Class: Float

Inherits:
Numeric show all
Defined in:
numeric.c

Overview

Float objects represent inexact real numbers using the native architecture's double-precision floating point representation.

Constant Summary

ROUNDS =
INT2FIX(FLT_ROUNDS)
RADIX =
INT2FIX(FLT_RADIX)
MANT_DIG =
INT2FIX(DBL_MANT_DIG)
DIG =
INT2FIX(DBL_DIG)
MIN_EXP =
INT2FIX(DBL_MIN_EXP)
MAX_EXP =
INT2FIX(DBL_MAX_EXP)
MIN_10_EXP =
INT2FIX(DBL_MIN_10_EXP)
MAX_10_EXP =
INT2FIX(DBL_MAX_10_EXP)
MIN =
DBL2NUM(DBL_MIN)
MAX =
DBL2NUM(DBL_MAX)
EPSILON =
DBL2NUM(DBL_EPSILON)
INFINITY =
DBL2NUM(INFINITY)
NAN =
DBL2NUM(NAN)

Instance Method Summary (collapse)

Methods inherited from Numeric

#+@, #abs2, #conj, #conjugate, #div, #i, #imag, #imaginary, #initialize_copy, #integer?, #nonzero?, #polar, #real, #real?, #rect, #rectangular, #remainder, #singleton_method_added, #step, #to_c

Methods included from Comparable

#between?

Instance Method Details

- (Float) %(other) - (Float) modulo(other)

Return the modulo after division of flt by other.

6543.21.modulo(137)      #=> 104.21
6543.21.modulo(137.24)   #=> 92.9299999999996


# File 'numeric.c'

/*
 *  call-seq:
 *     flt % other        ->  float
 *     flt.modulo(other)  ->  float
 *
 *  Return the modulo after division of <code>flt</code> by <code>other</code>.
 *
 *     6543.21.modulo(137)      #=> 104.21
 *     6543.21.modulo(137.24)   #=> 92.9299999999996
 */

static VALUE
flo_mod(VALUE x, VALUE y)
{
    double fy, mod;

    switch (TYPE(y)) {
      case T_FIXNUM:
    fy = (double)FIX2LONG(y);
    break;
      case T_BIGNUM:
    fy = rb_big2dbl(y);
    break;
      case T_FLOAT:
    fy = RFLOAT_VALUE(y);
    break;
      default:
    return rb_num_coerce_bin(x, y, '%');
    }
    flodivmod(RFLOAT_VALUE(x), fy, 0, &mod);
    return DBL2NUM(mod);
}

- (Float) *(other)

Returns a new float which is the product of float and other.



# File 'numeric.c'

/*
 * call-seq:
 *   float * other  ->  float
 *
 * Returns a new float which is the product of <code>float</code>
 * and <code>other</code>.
 */

static VALUE
flo_mul(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
    return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
      case T_BIGNUM:
    return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
      case T_FLOAT:
    return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
      default:
    return rb_num_coerce_bin(x, y, '*');
    }
}

- (Float) **(other)

Raises float the other power.

2.0**3      #=> 8.0


# File 'numeric.c'

/*
 * call-seq:
 *
 *  flt ** other  ->  float
 *
 * Raises <code>float</code> the <code>other</code> power.
 *
 *    2.0**3      #=> 8.0
 */

static VALUE
flo_pow(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
    return DBL2NUM(pow(RFLOAT_VALUE(x), (double)FIX2LONG(y)));
      case T_BIGNUM:
    return DBL2NUM(pow(RFLOAT_VALUE(x), rb_big2dbl(y)));
      case T_FLOAT:
    {
        double dx = RFLOAT_VALUE(x);
        double dy = RFLOAT_VALUE(y);
        if (dx < 0 && dy != round(dy))
        return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y);
        return DBL2NUM(pow(dx, dy));
    }
      default:
    return rb_num_coerce_bin(x, y, rb_intern("**"));
    }
}

- (Float) +(other)

Returns a new float which is the sum of float and other.



# File 'numeric.c'

/*
 * call-seq:
 *   float + other  ->  float
 *
 * Returns a new float which is the sum of <code>float</code>
 * and <code>other</code>.
 */

static VALUE
flo_plus(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
    return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
      case T_BIGNUM:
    return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
      case T_FLOAT:
    return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
      default:
    return rb_num_coerce_bin(x, y, '+');
    }
}

- (Float) -(other)

Returns a new float which is the difference of float and other.



