Class: Calc::Q

Inherits:
Numeric show all
Includes:
Comparable
Defined in:
ext/calc/q.c,
lib/calc/q.rb,
ext/calc/q.c

Overview

Calc rational number (fraction).

A rational number consists of an arbitrarily large numerator and denominator. The numerator and denominator are always in lowest terms, and the sign of the number is contained in the numerator.

Wraps the libcalc C type NUMBER*.

Constant Summary collapse

NEGONE = 
new(-1)
ZERO = 
new(0)
ONE = 
new(1)
TWO = 
new(2)

Instance Method Summary collapse

Methods inherited from Numeric

#%, #+@, #<<, #>>, #abs2, #ceil, #cmp, #coerce, #comb, #fdiv, #finite?, #floor, #ilog, #ilog10, #ilog2, #infinite?, #isint, #ln, #log, #log2, #mmin, #nonzero?, #polar, #quo, #rectangular, #root, #scale, #sgn, #sqrt, #to_int

Constructor Details

#initialize(*args) ⇒ Calc::Q

Creates a new rational number.

Arguments are either a numerator/denominator pair, or a single numerator. With a single parameter, a denominator of 1 is implied. Valid types are:

  • Integer

  • Rational

  • Calc::Q

  • String

  • Float

Strings can be in rational, floating point, exponential, hex or octal, eg:

Calc::Q("3/10")   #=> Calc::Q(0.3)
Calc::Q("0.5")    #=> Calc::Q(0.5)
Calc::Q("1e10")   #=> Calc::Q(10000000000)
Calc::Q("1e-10")  #=> Calc::Q(0.0000000001)
Calc::Q("0x2a")   #=> Calc::Q(42)
Calc::Q("052")    #=> Calc::Q(42)

Note that a Float cannot precisely equal many values; it will be converted the the closest rational number which may not be what you expect, eg:

Calc::Q(0.3)  #=> Calc::Q(~0.29999999999999998890)

for this reason, it is best to avoid Floats. Libcalc’s string parsing will work better:

Calc::Q("0.3")  #=> Calc::Q(0.3)

Parameters:

Raises:

  • (ZeroDivisionError) —

    if denominator of new number is zero



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# File 'ext/calc/q.c', line 93

static VALUE
cq_initialize(int argc, VALUE * argv, VALUE self)
{
    NUMBER *qself, *qnum, *qden;
    VALUE num, den;
    setup_math_error();

    if (rb_scan_args(argc, argv, "11", &num, &den) == 1) {
        /* single param */
        qself = value_to_number(num, 1);
    }
    else {
        /* 2 params. divide first by second. */
        qden = value_to_number(den, 1);
        if (qiszero(qden)) {
            qfree(qden);
            rb_raise(rb_eZeroDivError, "division by zero");
        }
        qnum = value_to_number(num, 1);
        qself = qqdiv(qnum, qden);
        qfree(qden);
        qfree(qnum);
    }
    DATA_PTR(self) = qself;

    return self;
}

Instance Method Details

#&(y) ⇒ Calc::Q

Bitwise AND

Examples:

Calc::Q(18) & 20 #=> Calc::Q(16)

Parameters:

  • y (Integer)

Returns:



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# File 'ext/calc/q.c', line 348

static VALUE
cq_and(VALUE x, VALUE y)
{
    return numeric_op(x, y, &qand, NULL, id_and);
}

#*(y) ⇒ Calc::Q

Performs multiplication.

@example:

Calc::Q(2) * 3 #=> Calc::Q(6)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 361

static VALUE
cq_multiply(VALUE x, VALUE y)
{
    return numeric_op(x, y, &qmul, &qmuli, id_multiply);
}

#**(other) ⇒ Object 



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# File 'lib/calc/q.rb', line 8

def **(other)
  power(other)
end

#+(y) ⇒ Calc::Q

Performs addition.

Examples:

Calc::Q(1) + 2 #=> Calc::Q(3)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 374

static VALUE
cq_add(VALUE x, VALUE y)
{
    /* fourth arg was &qaddi, but this segfaults with ruby 2.1.x */
    return numeric_op(x, y, &qqadd, NULL, id_add);
}

#-(y) ⇒ Calc::Q

Performs subtraction.

@example:

Calc::Q(1) - 2 #=> Calc::Q(-1)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 388

static VALUE
cq_subtract(VALUE x, VALUE y)
{
    return numeric_op(x, y, &qsub, NULL, id_subtract);
}

#-@ ⇒ Calc::Q

Unary minus. Returns the receiver’s value, negated.

Examples:

-Calc::Q(1) #=> Calc::Q(-1)

Returns:



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# File 'ext/calc/q.c', line 400

static VALUE
cq_uminus(VALUE self)
{
    setup_math_error();
    return wrap_number(qsub(&_qzero_, DATA_PTR(self)));
}

#/(y) ⇒ Calc::Q

Performs division.

@example:

Calc::Q(2) / 4 #=> Calc::Q(0.5)

Parameters:

Returns:

Raises:



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# File 'ext/calc/q.c', line 415

static VALUE
cq_divide(VALUE x, VALUE y)
{
    return numeric_op(x, y, &qqdiv, &qdivi, id_divide);
}

#<=>(other) ⇒ Integer?

Comparison - Returns -1, 0, +1 or nil depending on whether ‘y` is less than, equal to, or greater than `x`.

This is used by the ‘Comparable` module to implement `==`, `!=`, `<`, `<=`, `>` and `>=`.

nil is returned if the two values are incomparable.

@example:

Calc::Q(5) <=> 4     #=> 1
Calc::Q(5) <=> 5.1   #=> -1
Calc::Q(5) <=> 5     #=> 0
Calc::Q(5) <=> "cat" #=> nil

Parameters:

Returns:

  • (Integer, nil) 


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# File 'ext/calc/q.c', line 437

static VALUE
cq_spaceship(VALUE self, VALUE other)
{
    VALUE ary;
    NUMBER *qself, *qother;
    int result;
    setup_math_error();

    qself = DATA_PTR(self);
    /* qreli returns incorrect results if self > 0 and other == 0
       if (FIXNUM_P(other)) {
       result = qreli(qself, NUM2LONG(other));
       }
     */
    if (CALC_Q_P(other)) {
        result = qrel(qself, DATA_PTR(other));
    }
    else if (FIXNUM_P(other) || RB_TYPE_P(other, T_BIGNUM) || RB_TYPE_P(other, T_FLOAT)
             || RB_TYPE_P(other, T_RATIONAL)) {
        qother = value_to_number(other, 0);
        result = qrel(qself, qother);
        qfree(qother);
    }
    else if (rb_respond_to(other, id_coerce)) {
        if (RB_TYPE_P(other, T_COMPLEX)) {
            other = rb_funcall(cC, id_new, 1, other);
        }
        ary = rb_funcall(other, id_coerce, 1, self);
        if (!RB_TYPE_P(ary, T_ARRAY) || RARRAY_LEN(ary) != 2) {
            rb_raise(rb_eTypeError, "coerce must return [x, y]");
        }
        return rb_funcall(RARRAY_AREF(ary, 0), id_spaceship, 1, RARRAY_AREF(ary, 1));
    }
    else {
        return Qnil;
    }

    return INT2FIX(result);
}

#^(y) ⇒ Calc::Q

Bitwise exclusive or (xor)

Note that for ruby compatibility, ^ is an xor operator, unlike in calc where it is a power operator.

Examples:

Calc::Q(5).xor(3) #=> Calc::Q(6)

Returns:



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# File 'ext/calc/q.c', line 486

static VALUE
cq_xor(VALUE x, VALUE y)
{
    return numeric_op(x, y, &qxor, NULL, id_xor);
}

#abs ⇒ Calc::Q Also known as: magnitude

Absolute value

Examples:

Calc::Q(1).abs  #=> Calc::Q(1)
Calc::Q(-1).abs #=> Calc::Q(1)

Returns:



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# File 'ext/calc/q.c', line 527

static VALUE
cq_abs(VALUE self)
{
    setup_math_error();
    return wrap_number(qqabs(DATA_PTR(self)));
}

#acos(*args) ⇒ Calc::Q, Calc::C

Inverse trigonometric cosine

Examples:

Calc::Q(0.5).acos #=> Calc::Q(1.04719755119659774615)
Calc::Q(2.0).acos #=> Calc::C(1.31695789692481670863i)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 542

static VALUE
cq_acos(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qacos, &c_acos);
}

#acosh(*args) ⇒ Calc::Q, Calc::C

Inverse hyperbolic cosine

Examples:

Calc::Q(2).acosh #=> Calc::Q(1.31695789692481670862)
Calc::Q(0).acosh #=> Calc::C(1.57079632679489661923i)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 556

static VALUE
cq_acosh(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qacosh, &c_acosh);
}

#acot(*args) ⇒ Calc::Q

Inverse trigonometric cotangent

Examples:

Calc::Q(2).acot #=> Calc::Q(0.46364760900080611621)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 569

static VALUE
cq_acot(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qacot, NULL);
}

#acoth(*args) ⇒ Calc::Q, Calc::C

Inverse hyperbolic cotangent

Examples:

Calc::Q(2).acoth   #=> Calc::Q(0.5493061443340548457)
Calc::Q(0.5).acoth #=> Calc::C(0.5493061443340548457+1.57079632679489661923i)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 583

static VALUE
cq_acoth(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qacoth, &c_acoth);
}

#acsc(*args) ⇒ Calc::Q, Calc::C

Inverse trigonometric cosecant

Examples:

Calc::Q(2).acsc   #=> Calc::Q(0.52359877559829887308)
Calc::Q(0.5).acsc #=> Calc::C(1.57079632679489661923-1.31695789692481670863i)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 597

static VALUE
cq_acsc(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qacsc, &c_acsc);
}

#acsch(*args) ⇒ Calc::Q

Inverse hyperbolic cosecant

Examples:

Calc::Q(2).acsch #=> Calc::Q(0.4812118250596034475)

Parameters:

Returns:

Raises:



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# File 'ext/calc/q.c', line 611

static VALUE
cq_acsch(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qacsch, &c_acsch);
}

#agd(*args) ⇒ Calc::Q, Calc::C

Inverse gudermannian function

Examples:

Calc::Q(1).agd #=> Calc::Q(1.22619117088351707081)
Calc::Q(2).agd #=> Calc::C(1.5234524435626735209-3.14159265358979323846i)

Parameters:

  • eps (Calc::Q) —

    (optional) calculation accuracy

Returns:



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# File 'lib/calc/q.rb', line 19

def agd(*args)
  r = Calc::C(self).agd(*args)
  r.real? ? r.re : r
end

#appr(*args) ⇒ Object

Approximate numbers by multiples of a specified number

Returns the approximate value of self as specified by an error (defaults to Calc.config(:epsilon)) and rounding mode (defaults to Calc.config(:appr)).

Type “help appr” in calc for a description of the rounding modes.

