# class Float

A Float object represents a sometimes-inexact real number using the native architecture’s double-precision floating point representation.

Floating point has a different arithmetic and is an inexact number. So you should know its esoteric system. See following:

- docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

- github.com/rdp/ruby_tutorials_core/wiki/Ruby-Talk-FAQ#-why-are-rubys-floats-imprecise

- en.wikipedia.org/wiki/Floating_point#Accuracy_problems

You can create a Float object explicitly with:

- A floating-point literal.

You can convert certain objects to Floats with:

- Method `Float`.

## What’s Here¶ ↑

First, what’s elsewhere. Class Float:

- Inherits from class Numeric and class Object.

- Includes module Comparable.

Here, class Float provides methods for:

- Querying

- Comparing

- Converting

### Querying¶ ↑

- `finite?`: Returns whether `self` is finite.

- `hash`: Returns the integer hash code for `self`.

- `infinite?`: Returns whether `self` is infinite.

- `nan?`: Returns whether `self` is a NaN (not-a-number).

### Comparing¶ ↑

- `<`: Returns whether `self` is less than the given value.

- `<=`: Returns whether `self` is less than or equal to the given value.

- `<=>`: Returns a number indicating whether `self` is less than, equal to, or greater than the given value.

- `==` (aliased as `===` and `eql?`): Returns whether `self` is equal to the given value.

- `>`: Returns whether `self` is greater than the given value.

- `>=`: Returns whether `self` is greater than or equal to the given value.

### Converting¶ ↑

- `%` (aliased as `modulo`): Returns `self` modulo the given value.

- `*`: Returns the product of `self` and the given value.

- `**`: Returns the value of `self` raised to the power of the given value.

- `+`: Returns the sum of `self` and the given value.

- `-`: Returns the difference of `self` and the given value.

- `/`: Returns the quotient of `self` and the given value.

- `ceil`: Returns the smallest number greater than or equal to `self`.

- `coerce`: Returns a 2-element array containing the given value converted to a Float and `self`

- `divmod`: Returns a 2-element array containing the quotient and remainder results of dividing `self` by the given value.

- `fdiv`: Returns the Float result of dividing `self` by the given value.

- `floor`: Returns the greatest number smaller than or equal to `self`.

- `next_float`: Returns the next-larger representable Float.

- `prev_float`: Returns the next-smaller representable Float.

- `quo`: Returns the quotient from dividing `self` by the given value.

- `round`: Returns `self` rounded to the nearest value, to a given precision.

- `to_i` (aliased as `to_int`): Returns `self` truncated to an `Integer`.

- `to_s` (aliased as `inspect`): Returns a string containing the place-value representation of `self` in the given radix.

- `truncate`: Returns `self` truncated to a given precision.

### Constants

DIG

  The minimum number of significant decimal digits in a double-precision floating point.

  Usually defaults to 15.

EPSILON

  The difference between 1 and the smallest double-precision floating point number greater than 1.

  Usually defaults to 2.2204460492503131e-16.

INFINITY

  An expression representing positive infinity.

MANT_DIG

  The number of base digits for the `double` data type.

  Usually defaults to 53.

MAX

  The largest possible integer in a double-precision floating point number.

  Usually defaults to 1.7976931348623157e+308.

MAX_10_EXP

  The largest positive exponent in a double-precision floating point where 10 raised to this power minus 1.

  Usually defaults to 308.

MAX_EXP

  The largest possible exponent value in a double-precision floating point.

  Usually defaults to 1024.

MIN

  The smallest positive normalized number in a double-precision floating point.

  Usually defaults to 2.2250738585072014e-308.

  If the platform supports denormalized numbers, there are numbers between zero and `Float::MIN`. 0.0.next_float returns the smallest positive floating point number including denormalized numbers.

MIN_10_EXP

  The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1.

  Usually defaults to -307.

MIN_EXP

  The smallest possible exponent value in a double-precision floating point.

  Usually defaults to -1021.

NAN

  An expression representing a value which is “not a number”.

RADIX

  The base of the floating point, or number of unique digits used to represent the number.

  Usually defaults to 2 on most systems, which would represent a base-10 decimal.

### Public Instance Methods

self % other → float
Source

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

        if (FIXNUM_P(y)) {
            fy = (double)FIX2LONG(y);
        }
        else if (RB_BIGNUM_TYPE_P(y)) {
            fy = rb_big2dbl(y);
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            fy = RFLOAT_VALUE(y);
        }
        else {
            return rb_num_coerce_bin(x, y, '%');
        }
        return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
    }

Returns `self` modulo `other` as a float.

For float `f` and real number `r`, these expressions are equivalent:

    f % r
    f-r*(f/r).floor
    f.divmod(r)[1]

See `Numeric#divmod`.