# File 'numeric.c'

/*
 * call-seq:
 *   float - other  ->  float
 *
 * Returns a new float which is the difference of <code>float</code>
 * and <code>other</code>.
 */

static VALUE
flo_minus(VALUE x, VALUE y)
{
    switch (TYPE(y)) {
      case T_FIXNUM:
    return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
      case T_BIGNUM:
    return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
      case T_FLOAT:
    return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
      default:
    return rb_num_coerce_bin(x, y, '-');
    }
}

- (Float) -

Returns float, negated.



# File 'numeric.c'

/*
 * call-seq:
 *    -float  ->  float
 *
 * Returns float, negated.
 */

static VALUE
flo_uminus(VALUE flt)
{
    return DBL2NUM(-RFLOAT_VALUE(flt));
}

- (Float) /(other)

Returns a new float which is the result of dividing float by other.



# File 'numeric.c'

/*
 * call-seq:
 *   float / other  ->  float
 *
 * Returns a new float which is the result of dividing
 * <code>float</code> by <code>other</code>.
 */

static VALUE
flo_div(VALUE x, VALUE y)
{
    long f_y;
    double d;

    switch (TYPE(y)) {
      case T_FIXNUM:
    f_y = FIX2LONG(y);
    return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y);
      case T_BIGNUM:
    d = rb_big2dbl(y);
    return DBL2NUM(RFLOAT_VALUE(x) / d);
      case T_FLOAT:
    return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y));
      default:
    return rb_num_coerce_bin(x, y, '/');
    }
}

- (Boolean) <(real)

true if flt is less than real.



# File 'numeric.c'

/*
 * call-seq:
 *   flt < real  ->  true or false
 *
 * <code>true</code> if <code>flt</code> is less than <code>real</code>.
 */

static VALUE
flo_lt(VALUE x, VALUE y)
{
    double a, b;

    a = RFLOAT_VALUE(x);
    switch (TYPE(y)) {
      case T_FIXNUM:
    b = (double)FIX2LONG(y);
    break;

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

      case T_FLOAT:
    b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(b)) return Qfalse;
#endif
    break;

      default:
    return rb_num_coerce_relop(x, y, '<');
    }
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(a)) return Qfalse;
#endif
    return (a < b)?Qtrue:Qfalse;
}

- (Boolean) <=(real)

true if flt is less than or equal to real.



# File 'numeric.c'

/*
 * call-seq:
 *   flt <= real  ->  true or false
 *
 * <code>true</code> if <code>flt</code> is less than
 * or equal to <code>real</code>.
 */

static VALUE
flo_le(VALUE x, VALUE y)
{
    double a, b;

    a = RFLOAT_VALUE(x);
    switch (TYPE(y)) {
      case T_FIXNUM:
    b = (double)FIX2LONG(y);
    break;

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

      case T_FLOAT:
    b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(b)) return Qfalse;
#endif
    break;

      default:
    return rb_num_coerce_relop(x, y, rb_intern("<="));
    }
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(a)) return Qfalse;
#endif
    return (a <= b)?Qtrue:Qfalse;
}

- (-1, ...) <=>(real)

Returns -1, 0, +1 or nil depending on whether flt is less than, equal to, or greater than real. This is the basis for the tests in Comparable.



# File 'numeric.c'

/*
 *  call-seq:
 *     flt <=> real  ->  -1, 0, +1 or nil
 *
 *  Returns -1, 0, +1 or nil depending on whether <i>flt</i> is less
 *  than, equal to, or greater than <i>real</i>. This is the basis for
 *  the tests in <code>Comparable</code>.
 */

static VALUE
flo_cmp(VALUE x, VALUE y)
{
    double a, b;

    a = RFLOAT_VALUE(x);
    if (isnan(a)) return Qnil;
    switch (TYPE(y)) {
      case T_FIXNUM:
    b = (double)FIX2LONG(y);
    break;

      case T_BIGNUM:
    if (isinf(a)) {
        if (a > 0.0) return INT2FIX(1);
        else return INT2FIX(-1);
    }
    b = rb_big2dbl(y);
    break;

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

      default:
    if (isinf(a) && (!rb_respond_to(y, rb_intern("infinite?")) ||
             !RTEST(rb_funcall(y, rb_intern("infinite?"), 0, 0)))) {
        if (a > 0.0) return INT2FIX(1);
        return INT2FIX(-1);
    }
    return rb_num_coerce_cmp(x, y, rb_intern("<=>"));
    }
    return rb_dbl_cmp(a, b);
}

- (Boolean) ==(obj)

Returns true only if obj has the same value as flt. Contrast this with Float#eql?, which requires obj to be a Float.

