y);
    }
    if (!RBIGNUM_SIGN(x)) {
        x = rb_big_clone(x);
        get2comp(x);
    }
    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);
}

big * other => Numeric click to toggle source

Multiplies big and other, returning the result.

 
               VALUE
rb_big_mul(VALUE x, VALUE y)
{
    return bignorm(rb_big_mul0(x, y));
}

big ** exponent => numeric click to toggle source

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);
        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 = bigtrunc(bigsqr(z));
                if (yy & mask) {
                    z = z ? bigtrunc(rb_big_mul0(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));
}

big + other => Numeric click to toggle source

Adds big and other, returning the result.

 
               VALUE
rb_big_plus(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
        y = rb_int2big(FIX2LONG(y));
        /* fall through */
      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, '+');
    }
}

big - other => Numeric click to toggle source

Subtracts other from big, returning the result.

 
               VALUE
rb_big_minus(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
        y = rb_int2big(FIX2LONG(y));
        /* fall through */
      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, '-');
    }
}

-big => other_big click to toggle source

Unary minus (returns a new Bignum 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);
}

big / other => Numeric click to toggle source

Divides big by other, returning the result.

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

big << numeric => integer click to toggle source

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", Qtrue);
            break;
        }
        y = rb_to_int(y);
    }

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

big <=> numeric => -1, 0, +1 click to toggle source

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.

 
               VALUE
rb_big_cmp(VALUE x, VALUE y)
{
    long xlen = RBIGNUM_LEN(x);

    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);

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

big == obj => true or false click to toggle source

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

 
               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;
}

big == obj => true or false click to toggle source

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

 
               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;
}

big >> numeric => integer click to toggle source

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", Qtrue);
            break;
        }
        y = rb_to_int(y);
    }

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

big[n] → 0, 1 click to toggle source

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

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

produces:

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);
        if (RBIGNUM_LEN(bigtrunc(y)) > DIGSPERLONG) {
          out_of_range:
            return RBIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
        }
        shift = big2ulong(y, "long", Qfalse);
    }
    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);
}

big ^ numeric => integer click to toggle source

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 (FIXNUM_P(y)) {
        y = rb_int2big(FIX2LONG(y));
    }

    if (!RBIGNUM_SIGN(y)) {
        y = rb_big_clone(y);
        get2comp(y);
    }
    if (!RBIGNUM_SIGN(x)) {
        x = rb_big_clone(x);
        get2comp(x);
    }
    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 → aBignum click to toggle source

Returns the absolute value of big.

-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(p1) click to toggle source

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(p1) click to toggle source

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

divmod(numeric) => array click to toggle source

See Numeric#divmod.

 
               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) => true or false click to toggle source

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

 
               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? → true or false click to toggle source

Returns true if big is an even number.

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

fdiv(numeric) → float click to toggle source

Returns the floating point result of dividing big by numeric.

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

 
               static VALUE
rb_big_fdiv(VALUE x, VALUE y)
{
    double dx = big2dbl(x);
    double dy;

    if (isinf(dx)) {
#define DBL_BIGDIG ((DBL_MANT_DIG + BITSPERDIG) / BITSPERDIG)
        VALUE z;
        int ex, ey;

        ex = (RBIGNUM_LEN(bigtrunc(x)) - 1) * BITSPERDIG;
        ex += bdigbitsize(BDIGITS(x)[RBIGNUM_LEN(x) - 1]);
        ex -= 2 * DBL_BIGDIG * BITSPERDIG;
        if (ex) x = big_shift(x, ex);

        switch (TYPE(y)) {
          case T_FIXNUM:
            y = rb_int2big(FIX2LONG(y));
          case T_BIGNUM: {
            ey = (RBIGNUM_LEN(bigtrunc(y)) - 1) * BITSPERDIG;
            ey += bdigbitsize(BDIGITS(y)[RBIGNUM_LEN(y) - 1]);
            ey -= DBL_BIGDIG * BITSPERDIG;
            if (ey) y = big_shift(y, ey);
          bignum:
            bigdivrem(x, y, &z, 0);
            return DBL2NUM(ldexp(big2dbl(z), ex - ey));
          }
          case T_FLOAT:
            if (isnan(RFLOAT_VALUE(y))) return y;
            y = dbl2big(ldexp(frexp(RFLOAT_VALUE(y), &ey), DBL_MANT_DIG));
            ey -= DBL_MANT_DIG;
            goto bignum;
        }
    }
    switch (TYPE(y)) {
      case T_FIXNUM:
        dy = (double)FIX2LONG(y);
        break;

      case T_BIGNUM:
        dy = rb_big2dbl(y);
        break;

      case T_FLOAT:
        dy = RFLOAT_VALUE(y);
        break;

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

hash => fixnum click to toggle source

Compute a hash based on the value of big.

 
               static VALUE
rb_big_hash(VALUE x)
{
    int hash;

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

abs → aBignum click to toggle source

Returns the absolute value of big.

-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;
}

modulo(other) => Numeric click to toggle source

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? → true or false click to toggle source

Returns true if big is an odd number.

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

remainder(numeric) => number click to toggle source

Returns the remainder after dividing big by numeric.

-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 click to toggle source

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

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

to_f → float click to toggle source

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

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

to_s(base=10) => string click to toggle source

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"

 
               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);
}

big | numeric => integer click to toggle source

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 (FIXNUM_P(y)) {
        y = rb_int2big(FIX2LONG(y));
    }

    if (!RBIGNUM_SIGN(y)) {
        y = rb_big_clone(y);
        get2comp(y);
    }
    if (!RBIGNUM_SIGN(x)) {
        x = rb_big_clone(x);
        get2comp(x);
    }
    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]:(BIGRAD-1);
    }
    if (!RBIGNUM_SIGN(z)) get2comp(z);

    return bignorm(z);
}

~big => integer click to toggle source

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);
}

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