Examples:

    10.0 % 2              # => 0.0
    10.0 % 3              # => 1.0
    10.0 % 4              # => 2.0

    10.0 % -2             # => 0.0
    10.0 % -3             # => -2.0
    10.0 % -4             # => -2.0

    10.0 % 4.0            # => 2.0
    10.0 % Rational(4, 1) # => 2.0

Also aliased as: modulo
self * other → numeric
Source

    VALUE
    rb_float_mul(VALUE x, VALUE y)
    {
        if (FIXNUM_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
        }
        else if (RB_BIGNUM_TYPE_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
        }
        else {
            return rb_num_coerce_bin(x, y, '*');
        }
    }

Returns a new Float which is the product of `self` and `other`:

    f = 3.14
    f * 2              # => 6.28
    f * 2.0            # => 6.28
    f * Rational(1, 2) # => 1.57
    f * Complex(2, 0)  # => (6.28+0.0i)

self ** other → numeric
Source

    VALUE
    rb_float_pow(VALUE x, VALUE y)
    {
        double dx, dy;
        if (y == INT2FIX(2)) {
            dx = RFLOAT_VALUE(x);
            return DBL2NUM(dx * dx);
        }
        else if (FIXNUM_P(y)) {
            dx = RFLOAT_VALUE(x);
            dy = (double)FIX2LONG(y);
        }
        else if (RB_BIGNUM_TYPE_P(y)) {
            dx = RFLOAT_VALUE(x);
            dy = rb_big2dbl(y);
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            dx = RFLOAT_VALUE(x);
            dy = RFLOAT_VALUE(y);
            if (dx < 0 && dy != round(dy))
                return rb_dbl_complex_new_polar_pi(pow(-dx, dy), dy);
        }
        else {
            return rb_num_coerce_bin(x, y, idPow);
        }
        return DBL2NUM(pow(dx, dy));
    }

Raises `self` to the power of `other`:

    f = 3.14
    f ** 2              # => 9.8596
    f ** -2             # => 0.1014239928597509
    f ** 2.1            # => 11.054834900588839
    f ** Rational(2, 1) # => 9.8596
    f ** Complex(2, 0)  # => (9.8596+0i)

self + other → numeric
Source

    VALUE
    rb_float_plus(VALUE x, VALUE y)
    {
        if (FIXNUM_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
        }
        else if (RB_BIGNUM_TYPE_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
        }
        else {
            return rb_num_coerce_bin(x, y, '+');
        }
    }

Returns a new Float which is the sum of `self` and `other`:

    f = 3.14
    f + 1                 # => 4.140000000000001
    f + 1.0               # => 4.140000000000001
    f + Rational(1, 1)    # => 4.140000000000001
    f + Complex(1, 0)     # => (4.140000000000001+0i)

self - other → numeric
Source

    VALUE
    rb_float_minus(VALUE x, VALUE y)
    {
        if (FIXNUM_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
        }
        else if (RB_BIGNUM_TYPE_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
        }
        else {
            return rb_num_coerce_bin(x, y, '-');
        }
    }

Returns a new Float which is the difference of `self` and `other`:

    f = 3.14
    f - 1                 # => 2.14
    f - 1.0               # => 2.14
    f - Rational(1, 1)    # => 2.14
    f - Complex(1, 0)     # => (2.14+0i)

-float → float
Source

    # File numeric.rb, line 380
    def -@
      Primitive.attr! :leaf
      Primitive.cexpr! 'rb_float_uminus(self)'
    end

Returns `self`, negated.

self / other → numeric
Source

    VALUE
    rb_float_div(VALUE x, VALUE y)
    {
        double num = RFLOAT_VALUE(x);
        double den;
        double ret;

        if (FIXNUM_P(y)) {
            den = FIX2LONG(y);
        }
        else if (RB_BIGNUM_TYPE_P(y)) {
            den = rb_big2dbl(y);
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            den = RFLOAT_VALUE(y);
        }
        else {
            return rb_num_coerce_bin(x, y, '/');
        }

        ret = double_div_double(num, den);
        return DBL2NUM(ret);
    }

Returns a new Float which is the result of dividing `self` by `other`:

    f = 3.14
    f / 2              # => 1.57
    f / 2.0            # => 1.57
    f / Rational(2, 1) # => 1.57
    f / Complex(2, 0)  # => (1.57+0.0i)

self < other → true or false
Source

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

        a = RFLOAT_VALUE(x);
        if (RB_INTEGER_TYPE_P(y)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return RBOOL(-FIX2LONG(rel) < 0);
            return Qfalse;
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            b = RFLOAT_VALUE(y);
    #if MSC_VERSION_BEFORE(1300)
            if (isnan(b)) return Qfalse;
    #endif
        }
        else {
            return rb_num_coerce_relop(x, y, '<');
        }
    #if MSC_VERSION_BEFORE(1300)
        if (isnan(a)) return Qfalse;
    #endif
        return RBOOL(a < b);
    }