1.0 == 1   #=> true


# File 'numeric.c'

/*
 *  call-seq:
 *     flt == obj  ->  true or false
 *
 *  Returns <code>true</code> only if <i>obj</i> has the same value
 *  as <i>flt</i>. Contrast this with <code>Float#eql?</code>, which
 *  requires <i>obj</i> to be a <code>Float</code>.
 *
 *     1.0 == 1   #=> true
 *
 */

static VALUE
flo_eq(VALUE x, VALUE y)
{
    volatile double a, b;

    switch (TYPE(y)) {
      case T_FIXNUM:
    b = (double)FIX2LONG(y);
    break;
      case T_BIGNUM:
    b = rb_big2dbl(y);
    break;
      case T_FLOAT:
    b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(b)) return Qfalse;
#endif
    break;
      default:
    return num_equal(x, y);
    }
    a = RFLOAT_VALUE(x);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(a)) return Qfalse;
#endif
    return (a == b)?Qtrue:Qfalse;
}

- (Boolean) ==(obj)

Returns true only if obj has the same value as flt. Contrast this with Float#eql?, which requires obj to be a Float.

1.0 == 1   #=> true


# File 'numeric.c'

/*
 *  call-seq:
 *     flt == obj  ->  true or false
 *
 *  Returns <code>true</code> only if <i>obj</i> has the same value
 *  as <i>flt</i>. Contrast this with <code>Float#eql?</code>, which
 *  requires <i>obj</i> to be a <code>Float</code>.
 *
 *     1.0 == 1   #=> true
 *
 */

static VALUE
flo_eq(VALUE x, VALUE y)
{
    volatile double a, b;

    switch (TYPE(y)) {
      case T_FIXNUM:
    b = (double)FIX2LONG(y);
    break;
      case T_BIGNUM:
    b = rb_big2dbl(y);
    break;
      case T_FLOAT:
    b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(b)) return Qfalse;
#endif
    break;
      default:
    return num_equal(x, y);
    }
    a = RFLOAT_VALUE(x);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(a)) return Qfalse;
#endif
    return (a == b)?Qtrue:Qfalse;
}

- (Boolean) >(real)

true if flt is greater than real.



# File 'numeric.c'

/*
 * call-seq:
 *   flt > real  ->  true or false
 *
 * <code>true</code> if <code>flt</code> is greater than <code>real</code>.
 */

static VALUE
flo_gt(VALUE x, VALUE y)
{
    double a, b;

    a = RFLOAT_VALUE(x);
    switch (TYPE(y)) {
      case T_FIXNUM:
    b = (double)FIX2LONG(y);
    break;

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

      case T_FLOAT:
    b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(b)) return Qfalse;
#endif
    break;

      default:
    return rb_num_coerce_relop(x, y, '>');
    }
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(a)) return Qfalse;
#endif
    return (a > b)?Qtrue:Qfalse;
}

- (Boolean) >=(real)

true if flt is greater than or equal to real.



# File 'numeric.c'

/*
 * call-seq:
 *   flt >= real  ->  true or false
 *
 * <code>true</code> if <code>flt</code> is greater than
 * or equal to <code>real</code>.
 */

static VALUE
flo_ge(VALUE x, VALUE y)
{
    double a, b;

    a = RFLOAT_VALUE(x);
    switch (TYPE(y)) {
      case T_FIXNUM:
    b = (double)FIX2LONG(y);
    break;

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

      case T_FLOAT:
    b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(b)) return Qfalse;
#endif
    break;

      default:
    return rb_num_coerce_relop(x, y, rb_intern(">="));
    }
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(a)) return Qfalse;
#endif
    return (a >= b)?Qtrue:Qfalse;
}

- (Float) abs - (Float) magnitude

Returns the absolute value of flt.

(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.abs        ->  float
 *     flt.magnitude  ->  float
 *
 *  Returns the absolute value of <i>flt</i>.
 *
 *     (-34.56).abs   #=> 34.56
 *     -34.56.abs     #=> 34.56
 *
 */

static VALUE
flo_abs(VALUE flt)
{
    double val = fabs(RFLOAT_VALUE(flt));
    return DBL2NUM(val);
}

- (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.



# File 'complex.c'

/*
 * call-seq:
 *    flo.arg    ->  0 or float
 *    flo.angle  ->  0 or float
 *    flo.phase  ->  0 or float
 *
 * Returns 0 if the value is positive, pi otherwise.
 */
static VALUE
float_arg(VALUE self)
{
    if (isnan(RFLOAT_VALUE(self)))
    return self;
    if (f_tpositive_p(self))
    return INT2FIX(0);
    return rb_const_get(rb_mMath, id_PI);
}

- (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.