Examples:

Calc::Q("5.44").appr("0.1",0) #=> Calc::Q(5.4)

Parameters:

  • y (Numeric, Calc::Q) —

    (optional) error

  • z (Interger) —

    (optional) rounding mode



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# File 'ext/calc/q.c', line 629

static VALUE
cq_appr(int argc, VALUE * argv, VALUE self)
{
    VALUE result, epsilon, rounding;
    NUMBER *qepsilon, *qrounding;
    long R = 0;
    int n;
    setup_math_error();

    n = rb_scan_args(argc, argv, "02", &epsilon, &rounding);
    if (n == 2) {
        if (FIXNUM_P(rounding)) {
            R = FIX2LONG(rounding);
        }
        else {
            qrounding = value_to_number(rounding, 1);
            if (qisfrac(qrounding)) {
                rb_raise(e_MathError, "fractional rounding for appr");
            }
            R = qtoi(DATA_PTR(qrounding));
            qfree(qrounding);
        }
    }
    else {
        R = conf->appr;
    }
    if (n >= 1) {
        qepsilon = value_to_number(epsilon, 1);
    }
    else {
        qepsilon = NULL;
    }
    result = wrap_number(qmappr(DATA_PTR(self), qepsilon ? qepsilon : conf->epsilon, R));
    if (qepsilon) {
        qfree(qepsilon);
    }
    return result;
}

#arg(*args) ⇒ Calc::Q Also known as: angle, phase

Returns the argument (the angle or phase) of a complex number in radians

This method is used by non-complex classes, it will be 0 for positive values, pi() otherwise.

Examples:

Calc::Q(-1).arg #=> Calc::Q(3.14159265358979323846)
Calc::Q(1).arg  #=> Calc::Q(0)

Parameters:

  • eps (Calc::Q) —

    (optional) calculation accuracy

Returns:



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# File 'lib/calc/q.rb', line 34

def arg(*args)
  if self < 0
    Calc.pi(*args)
  else
    ZERO
  end
end

#asec(*args) ⇒ Calc::Q, Calc::C

Inverse trigonometric secant

Examples:

Calc::Q(2).asec #=> Calc::Q(1.04719755119659774615)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 675

static VALUE
cq_asec(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qasec, &c_asec);
}

#asech(*args) ⇒ Calc::Q, Calc::C

Inverse hyperbolic secant

Examples:

Calc::Q(0.5).asech #=> Calc::Q(1.31695789692481670862)

Parameters:

Returns:

Raises:



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# File 'ext/calc/q.c', line 689

static VALUE
cq_asech(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qasech, &c_asech);
}

#asin(*args) ⇒ Calc::Q, Calc::C

Inverse trigonometric sine

Examples:

Calc::Q(0.5).asin #=> Calc::Q(0.52359877559829887308)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 702

static VALUE
cq_asin(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qasin, &c_asin);
}

#asinh(*args) ⇒ Calc::Q

Inverse hyperbolic sine

Examples:

Calc::Q(2).asinh #=> Calc::Q(1.44363547517881034249)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 715

static VALUE
cq_asinh(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qasinh, NULL);
}

#atan(*args) ⇒ Calc::Q

Inverse trigonometric tangent

Examples:

Calc::Q(2).atan #=> Calc::Q(1.10714871779409050302)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 728

static VALUE
cq_atan(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qatan, NULL);
}

#atan2(*args) ⇒ Calc::Q

Angle to point (arctangent with 2 arguments)

To match normal calling conventions, ‘y.atan2(x)` is equivalent to `Math.atan2(y,x)`. To avoid confusion, the class method may be preferrable: `Calc::Q.atan2(y,x)`.

Examples:

Calc::Q(0).atan2(0)   #=> Calc::Q(0)
Calc::Q(17).atan2(52) #=> Calc::Q(0.31597027195298044266)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 746

static VALUE
cq_atan2(int argc, VALUE * argv, VALUE self)
{
    return trans_function2(argc, argv, self, &qatan2);
}

#atanh(*args) ⇒ Calc::Q, Calc::C

Inverse hyperbolic tangent

Examples:

Calc::Q(0.5).atanh #=> Calc::Q(0.87758256189037271612)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 759

static VALUE
cq_atanh(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qatanh, &c_atanh);
}

#bernoulli ⇒ Calc::Q

Returns the bernoulli number with index self. Self must be an integer, and < 2^31 if even.

Examples:

Calc::Q(20).bernoulli.to_s(:frac) #=> "-174611/330"

Returns:

Raises:



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# File 'ext/calc/q.c', line 773

static VALUE
cq_bernoulli(VALUE self)
{
    NUMBER *qself, *qresult;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "Non-integer argument for bernoulli");
    }
    qresult = qbern(qself->num);
    if (!qresult) {
        rb_raise(e_MathError, "Bad argument for bern");
    }
    return wrap_number(qresult);
}

#bit(y) ⇒ Calc::Q Also known as: []

Returns 1 if binary bit y is set in self, otherwise 0.

Examples:

Calc::Q(9).bit(0) #=> Calc::Q(1)
Calc::Q(9).bit(1) #=> Calc::Q(0)

Parameters:

Returns:

See Also:



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# File 'lib/calc/q.rb', line 52

def bit(y)
  bit?(y) ? ONE : ZERO
end

#bit?(y) ⇒ Boolean

Returns true if binary bit y is set in self, otherwise false.

Examples:

Calc::Q(9).bit?(0) #=> true
Calc::Q(9).bit?(1) #=> false

Parameters:

Returns:

  • (Boolean)

See Also:



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# File 'ext/calc/q.c', line 799

static VALUE
cq_bitp(VALUE self, VALUE y)
{
    /* this is an "opcode" in calc rather than a builtin ("help bit" is
     * wrong!).  this is based on calc's opcodes.c#o_bit() */
    NUMBER *qself, *qy;
    long index;
    int r;
    setup_math_error();

    qself = DATA_PTR(self);
    qy = value_to_number(y, 0);
    if (qisfrac(qy)) {
        qfree(qy);
        rb_raise(e_MathError, "Bad argument type for bit");     /* E_BIT1 */
    }
    if (zge31b(qy->num)) {
        qfree(qy);
        rb_raise(e_MathError, "Index too large for bit");       /* E_BIT2 */
    }
    index = qtoi(qy);
    qfree(qy);
    r = qisset(qself, index);
    return r ? Qtrue : Qfalse;
}

#bit_length ⇒ Calc::Q

Returns the number of bits in the integer part of ‘self`

Note that this is compatible with ruby’s Integer#bit_length. Libcalc provides a similar function called ‘highbit` with different semantics.

This returns the bit position of the highest bit which is different to the sign bit. If there is no such bit (zero or -1), zero is returned.

Examples:

Calc::Q(0xff).bit_length #=> Calc::Q(8)

Returns:



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# File 'lib/calc/q.rb', line 68

def bit_length
  (negative? ? -self : self + ONE).log2.ceil
end

#bround(*args) ⇒ Calc::Q

Round to a specified number of binary digits

Rounds self rounded to the specified number of significant binary digits. For the meanings of the rounding flags, see “help bround”.

Examples:

Calc::Q(7,32).bround(3)  #=> Calc::Q(0.25)

Parameters:

  • places (Integer) —

    number of binary digits to round to (default 0)

  • rnd (Integer) —

    rounding flags (default Calc.config(:round)

Returns:



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# File 'ext/calc/q.c', line 836

static VALUE
cq_bround(int argc, VALUE * argv, VALUE self)
{
    return rounding_function(argc, argv, self, &qbround);
}

#btrunc(*args) ⇒ Calc::Q

Truncate to a number of binary places

Truncates to j binary places. If j is omitted, 0 places is assumed. Truncation of a non-integer prouces values nearer to zero.

Examples:

Calc.pi.btrunc    #=> Calc::Q(3)
Calc.pi.btrunc(5) #=> Calc::Q(3.125)

Parameters:

  • j (Integer)

Returns:



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# File 'ext/calc/q.c', line 853

static VALUE
cq_btrunc(int argc, VALUE * argv, VALUE self)
{
    return trunc_function(argc, argv, self, &qbtrunc);
}

#catalan ⇒ Calc::Q

Returns the Catalan number for index self. If self is negative, zero is returned.

Examples:

Calc::Q(2).catalan  #=> Calc::Q(2)
Calc::Q(5).catalan  #=> Calc::Q(42)
Calc::Q(20).catalan #=> Calc::Q(6564120420)

Returns:

Raises:



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# File 'ext/calc/q.c', line 869

static VALUE
cq_catalan(VALUE self)
{
    NUMBER *qself, *qresult;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "Non-integer value for catalan");
    }
    else if (zge31b(qself->num)) {
        rb_raise(e_MathError, "Value too large for catalan");
    }
    qresult = qcatalan(qself);
    if (!qresult) {
        rb_raise(e_MathError, "qcatalan() returned NULL");
    }
    return wrap_number(qresult);
}

#cfappr(*args) ⇒ Calc::Q

Approximation using continued fractions

If self is an integer or eps is zero, returns x.

If abs(eps) < 1, returns the smallest denominator number in one of the three intervals [self, self+abs(eps)], [self-abs(eps), self], [self-abs(eps)/2, self+abs(eps)/2].

If eps >= 1 and den(self) > n, returns the nearest above, below or approximation with denominatior less than or equal to n.

If den(self) <= eps, returns self.

When the result is not self, the rounding is controlled by the final parameter; see “help cfappr” for details.

Examples:

Calc.pi.cfappr(1).to_s(:frac)   #=> "3"
Calc.pi.cfappr(10).to_s(:frac)  #=> "25/8"
Calc.pi.cfappr(50).to_s(:frac)  #=> "157/50"
Calc.pi.cfappr(100).to_s(:frac) #=> "311/99"

Parameters:

  • eps (Numeric) —

    epsilon or upper limit of denominator (default: Calc.config(“epsilon”))

  • rnd (Integer) —

    rounding flags (default: Calc.config(“cfappr”))

Returns:



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# File 'ext/calc/q.c', line 914

static VALUE
cq_cfappr(int argc, VALUE * argv, VALUE self)
{
    VALUE eps, rnd, result;
    NUMBER *q;
    long n, R;
    setup_math_error();

    n = rb_scan_args(argc, argv, "02", &eps, &rnd);
    q = (n >= 1) ? value_to_number(eps, 1) : conf->epsilon;
    R = (n == 2) ? value_to_long(rnd) : conf->cfappr;
    result = wrap_number(qcfappr(DATA_PTR(self), q, R));
    if (n >= 1) {
        qfree(q);
    }
    return result;
}

#cfsim(*args) ⇒ Calc::Q

Simplify using continued fractions

If self is not an integer, returns either the nearest above or below number with denominator less than self.den.

Rounding is controlled by rnd (default: Calc.config(:cfsim)).

See “help cfsim” for details of rounding values.

Repeated calls to cfsim give a sequence of good approximations with decreasing denominators and correspondinlgy decreasing accuracy.

Examples:

x = Calc.pi; while (!x.int?) do; x = x.cfsim; puts x.to_s(:frac) if x.den < 1e6; end
1146408/364913
312689/99532
104348/33215
355/113
22/7
3

Parameters:

  • rnd (Integer) —

    rounding flags (default: Calc.config(:cfsim))

Returns:



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# File 'ext/calc/q.c', line 955

static VALUE
cq_cfsim(int argc, VALUE * argv, VALUE self)
{
    VALUE rnd;
    long n, R;
    setup_math_error();

    n = rb_scan_args(argc, argv, "01", &rnd);
    R = (n >= 1) ? value_to_long(rnd) : conf->cfsim;
    return wrap_number(qcfsim(DATA_PTR(self), R));
}

#char ⇒ String

Returns a string containing the character corresponding to a value

Note that this is for compatibility with calc, normally in ruby you should just #chr

Examples:

Calc::Q(88).char #=> "X"

Returns:

  • (String)

Raises:



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# File 'lib/calc/q.rb', line 80

def char
  raise MathError, "Non-integer for char" unless int?
  raise MathError, "Out of range for char" unless between?(0, 255)
  if zero?
    ""
  else
    to_i.chr
  end
end

#chr(*args) ⇒ String

Returns a string containing the character represented by ‘self` value according to encoding.

