Class: Bignum

Inherits:
Integer show all
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.

Constant Summary collapse

GMP_VERSION =

The version of loaded GMP.

rb_sprintf("GMP %s", gmp_version)

Instance Method Summary collapse

Methods inherited from Integer

#ceil, #chr, #denominator, #downto, #floor, #gcd, #gcdlcm, #integer?, #lcm, #next, #numerator, #ord, #pred, #rationalize, #round, #succ, #times, #to_i, #to_int, #to_r, #truncate, #upto

Methods inherited from Numeric

#+@, #abs2, #angle, #arg, #ceil, #conj, #conjugate, #denominator, #floor, #i, #imag, #imaginary, #initialize_copy, #integer?, #nonzero?, #numerator, #phase, #polar, #quo, #real, #real?, #rect, #rectangular, #round, #singleton_method_added, #step, #to_c, #to_int, #truncate, #zero?

Methods included from Comparable

#between?

Instance Method Details

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

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

Overloads:



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# File 'bignum.c', line 6080

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

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else if (!RB_BIGNUM_TYPE_P(y)) {
	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:



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# File 'bignum.c', line 6370

VALUE
rb_big_and(VALUE x, VALUE y)
{
    VALUE z;
    BDIGIT *ds1, *ds2, *zds;
    long i, xn, yn, n1, n2;
    BDIGIT hibitsx, hibitsy;
    BDIGIT hibits1, hibits2;
    VALUE tmpv;
    BDIGIT tmph;
    long tmpn;

    if (!FIXNUM_P(y) && !RB_BIGNUM_TYPE_P(y)) {
	return rb_num_coerce_bit(x, y, '&');
    }

    hibitsx = abs2twocomp(&x, &xn);
    if (FIXNUM_P(y)) {
	return bigand_int(x, xn, hibitsx, FIX2LONG(y));
    }
    hibitsy = abs2twocomp(&y, &yn);
    if (xn > yn) {
        tmpv = x; x = y; y = tmpv;
        tmpn = xn; xn = yn; yn = tmpn;
        tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
    }
    n1 = xn;
    n2 = yn;
    ds1 = BDIGITS(x);
    ds2 = BDIGITS(y);
    hibits1 = hibitsx;
    hibits2 = hibitsy;

    if (!hibits1)
        n2 = n1;

    z = bignew(n2, 0);
    zds = BDIGITS(z);

    for (i=0; i<n1; i++) {
	zds[i] = ds1[i] & ds2[i];
    }
    for (; i<n2; i++) {
	zds[i] = hibits1 & ds2[i];
    }
    twocomp2abs_bang(z, hibits1 && hibits2);
    RB_GC_GUARD(x);
    RB_GC_GUARD(y);
    return bignorm(z);
}

#*(other) ⇒ Numeric

Multiplies big and other, returning the result.

Returns:



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# File 'bignum.c', line 5888

VALUE
rb_big_mul(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	return DBL2NUM(rb_big2dbl(x) * RFLOAT_VALUE(y));
    }
    else {
	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:



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# File 'bignum.c', line 6254

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

  again:
    if (y == INT2FIX(0)) return INT2FIX(1);
    if (RB_FLOAT_TYPE_P(y)) {
	d = RFLOAT_VALUE(y);
	if ((!BIGNUM_SIGN(x) && !BIGZEROP(x)) && d != round(d))
	    return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y);
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	y = bignorm(y);
	if (FIXNUM_P(y))
	    goto again;
	rb_warn("in a**b, b may be too big");
	d = rb_big2dbl(y);
    }
    else if (FIXNUM_P(y)) {
	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 size_t xbits = rb_absint_numwords(x, 1, NULL);
	    const size_t BIGLEN_LIMIT = 32*1024*1024;

	    if (xbits == (size_t)-1 ||
                (xbits > BIGLEN_LIMIT) ||
                (xbits * yy > BIGLEN_LIMIT)) {
		rb_warn("in a**b, b may be too big");
		d = (double)yy;
	    }
	    else {
		for (mask = FIXNUM_MAX + 1; mask; mask >>= 1) {
		    if (z) z = bigsq(z);
		    if (yy & mask) {
			z = z ? bigtrunc(bigmul0(z, x)) : x;
		    }
		}
		return bignorm(z);
	    }
	}
    }
    else {
	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:



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# File 'bignum.c', line 5758

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

    if (FIXNUM_P(y)) {
	n = FIX2LONG(y);
	if ((n > 0) != BIGNUM_SIGN(x)) {
	    if (n < 0) {
		n = -n;
	    }
	    return bigsub_int(x, n);
	}
	if (n < 0) {
	    n = -n;
	}
	return bigadd_int(x, n);
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	return bignorm(bigadd(x, y, 1));
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	return DBL2NUM(rb_big2dbl(x) + RFLOAT_VALUE(y));
    }
    else {
	return rb_num_coerce_bin(x, y, '+');
    }
}

#-(other) ⇒ Numeric

Subtracts other from big, returning the result.

Returns:



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# File 'bignum.c', line 5794

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

    if (FIXNUM_P(y)) {
	n = FIX2LONG(y);
	if ((n > 0) != BIGNUM_SIGN(x)) {
	    if (n < 0) {
		n = -n;
	    }
	    return bigadd_int(x, n);
	}
	if (n < 0) {
	    n = -n;
	}
	return bigsub_int(x, n);
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	return bignorm(bigadd(x, y, 0));
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	return DBL2NUM(rb_big2dbl(x) - RFLOAT_VALUE(y));
    }
    else {
	return rb_num_coerce_bin(x, y, '-');
    }
}

#- ⇒ Integer

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

Returns:



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# File 'bignum.c', line 5469

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

    BIGNUM_SET_SIGN(z, !BIGNUM_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:



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# File 'bignum.c', line 6052

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) 


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# File 'bignum.c', line 5389

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

#<<(numeric) ⇒ Integer

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

Returns:



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# File 'bignum.c', line 6651

VALUE
rb_big_lshift(VALUE x, VALUE y)
{
    int lshift_p;
    size_t shift_numdigits;
    int shift_numbits;

    for (;;) {
	if (FIXNUM_P(y)) {
	    long l = FIX2LONG(y);
            unsigned long shift;
	    if (0 <= l) {
		lshift_p = 1;
                shift = l;
            }
            else {
		lshift_p = 0;
		shift = 1+(unsigned long)(-(l+1));
	    }
            shift_numbits = (int)(shift & (BITSPERDIG-1));
            shift_numdigits = shift >> bit_length(BITSPERDIG-1);
            return bignorm(big_shift3(x, lshift_p, shift_numdigits, shift_numbits));
	}
	else if (RB_BIGNUM_TYPE_P(y)) {
            return bignorm(big_shift2(x, 1, y));
	}
	y = rb_to_int(y);
    }
}

#<=(real) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'bignum.c', line 5403

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

#<=>(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.

nil is returned if the two values are incomparable.

Returns:

  • (-1, 0, +1, nil) 


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# File 'bignum.c', line 5275

VALUE
rb_big_cmp(VALUE x, VALUE y)
{
    int cmp;

    if (FIXNUM_P(y)) {
        x = bignorm(x);
        if (FIXNUM_P(x)) {
            if (FIX2LONG(x) > FIX2LONG(y)) return INT2FIX(1);
            if (FIX2LONG(x) < FIX2LONG(y)) return INT2FIX(-1);
            return INT2FIX(0);
        }
        else {
            if (BIGNUM_NEGATIVE_P(x)) return INT2FIX(-1);
            return INT2FIX(1);
        }
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
    }
    else if (RB_FLOAT_TYPE_P(y)) {
        return rb_integer_float_cmp(x, y);
    }
    else {
	return rb_num_coerce_cmp(x, y, rb_intern("<=>"));
    }