# File 'complex.c'

/*
 * call-seq:
 *    flo.arg    ->  0 or float
 *    flo.angle  ->  0 or float
 *    flo.phase  ->  0 or float
 *
 * Returns 0 if the value is positive, pi otherwise.
 */
static VALUE
float_arg(VALUE self)
{
    if (isnan(RFLOAT_VALUE(self)))
    return self;
    if (f_tpositive_p(self))
    return INT2FIX(0);
    return rb_const_get(rb_mMath, id_PI);
}

- (Integer) ceil

Returns the smallest Integer greater than or equal to flt.

1.2.ceil      #=> 2
2.0.ceil      #=> 2
(-1.2).ceil   #=> -1
(-2.0).ceil   #=> -2


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.ceil  ->  integer
 *
 *  Returns the smallest <code>Integer</code> greater than or equal to
 *  <i>flt</i>.
 *
 *     1.2.ceil      #=> 2
 *     2.0.ceil      #=> 2
 *     (-1.2).ceil   #=> -1
 *     (-2.0).ceil   #=> -2
 */

static VALUE
flo_ceil(VALUE num)
{
    double f = ceil(RFLOAT_VALUE(num));
    long val;

    if (!FIXABLE(f)) {
    return rb_dbl2big(f);
    }
    val = (long)f;
    return LONG2FIX(val);
}

- (Object) coerce

MISSING: documentation



# File 'numeric.c'

/*
 * MISSING: documentation
 */

static VALUE
flo_coerce(VALUE x, VALUE y)
{
    return rb_assoc_new(rb_Float(y), x);
}

- (Integer) denominator

Returns the denominator (always positive). The result is machine dependent.

See numerator.



# File 'rational.c'

/*
 * call-seq:
 *    flo.denominator  ->  integer
 *
 * Returns the denominator (always positive).  The result is machine
 * dependent.
 *
 * See numerator.
 */
static VALUE
float_denominator(VALUE self)
{
    double d = RFLOAT_VALUE(self);
    if (isinf(d) || isnan(d))
    return INT2FIX(1);
    return rb_call_super(0, 0);
}

- (Array) divmod(numeric)

See Numeric#divmod.



# File 'numeric.c'

/*
 *  call-seq:
 *     flt.divmod(numeric)  ->  array
 *
 *  See <code>Numeric#divmod</code>.
 */

static VALUE
flo_divmod(VALUE x, VALUE y)
{
    double fy, div, mod;
    volatile VALUE a, b;

    switch (TYPE(y)) {
      case T_FIXNUM:
    fy = (double)FIX2LONG(y);
    break;
      case T_BIGNUM:
    fy = rb_big2dbl(y);
    break;
      case T_FLOAT:
    fy = RFLOAT_VALUE(y);
    break;
      default:
    return rb_num_coerce_bin(x, y, rb_intern("divmod"));
    }
    flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
    a = dbl2ival(div);
    b = DBL2NUM(mod);
    return rb_assoc_new(a, b);
}

- (Boolean) eql?(obj)

Returns true only if obj is a Float with the same value as flt. Contrast this with Float#==, which performs type conversions.

1.0.eql?(1)   #=> false


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.eql?(obj)  ->  true or false
 *
 *  Returns <code>true</code> only if <i>obj</i> is a
 *  <code>Float</code> with the same value as <i>flt</i>. Contrast this
 *  with <code>Float#==</code>, which performs type conversions.
 *
 *     1.0.eql?(1)   #=> false
 */

static VALUE
flo_eql(VALUE x, VALUE y)
{
    if (TYPE(y) == T_FLOAT) {
    double a = RFLOAT_VALUE(x);
    double b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
    if (isnan(a) || isnan(b)) return Qfalse;
#endif
    if (a == b)
        return Qtrue;
    }
    return Qfalse;
}

- (Float) quo(numeric)

Returns float / numeric.



# File 'numeric.c'

/*
 *  call-seq:
 *     float.quo(numeric)  ->  float
 *
 *  Returns float / numeric.
 */

static VALUE
flo_quo(VALUE x, VALUE y)
{
    return rb_funcall(x, '/', 1, y);
}

- (Boolean) finite?

Returns true if flt is a valid IEEE floating point number (it is not infinite, and nan? is false).



# File 'numeric.c'

/*
 *  call-seq:
 *     flt.finite?  ->  true or false
 *
 *  Returns <code>true</code> if <i>flt</i> is a valid IEEE floating
 *  point number (it is not infinite, and <code>nan?</code> is
 *  <code>false</code>).
 *
 */

static VALUE
flo_is_finite_p(VALUE num)
{
    double value = RFLOAT_VALUE(num);

#if HAVE_FINITE
    if (!finite(value))
    return Qfalse;
#else
    if (isinf(value) || isnan(value))
    return Qfalse;
#endif

    return Qtrue;
}

- (Integer) floor

Returns the largest integer less than or equal to flt.