Unlike the calc version (‘char`), this allows numbers greater than 255 if an encoding is specified.

Examples:

Calc::Q(88).chr                   #=> "X"
Calc::Q(300).chr(Encoding::UTF_8) #=> Unicode I-breve

Parameters:

  • encoding (Encoding)

Returns:

  • (String) 


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# File 'lib/calc/q.rb', line 101

def chr(*args)
  to_i.chr(*args)
end

#clamp(min, max) ⇒ Object 



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# File 'lib/calc/q.rb', line 108

def clamp(min, max)
  super(Q.new(min), Q.new(max))
end

#conj ⇒ Calc::Q Also known as: conjugate

Complex conjugate

As the conjugate of real x is x, this method returns self.

Examples:

Calc::Q(3).conj #=> 3

Returns:



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# File 'lib/calc/q.rb', line 120

def conj
  self
end

#cos(*args) ⇒ Calc::Q

Cosine

Examples:

Calc::Q(1).cos #=> Calc::Q(0.5403023058681397174)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 974

static VALUE
cq_cos(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qcos, NULL);
}

#cosh(*args) ⇒ Calc::Q

Hyperbolic cosine

Examples:

Calc::Q(1).cosh #=> Calc::Q(1.54308063481524377848)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 987

static VALUE
cq_cosh(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qcosh, NULL);
}

#cot(*args) ⇒ Calc::Q

Trigonometric cotangent

Examples:

Calc::Q(1).cot #=> Calc::Q(0.64209261593433070301)

Parameters:

Returns:

Raises:



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# File 'ext/calc/q.c', line 1001

static VALUE
cq_cot(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qcot, NULL);
}

#coth(*args) ⇒ Calc::Q

Hyperbolic cotangent

Examples:

Calc::Q(1).coth #=> Calc::Q(1.31303528549933130364)

Parameters:

Returns:

Raises:



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# File 'ext/calc/q.c', line 1015

static VALUE
cq_coth(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qcoth, NULL);
}

#csc(*args) ⇒ Calc::Q

Trigonometric cosecant

Examples:

Calc::Q(1).csc #=> Calc::Q(1.18839510577812121626)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 1028

static VALUE
cq_csc(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qcsc, NULL);
}

#csch(*args) ⇒ Calc::Q

Hyperbolic cosecant

Examples:

Calc::Q(1).csch #=> Calc::Q(0.85091812823932154513)

Parameters:

Returns:

Raises:



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# File 'ext/calc/q.c', line 1042

static VALUE
cq_csch(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qcsch, NULL);
}

#den ⇒ Calc::Q Also known as: denominator

Returns the denominator. Always positive.

@example:

Calc::Q(1,3).den  #=> Calc::Q(3)
Calc::Q(-1,3).den #=> Calc::Q(3)

Returns:



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# File 'ext/calc/q.c', line 1055

static VALUE
cq_den(VALUE self)
{
    setup_math_error();
    return wrap_number(qden(DATA_PTR(self)));
}

#digit(*args) ⇒ Calc::Q

Returns the digit at the specified position on decimal or any other base.

Examples:

Calc::Q("123456.789").digit(3)  #=> Calc::Q(3)
Calc::Q("123456.789").digit(-3) #=> Calc::Q(9)

Parameters:

  • n (Integer) —

    index. negative indices are to the right of any decimal point

  • b (Integer) —

    (optional) base >= 2 (default 10)

Returns:



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# File 'ext/calc/q.c', line 1071

static VALUE
cq_digit(int argc, VALUE * argv, VALUE self)
{
    VALUE pos, base;
    NUMBER *qpos, *qbase, *qresult;
    long n;
    setup_math_error();

    n = rb_scan_args(argc, argv, "11", &pos, &base);
    qpos = value_to_number(pos, 1);
    if (qisfrac(qpos)) {
        qfree(qpos);
        rb_raise(e_MathError, "non-integer position for digit");
    }
    if (n >= 2) {
        qbase = value_to_number(base, 1);
        if (qisfrac(qbase)) {
            qfree(qpos);
            qfree(qbase);
            rb_raise(e_MathError, "non-integer base for digit");
        }
    }
    else {
        qbase = NULL;
    }
    qresult = qdigit(DATA_PTR(self), qpos->num, qbase ? qbase->num : _ten_);
    qfree(qpos);
    if (qbase)
        qfree(qbase);
    if (qresult == NULL) {
        rb_raise(e_MathError, "Invalid arguments for digit");
    }
    return wrap_number(qresult);
}

#digits(*args) ⇒ Calc::Q

Returns the number of digits of the integral part of self in decimal or another base

Note that this is unlike the ruby’s ‘Integer#digits`. For an equivalent, see `Q#digits_r`.

Examples:

Calc::Q("12.3456").digits   #=> Calc::Q(2)
Calc::Q(-1234).digits       #=> Calc::Q(4)
Calc::Q(0).digits           #=> Calc::Q(1)
Calc::Q("-0.123").digits    #=> Calc::Q(1)

Parameters:

  • b (Integer) —

    (optional) base >= 2 (default 10)

Returns:



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# File 'ext/calc/q.c', line 1119

static VALUE
cq_digits(int argc, VALUE * argv, VALUE self)
{
    VALUE base;
    NUMBER *qbase, *qresult;
    long n;
    setup_math_error();

    n = rb_scan_args(argc, argv, "01", &base);
    if (n >= 1) {
        qbase = value_to_number(base, 1);
        if (qisfrac(qbase) || qiszero(qbase) || qisunit(qbase)) {
            qfree(qbase);
            rb_raise(e_MathError, "base must be integer greater than 1 for digits");
        }
    }
    qresult = itoq(qdigits(DATA_PTR(self), n >= 1 ? qbase->num : _ten_));
    if (n >= 1)
        qfree(qbase);
    return wrap_number(qresult);
}

#digits_r(b = 10) ⇒ Array

Returns an array of digits in base b making up self

This is compatible with ruby’s ‘Integer#digits`. Note that `Q#digits` implements the libcalc function `digits`, which is different. Any fractional part of self is truncated.

Requires ruby 2.4.

Examples:

Calc::Q(1234).digits_r      #=> [Calc::Q(4), Calc::Q(3), Calc::Q(2), Calc::Q(1)]
Calc::Q(1234).digits_r(7)   #=> [Calc::Q(2), Calc::Q(1), Calc::Q(4), Calc::Q(3)]
Calc::Q(1234).digits_r(100) #=> [Calc::Q(34), Calc::Q(12)]

Parameters:

  • b (Integer) (defaults to: 10) —

    (optional) base, default 10

Returns:

  • (Array) 


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# File 'lib/calc/q.rb', line 140

def digits_r(b = 10)
  to_i.digits(b).map { |d| Q.new(d) }
end

#div(y) ⇒ Object

Ruby compatible integer division

Calls ‘quo` to get the quotient of integer division, with rounding mode which specifies behaviour compatible with ruby’s Numeric#div

Examples:

Calc::Q(13).div(4)     #=> Calc::Q(3)
Calc::Q("11.5").div(4) #=> Calc::Q(2)

Parameters:

See Also:

  • #quo


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# File 'lib/calc/q.rb', line 155

def div(y)
  quo(y, ZERO)
end

#divmod(y) ⇒ Object

Ruby compatible quotient/modulus

Returns an array containing the quotient and modulus by dividing ‘self` by `y`. Rounding is compatible with the ruby method `Numeric#divmod`.

Unlike ‘quomod`, this is not affected by `Calc.config(:quomod)`.

Examples:

Calc::Q(11).divmod(3)  #=> [Calc::Q(3), Calc::Q(2)]
Calc::Q(11).divmod(-3) #=> [Calc::Q(-4), Calc::Q(-1)]

Parameters:



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# File 'lib/calc/q.rb', line 170

def divmod(y)
  quomod(y, ZERO)
end

#downto(limit, &block) ⇒ Enumerator?

Iterates the given block, yielding values from ‘self` decreasing by 1 down to and including `limit`

x.downto(limit) is equivalent to x.step(by: -1, to: limit)

If no block is given, an Enumerator is returned instead.

Examples:

Calc::Q(10).downto(5) { |i| print i, " " } #=> 10 9 8 7 6 5

Parameters:

  • limit (Numeric) —

    lowest value to return

Returns:

  • (Enumerator, nil) 


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# File 'lib/calc/q.rb', line 185

def downto(limit, &block)
  step(limit, NEGONE, &block)
end

#estr ⇒ String

Returns a string which if evaluated creates a new object with the original value

Examples:

Calc::Q(0.5).estr #=> "Calc::Q(1,2)"

Returns:

  • (String) 


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# File 'lib/calc/q.rb', line 194

def estr
  s = self.class.name
  s << "("
  s << (int? ? num.to_s : "#{ num },#{ den }")
  s << ")"
  s
end

#euler ⇒ Object

Euler number

Returns the euler number of a specified index.

Considerable runtime and memory are required for calculating the euler number for large even indices. Calculated values are stored in a table so that later calls are executed quickly. This memory can be freed with ‘Calc.freeeuler`.

Examples:

Calc::Q(18).euler   #=> Calc::Q(-2404879675441)
Calc::Q(19).euler   #=> Calc::Q(0)
Calc::Q(20).euler   #=> Calc::Q(370371188237525)


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# File 'ext/calc/q.c', line 1155

static VALUE
cq_euler(VALUE self)
{
    NUMBER *qself, *qresult;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "non-integer value for euler");
    }
    qresult = qeuler(qself->num);
    if (qresult == NULL) {
        rb_raise(e_MathError, "number too big or out of memory for euler");
    }
    return wrap_number(qresult);
}

#even? ⇒ Boolean

Returns true if the number is an even integer

Examples:

Calc::Q(1).even? #=> false
Calc::Q(2).even? #=> true

Returns:

  • (Boolean) 


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# File 'ext/calc/q.c', line 1179

static VALUE
cq_evenp(VALUE self)
{
    return qiseven((NUMBER *) DATA_PTR(self)) ? Qtrue : Qfalse;
}

#exp(*args) ⇒ Calc::Q

Exponential function

Examples:

Calc::Q(1).exp #=> Calc::Q(2.71828182845904523536)
Calc::Q(2).exp #=> Calc::Q(7.38905609893065022723)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 1193

static VALUE
cq_exp(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qexp, NULL);
}

#fact ⇒ Calc::Q

Returns the factorial of a number.

@example:

Calc::Q(10).fact #=> Calc::Q(3628800)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1207

static VALUE
cq_fact(VALUE self)
{
    setup_math_error();
    return wrap_number(qfact(DATA_PTR(self)));
}

#factor(*args) ⇒ Calc::Q

Smallest prime factor not exceeding specified limit

Ignoring signs of self and limit; if self has a prime factor less than or equal to limit, then returns the smallest such factor.

