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 =

rb_sprintf("GMP %s", gmp_version)

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 ⇒ Object

Returns the absolute value of big.
#bit_length ⇒ Integer

Returns the number of bits of the value of int.
#coerce(numeric) ⇒ Array

Returns an array with both a numeric and a big represented as Bignum objects.
#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.
#magnitude ⇒ Object

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 (also: #inspect)

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', line 6188

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:

(Integer)

# File 'bignum.c', line 6478

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:

(Numeric)

# File 'bignum.c', line 5996

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:

(Numeric)

# File 'bignum.c', line 6362

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 ((!RBIGNUM_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:

(Numeric)

# File 'bignum.c', line 5866

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

    if (FIXNUM_P(y)) {
	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);
    }
    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:

(Numeric)

# File 'bignum.c', line 5902

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

    if (FIXNUM_P(y)) {
	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);
    }
    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:

(Integer)

# File 'bignum.c', line 5577

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', line 6160

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', line 5497

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:

(Integer)

# File 'bignum.c', line 6759

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)

# File 'bignum.c', line 5511

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)

# File 'bignum.c', line 5392

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

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    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 (RBIGNUM_SIGN(x) > RBIGNUM_SIGN(y)) return INT2FIX(1);
    if (RBIGNUM_SIGN(x) < RBIGNUM_SIGN(y)) return INT2FIX(-1);

    cmp = bary_cmp(BDIGITS(x), RBIGNUM_LEN(x), BDIGITS(y), RBIGNUM_LEN(y));
    if (RBIGNUM_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)

# File 'bignum.c', line 5528

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 (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', line 5528

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 (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', line 5469

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)

# File 'bignum.c', line 5483

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:

(Integer)

# File 'bignum.c', line 6797

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)

# File 'bignum.c', line 6846

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

    if (RB_BIGNUM_TYPE_P(y)) {
	if (!RBIGNUM_SIGN(y))
	    return INT2FIX(0);
	bigtrunc(y);
	if (BIGSIZE(y) > sizeof(long)) {
	  out_of_range:
	    return RBIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
	}
	shift = big2ulong(y, "long");
    }
    else {
	i = NUM2LONG(y);
	if (i < 0) return INT2FIX(0);
	shift = i;
    }
    s1 = shift/BITSPERDIG;
    s2 = shift%BITSPERDIG;
    bit = (BDIGIT)1 << s2;

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

    xds = BDIGITS(x);
    if (RBIGNUM_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:

(Integer)

# File 'bignum.c', line 6704

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:

#abs ⇒ Bignum
Returns:
- (Bignum)
#magnitude ⇒ Bignum
Returns:
- (Bignum)

# File 'bignum.c', line 6939

static VALUE
rb_big_abs(VALUE x)
{
    if (!RBIGNUM_SIGN(x)) {
	x = rb_big_clone(x);
	RBIGNUM_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

Returns:

(Integer)

# File 'bignum.c', line 6998

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 (RBIGNUM_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:

(Array)

# File 'bignum.c', line 6916

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:

(Integer)

# File 'bignum.c', line 6173

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', line 6236

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)

# File 'bignum.c', line 5560

VALUE
rb_big_eql(VALUE x, VALUE y)
{
    if (!RB_BIGNUM_TYPE_P(y)) 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)

Returns:

(Boolean)

# File 'bignum.c', line 7062

static VALUE
rb_big_even_p(VALUE num)
{
    if (RBIGNUM_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:

(Float)

# File 'bignum.c', line 6320

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.

Returns:

(Fixnum)

# File 'bignum.c', line 6893

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` #magnitude ⇒ `Bignum`

Returns the absolute value of big.

-1234567890987654321.abs   #=> 1234567890987654321

Overloads:

#abs ⇒ Bignum
Returns:
- (Bignum)
#magnitude ⇒ Bignum
Returns:
- (Bignum)

# File 'bignum.c', line 6939

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', line 6188

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)

# File 'bignum.c', line 7046

static VALUE
rb_big_odd_p(VALUE num)
{
    if (RBIGNUM_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:

(Numeric)

# File 'bignum.c', line 6213

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:

(Integer)

# File 'bignum.c', line 6961

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:

(Float)

# File 'bignum.c', line 5292

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:

(String)

# File 'bignum.c', line 5033

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', line 6604

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:

(Integer)

# File 'bignum.c', line 5599

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

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

    if (RBIGNUM_POSITIVE_P(z)) {
        if (bary_add_one(ds, n)) {
            big_extend_carry(z);
        }
        RBIGNUM_SET_NEGATIVE_SIGN(z);
    }
    else {
        bary_neg(ds, n);
        if (bary_add_one(ds, n))
            return INT2FIX(-1);
        bary_neg(ds, n);
        RBIGNUM_SET_POSITIVE_SIGN(z);
    }

    return bignorm(z);
}

Class: Bignum

Overview

Constant Summary collapse

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 #magnitude ⇒ Bignum

#bit_length ⇒ Integer

#coerce(numeric) ⇒ Array

#div(other) ⇒ Integer

#divmod(numeric) ⇒ Array

#eql?(obj) ⇒ Boolean

#even? ⇒ Boolean

#fdiv(numeric) ⇒ Float

#hash ⇒ Fixnum

#abs ⇒ Bignum #magnitude ⇒ Bignum

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

#odd? ⇒ Boolean

#remainder(numeric) ⇒ Numeric

#size ⇒ Integer

#to_f ⇒ Float

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

#|(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` #magnitude ⇒ `Bignum`

#bit_length ⇒ `Integer`

#coerce(numeric) ⇒ `Array`

#div(other) ⇒ `Integer`

#divmod(numeric) ⇒ `Array`

#eql?(obj) ⇒ `Boolean`

#even? ⇒ `Boolean`

#fdiv(numeric) ⇒ `Float`

#hash ⇒ `Fixnum`

#abs ⇒ `Bignum` #magnitude ⇒ `Bignum`

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

#odd? ⇒ `Boolean`

#remainder(numeric) ⇒ `Numeric`

#size ⇒ `Integer`

#to_f ⇒ `Float`

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

#|(numeric) ⇒ `Integer`

#~ ⇒ `Integer`