1.2.floor      #=> 1
2.0.floor      #=> 2
(-1.2).floor   #=> -2
(-2.0).floor   #=> -2


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.floor  ->  integer
 *
 *  Returns the largest integer less than or equal to <i>flt</i>.
 *
 *     1.2.floor      #=> 1
 *     2.0.floor      #=> 2
 *     (-1.2).floor   #=> -2
 *     (-2.0).floor   #=> -2
 */

static VALUE
flo_floor(VALUE num)
{
    double f = floor(RFLOAT_VALUE(num));
    long val;

    if (!FIXABLE(f)) {
    return rb_dbl2big(f);
    }
    val = (long)f;
    return LONG2FIX(val);
}

- (Integer) hash

Returns a hash code for this float.



# File 'numeric.c'

/*
 * call-seq:
 *   flt.hash  ->  integer
 *
 * Returns a hash code for this float.
 */

static VALUE
flo_hash(VALUE num)
{
    double d;
    st_index_t hash;

    d = RFLOAT_VALUE(num);
    /* normalize -0.0 to 0.0 */
    if (d == 0.0) d = 0.0;
    hash = rb_memhash(&d, sizeof(d));
    return LONG2FIX(hash);
}

- (nil, ...) infinite?

Returns nil, -1, or +1 depending on whether flt is finite, -infinity, or +infinity.

(0.0).infinite?        #=> nil
(-1.0/0.0).infinite?   #=> -1
(+1.0/0.0).infinite?   #=> 1


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.infinite?  ->  nil, -1, +1
 *
 *  Returns <code>nil</code>, -1, or +1 depending on whether <i>flt</i>
 *  is finite, -infinity, or +infinity.
 *
 *     (0.0).infinite?        #=> nil
 *     (-1.0/0.0).infinite?   #=> -1
 *     (+1.0/0.0).infinite?   #=> 1
 */

static VALUE
flo_is_infinite_p(VALUE num)
{
    double value = RFLOAT_VALUE(num);

    if (isinf(value)) {
    return INT2FIX( value < 0 ? -1 : 1 );
    }

    return Qnil;
}

- (Float) abs - (Float) magnitude

Returns the absolute value of flt.

(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.abs        ->  float
 *     flt.magnitude  ->  float
 *
 *  Returns the absolute value of <i>flt</i>.
 *
 *     (-34.56).abs   #=> 34.56
 *     -34.56.abs     #=> 34.56
 *
 */

static VALUE
flo_abs(VALUE flt)
{
    double val = fabs(RFLOAT_VALUE(flt));
    return DBL2NUM(val);
}

- (Float) %(other) - (Float) modulo(other)

Return the modulo after division of flt by other.

6543.21.modulo(137)      #=> 104.21
6543.21.modulo(137.24)   #=> 92.9299999999996


# File 'numeric.c'

/*
 *  call-seq:
 *     flt % other        ->  float
 *     flt.modulo(other)  ->  float
 *
 *  Return the modulo after division of <code>flt</code> by <code>other</code>.
 *
 *     6543.21.modulo(137)      #=> 104.21
 *     6543.21.modulo(137.24)   #=> 92.9299999999996
 */

static VALUE
flo_mod(VALUE x, VALUE y)
{
    double fy, mod;

    switch (TYPE(y)) {
      case T_FIXNUM:
    fy = (double)FIX2LONG(y);
    break;
      case T_BIGNUM:
    fy = rb_big2dbl(y);
    break;
      case T_FLOAT:
    fy = RFLOAT_VALUE(y);
    break;
      default:
    return rb_num_coerce_bin(x, y, '%');
    }
    flodivmod(RFLOAT_VALUE(x), fy, 0, &mod);
    return DBL2NUM(mod);
}

- (Boolean) nan?

Returns true if flt is an invalid IEEE floating point number.

a = -1.0      #=> -1.0
a.nan?        #=> false
a = 0.0/0.0   #=> NaN
a.nan?        #=> true


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.nan?  ->  true or false
 *
 *  Returns <code>true</code> if <i>flt</i> is an invalid IEEE floating
 *  point number.
 *
 *     a = -1.0      #=> -1.0
 *     a.nan?        #=> false
 *     a = 0.0/0.0   #=> NaN
 *     a.nan?        #=> true
 */

static VALUE
flo_is_nan_p(VALUE num)
{
    double value = RFLOAT_VALUE(num);

    return isnan(value) ? Qtrue : Qfalse;
}

- (Integer) numerator

Returns the numerator. The result is machine dependent.