Examples:

Calc::Q(2).power(32).+(1).factor #=> Calc::Q(641)

Parameters:

  • limit (Numeric) —

    (optional) limit, defaults to 2^32-1

Returns:

Raises:



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# File 'ext/calc/q.c', line 1226

static VALUE
cq_factor(int argc, VALUE * argv, VALUE self)
{
    VALUE limit;
    NUMBER *qself, *qlimit, *qfactor;
    ZVALUE zlimit;
    long a;
    int res;
    setup_math_error();

    a = rb_scan_args(argc, argv, "01", &limit);
    if (a >= 1) {
        qlimit = value_to_number(limit, 0);
        if (qisfrac(qlimit)) {
            qfree(qlimit);
            rb_raise(e_MathError, "non-integer limit for factor");
        }
        zcopy(qlimit->num, &zlimit);
        qfree(qlimit);
    }
    else {
        /* default limit is 2^32-1 */
        utoz((FULL) 0xffffffff, &zlimit);
    }
    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        zfree(zlimit);
        rb_raise(e_MathError, "non-integer for factor");
    }

    qfactor = qalloc();
    res = zfactor(qself->num, zlimit, &(qfactor->num));
    if (res < 0) {
        qfree(qfactor);
        zfree(zlimit);
        rb_raise(e_MathError, "limit >= 2^32 for factor");
    }
    zfree(zlimit);
    return wrap_number(qfactor);
}

#fcnt(y) ⇒ Calc::Q

Count number of times an integer divides self.

Returns the greatest non-negative n for which y^n is a divisor of self. Zero is returns if self is not divisible by y.

Examples:

Calc::Q(24).fcnt(4) #=> Calc::Q(1)
Calc::Q(48).fcnt(4) #=> Calc::Q(2)

Parameters:

  • y (Integer)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1279

static VALUE
cq_fcnt(VALUE self, VALUE y)
{
    VALUE result;
    NUMBER *qself, *qy;
    setup_math_error();

    qself = DATA_PTR(self);
    qy = value_to_number(y, 0);
    if (qisfrac(qself) || qisfrac(qy)) {
        qfree(qy);
        rb_raise(e_MathError, "non-integral argument for fcnt");
    }
    result = wrap_number(itoq(zdivcount(qself->num, qy->num)));
    qfree(qy);
    return result;
}

#fib ⇒ Calc::Q

Returns the Fibonacci number with index self.

Examples:

Calc::Q(10).fib #=> Calc::Q(55)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1349

static VALUE
cq_fib(VALUE self)
{
    setup_math_error();
    return wrap_number(qfib(DATA_PTR(self)));
}

#frac ⇒ Calc::Q

Return the fractional part of self

Examples:

Calc::Q(22,7).frac.to_s(:frac) #=> "1/7"

Returns:



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# File 'ext/calc/q.c', line 1303

static VALUE
cq_frac(VALUE self)
{
    NUMBER *qself;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisint(qself)) {
        return wrap_number(qlink(&_qzero_));
    }
    else {
        return wrap_number(qfrac(qself));
    }
}

#frem(y) ⇒ Calc::Q

Remove specified integer factors from self.

Examples:

Calc::Q(7).frem(4)   #=> 7
Calc::Q(24).frem(4)  #=> 6
Calc::Q(48).frem(4)  #=> 3
Calc::Q(-48).frem(4) #=> 3

Parameters:

  • y (Integer)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1329

static VALUE
cq_frem(VALUE self, VALUE y)
{
    VALUE result;
    NUMBER *qy;

    qy = value_to_number(y, 0);
    result = wrap_number(qfacrem(DATA_PTR(self), qy));
    qfree(qy);
    return result;
}

#gcd(*args) ⇒ Calc::Q

Greatest common divisor

Returns the greatest common divisor of self and all arguments. If no arguments, returns self.

Examples:

Calc::Q(12).gcd(8)               #=> Calc::Q(4)
Calc::Q(12).gcd(8, 6)            #=> Calc::Q(2)
Calc.gcd("9/10", "11/5", "4/25") #=> Calc::Q(0.02)

Returns:



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# File 'ext/calc/q.c', line 1367

static VALUE
cq_gcd(int argc, VALUE * argv, VALUE self)
{
    NUMBER *qresult, *qarg, *qtmp;
    int i;
    setup_math_error();

    qresult = qqabs(DATA_PTR(self));
    for (i = 0; i < argc; i++) {
        qarg = value_to_number(argv[i], 1);
        qtmp = qgcd(qresult, qarg);
        qfree(qarg);
        qfree(qresult);
        qresult = qtmp;
    }
    return wrap_number(qresult);
}

#gcdlcm(*args) ⇒ Array

Returns an array; [gcd, lcm]

This method exists for compatibility with ruby’s Integer class, however note that the libcalc version works on rational numbers and the lcm can be negative. You can also pass more than one value.

Examples:

Calc::Q(2).gcdlcm(2)  #=> [Calc::Q(2), Calc::Q(2)]
Calc::Q(3).gcdlcm(-7) #=> [Calc::Q(1), Calc::Q(-21)]

Returns:

  • (Array) 


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# File 'lib/calc/q.rb', line 212

def gcdlcm(*args)
  [gcd(*args), lcm(*args)]
end

#gcdrem(other) ⇒ Calc::Q

Returns greatest integer divisor of self relatively prime to other

Examples:

Calc::Q(6).gcdrem(15) #=> Calc::Q(2)
Calc::Q(15).gcdrem(6) #=> Calc::Q(5)

Returns:



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# File 'ext/calc/q.c', line 1392

static VALUE
cq_gcdrem(VALUE self, VALUE other)
{
    NUMBER *qother, *qresult;
    setup_math_error();

    qother = value_to_number(other, 0);
    qresult = qgcdrem(DATA_PTR(self), qother);
    qfree(qother);
    return wrap_number(qresult);
}

#gd(*args) ⇒ Calc::Q

Gudermannian function

Examples:

Calc::Q(1).gd #=> Calc::Q(0.86576948323965862429)

Parameters:

  • eps (Calc::Q) —

    (optional) calculation accuracy

Returns:



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# File 'lib/calc/q.rb', line 222

def gd(*args)
  r = Calc::C(self).gd(*args)
  r.real? ? r.re : r
end

#highbit ⇒ Calc::Q

Returns index of highest bit in binary representation of self

If self is a non-zero integer, higbit returns the index of the highest bit in the binary representation of abs(self). Equivalently, x.highbit = n if 2^n <= abs(x) < 2^(n+1); the binary representation of x then has n + 1 digits.

Examples:

Calc::Q(4).highbit        #=> Calc::Q(2)
Calc::Q(2).**(27).highbit #=> Calc::Q(27)

Returns:



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# File 'ext/calc/q.c', line 1416

static VALUE
cq_highbit(VALUE self)
{
    NUMBER *qself;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "non-integer argument for highbit");
    }
    if (qiszero(qself)) {
        return wrap_number(qlink(&_qnegone_));
    }
    else {
        return wrap_number(itoq(zhighbit(qself->num)));
    }
}

#hypot(*args) ⇒ Calc::Q

Returns the hypotenuse of a right-angled triangle given the other sides

@example:

Calc::Q(3).hypot(4)  #=> Calc::Q(5)
Calc::Q(2).hypot(-3) #=> Calc::Q(3.60555127546398929312)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 1442

static VALUE
cq_hypot(int argc, VALUE * argv, VALUE self)
{
    return trans_function2(argc, argv, self, &qhypot);
}

#i ⇒ Calc::C

Returns the corresponding imaginary number

Examples:

Calc::Q(1).i #=> Calc::C(1i)

Returns:



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# File 'lib/calc/q.rb', line 232

def i
  Calc::C(ZERO, self)
end

#im ⇒ Object Also known as: imaginary, imag 



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# File 'lib/calc/q.rb', line 236

def im
  ZERO
end

#imag? ⇒ Boolean

Returns true if the number is imaginary. Instances of this class always return false.

Examples:

Calc::Q(1).imag? #=> false

Returns:

  • (Boolean) 


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# File 'lib/calc/q.rb', line 247

def imag?
  false
end

#initialize_copy(orig) ⇒ Object 



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# File 'ext/calc/q.c', line 121

static VALUE
cq_initialize_copy(VALUE obj, VALUE orig)
{
    NUMBER *qorig, *qobj;

    if (obj == orig) {
        return obj;
    }
    if (!CALC_Q_P(orig)) {
        rb_raise(rb_eTypeError, "wrong argument type");
    }

    qorig = DATA_PTR(orig);
    qobj = qlink(qorig);
    DATA_PTR(obj) = qobj;

    return obj;
}

#inspect ⇒ Object 



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# File 'lib/calc/q.rb', line 251

def inspect
  "Calc::Q(#{ self })"
end

#int ⇒ Calc::Q

Integer part of the number

Examples:

Calc::Q(3).int      #=> Calc::Q(3)
Calc::Q("30/7").int #=> Calc::Q(4)
Calc::Q(-3.125).int #=> Calc::Q(-3)

Returns:



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# File 'ext/calc/q.c', line 1456

static VALUE
cq_int(VALUE self)
{
    NUMBER *qself;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisint(qself)) {
        return self;
    }
    return wrap_number(qint(qself));
}

#int? ⇒ Boolean Also known as: integer?

Returns true if the number is an integer.

Examples:

Calc::Q(2).int?     #=> true
Calc::Q(0.1).int?   #=> false

Returns:

  • (Boolean) 


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# File 'ext/calc/q.c', line 1476

static VALUE
cq_intp(VALUE self)
{
    return qisint((NUMBER *) DATA_PTR(self)) ? Qtrue : Qfalse;
}

#inverse ⇒ Calc::Q

Inverse of a real number

@example:

Calc::Q(3).inverse #=> Calc::Q(0.25)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1489

static VALUE
cq_inverse(VALUE self)
{
    setup_math_error();
    return wrap_number(qinv(DATA_PTR(self)));
}

#iroot(other) ⇒ Calc::Q

Integer part of specified root

x.iroot(n) returns the greatest integer v for which v^n <= x.

Examples:

Calc::Q(100).iroot(3) #=> Calc::Q(4)

Parameters:

  • n (Integer)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1506

static VALUE
cq_iroot(VALUE self, VALUE other)
{
    NUMBER *qother, *qresult;
    setup_math_error();

    qother = value_to_number(other, 0);
    qresult = qiroot(DATA_PTR(self), qother);
    qfree(qother);
    return wrap_number(qresult);
}

#iseven ⇒ Object 



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# File 'lib/calc/q.rb', line 255

def iseven
  even? ? ONE : ZERO
end

#isimag ⇒ Calc::Q

Returns 1 if the number is imaginary, otherwise returns 0. Instance of this class always return 0.

Examples:

Calc::Q(1).isimag #=> Calc::Q(0)

Returns:



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# File 'lib/calc/q.rb', line 265

def isimag
  ZERO
end

#ismult(y) ⇒ Calc::Q

Returns 1 if self exactly divides y, otherwise return 0.

Examples:

Calc::Q(6).ismult(2) #=> Calc::Q(1)
Calc::Q(2).ismult(6) #=> Calc::Q(0)

Returns:

See Also:



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# File 'lib/calc/q.rb', line 276

def ismult(y)
  mult?(y) ? ONE : ZERO
end

#isodd ⇒ Object 



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# File 'lib/calc/q.rb', line 280

def isodd
  odd? ? ONE : ZERO
end

#isprime ⇒ Calc::Q

Returns 1 if self is prime, 0 if it is not prime. This function can’t be used for odd numbers > 2^32.

Examples:

Calc::Q(2**31 - 9).isprime #=> Calc::Q(0)
Calc::Q(2**31 - 1).isprime #=> Calc::Q(1)

Returns:

Raises:



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# File 'lib/calc/q.rb', line 292

def isprime
  prime? ? ONE : ZERO
end

#isqrt ⇒ Calc::Q

Integer part of square root

x.isqrt returns the greatest integer n for which n^2 <= x.