    if (BIGNUM_SIGN(x) > BIGNUM_SIGN(y)) return INT2FIX(1);
    if (BIGNUM_SIGN(x) < BIGNUM_SIGN(y)) return INT2FIX(-1);

    cmp = bary_cmp(BDIGITS(x), BIGNUM_LEN(x), BDIGITS(y), BIGNUM_LEN(y));
    if (BIGNUM_SIGN(x))
        return INT2FIX(cmp);
    else
        return INT2FIX(-cmp);
}

#==(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) 


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# File 'bignum.c', line 5420

VALUE
rb_big_eq(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
	if (bignorm(x) == y) return Qtrue;
	y = rb_int2big(FIX2LONG(y));
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
    }
    else if (RB_FLOAT_TYPE_P(y)) {
        return rb_integer_float_eq(x, y);
    }
    else {
	return rb_equal(y, x);
    }
    if (BIGNUM_SIGN(x) != BIGNUM_SIGN(y)) return Qfalse;
    if (BIGNUM_LEN(x) != BIGNUM_LEN(y)) return Qfalse;
    if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,BIGNUM_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) 


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# File 'bignum.c', line 5420

VALUE
rb_big_eq(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
	if (bignorm(x) == y) return Qtrue;
	y = rb_int2big(FIX2LONG(y));
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
    }
    else if (RB_FLOAT_TYPE_P(y)) {
        return rb_integer_float_eq(x, y);
    }
    else {
	return rb_equal(y, x);
    }
    if (BIGNUM_SIGN(x) != BIGNUM_SIGN(y)) return Qfalse;
    if (BIGNUM_LEN(x) != BIGNUM_LEN(y)) return Qfalse;
    if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,BIGNUM_LEN(y)) != 0) return Qfalse;
    return Qtrue;
}

#>(real) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'bignum.c', line 5361

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

#>=(real) ⇒ Boolean

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

Returns:

  • (Boolean) 


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# File 'bignum.c', line 5375

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

#>>(numeric) ⇒ Integer

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

Returns:



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# File 'bignum.c', line 6689

VALUE
rb_big_rshift(VALUE x, VALUE y)
{
    int lshift_p;
    size_t shift_numdigits;
    int shift_numbits;

    for (;;) {
	if (FIXNUM_P(y)) {
	    long l = FIX2LONG(y);
            unsigned long shift;
            if (0 <= l) {
                lshift_p = 0;
                shift = l;
            }
            else {
                lshift_p = 1;
		shift = 1+(unsigned long)(-(l+1));
	    }
            shift_numbits = (int)(shift & (BITSPERDIG-1));
            shift_numdigits = shift >> bit_length(BITSPERDIG-1);
            return bignorm(big_shift3(x, lshift_p, shift_numdigits, shift_numbits));
	}
	else if (RB_BIGNUM_TYPE_P(y)) {
            return bignorm(big_shift2(x, 0, y));
	}
	y = rb_to_int(y);
    }
}

#[](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) 


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# File 'bignum.c', line 6738

static VALUE
rb_big_aref(VALUE x, VALUE y)
{
    BDIGIT *xds;
    size_t shift;
    size_t i, s1, s2;
    long l;
    BDIGIT bit;

    if (RB_BIGNUM_TYPE_P(y)) {
	if (!BIGNUM_SIGN(y))
	    return INT2FIX(0);
	bigtrunc(y);
	if (BIGSIZE(y) > sizeof(size_t)) {
	  out_of_range:
	    return BIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
	}
#if SIZEOF_SIZE_T <= SIZEOF_LONG
	shift = big2ulong(y, "long");
#else
	shift = big2ull(y, "long long");
#endif
    }
    else {
	l = NUM2LONG(y);
	if (l < 0) return INT2FIX(0);
	shift = (size_t)l;
    }
    s1 = shift/BITSPERDIG;
    s2 = shift%BITSPERDIG;
    bit = (BDIGIT)1 << s2;