For example:

n = 0.3.numerator    #=> 5404319552844595
d = 0.3.denominator  #=> 18014398509481984
n.fdiv(d)            #=> 0.3


# File 'rational.c'

/*
 * call-seq:
 *    flo.numerator  ->  integer
 *
 * Returns the numerator.  The result is machine dependent.
 *
 * For example:
 *
 *    n = 0.3.numerator    #=> 5404319552844595
 *    d = 0.3.denominator  #=> 18014398509481984
 *    n.fdiv(d)            #=> 0.3
 */
static VALUE
float_numerator(VALUE self)
{
    double d = RFLOAT_VALUE(self);
    if (isinf(d) || isnan(d))
    return self;
    return rb_call_super(0, 0);
}

- (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.



# File 'complex.c'

/*
 * call-seq:
 *    flo.arg    ->  0 or float
 *    flo.angle  ->  0 or float
 *    flo.phase  ->  0 or float
 *
 * Returns 0 if the value is positive, pi otherwise.
 */
static VALUE
float_arg(VALUE self)
{
    if (isnan(RFLOAT_VALUE(self)))
    return self;
    if (f_tpositive_p(self))
    return INT2FIX(0);
    return rb_const_get(rb_mMath, id_PI);
}

- (Float) quo(numeric)

Returns float / numeric.



# File 'numeric.c'

/*
 *  call-seq:
 *     float.quo(numeric)  ->  float
 *
 *  Returns float / numeric.
 */

static VALUE
flo_quo(VALUE x, VALUE y)
{
    return rb_funcall(x, '/', 1, y);
}

- (Object) rationalize([eps])

Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|). if eps is not given, it will be chosen automatically.

For example:

0.3.rationalize          #=> (3/10)
1.333.rationalize        #=> (1333/1000)
1.333.rationalize(0.01)  #=> (4/3)


# File 'rational.c'

/*
 * call-seq:
 *    flt.rationalize([eps])  ->  rational
 *
 * Returns a simpler approximation of the value (flt-|eps| <= result
 * <= flt+|eps|).  if eps is not given, it will be chosen
 * automatically.
 *
 * For example:
 *
 *    0.3.rationalize          #=> (3/10)
 *    1.333.rationalize        #=> (1333/1000)
 *    1.333.rationalize(0.01)  #=> (4/3)
 */
static VALUE
float_rationalize(int argc, VALUE *argv, VALUE self)
{
    VALUE e, a, b, p, q;

    if (f_negative_p(self))
    return f_negate(float_rationalize(argc, argv, f_abs(self)));

    rb_scan_args(argc, argv, "01", &e);

    if (argc != 0) {
    e = f_abs(e);
    a = f_sub(self, e);
    b = f_add(self, e);
    }
    else {
    VALUE f, n;

    float_decode_internal(self, &f, &n);
    if (f_zero_p(f) || f_positive_p(n))
        return rb_rational_new1(f_lshift(f, n));

#if FLT_RADIX == 2
    a = rb_rational_new2(f_sub(f_mul(TWO, f), ONE),
                 f_lshift(ONE, f_sub(ONE, n)));
    b = rb_rational_new2(f_add(f_mul(TWO, f), ONE),
                 f_lshift(ONE, f_sub(ONE, n)));
#else
    a = rb_rational_new2(f_sub(f_mul(INT2FIX(FLT_RADIX), f),
                   INT2FIX(FLT_RADIX - 1)),
                 f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n)));
    b = rb_rational_new2(f_add(f_mul(INT2FIX(FLT_RADIX), f),
                   INT2FIX(FLT_RADIX - 1)),
                 f_expt(INT2FIX(FLT_RADIX), f_sub(ONE, n)));
#endif
    }

    if (f_eqeq_p(a, b))
    return f_to_r(self);

    nurat_rationalize_internal(a, b, &p, &q);
    return rb_rational_new2(p, q);
}

- (Integer, Float) round([ndigits])

Rounds flt to a given precision in decimal digits (default 0 digits). Precision may be negative. Returns a floating point number when ndigits is more than zero.