Examples:

Calc::Q("8.5").isqrt #=> Calc::Q(2)
Calc::Q(200).isqrt   #=> Calc::Q(14)
Calc::Q("2e6").isqrt #=> Calc::Q(1414)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1529

static VALUE
cq_isqrt(VALUE self)
{
    setup_math_error();
    return wrap_number(qisqrt(DATA_PTR(self)));
}

#isreal ⇒ Calc::Q

Returns 1 if this number has zero imaginary part, otherwise returns 0. Instances of this class always return 1.

Examples:

Calc::Q(1).isreal #=> Calc::Q(1)

Returns:



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# File 'lib/calc/q.rb', line 302

def isreal
  ONE
end

#isrel(y) ⇒ Calc::Q

Returns 1 if both values are relatively prime

Examples:

Calc::Q(6).isrel(5) #=> Calc::Q(1)
Calc::Q(6).isrel(2) #=> Calc::Q(0)

Parameters:

  • other (Integer)

Returns:

Raises:

See Also:



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# File 'lib/calc/q.rb', line 315

def isrel(y)
  rel?(y) ? ONE : ZERO
end

#issq ⇒ Calc::Q

Returns 1 if this value is a square

Examples:

Calc::Q(25).issq     #=> Calc::Q(1)
Calc::Q(3).issq      #=> Calc::Q(0)
Calc::Q("4/25").issq #=> Calc::Q(1)

Returns:

See Also:



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# File 'lib/calc/q.rb', line 327

def issq
  sq? ? ONE : ZERO
end

#jacobi(y) ⇒ Calc::Q

Compute the Jacobi function (x = self / y)

Returns: -1 if x is not quadratic residue mod y

1 if y is composite, or x is a quadratic residue of y]
0 if y is even or y is < 0

Examples:

Calc::Q(2).jacobi(5)  #=> Calc::Q(-1)
Calc::Q(2).jacobi(15) #=> Calc::Q(1)

Parameters:

  • y (Integer)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1550

static VALUE
cq_jacobi(VALUE self, VALUE y)
{
    NUMBER *qy, *qresult;
    setup_math_error();

    qy = value_to_number(y, 0);
    qresult = qjacobi(DATA_PTR(self), qy);
    qfree(qy);
    return wrap_number(qresult);
}

#lcm(*args) ⇒ Calc::Q

Least common multiple

If no value is zero, lcm returns the least positive number which is a multiple of all values. If at least one value is zero, the lcm is zero.

Examples:

Calc::Q(12).lcm(24, 30) #=> Calc::Q(120)

Parameters:

  • v (Numeric) —

    zero or more values

Returns:



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# File 'ext/calc/q.c', line 1572

static VALUE
cq_lcm(int argc, VALUE * argv, VALUE self)
{
    NUMBER *qresult, *qarg, *qtmp;
    int i;
    setup_math_error();

    qresult = qqabs(DATA_PTR(self));
    for (i = 0; i < argc; i++) {
        qarg = value_to_number(argv[i], 1);
        qtmp = qlcm(qresult, qarg);
        qfree(qarg);
        qfree(qresult);
        qresult = qtmp;
        if (qiszero(qresult))
            break;
    }
    return wrap_number(qresult);
}

#lcmfact ⇒ Calc::Q

Least common multiple of positive integers up to specified integer

Retrurns the lcm of the integers 1, 2, …, self

Examples:

Calc::Q(6).lcmfact #=> Calc::Q(60)
Calc::Q(7).lcmfact #=> Calc::Q(420)

Returns:



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# File 'ext/calc/q.c', line 1601

static VALUE
cq_lcmfact(VALUE self)
{
    setup_math_error();
    return wrap_number(qlcmfact(DATA_PTR(self)));
}

#lfactor(other) ⇒ Calc::Q

Smallest prime factor in first specified number of primes

If n is nonzero and abs(n) has a prime factor in the first m primes (2, 3, 5, …), then n.lfactor(m) returns the smallest such factor. Otherwise it returns 1.

Examples:

Calc::Q(2**32 + 1).lfactor(116) #=> Calc::Q(641)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 1619

static VALUE
cq_lfactor(VALUE self, VALUE other)
{
    NUMBER *qother, *qresult;
    setup_math_error();

    qother = value_to_number(other, 1);
    qresult = qlowfactor(DATA_PTR(self), qother);
    qfree(qother);
    return wrap_number(qresult);
}

#lowbit ⇒ Calc::Q

Index of lowest nonzero bit in binary representation

Returns the index of the lowest nonzero bit in the binary representation of abs(self). If self is zero, returns -1.

Examples:

Calc::Q(2).lowbit     #=> Calc::Q(1)
Calc::Q(2**27).lowbit #=> Calc::Q(27)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1642

static VALUE
cq_lowbit(VALUE self)
{
    NUMBER *qself;
    long index;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qiszero(qself)) {
        index = -1;
    }
    else if (qisfrac(qself)) {
        rb_raise(e_MathError, "non-integer argument for lowbit");
    }
    else {
        index = zlowbit(qself->num);
    }
    return wrap_number(itoq(index));
}

#ltol(*args) ⇒ Calc::Q

leg-to-leg - third side of a right angled triangle

Returns the third side of a right-angled triangle with unit hypotenuse, given one other side. x.ltol is equivalent to sqrt(1 - x**2). Result is to nearest multiple of eps which defaults to Calc.config(:epsilon).

Examples:

Calc::Q("0.5").ltol #=> Calc::Q(0.86602540378443864676)

Parameters:

  • eps (Numeric) —

    (optional) calculation accuracy

Returns:

Raises:



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# File 'ext/calc/q.c', line 1674

static VALUE
cq_ltol(int argc, VALUE * argv, VALUE self)
{
    VALUE epsilon;
    NUMBER *qresult, *qepsilon;
    setup_math_error();

    if (rb_scan_args(argc, argv, "01", &epsilon) == 0) {
        qresult = qlegtoleg(DATA_PTR(self), conf->epsilon, FALSE);
    }
    else {
        qepsilon = value_to_number(epsilon, 1);
        qresult = qlegtoleg(DATA_PTR(self), qepsilon, FALSE);
        qfree(qepsilon);
    }
    return wrap_number(qresult);
}

#meq(y, md) ⇒ Calc::Q

test for equaility modulo a specific number

Returns 1 if self is congruent to y modulo md, otherwise 0.

Examples:

Calc::Q(5).meq(33, 7) #=> Calc::Q(1)
Calc::Q(5).meq(32, 7) #=> Calc::Q(0)

Parameters:

Returns:

See Also:



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# File 'lib/calc/q.rb', line 342

def meq(y, md)
  meq?(y, md) ? ONE : ZERO
end

#meq?(y, md) ⇒ Boolean

test for equality modulo a specific number

Returns true if self is congruent to y modulo md.

Examples:

Calc::Q(5).meq?(33, 7) #=> true
Calc::Q(5).meq?(32, 7) #=> false

Parameters:

Returns:

  • (Boolean)

See Also:



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# File 'ext/calc/q.c', line 1704

static VALUE
cq_meqp(VALUE self, VALUE y, VALUE md)
{
    VALUE result;
    NUMBER *qy, *qmd, *qtmp;
    setup_math_error();

    qy = value_to_number(y, 1);
    qmd = value_to_number(md, 1);
    qtmp = qsub(DATA_PTR(self), qy);
    result = qdivides(qtmp, qmd) ? Qtrue : Qfalse;
    qfree(qtmp);
    qfree(qmd);
    qfree(qy);
    return result;
}

#minv(md) ⇒ Calc::Q

Inverse of an integer modulo a specified integer

Finds x such that:

self * x = 1 (mod md)

If self and md are not relatively prime, zero is returned.

The canonical residues modulo md are determined by Calc.config(:mod) (run “help minv” in calc for details).

Examples:

Calc::Q(3).minv(10)  #=> Calc::Q(7)
Calc::Q(-3).minv(10) #=> Calc::Q(3)

Parameters:

  • md (Integer)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1737

static VALUE
cq_minv(VALUE self, VALUE md)
{
    NUMBER *qmd, *qresult;
    setup_math_error();

    qmd = value_to_number(md, 1);
    qresult = qminv(DATA_PTR(self), qmd);
    qfree(qmd);
    return wrap_number(qresult);
}

#mne(y, md) ⇒ Calc::Q

test for inequality modulo a specific number

Reurns 1 if self is not congruent to y modulo md, otherwise 0. This is the opposite of #meq.

Examples:

Calc::Q(5).mne(33, 7) #=> Calc::Q(0)
Calc::Q(5).mne(32, 7) #=> Calc::Q(1)

Parameters:

Returns:

See Also:



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# File 'lib/calc/q.rb', line 358

def mne(y, md)
  meq?(y, md) ? ZERO : ONE
end

#mne?(y, md) ⇒ Boolean

test for inequality modulo a specific number

Returns true of self is not congruent to y modulo md. This is the opposiute of #meq?.

Examples:

Calc::Q(5).mne?(33, 7) #=> false
Calc::Q(5).mne?(32, 6) #=> true

Parameters:

Returns:

  • (Boolean) 


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# File 'lib/calc/q.rb', line 373

def mne?(y, md)
  !meq?(y, md)
end

#mod(*args) ⇒ Calc::Q

Computes the remainder for an integer quotient

@example:

Calc::Q(11).mod(5) #=> Calc::Q(1)

Parameters:

  • y (Numeric, Calc::Q)
  • rnd (Integer) —

    rounding flags (default Calc.config(:mod))

Returns:



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# File 'ext/calc/q.c', line 1757

static VALUE
cq_mod(int argc, VALUE * argv, VALUE self)
{
    VALUE other, rnd;
    NUMBER *qother, *qresult;
    long n;
    setup_math_error();

    n = rb_scan_args(argc, argv, "11", &other, &rnd);
    qother = value_to_number(other, 0);
    if (qiszero(qother)) {
        qfree(qother);
        rb_raise(rb_eZeroDivError, "division by zero in mod");
    }
    qresult = qmod(DATA_PTR(self), qother, (n == 2) ? value_to_long(rnd) : conf->mod);
    qfree(qother);
    return wrap_number(qresult);
}

#modulo(y) ⇒ Object

Ruby compatible modulus

Returns the modulus of ‘self` divided by `y`.

Rounding is compatible with the ruby method Numeric#modulo. Unlike ‘mod`, this is not affected by `Calc.confg(:mod)`.

Examples:

Calc::Q(13).modulo(4)  #=> Calc::Q(1)
Calc::Q(13).modulo(-4) #=> Calc::Q(-3)

Parameters:



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# File 'lib/calc/q.rb', line 388

def modulo(y)
  mod(y, ZERO)
end

#mult?(other) ⇒ Boolean

Returns true if self exactly divides y, otherwise return false.