    if (s1 >= BIGNUM_LEN(x)) goto out_of_range;

    xds = BDIGITS(x);
    if (BIGNUM_POSITIVE_P(x))
        return (xds[s1] & bit) ? INT2FIX(1) : INT2FIX(0);
    if (xds[s1] & (bit-1))
        return (xds[s1] & bit) ? INT2FIX(0) : INT2FIX(1);
    for (i = 0; i < s1; i++)
        if (xds[i])
            return (xds[s1] & bit) ? INT2FIX(0) : INT2FIX(1);
    return (xds[s1] & bit) ? INT2FIX(1) : INT2FIX(0);
}

#^(numeric) ⇒ Integer

Performs bitwise exclusive or between big and numeric.

Returns:



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# File 'bignum.c', line 6596

VALUE
rb_big_xor(VALUE x, VALUE y)
{
    VALUE z;
    BDIGIT *ds1, *ds2, *zds;
    long i, xn, yn, n1, n2;
    BDIGIT hibitsx, hibitsy;
    BDIGIT hibits1, hibits2;
    VALUE tmpv;
    BDIGIT tmph;
    long tmpn;

    if (!FIXNUM_P(y) && !RB_BIGNUM_TYPE_P(y)) {
	return rb_num_coerce_bit(x, y, '^');
    }

    hibitsx = abs2twocomp(&x, &xn);
    if (FIXNUM_P(y)) {
	return bigxor_int(x, xn, hibitsx, FIX2LONG(y));
    }
    hibitsy = abs2twocomp(&y, &yn);
    if (xn > yn) {
        tmpv = x; x = y; y = tmpv;
        tmpn = xn; xn = yn; yn = tmpn;
        tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
    }
    n1 = xn;
    n2 = yn;
    ds1 = BDIGITS(x);
    ds2 = BDIGITS(y);
    hibits1 = hibitsx;
    hibits2 = hibitsy;

    z = bignew(n2, 0);
    zds = BDIGITS(z);

    for (i=0; i<n1; i++) {
	zds[i] = ds1[i] ^ ds2[i];
    }
    for (; i<n2; i++) {
	zds[i] = hibitsx ^ ds2[i];
    }
    twocomp2abs_bang(z, (hibits1 ^ hibits2) != 0);
    RB_GC_GUARD(x);
    RB_GC_GUARD(y);
    return bignorm(z);
}

#abs ⇒ Bignum #magnitude ⇒ Bignum

Returns the absolute value of big.

-1234567890987654321.abs   #=> 1234567890987654321

Overloads:



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# File 'bignum.c', line 6838

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

#bit_length ⇒ Integer

Returns the number of bits of the value of int.

“the number of bits” means that the bit position of the highest bit which is different to the sign bit. (The bit position of the bit 2**n is n+1.) If there is no such bit (zero or minus one), zero is returned.

I.e. This method returns ceil(log2(int < 0 ? -int : int+1)).

(-2**10000-1).bit_length  #=> 10001
(-2**10000).bit_length    #=> 10000
(-2**10000+1).bit_length  #=> 10000

(-2**1000-1).bit_length   #=> 1001
(-2**1000).bit_length     #=> 1000
(-2**1000+1).bit_length   #=> 1000

(2**1000-1).bit_length    #=> 1000
(2**1000).bit_length      #=> 1001
(2**1000+1).bit_length    #=> 1001

(2**10000-1).bit_length   #=> 10000
(2**10000).bit_length     #=> 10001
(2**10000+1).bit_length   #=> 10001

This method can be used to detect overflow in Array#pack as follows.

if n.bit_length < 32
  [n].pack("l") # no overflow
else
  raise "overflow"
end

Returns:



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# File 'bignum.c', line 6904

static VALUE
rb_big_bit_length(VALUE big)
{
    int nlz_bits;
    size_t numbytes;

    static const BDIGIT char_bit[1] = { CHAR_BIT };
    BDIGIT numbytes_bary[bdigit_roomof(sizeof(size_t))];
    BDIGIT nlz_bary[1];
    BDIGIT result_bary[bdigit_roomof(sizeof(size_t)+1)];

    numbytes = rb_absint_size(big, &nlz_bits);

    if (numbytes == 0)
        return LONG2FIX(0);

    if (BIGNUM_NEGATIVE_P(big) && rb_absint_singlebit_p(big)) {
        if (nlz_bits != CHAR_BIT-1) {
            nlz_bits++;
        }
        else {
            nlz_bits = 0;
            numbytes--;
        }
    }

    if (numbytes <= SIZE_MAX / CHAR_BIT) {
        return SIZET2NUM(numbytes * CHAR_BIT - nlz_bits);
    }

    nlz_bary[0] = nlz_bits;

    bary_unpack(BARY_ARGS(numbytes_bary), &numbytes, 1, sizeof(numbytes), 0,
            INTEGER_PACK_NATIVE_BYTE_ORDER);
    BARY_SHORT_MUL(result_bary, numbytes_bary, char_bit);
    BARY_SUB(result_bary, result_bary, nlz_bary);

    return rb_integer_unpack(result_bary, numberof(result_bary), sizeof(BDIGIT), 0,
            INTEGER_PACK_LSWORD_FIRST|INTEGER_PACK_NATIVE_BYTE_ORDER);
}

#coerce(numeric) ⇒ Array

Returns an array with both a numeric and a big represented as Bignum objects.

This is achieved by converting numeric to a Bignum.

A TypeError is raised if the numeric is not a Fixnum or Bignum type.

(0x3FFFFFFFFFFFFFFF+1).coerce(42)   #=> [42, 4611686018427387904]

Returns:



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# File 'bignum.c', line 6815

static VALUE
rb_big_coerce(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else if (!RB_BIGNUM_TYPE_P(y)) {
	rb_raise(rb_eTypeError, "can't coerce %s to Bignum",
		 rb_obj_classname(y));
    }
    return rb_assoc_new(y, x);
}

#div(other) ⇒ Integer

Performs integer division: returns integer value.

Returns:



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# File 'bignum.c', line 6065

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

#divmod(numeric) ⇒ Array

See Numeric#divmod.

Returns:



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# File 'bignum.c', line 6128

VALUE
rb_big_divmod(VALUE x, VALUE y)
{
    VALUE div, mod;

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else if (!RB_BIGNUM_TYPE_P(y)) {
	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)

Returns:

  • (Boolean) 


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# File 'bignum.c', line 5452

VALUE
rb_big_eql(VALUE x, VALUE y)
{
    if (!RB_BIGNUM_TYPE_P(y)) return Qfalse;
    if (BIGNUM_SIGN(x) != BIGNUM_SIGN(y)) return Qfalse;
    if (BIGNUM_LEN(x) != BIGNUM_LEN(y)) return Qfalse;
    if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,BIGNUM_LEN(y)) != 0) return Qfalse;
    return Qtrue;
}

#even? ⇒ Boolean

Returns true if big is an even number.

Returns:

  • (Boolean)

Returns:

  • (Boolean) 


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# File 'bignum.c', line 6968

static VALUE
rb_big_even_p(VALUE num)
{
    if (BIGNUM_LEN(num) != 0 && 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:



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# File 'bignum.c', line 6212

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

    dx = big2dbl(x);
    if (FIXNUM_P(y)) {
	dy = (double)FIX2LONG(y);
	if (isinf(dx))
	    return big_fdiv_int(x, rb_int2big(FIX2LONG(y)));
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	dy = rb_big2dbl(y);
	if (isinf(dx) || isinf(dy))
	    return big_fdiv_int(x, y);
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	dy = RFLOAT_VALUE(y);
	if (isnan(dy))
	    return y;
	if (isinf(dx))
	    return big_fdiv_float(x, y);
    }
    else {
	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.

