/*
 *  call-seq:
 *     Math.acos(x)    => float
 *  
 *  Computes the arc cosine of <i>x</i>. Returns 0..PI.
 */

static VALUE
math_acos(obj, x)
    VALUE obj, x;
{
    double d;

    Need_Float(x);
    errno = 0;
    d = acos(RFLOAT(x)->value);
    domain_check(d, "acos");
    return rb_float_new(d);
}

/*
 *  call-seq:
 *     Math.acosh(x)    => float
 *  
 *  Computes the inverse hyperbolic cosine of <i>x</i>.
 */

static VALUE
math_acosh(obj, x)
    VALUE obj, x;
{
    double d;

    Need_Float(x);
    errno = 0;
    d = acosh(RFLOAT(x)->value);
    domain_check(d, "acosh");
    return rb_float_new(d);
}

/*
 *  call-seq:
 *     Math.asin(x)    => float
 *  
 *  Computes the arc sine of <i>x</i>. Returns -{PI/2} .. {PI/2}.
 */

static VALUE
math_asin(obj, x)
    VALUE obj, x;
{
    double d;

    Need_Float(x);
    errno = 0;
    d = asin(RFLOAT(x)->value);
    domain_check(d, "asin");
    return rb_float_new(d);
}

/*
 *  call-seq:
 *     Math.asinh(x)    => float
 *  
 *  Computes the inverse hyperbolic sine of <i>x</i>.
 */

static VALUE
math_asinh(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(asinh(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.atan(x)    => float
 *  
 *  Computes the arc tangent of <i>x</i>. Returns -{PI/2} .. {PI/2}.
 */

static VALUE
math_atan(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(atan(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.atan2(y, x)  => float
 *  
 *  Computes the arc tangent given <i>y</i> and <i>x</i>. Returns
 *  -PI..PI.
 *     
 */

static VALUE
math_atan2(obj, y, x)
    VALUE obj, x, y;
{
    Need_Float2(y, x);
    return rb_float_new(atan2(RFLOAT(y)->value, RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.atanh(x)    => float
 *  
 *  Computes the inverse hyperbolic tangent of <i>x</i>.
 */

static VALUE
math_atanh(obj, x)
    VALUE obj, x;
{
    double d;

    Need_Float(x);
    errno = 0;
    d = atanh(RFLOAT(x)->value);
    domain_check(d, "atanh");
    return rb_float_new(d);
}

/*
 *  call-seq:
 *     Math.cos(x)    => float
 *  
 *  Computes the cosine of <i>x</i> (expressed in radians). Returns
 *  -1..1.
 */

static VALUE
math_cos(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(cos(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.cosh(x)    => float
 *  
 *  Computes the hyperbolic cosine of <i>x</i> (expressed in radians).
 */

static VALUE
math_cosh(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    
    return rb_float_new(cosh(RFLOAT(x)->value));
}

/*
 * call-seq:
 *    Math.erf(x)  => float
 *
 *  Calculates the error function of x.
 */

static VALUE
math_erf(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(erf(RFLOAT(x)->value));
}

/*
 * call-seq:
 *    Math.erfc(x)  => float
 *
 *  Calculates the complementary error function of x.
 */

static VALUE
math_erfc(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(erfc(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.exp(x)    => float
 *  
 *  Returns e**x.
 */

static VALUE
math_exp(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(exp(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.frexp(numeric)    => [ fraction, exponent ]
 *  
 *  Returns a two-element array containing the normalized fraction (a
 *  <code>Float</code>) and exponent (a <code>Fixnum</code>) of
 *  <i>numeric</i>.
 *     
 *     fraction, exponent = Math.frexp(1234)   #=> [0.6025390625, 11]
 *     fraction * 2**exponent                  #=> 1234.0
 */

static VALUE
math_frexp(obj, x)
    VALUE obj, x;
{
    double d;
    int exp;

    Need_Float(x);
    
    d = frexp(RFLOAT(x)->value, &exp);
    return rb_assoc_new(rb_float_new(d), INT2NUM(exp));
}

/*
 *  call-seq:
 *     Math.hypot(x, y)    => float
 *  
 *  Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle
 *  with sides <i>x</i> and <i>y</i>.
 *     
 *     Math.hypot(3, 4)   #=> 5.0
 */

static VALUE
math_hypot(obj, x, y)
    VALUE obj, x, y;
{
    Need_Float2(x, y);
    return rb_float_new(hypot(RFLOAT(x)->value, RFLOAT(y)->value));
}

/*
 *  call-seq:
 *     Math.ldexp(flt, int) -> float
 *  
 *  Returns the value of <i>flt</i>*(2**<i>int</i>).
 *     
 *     fraction, exponent = Math.frexp(1234)
 *     Math.ldexp(fraction, exponent)   #=> 1234.0
 */

static VALUE
math_ldexp(obj, x, n)
    VALUE obj, x, n;
{
    Need_Float(x);
    return rb_float_new(ldexp(RFLOAT(x)->value, NUM2INT(n)));
}

/*
 *  call-seq:
 *     Math.log(numeric)    => float
 *  
 *  Returns the natural logarithm of <i>numeric</i>.
 */

static VALUE
math_log(obj, x)
    VALUE obj, x;
{
    double d;

    Need_Float(x);
    errno = 0;
    d = log(RFLOAT(x)->value);
    domain_check(d, "log");
    return rb_float_new(d);
}

/*
 *  call-seq:
 *     Math.log10(numeric)    => float
 *  
 *  Returns the base 10 logarithm of <i>numeric</i>.
 */

static VALUE
math_log10(obj, x)
    VALUE obj, x;
{
    double d;