Examples:

Calc::Q(6).mult?(2) #=> true
Calc::Q(2).mult?(6) #=> false

Returns:

  • (Boolean)

See Also:



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# File 'ext/calc/q.c', line 1784

static VALUE
cq_multp(VALUE self, VALUE other)
{
    VALUE result;
    NUMBER *qother;
    setup_math_error();

    qother = value_to_number(other, 0);
    result = qdivides(DATA_PTR(self), qother) ? Qtrue : Qfalse;
    qfree(qother);
    return result;
}

#near(*args) ⇒ Calc::Q

Compare nearness of two numbers with a standard

Returns:

-1 if abs(self - other) < abs(eps)
 0 if abs(self - other) = abs(eps)
 1 if abs(self - other) > abs(eps)

Examples:

Calc::Q("22/7").near("3.15", ".01")  #=> Calc::Q(-1)
Calc::Q("22/7").near("3.15", ".005") #=> Calc::Q(1)

Parameters:

  • other (Numeric)
  • eps (Numeric) —

    (optional) defaults to Calc.config(:epsilon)

Returns:



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# File 'ext/calc/q.c', line 1811

static VALUE
cq_near(int argc, VALUE * argv, VALUE self)
{
    VALUE other, epsilon;
    NUMBER *qother, *qepsilon, *qresult;
    int n;
    setup_math_error();

    n = rb_scan_args(argc, argv, "11", &other, &epsilon);
    qother = value_to_number(other, 1);
    qepsilon = (n == 2) ? value_to_number(epsilon, 1) : conf->epsilon;
    qresult = itoq((long) qnear(DATA_PTR(self), qother, qepsilon));
    qfree(qother);
    if (n == 2)
        qfree(qepsilon);
    return wrap_number(qresult);
}

#negative? ⇒ Boolean

Return true if ‘self` is less than zero.

This method exists for ruby Integer/Rational compatibility

Examples:

Calc::Q(-1).negative? #=> true
Calc::Q(0).negative?  #=> false
Calc::Q(1).negative?  #=> false

Returns:

  • (Boolean) 


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# File 'lib/calc/q.rb', line 401

def negative?
  self < ZERO
end

#nextcand(*args) ⇒ Calc::Q

Next candidate for primeness

Returns the least positive integer i greater than abs(self) expressible as residue + k * modulus, where k is an integer, for which i.ptest?(count, skip) is true, or if there is no such integer i, nil.

See ‘ptest?` for a description of `count` and `skip`. For basic purposes, use default values and count > 1. Higher counts increase the probability that the returned value is prime.

Examples:

Calc::Q(100).nextcand(10)        #=> Calc::Q(101)
Calc::Q(5000000000).nextcand(10) #=> Calc::Q(5000000029)

Parameters:

  • count (Integer) —

    number of tests for ptest (default 1)

  • skip (Integer) —

    base selection mode for ptest (default 1)

  • residue (Integer) —

    (default 0)

  • modulus (Integer) —

    (default 1)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1849

static VALUE
cq_nextcand(int argc, VALUE * argv, VALUE self)
{
    return cand_navigation(argc, argv, self, &znextcand);
}

#nextprime ⇒ Calc::Q

Next prime number

If self is >= 2**32, raises an exception. Otherwise returns the next prime number.

Examples:

Calc::Q(2).nextprime         #=> Calc::Q(3)
Calc::Q(10).nextprime        #=> Calc::Q(11)
Calc::Q(100).nextprime       #=> Calc::Q(101)
Calc::Q("1e6").nextprime     #=> Calc::Q(1000003)
Calc::Q(2**32 - 1).nextprime #=> Calc::Q(4294967311)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1872

static VALUE
cq_nextprime(VALUE self)
{
    NUMBER *qself;
    FULL next_prime;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "non-integral for nextprime");
    }
    next_prime = znprime(qself->num);
    if (next_prime == 0) {
        /* return 2^32+15 */
        return wrap_number(qlink(&_nxtprime_));
    }
    else if (next_prime == 1) {
        rb_raise(e_MathError, "nextprime arg is >= 2^32");
    }
    return wrap_number(utoq(next_prime));
}

#norm ⇒ Calc::Q

Norm of a value

For real values, norm is the square of the absolute value.

Examples:

Calc::Q("3.4").norm  #=> Calc::Q(11.56)
Calc::Q("-3.4").norm #=> Calc::Q(11.56)

Returns:



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# File 'ext/calc/q.c', line 1903

static VALUE
cq_norm(VALUE self)
{
    setup_math_error();
    return wrap_number(qsquare(DATA_PTR(self)));
}

#num ⇒ Calc::Q Also known as: numerator

Returns the numerator. Return value has the same sign as self.

@example:

Calc::Q(1,3).num  #=> Calc::Q(1)
Calc::Q(-1,3).num #=> Calc::Q(-1)

Returns:



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# File 'ext/calc/q.c', line 1917

static VALUE
cq_num(VALUE self)
{
    setup_math_error();
    return wrap_number(qnum(DATA_PTR(self)));
}

#odd? ⇒ Boolean

Returns true if the number is an odd integer

Examples:

Calc::Q(1).odd? #=> true
Calc::Q(2).odd? #=> false

Returns:

  • (Boolean) 


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# File 'ext/calc/q.c', line 1931

static VALUE
cq_oddp(VALUE self)
{
    return qisodd((NUMBER *) DATA_PTR(self)) ? Qtrue : Qfalse;
}

#ord ⇒ Calc::Q

Returns self.

This method is for ruby Integer compatibility

Returns:



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# File 'lib/calc/q.rb', line 410

def ord
  self
end

#perm(other) ⇒ Calc::Q

Permutation number

Returns the number of permutations in which ‘other` things may be chosen from `self` items where order in which they are chosen matters.

Examples:

Calc::Q(7).perm(3) #=> Calc::Q(210)

Parameters:

  • other (Integer)

Returns:



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# File 'ext/calc/q.c', line 1947

static VALUE
cq_perm(VALUE self, VALUE other)
{
    NUMBER *qresult, *qother;
    setup_math_error();

    qother = value_to_number(other, 0);
    qresult = qperm(DATA_PTR(self), qother);
    qfree(qother);
    return wrap_number(qresult);
}

#pfact ⇒ Calc::Q

Product of primes up to specified integer

Examples:

Calc::Q(2).pfact   #=> Calc::Q(2)
Calc::Q(10).pfact  #=> Calc::Q(210)
Calc::Q(100).pfact #=> Calc::Q(2305567963945518424753102147331756070)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1968

static VALUE
cq_pfact(VALUE self)
{
    setup_math_error();
    return wrap_number(qpfact(DATA_PTR(self)));
}

#pix ⇒ Calc::Q

Number of primes not exceeded specified number

Examples:

Calc::Q(10).pix    #=> Calc::Q(4)
Calc::Q(100).pix   #=> Calc::Q(25)
Calc::Q(10**9).pix #=> Calc::Q(50847534)

Returns:

Raises:



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# File 'ext/calc/q.c', line 1984

static VALUE
cq_pix(VALUE self)
{
    NUMBER *qself;
    long value;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "non-integer value for pix");
    }
    value = zpix(qself->num);
    if (value >= 0) {
        return wrap_number(utoq(value));
    }
    rb_raise(e_MathError, "pix arg is >= 2^32");
}

#places(*args) ⇒ Calc::Q

Number of decimal (or other) places in fractional part

Returns the number of digits needed to express the fractional part of this number in base b. If self is an integer, returns 0. If the expansion in base b is infinite, returns nil.

Examples:

Calc::Q(3).places           #=> Calc::Q(0)
Calc::Q("0.0123").places    #=> Calc::Q(4)
Calc::Q("0.0123").places(2) #=> nil
Calc::Q(".625").places(2)   #=> Calc::Q(3)

Parameters:

  • b (Integer) —

    base (default 10)

Returns:

Raises:



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# File 'ext/calc/q.c', line 2017

static VALUE
cq_places(int argc, VALUE * argv, VALUE self)
{
    VALUE base;
    NUMBER *qbase;
    long places;
    setup_math_error();

    if (rb_scan_args(argc, argv, "01", &base) == 0) {
        places = qdecplaces(DATA_PTR(self));
    }
    else {
        qbase = value_to_number(base, 0);
        if (qisfrac(qbase)) {
            qfree(qbase);
            rb_raise(e_MathError, "non-integer base for places");
        }
        places = qplaces(DATA_PTR(self), qbase->num);
        qfree(qbase);
        if (places == -2) {
            rb_raise(e_MathError, "invalid base for places");
        }
    }
    if (places == -1) {
        return Qnil;
    }
    return wrap_number(itoq(places));
}

#pmod(n, md) ⇒ Calc::Q

Integral power of an interger modulo a specified integer

x.pmod(n, md) returns the integer value of the canonical reidue of x^n modulo md. The canonical residue is determined by Calc.config(:mod). See “help pmod” for full details.

Examples:

Calc::Q(2).pmod(3, 10) #=> Calc::Q(8)
Calc::Q(2).pmod(5, 10) #=> Calc::Q(2)

Parameters:

  • n (Integer)
  • md (Integer)

Returns:



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# File 'ext/calc/q.c', line 2059

static VALUE
cq_pmod(VALUE self, VALUE n, VALUE md)
{
    NUMBER *qn, *qmd, *qresult;
    setup_math_error();

    qn = value_to_number(n, 0);
    qmd = value_to_number(md, 0);
    qresult = qpowermod(DATA_PTR(self), qn, qmd);
    qfree(qn);
    qfree(qmd);
    return wrap_number(qresult);
}

#popcnt(*args) ⇒ Calc::Q

Number of bits that match 0 or 1

Counts of number of bits in abs(self) that match bitval (1 or 0, default 1)

Examples:

Calc::Q(32767).popcnt    #=> Calc::Q(15)
Calc::Q(32767).popcnt(0) #=> Calc::Q(0)

Parameters:

  • bitval (Integer) —

    0 or 1 (default 1)

Returns:



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# File 'ext/calc/q.c', line 2083

static VALUE
cq_popcnt(int argc, VALUE * argv, VALUE self)
{
    VALUE bitval;
    NUMBER *qself, *qbitval, *qresult;
    int b = 1;
    setup_math_error();

    if (rb_scan_args(argc, argv, "01", &bitval) == 1) {
        qbitval = value_to_number(bitval, 0);
        if (qiszero(qbitval)) {
            b = 0;
        }
        qfree(qbitval);
    }
    qself = DATA_PTR(self);
    if (qisint(qself)) {
        qresult = itoq(zpopcnt(qself->num, b));
    }
    else {
        qresult = itoq(zpopcnt(qself->num, b) + zpopcnt(qself->den, b));
    }
    return wrap_number(qresult);
}

#positive? ⇒ Boolean

Return true if ‘self` is greater than zero.

This method exists for ruby Integer/Rational compatibility

Examples:

Calc::Q(-1).positive? #=> false
Calc::Q(0).positive?  #=> false
Calc::Q(1).positive?  #=> true

Returns:

  • (Boolean) 


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# File 'lib/calc/q.rb', line 423

def positive?
  self > ZERO
end

#power(*args) ⇒ Calc::Q, Calc::C

Evaluates a numeric power

Examples:

Calc::Q("1.2345").power(10) #=> Calc::Q(8.2207405646327461795)
Calc::Q(-1).power("0.1")    #=> Calc::C(0.95105651629515357212+0.3090169943749474241i)

Parameters:

Returns:

Raises:



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# File 'ext/calc/q.c', line 2118

static VALUE
cq_power(int argc, VALUE * argv, VALUE self)
{
    /* ref: powervalue() in calc value.c.  handle cases NUM,NUM and NUM,COM */
    VALUE arg, epsilon, result;
    NUMBER *qself, *qarg, *qepsilon;
    COMPLEX *cself, *carg;
    setup_math_error();

    if (rb_scan_args(argc, argv, "11", &arg, &epsilon) == 1) {
        qepsilon = NULL;
    }
    else {
        qepsilon = value_to_number(epsilon, 1);
    }
    qself = DATA_PTR(self);
    if (CALC_C_P(arg) || RB_TYPE_P(arg, T_COMPLEX) || qisneg(qself)) {
        cself = comalloc();
        qfree(cself->real);
        cself->real = qlink(qself);
        if (RB_TYPE_P(arg, T_STRING)) {
            carg = comalloc();
            qfree(carg->real);
            carg->real = value_to_number(arg, 1);
        }
        else {
            carg = value_to_complex(arg);
        }
        result = wrap_complex(c_power(cself, carg, qepsilon ? qepsilon : conf->epsilon));
        comfree(cself);
        comfree(carg);
    }
    else {
        qarg = value_to_number(arg, 1);
        result = wrap_number(qpower(qself, qarg, qepsilon ? qepsilon : conf->epsilon));
        qfree(qarg)
    }
    if (qepsilon) {
        qfree(qepsilon);
    }
    return result;
}

#pred ⇒ Calc::Q

Returns one less than self.