1.4.round      #=> 1
1.5.round      #=> 2
1.6.round      #=> 2
(-1.5).round   #=> -2

1.234567.round(2)  #=> 1.23
1.234567.round(3)  #=> 1.235
1.234567.round(4)  #=> 1.2346
1.234567.round(5)  #=> 1.23457

34567.89.round(-5) #=> 0
34567.89.round(-4) #=> 30000
34567.89.round(-3) #=> 35000
34567.89.round(-2) #=> 34600
34567.89.round(-1) #=> 34570
34567.89.round(0)  #=> 34568
34567.89.round(1)  #=> 34567.9
34567.89.round(2)  #=> 34567.89
34567.89.round(3)  #=> 34567.89


# File 'numeric.c'

/*
 *  call-seq:
 *     flt.round([ndigits])  ->  integer or float
 *
 *  Rounds <i>flt</i> to a given precision in decimal digits (default 0 digits).
 *  Precision may be negative.  Returns a floating point number when ndigits
 *  is more than zero.
 *
 *     1.4.round      #=> 1
 *     1.5.round      #=> 2
 *     1.6.round      #=> 2
 *     (-1.5).round   #=> -2
 *
 *     1.234567.round(2)  #=> 1.23
 *     1.234567.round(3)  #=> 1.235
 *     1.234567.round(4)  #=> 1.2346
 *     1.234567.round(5)  #=> 1.23457
 *
 *     34567.89.round(-5) #=> 0
 *     34567.89.round(-4) #=> 30000
 *     34567.89.round(-3) #=> 35000
 *     34567.89.round(-2) #=> 34600
 *     34567.89.round(-1) #=> 34570
 *     34567.89.round(0)  #=> 34568
 *     34567.89.round(1)  #=> 34567.9
 *     34567.89.round(2)  #=> 34567.89
 *     34567.89.round(3)  #=> 34567.89
 *
 */

static VALUE
flo_round(int argc, VALUE *argv, VALUE num)
{
    VALUE nd;
    double number, f;
    int ndigits = 0, i;
    long val;

    if (argc > 0 && rb_scan_args(argc, argv, "01", &nd) == 1) {
    ndigits = NUM2INT(nd);
    }
    number  = RFLOAT_VALUE(num);
    f = 1.0;
    i = abs(ndigits);
    while  (--i >= 0)
    f = f*10.0;

    if (isinf(f)) {
    if (ndigits < 0) number = 0;
    }
    else {
    if (ndigits < 0) number /= f;
    else number *= f;
    number = round(number);
    if (ndigits < 0) number *= f;
    else number /= f;
    }

    if (ndigits > 0) return DBL2NUM(number);

    if (!FIXABLE(number)) {
    return rb_dbl2big(number);
    }
    val = (long)number;
    return LONG2FIX(val);
}

- (Float) to_f

As flt is already a float, returns self.



# File 'numeric.c'

/*
 * call-seq:
 *   flt.to_f  ->  self
 *
 * As <code>flt</code> is already a float, returns +self+.
 */

static VALUE
flo_to_f(VALUE num)
{
    return num;
}

- (Integer) to_i - (Integer) to_int - (Integer) truncate

Returns flt truncated to an Integer.



# File 'numeric.c'

/*
 *  call-seq:
 *     flt.to_i      ->  integer
 *     flt.to_int    ->  integer
 *     flt.truncate  ->  integer
 *
 *  Returns <i>flt</i> truncated to an <code>Integer</code>.
 */

static VALUE
flo_truncate(VALUE num)
{
    double f = RFLOAT_VALUE(num);
    long val;

    if (f > 0.0) f = floor(f);
    if (f < 0.0) f = ceil(f);

    if (!FIXABLE(f)) {
    return rb_dbl2big(f);
    }
    val = (long)f;
    return LONG2FIX(val);
}

- (Integer) to_i - (Integer) to_int - (Integer) truncate

Returns flt truncated to an Integer.



# File 'numeric.c'

/*
 *  call-seq:
 *     flt.to_i      ->  integer
 *     flt.to_int    ->  integer
 *     flt.truncate  ->  integer
 *
 *  Returns <i>flt</i> truncated to an <code>Integer</code>.
 */

static VALUE
flo_truncate(VALUE num)
{
    double f = RFLOAT_VALUE(num);
    long val;

    if (f > 0.0) f = floor(f);
    if (f < 0.0) f = ceil(f);

    if (!FIXABLE(f)) {
    return rb_dbl2big(f);
    }
    val = (long)f;
    return LONG2FIX(val);
}

- (Object) to_r

Returns the value as a rational.

NOTE: 0.3.to_r isn't the same as '0.3'.to_r. The latter is equivalent to '3/10'.to_r, but the former isn't so.