See also Object#hash.

Returns:



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# File 'bignum.c', line 6792

static VALUE
rb_big_hash(VALUE x)
{
    st_index_t hash;

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

#abs ⇒ Bignum #magnitude ⇒ Bignum

Returns the absolute value of big.

-1234567890987654321.abs   #=> 1234567890987654321

Overloads:



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# File 'bignum.c', line 6838

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

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

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

Overloads:



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# File 'bignum.c', line 6080

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

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else if (!RB_BIGNUM_TYPE_P(y)) {
	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)

Returns:

  • (Boolean) 


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# File 'bignum.c', line 6952

static VALUE
rb_big_odd_p(VALUE num)
{
    if (BIGNUM_LEN(num) != 0 && 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:



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# File 'bignum.c', line 6105

static VALUE
rb_big_remainder(VALUE x, VALUE y)
{
    VALUE z;

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else if (!RB_BIGNUM_TYPE_P(y)) {
	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:



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# File 'bignum.c', line 6860

static VALUE
rb_big_size(VALUE big)
{
    return SIZET2NUM(BIGSIZE(big));
}

#to_f ⇒ Float

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

Returns:



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# File 'bignum.c', line 5175

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

#to_s(base = 10) ⇒ String Also known as: inspect

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:



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# File 'bignum.c', line 4926

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:



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# File 'bignum.c', line 6496

VALUE
rb_big_or(VALUE x, VALUE y)
{
    VALUE z;
    BDIGIT *ds1, *ds2, *zds;
    long i, xn, yn, n1, n2;
    BDIGIT hibitsx, hibitsy;
    BDIGIT hibits1, hibits2;
    VALUE tmpv;
    BDIGIT tmph;
    long tmpn;

    if (!FIXNUM_P(y) && !RB_BIGNUM_TYPE_P(y)) {
	return rb_num_coerce_bit(x, y, '|');
    }

    hibitsx = abs2twocomp(&x, &xn);
    if (FIXNUM_P(y)) {
	return bigor_int(x, xn, hibitsx, FIX2LONG(y));
    }
    hibitsy = abs2twocomp(&y, &yn);
    if (xn > yn) {
        tmpv = x; x = y; y = tmpv;
        tmpn = xn; xn = yn; yn = tmpn;
        tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
    }
    n1 = xn;
    n2 = yn;
    ds1 = BDIGITS(x);
    ds2 = BDIGITS(y);
    hibits1 = hibitsx;
    hibits2 = hibitsy;

    if (hibits1)
        n2 = n1;

    z = bignew(n2, 0);
    zds = BDIGITS(z);

    for (i=0; i<n1; i++) {
	zds[i] = ds1[i] | ds2[i];
    }
    for (; i<n2; i++) {
	zds[i] = hibits1 | ds2[i];
    }
    twocomp2abs_bang(z, hibits1 || hibits2);
    RB_GC_GUARD(x);
    RB_GC_GUARD(y);
    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:



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# File 'bignum.c', line 5491

static VALUE
rb_big_neg(VALUE x)
{
    VALUE z = rb_big_clone(x);
    BDIGIT *ds = BDIGITS(z);
    long n = BIGNUM_LEN(z);

    if (!n) return INT2FIX(-1);

    if (BIGNUM_POSITIVE_P(z)) {
        if (bary_add_one(ds, n)) {
            big_extend_carry(z);
        }
        BIGNUM_SET_NEGATIVE_SIGN(z);
    }
    else {
        bary_neg(ds, n);
        if (bary_add_one(ds, n))
            return INT2FIX(-1);
        bary_neg(ds, n);
        BIGNUM_SET_POSITIVE_SIGN(z);
    }

    return bignorm(z);
}