This method exists for ruby Integer compatibility.

Examples:

Calc::Q(1).pred #=> Calc::Q(0)

Returns:



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# File 'lib/calc/q.rb', line 434

def pred
  self - ONE
end

#prevcand(*args) ⇒ Calc::Q

Previous candidate for primeness

Returns the greatest positive integer i less than abs(self) expressible as residue + k * modulus, where k is an integer, for which ptest?(count, skip) is true, or if there is no such integer i, nil.

See ‘ptest?` for a description of `count` and `skip`. For basic purposes, use default values and count > 1. Higher counts increase the probability that the returned value is prime.

Examples:

Calc::Q(100).prevcand(10)        #=> Calc::Q(97)
Calc::Q(5000000000).prevcand(10) #=> Calc::Q(4999999937)

Parameters:

  • count (Integer) —

    number of tests for ptest (default 1)

  • skip (Integer) —

    base selection mode for ptest (default 1)

  • residue (Integer) —

    (default 0)

  • modulus (Integer) —

    (default 1)

Returns:

Raises:



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# File 'ext/calc/q.c', line 2181

static VALUE
cq_prevcand(int argc, VALUE * argv, VALUE self)
{
    return cand_navigation(argc, argv, self, &zprevcand);
}

#prevprime ⇒ Calc::Q

Previous prime number

If self <= 2, returns nil. If self is >= 2**32, raises an exception. Otherwise returns the previous prime number.

Examples:

Calc::Q(2).prevprime         #=> nil
Calc::Q(10).prevprime        #=> Calc::Q(7)
Calc::Q(100).prevprime       #=> Calc::Q(97)
Calc::Q("1e6").prevprime     #=> Calc::Q(999983)
Calc::Q(2**32 - 1).prevprime #=> Calc::Q(4294967291)

Returns:

Raises:



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# File 'ext/calc/q.c', line 2201

static VALUE
cq_prevprime(VALUE self)
{
    NUMBER *qself;
    FULL prev_prime;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "non-integral for prevprime");
    }
    prev_prime = zpprime(qself->num);
    if (prev_prime == 0) {
        return Qnil;
    }
    else if (prev_prime == 1) {
        rb_raise(e_MathError, "prevprime arg is >= 2^32");
    }
    return wrap_number(utoq(prev_prime));
}

#prime? ⇒ Boolean

Small integer prime test

Returns true if self is prime, false if it is not prime. This function can’t be used for odd numbers > 2^32.

Examples:

Calc::Q(2**31 - 9).prime? #=> false
Calc::Q(2**31 - 1).prime? #=> true

Returns:

  • (Boolean)

Raises:

See Also:



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# File 'ext/calc/q.c', line 2234

static VALUE
cq_primep(VALUE self)
{
    NUMBER *qself;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisfrac(qself)) {
        rb_raise(e_MathError, "non-integral for prime?");
    }
    switch (zisprime(qself->num)) {
    case 0:
        return Qfalse;
    case 1:
        return Qtrue;
    default:
        rb_raise(e_MathError, "prime? argument is an odd value > 2^32");
    }
}

#ptest(*args) ⇒ Calc::Q

Probabilistic primacy test

Returns 1 if ptest? would have returned true, otherwise 0.

Parameters:

  • count (Integer)
  • skip (Integer)

Returns:

See Also:



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# File 'lib/calc/q.rb', line 446

def ptest(*args)
  ptest?(*args) ? ONE : ZERO
end

#ptest?(*args) ⇒ Boolean

Probabilistic test of primality

Returns false if self is definitely not a prime. Returns true if self is probably prime.

If self is < 2**32, essentially calles prime? and returns true only if self is prime.

If self is > 2**32 and is divisible by a prime <= 101, returns false.

In other cases, performs abs(count) tests of bases of possible primality.

‘skip` specifies how to select bases for testing:

0: random in [2, self-2]
1: successive primes [2, 3, 5, ...] not exceeding min(self, 65536)
otherwise: integers starting from `skip`

For a full explanation of the tests, see “help ptest”.

Returning true from this function means self is either prime or a strong psuedoprime. The probability that a composite number returns true is less than (1/4)**count. For example, ptest(10) incorrectly returns true less than once in a million numbers; ptest(20) incorrectly returns true less than once in a quadrillion numbers.

Examples:

Calc::Q(4294967291).ptest?(10) #=> true

Parameters:

  • count (Integer) —

    (optional: default 1)

  • skip (Integer) —

    (optional: default 1)

Returns:

  • (Boolean) 


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# File 'ext/calc/q.c', line 2285

static VALUE
cq_ptestp(int argc, VALUE * argv, VALUE self)
{
    VALUE count, skip, result;
    NUMBER *qcount, *qskip;
    int n;
    setup_math_error();

    n = rb_scan_args(argc, argv, "02", &count, &skip);
    qcount = (n >= 1) ? value_to_number(count, 0) : qlink(&_qone_);
    qskip = (n >= 2) ? value_to_number(skip, 0) : qlink(&_qone_);
    result = qprimetest(DATA_PTR(self), qcount, qskip) ? Qtrue : Qfalse;
    qfree(qcount);
    qfree(qskip);
    return result;
}

#quomod(*args) ⇒ Array<Calc::Q>

TODO:

add parameter to control rounding

Returns the quotient and remainder from division

Examples:

Calc::Q(13).quomod(5) #=> [Calc::Q(2), Calc::Q(3)]

Parameters:

  • y (Numeric, Calc::Q) —

    number to divide by

  • rnd (Integer) —

    optional rounding mode, default Calc.config(:quomod)

Returns:

  • (Array<Calc::Q>) —

    Array containing quotient and remainder



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# File 'ext/calc/q.c', line 2311

static VALUE
cq_quomod(int argc, VALUE * argv, VALUE self)
{
    VALUE other, rnd;
    NUMBER *qother, *qquo, *qmod;
    long r;
    setup_math_error();

    if (rb_scan_args(argc, argv, "11", &other, &rnd) == 2) {
        r = value_to_long(rnd);
    }
    else {
        r = conf->quomod;
    }
    qother = value_to_number(other, 0);
    if (qiszero(qother)) {
        qfree(qother);
        rb_raise(rb_eZeroDivError, "division by zero in quomod");
    }
    qquomod(DATA_PTR(self), qother, &qquo, &qmod, r);
    qfree(qother);
    return rb_assoc_new(wrap_number(qquo), wrap_number(qmod));
}

#rationalize(eps = nil) ⇒ Calc::Q

Returns a simpler approximation of the value if the optional argument eps is given (rat-|eps| <= result <= rat+|eps|), self otherwise.

Note that this method exists for ruby Numeric compatibility. Libcalc has an alternative approximation method with different semantics, see ‘appr`.

Examples:

Calc::Q(5033165, 16777216).rationalize                   #=> Calc::Q(5033165/16777216)
Calc::Q(5033165, 16777216).rationalize(Rational('0.01')) #=> Calc::Q(3/10)
Calc::Q(5033165, 16777216).rationalize(Rational('0.1'))  #=> Calc::Q(1/3)

Parameters:

  • eps (Float, Rational) (defaults to: nil)

Returns:



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# File 'lib/calc/q.rb', line 462

def rationalize(eps = nil)
  eps ? Q.new(to_r.rationalize(eps)) : self
end

#re ⇒ Object Also known as: real 



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# File 'lib/calc/q.rb', line 466

def re
  self
end

#real? ⇒ Boolean

Returns true if this number has zero imaginary part. Instances of this class always return true.

Examples:

Calc::Q(1).real? #=> true

Returns:

  • (Boolean) 


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# File 'lib/calc/q.rb', line 476

def real?
  true
end

#rel?(other) ⇒ Boolean

Returns true if both values are relatively prime

Examples:

Calc::Q(6).rel?(5) #=> true
Calc::Q(6).rel?(2) #=> false

Parameters:

  • other (Integer)

Returns:

  • (Boolean)

Raises:

See Also:



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# File 'ext/calc/q.c', line 2345

static VALUE
cq_relp(VALUE self, VALUE other)
{
    VALUE result;
    NUMBER *qself, *qother;
    setup_math_error();

    qself = DATA_PTR(self);
    qother = value_to_number(other, 0);
    if (qisfrac(qself) || qisfrac(qother)) {
        qfree(qother);
        rb_raise(e_MathError, "non-integer for rel?");
    }
    result = zrelprime(qself->num, qother->num) ? Qtrue : Qfalse;
    qfree(qother);
    return result;
}

#remainder(y) ⇒ Calc::C, Calc::Q

Remainder of ‘self` divided by `y`

This method is provided for compatibility with ruby’s ‘Numeric#remainder`. Unlike `%` and `mod`, this method behaves the same as the ruby version, unaffected by `Calc.config(:mod).

Examples:

Calc::Q(13).remainder(4) #=> Calc::Q(1)

Parameters:

Returns:



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# File 'lib/calc/q.rb', line 490

def remainder(y)
  z = modulo(y)
  if !z.zero? && ((self < 0 && y > 0) || (self > 0 && y < 0))
    z - y
  else
    z
  end
end

#round(*args) ⇒ Calc::Q

Round to a specified number of decimal places

Rounds self rounded to the specified number of significant binary digits. For the meanings of the rounding flags, see “help round”.

Examples:

Calc::Q(7,32).round(3)  #=> Calc::Q(0.219)

Parameters:

  • places (Integer) —

    number of decimal digits to round to (default 0)

  • rnd (Integer) —

    rounding flags (default Calc.config(:round))

Returns:



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# File 'ext/calc/q.c', line 2374

static VALUE
cq_round(int argc, VALUE * argv, VALUE self)
{
    return rounding_function(argc, argv, self, &qround);
}

#sec(*args) ⇒ Calc::Q

Trigonometric secant

Examples:

Calc::Q(1).sec #=> Calc::Q(1.85081571768092561791)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 2387

static VALUE
cq_sec(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qsec, NULL);
}

#sech(*args) ⇒ Calc::Q

Hyperbolic secant

Examples:

Calc::Q(1).sech #=> Calc::Q(0.64805427366388539958)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 2400

static VALUE
cq_sech(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qsech, NULL);
}

#sin(*args) ⇒ Calc::Q

Trigonometric sine

Examples:

Calc::Q(1).sin #=> Calc::Q(0.84147098480789650665)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 2413

static VALUE
cq_sin(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qsin, NULL);
}

#sinh(*args) ⇒ Calc::Q

Hyperbolic sine

Examples:

Calc::Q(1).sin #=> Calc::Q(1.17520119364380145688)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 2426

static VALUE
cq_sinh(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qsinh, NULL);
}

#size ⇒ Calc::Q

Returns the number of bytes in the machine representation of ‘self`

This method acts like ruby’s Integer#size, except that is works on fractions in which case the result is the number of bytes for both the numerator and denominator. As the internal representation of numbers differs between ruby and libcalc, it wil not necessary return the same values as Integer#size.