For example:

2.0.to_r    #=> (2/1)
2.5.to_r    #=> (5/2)
-0.75.to_r  #=> (-3/4)
0.0.to_r    #=> (0/1)


# File 'rational.c'

/*
 * call-seq:
 *    flt.to_r  ->  rational
 *
 * Returns the value as a rational.
 *
 * NOTE: 0.3.to_r isn't the same as '0.3'.to_r.  The latter is
 * equivalent to '3/10'.to_r, but the former isn't so.
 *
 * For example:
 *
 *    2.0.to_r    #=> (2/1)
 *    2.5.to_r    #=> (5/2)
 *    -0.75.to_r  #=> (-3/4)
 *    0.0.to_r    #=> (0/1)
 */
static VALUE
float_to_r(VALUE self)
{
    VALUE f, n;

    float_decode_internal(self, &f, &n);
#if FLT_RADIX == 2
    {
    long ln = FIX2LONG(n);

    if (ln == 0)
        return f_to_r(f);
    if (ln > 0)
        return f_to_r(f_lshift(f, n));
    ln = -ln;
    return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln)));
    }
#else
    return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n)));
#endif
}

- (String) to_s

Returns a string containing a representation of self. As well as a fixed or exponential form of the number, the call may return "NaN'', "Infinity'', and "-Infinity''.



# File 'numeric.c'

/*
 *  call-seq:
 *     flt.to_s  ->  string
 *
 *  Returns a string containing a representation of self. As well as a
 *  fixed or exponential form of the number, the call may return
 *  ``<code>NaN</code>'', ``<code>Infinity</code>'', and
 *  ``<code>-Infinity</code>''.
 */

static VALUE
flo_to_s(VALUE flt)
{
    char *ruby_dtoa(double d_, int mode, int ndigits, int *decpt, int *sign, char **rve);
    enum {decimal_mant = DBL_MANT_DIG-DBL_DIG};
    enum {float_dig = DBL_DIG+1};
    char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10];
    double value = RFLOAT_VALUE(flt);
    VALUE s;
    char *p, *e;
    int sign, decpt, digs;

    if (isinf(value))
    return rb_usascii_str_new2(value < 0 ? "-Infinity" : "Infinity");
    else if (isnan(value))
    return rb_usascii_str_new2("NaN");

    p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e);
    s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0);
    if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1;
    memcpy(buf, p, digs);
    xfree(p);
    if (decpt > 0) {
    if (decpt < digs) {
        memmove(buf + decpt + 1, buf + decpt, digs - decpt);
        buf[decpt] = '.';
        rb_str_cat(s, buf, digs + 1);
    }
    else if (decpt - digs < float_dig) {
        long len;
        char *ptr;
        rb_str_cat(s, buf, digs);
        rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2);
        ptr = RSTRING_PTR(s) + len;
        if (decpt > digs) {
        memset(ptr, '0', decpt - digs);
        ptr += decpt - digs;
        }
        memcpy(ptr, ".0", 2);
    }
    else {
        goto exp;
    }
    }
    else if (decpt > -4) {
    long len;
    char *ptr;
    rb_str_cat(s, "0.", 2);
    rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs);
    ptr = RSTRING_PTR(s);
    memset(ptr += len, '0', -decpt);
    memcpy(ptr -= decpt, buf, digs);
    }
    else {
      exp:
    if (digs > 1) {
        memmove(buf + 2, buf + 1, digs - 1);
    }
    else {
        buf[2] = '0';
        digs++;
    }
    buf[1] = '.';
    rb_str_cat(s, buf, digs + 1);
    rb_str_catf(s, "e%+03d", decpt - 1);
    }
    return s;
}

- (Integer) to_i - (Integer) to_int - (Integer) truncate

Returns flt truncated to an Integer.



# File 'numeric.c'

/*
 *  call-seq:
 *     flt.to_i      ->  integer
 *     flt.to_int    ->  integer
 *     flt.truncate  ->  integer
 *
 *  Returns <i>flt</i> truncated to an <code>Integer</code>.
 */

static VALUE
flo_truncate(VALUE num)
{
    double f = RFLOAT_VALUE(num);
    long val;

    if (f > 0.0) f = floor(f);
    if (f < 0.0) f = ceil(f);

    if (!FIXABLE(f)) {
    return rb_dbl2big(f);
    }
    val = (long)f;
    return LONG2FIX(val);
}

- (Boolean) zero?

Returns true if flt is 0.0.



# File 'numeric.c'

/*
 *  call-seq:
 *     flt.zero?  ->  true or false
 *
 *  Returns <code>true</code> if <i>flt</i> is 0.0.
 *
 */

static VALUE
flo_zero_p(VALUE num)
{
    if (RFLOAT_VALUE(num) == 0.0) {
    return Qtrue;
    }
    return Qfalse;
}