    Need_Float(x);
    errno = 0;
    d = log10(RFLOAT(x)->value);
    domain_check(d, "log10");
    return rb_float_new(d);
}

/*
 *  call-seq:
 *     Math.sin(x)    => float
 *  
 *  Computes the sine of <i>x</i> (expressed in radians). Returns
 *  -1..1.
 */

static VALUE
math_sin(obj, x)
    VALUE obj, x;
{
    Need_Float(x);

    return rb_float_new(sin(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.sinh(x)    => float
 *  
 *  Computes the hyperbolic sine of <i>x</i> (expressed in
 *  radians).
 */

static VALUE
math_sinh(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(sinh(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.sqrt(numeric)    => float
 *  
 *  Returns the non-negative square root of <i>numeric</i>.
 */

static VALUE
math_sqrt(obj, x)
    VALUE obj, x;
{
    double d;

    Need_Float(x);
    errno = 0;
    d = sqrt(RFLOAT(x)->value);
    domain_check(d, "sqrt");
    return rb_float_new(d);
}

/*
 *  call-seq:
 *     Math.tan(x)    => float
 *  
 *  Returns the tangent of <i>x</i> (expressed in radians).
 */

static VALUE
math_tan(obj, x)
    VALUE obj, x;
{
    Need_Float(x);

    return rb_float_new(tan(RFLOAT(x)->value));
}

/*
 *  call-seq:
 *     Math.tanh()    => float
 *  
 *  Computes the hyperbolic tangent of <i>x</i> (expressed in
 *  radians).
 */

static VALUE
math_tanh(obj, x)
    VALUE obj, x;
{
    Need_Float(x);
    return rb_float_new(tanh(RFLOAT(x)->value));
}

# File lib/complex.rb, line 566
  def acos(z)
    if Complex.generic?(z) and z >= -1 and z <= 1
      acos!(z)
    else
      -1.0.im * log( z + 1.0.im * sqrt(1.0-z*z) )
    end
  end

# File lib/complex.rb, line 598
  def acosh(z)
    if Complex.generic?(z) and z >= 1
      acosh!(z)
    else
      log( z + sqrt(z*z-1.0) )
    end
  end

# File lib/complex.rb, line 574
  def asin(z)
    if Complex.generic?(z) and z >= -1 and z <= 1
      asin!(z)
    else
      -1.0.im * log( 1.0.im * z + sqrt(1.0-z*z) )
    end
  end

# File lib/complex.rb, line 606
  def asinh(z)
    if Complex.generic?(z)
      asinh!(z)
    else
      log( z + sqrt(1.0+z*z) )
    end
  end

# File lib/complex.rb, line 582
  def atan(z)
    if Complex.generic?(z)
      atan!(z)
    else
      1.0.im * log( (1.0.im+z) / (1.0.im-z) ) / 2.0
    end
  end

# File lib/complex.rb, line 590
  def atan2(y,x)
    if Complex.generic?(y) and Complex.generic?(x)
      atan2!(y,x)
    else
      -1.0.im * log( (x+1.0.im*y) / sqrt(x*x+y*y) )
    end
  end

# File lib/complex.rb, line 614
  def atanh(z)
    if Complex.generic?(z) and z >= -1 and z <= 1
      atanh!(z)
    else
      log( (1.0+z) / (1.0-z) ) / 2.0
    end
  end

# File lib/complex.rb, line 495
  def cos(z)
    if Complex.generic?(z)
      cos!(z)
    else
      Complex(cos!(z.real)*cosh!(z.image),
              -sin!(z.real)*sinh!(z.image))
    end
  end

# File lib/complex.rb, line 531
  def cosh(z)
    if Complex.generic?(z)
      cosh!(z)
    else
      Complex( cosh!(z.real)*cos!(z.image), sinh!(z.real)*sin!(z.image) )
    end
  end

# File lib/complex.rb, line 486
  def exp(z)
    if Complex.generic?(z)
      exp!(z)
    else
      Complex(exp!(z.real) * cos!(z.image), exp!(z.real) * sin!(z.image))
    end
  end

# File lib/complex.rb, line 548
  def log(z)
    if Complex.generic?(z) and z >= 0
      log!(z)
    else
      r, theta = z.polar
      Complex(log!(r.abs), theta)
    end
  end

# File lib/complex.rb, line 558
  def log10(z)
    if Complex.generic?(z)
      log10!(z)
    else
      log(z)/log!(10)
    end
  end

# File lib/complex.rb, line 505
  def sin(z)
    if Complex.generic?(z)
      sin!(z)
    else
      Complex(sin!(z.real)*cosh!(z.image),
              cos!(z.real)*sinh!(z.image))
    end
  end

# File lib/complex.rb, line 523
  def sinh(z)
    if Complex.generic?(z)
      sinh!(z)
    else
      Complex( sinh!(z.real)*cos!(z.image), cosh!(z.real)*sin!(z.image) )
    end
  end

# File lib/complex.rb, line 467
  def sqrt(z)
    if Complex.generic?(z)
      if z >= 0
        sqrt!(z)
      else
        Complex(0,sqrt!(-z))
      end
    else
      if z.image < 0
        sqrt(z.conjugate).conjugate
      else
        r = z.abs
        x = z.real
        Complex( sqrt!((r+x)/2), sqrt!((r-x)/2) )
      end
    end
  end

# File lib/complex.rb, line 515
  def tan(z)
    if Complex.generic?(z)
      tan!(z)
    else
      sin(z)/cos(z)
    end
  end

# File lib/complex.rb, line 539
  def tanh(z)
    if Complex.generic?(z)
      tanh!(z)
    else
      sinh(z)/cosh(z)
    end
  end