Examples:

Calc::Q(1).size     #=> Calc::Q(4)
Calc::Q(2**32).size #=> Calc::Q(8)
Calc::Q("1/3").size #=> Calc::Q(8)

Returns:



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# File 'ext/calc/q.c', line 2446

static VALUE
cq_size(VALUE self)
{
    NUMBER *qself;
    size_t s;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisint(qself)) {
        s = qself->num.len * sizeof(HALF);
    }
    else {
        s = (qself->num.len + qself->den.len) * sizeof(HALF);
    }
    return wrap_number(itoq(s));
}

#sq? ⇒ Boolean

Return true if this value is a square

Returns true if there exists integers, b such that:

self == a^2 / b^2  (b != 0)

Note that this function works on rationals, so:

Calc::Q(25, 15).sq? #=> true

If you want to test for perfect square integers, you need to exclude non-integer values before you test.

Examples:

Calc::Q(25).sq?     #=> true
Calc::Q(3).sq?      #=> false
Calc::Q("4/25").sq? #=> true

Returns:

  • (Boolean)

See Also:



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# File 'ext/calc/q.c', line 2481

static VALUE
cq_sqp(VALUE self)
{
    setup_math_error();
    return qissquare(DATA_PTR(self)) ? Qtrue : Qfalse;
}

#step(a1 = nil, a2 = ONE) ⇒ Enumerator?

Invokes the given block with the sequence of numbers starting at self incrementing by step (default 1) on each call.

In the first format, uses keyword parameters:

x.step(by: step, to: limit)

In the second format, uses positional parameters:

x.step(limit = nil, step = 1)

If step is negative, the sequence decrements instead of incrementing. If step is zero, the sequence will yield self forever.

If limit exists, the sequence will stop once the next item yielded would be higher than limit (if step is positive) or lower than limit (if step is negative). If limit is nil, the sequence never stops.

If no block is givem, an Enumerator is returned instead.

This method was added for ruby Numeric compatibiliy; unlike Numeric#step, it is not an error for step to be zero in the positional format.

prints:

2.71828182845904523536 2.91828182845904523536 3.11828182845904523536

Examples:

Calc::Q(1).step(10, 3).to_a      #=> [Calc::Q(1), Calc::Q(4), Calc::Q(7), Calc::Q(10)]
Calc::Q(10).step(by: -2).take(4) #=> [Calc::Q(10), Calc::Q(8), Calc::Q(6), Calc::Q(4)]
Calc::Q(1).exp.step(to: Calc.pi, by: "0.2") { |q| print q, " " } #=> nil

Parameters:

  • by (Numeric) —

    amount to add to sequence each iteration

  • to (Numeric) —

    end of sequence value

Returns:

  • (Enumerator, nil) 


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# File 'lib/calc/q.rb', line 529

def step(a1 = nil, a2 = ONE)
  return to_enum(:step, a1, a2) unless block_given?
  to, by = step_args(a1, a2)
  loop { yield self } if by.zero?
  i = self
  loop do
    break if to && ((by.positive? && i > to) || (by.negative? && i < to))
    yield i
    i += by
  end
end

#succ ⇒ Calc::Q Also known as: next

Returns one more than self.

This method exists for ruby Integer compatibility.

Examples:

Calc::Q(1).pred #=> Calc::Q(2)

Returns:



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# File 'lib/calc/q.rb', line 566

def succ
  self + ONE
end

#tan(*args) ⇒ Calc::Q

Trigonometric tangent

Examples:

Calc::Q(1).tan #=> Calc::Q(1.55740772465490223051)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 2495

static VALUE
cq_tan(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qtan, NULL);
}

#tanh(*args) ⇒ Calc::Q

Hyperbolic tangent

Examples:

Calc::Q(1).tanh #=> Calc::Q(0.76159415595576488812)

Parameters:

Returns:



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# File 'ext/calc/q.c', line 2508

static VALUE
cq_tanh(int argc, VALUE * argv, VALUE self)
{
    return trans_function(argc, argv, self, &qtanh, NULL);
}

#times ⇒ Enumerator?

Iterates the given block ‘self` times, passing in values from zero to self - 1

If no block is given, an Enumerator is returned instead.

Examples:

Calc::Q(5).times { |i| print i, " " }
#=> 0 1 2 3 4

Returns:

  • (Enumerator, nil) 


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# File 'lib/calc/q.rb', line 580

def times
  return to_enum(:times) unless block_given?
  i = ZERO
  while i < self
    yield i
    i += ONE
  end
end

#to_c ⇒ Complex

Returns a ruby Complex number with self as the real part and zero imaginary part.

Examples:

Calc::Q(2).to_c    #=> (2+0i)
Calc::Q(2.5).to_c  #=> ((5/2)+0i)

Returns:

  • (Complex) 


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# File 'lib/calc/q.rb', line 596

def to_c
  Complex(int? ? to_i : to_r, 0)
end

#to_complex ⇒ Calc::C

Returns a Calc::C complex number with self as the real part and zero imaginary part.

Examples:

Calc::Q(2).to_complex #=> Calc::C(2)

Returns:



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# File 'lib/calc/q.rb', line 606

def to_complex
  C.new(self, 0)
end

#to_f ⇒ Object

libcalc has no concept of floating point numbers. so we use ruby’s Rational#to_f



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# File 'lib/calc/q.rb', line 612

def to_f
  to_r.to_f
end

#to_i ⇒ Integer

Converts this number to a core ruby Integer.

If self is a fraction, the fractional part is truncated.

Note that the return value is a ruby Integer. If you want to convert to an integer but have the result be a ‘Calc::Q` object, use `trunc` or `round`.

Examples:

Calc::Q(42).to_i     #=> 42
Calc::Q("1e19").to_i #=> 10000000000000000000
Calc::Q(1,2).to_i    #=> 0

Returns:

  • (Integer) 


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# File 'ext/calc/q.c', line 2528

static VALUE
cq_to_i(VALUE self)
{
    NUMBER *qself;
    ZVALUE ztmp;
    VALUE string, result;
    char *s;
    setup_math_error();

    qself = DATA_PTR(self);
    if (qisint(qself)) {
        zcopy(qself->num, &ztmp);
    }
    else {
        zquo(qself->num, qself->den, &ztmp, 0);
    }
    if (zgtmaxlong(ztmp)) {
        /* too big to fit in a long, ztoi would return MAXLONG.  use a string
         * intermediary */
        math_divertio();
        zprintval(ztmp, 0, 0);
        s = math_getdivertedio();
        string = rb_str_new2(s);
        free(s);
        result = rb_funcall(string, rb_intern("to_i"), 0);
    }
    else {
        result = LONG2NUM(ztoi(ztmp));
    }
    zfree(ztmp);
    return result;
}

#to_r ⇒ Object

convert to a core ruby Rational



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# File 'lib/calc/q.rb', line 617

def to_r
  Rational(numerator.to_i, denominator.to_i)
end

#to_s(*args) ⇒ String

Converts this number to a string.

Format depends on the configuration parameters “mode” and “display. The mode can be overridden for individual calls.

Examples:

Calc::Q(1,2).to_s        #=> "0.5"
Calc::Q(1,2).to_s(:frac) #=> "1/2"
Calc::Q(42).to_s(:hex)   #=> "0x2a"
Calc::Q(42).to_s(8)      #=> "52"

Parameters:

  • mode (String, Symbol, Integer) —

    (optional) output mode, see [Calc::Config]

Returns:

  • (String) 


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# File 'ext/calc/q.c', line 2574

static VALUE
cq_to_s(int argc, VALUE * argv, VALUE self)
{
    NUMBER *qself = DATA_PTR(self);
    char *s;
    int args;
    VALUE rs, mode;
    setup_math_error();

    args = rb_scan_args(argc, argv, "01", &mode);
    if (args == 1 && FIXNUM_P(mode)) {
        if (qisint((NUMBER *) DATA_PTR(self))) {
            rs = rb_funcall(cq_to_i(self), rb_intern("to_s"), 1, mode);
        }
        else {
            rb_raise(rb_eArgError, "can't convert non-integer to string with base");
        }
    }
    else {
        math_divertio();
        if (args == 0) {
            qprintnum(qself, MODE_DEFAULT);
        }
        else {
            qprintnum(qself, (int) value_to_mode(mode));
        }
        s = math_getdivertedio();
        rs = rb_str_new2(s);
        free(s);
    }

    return rs;
}

#trunc(*args) ⇒ Calc::Q Also known as: truncate

Truncate to a number of decimal places

Truncates to j decimal places. If j is omitted, 0 places is assumed. Truncation of a non-integer prouces values nearer to zero.

Examples:

Calc.pi.trunc    #=> Calc::Q(3)
Calc.pi.trunc(5) #=> Calc::Q(3.14159)

Parameters:

  • j (Integer)

Returns:



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# File 'ext/calc/q.c', line 2619

static VALUE
cq_trunc(int argc, VALUE * argv, VALUE self)
{
    return trunc_function(argc, argv, self, &qtrunc);
}

#upto(limit, &block) ⇒ Enumerator?

Iterates the given block, yielding values from ‘self` increasing by 1 up to and including `limit`

x.upto(limit) is equivalent to x.step(by: 1, to: limit)

If no block is given, an Enumerator is returned instead.

Examples:

Calc::Q(5).upto(10) { |i| print i, " " } #=> 5 6 7 8 9 10

Parameters:

  • limit (Numeric) —

    highest value to return

Returns:

  • (Enumerator, nil) 


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# File 'lib/calc/q.rb', line 634

def upto(limit, &block)
  step(limit, ONE, &block)
end

#xor(*args) ⇒ Calc::Q

Bitwise exclusive or of a set of integers

xor(a, b, c, …) is equivalent to (((a ^ b) ^ c) … ) note that ^ is the ruby xor operator, not the calc power operator.

Examples:

Calc::Q(3).xor(5)           #=> Calc::Q(6)
Calc::Q(5).xor(3, -7, 2, 9) #=> Calc::Q(-12)

Returns:



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# File 'lib/calc/q.rb', line 647

def xor(*args)
  args.inject(self, :^)
end

#zero? ⇒ Calc::Q

Returns true if self is zero

Examples:

Calc::Q(0).zero? #=> true
Calc::Q(1).zero? #=> false

Parameters:

Returns:



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# File 'ext/calc/q.c', line 2633

static VALUE
cq_zerop(VALUE self)
{
    return qiszero((NUMBER *) DATA_PTR(self)) ? Qtrue : Qfalse;
}

#|(y) ⇒ Calc::Q

Bitwise OR

Examples:

Calc::Q(18) | 20 #=> Calc::Q(22)

Parameters:

  • y (Integer)

Returns:



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# File 'ext/calc/q.c', line 499

static VALUE
cq_or(VALUE x, VALUE y)
{
    return numeric_op(x, y, &qor, NULL, id_or);
}

#~ ⇒ Object

Bitwise NOT (complement)

This is ‘-self - 1` if self is an integer, `-self` otherwise.

Examples:

~Calc::Q(7)   #=> Calc::Q(-8)
~Calc::Q(0.5) #=> Calc::Q(-0.5)


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# File 'ext/calc/q.c', line 513

static VALUE
cq_comp(VALUE self)
{
    setup_math_error();
    return wrap_number(qcomp(DATA_PTR(self)));
}