Returns `true` if `self` is numerically less than `other`:

    2.0 < 3              # => true
    2.0 < 3.0            # => true
    2.0 < Rational(3, 1) # => true
    2.0 < 2.0            # => false

`Float::NAN < Float::NAN` returns an implementation-dependent value.

self <= other → true or false
Source

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

        a = RFLOAT_VALUE(x);
        if (RB_INTEGER_TYPE_P(y)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return RBOOL(-FIX2LONG(rel) <= 0);
            return Qfalse;
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            b = RFLOAT_VALUE(y);
    #if MSC_VERSION_BEFORE(1300)
            if (isnan(b)) return Qfalse;
    #endif
        }
        else {
            return rb_num_coerce_relop(x, y, idLE);
        }
    #if MSC_VERSION_BEFORE(1300)
        if (isnan(a)) return Qfalse;
    #endif
        return RBOOL(a <= b);
    }

Returns `true` if `self` is numerically less than or equal to `other`:

    2.0 <= 3              # => true
    2.0 <= 3.0            # => true
    2.0 <= Rational(3, 1) # => true
    2.0 <= 2.0            # => true
    2.0 <= 1.0            # => false

`Float::NAN <= Float::NAN` returns an implementation-dependent value.

self <=> other → -1, 0, +1, or nil
Source

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

        a = RFLOAT_VALUE(x);
        if (isnan(a)) return Qnil;
        if (RB_INTEGER_TYPE_P(y)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return LONG2FIX(-FIX2LONG(rel));
            return rel;
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            b = RFLOAT_VALUE(y);
        }
        else {
            if (isinf(a) && !UNDEF_P(i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0))) {
                if (RTEST(i)) {
                    int j = rb_cmpint(i, x, y);
                    j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1);
                    return INT2FIX(j);
                }
                if (a > 0.0) return INT2FIX(1);
                return INT2FIX(-1);
            }
            return rb_num_coerce_cmp(x, y, id_cmp);
        }
        return rb_dbl_cmp(a, b);
    }

Returns a value that depends on the numeric relation between `self` and `other`:

- -1, if `self` is less than `other`.

- 0, if `self` is equal to `other`.

- 1, if `self` is greater than `other`.

- `nil`, if the two values are incommensurate.

Examples:

    2.0 <=> 2              # => 0
    2.0 <=> 2.0            # => 0
    2.0 <=> Rational(2, 1) # => 0
    2.0 <=> Complex(2, 0)  # => 0
    2.0 <=> 1.9            # => 1
    2.0 <=> 2.1            # => -1
    2.0 <=> 'foo'          # => nil

This is the basis for the tests in the `Comparable` module.

`Float::NAN <=> Float::NAN` returns an implementation-dependent value.

self == other → true or false
Source

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

        if (RB_INTEGER_TYPE_P(y)) {
            return rb_integer_float_eq(y, x);
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            b = RFLOAT_VALUE(y);
    #if MSC_VERSION_BEFORE(1300)
            if (isnan(b)) return Qfalse;
    #endif
        }
        else {
            return num_equal(x, y);
        }
        a = RFLOAT_VALUE(x);
    #if MSC_VERSION_BEFORE(1300)
        if (isnan(a)) return Qfalse;
    #endif
        return RBOOL(a == b);
    }

Returns `true` if `other` has the same value as `self`, `false` otherwise:

    2.0 == 2              # => true
    2.0 == 2.0            # => true
    2.0 == Rational(2, 1) # => true
    2.0 == Complex(2, 0)  # => true

`Float::NAN == Float::NAN` returns an implementation-dependent value.

Related: `Float#eql?` (requires `other` to be a Float).

Also aliased as: ===
===
Alias for: ==
self > other → true or false
Source

    VALUE
    rb_float_gt(VALUE x, VALUE y)
    {
        double a, b;

        a = RFLOAT_VALUE(x);
        if (RB_INTEGER_TYPE_P(y)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return RBOOL(-FIX2LONG(rel) > 0);
            return Qfalse;
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            b = RFLOAT_VALUE(y);
    #if MSC_VERSION_BEFORE(1300)
            if (isnan(b)) return Qfalse;
    #endif
        }
        else {
            return rb_num_coerce_relop(x, y, '>');
        }
    #if MSC_VERSION_BEFORE(1300)
        if (isnan(a)) return Qfalse;
    #endif
        return RBOOL(a > b);
    }

Returns `true` if `self` is numerically greater than `other`:

    2.0 > 1              # => true
    2.0 > 1.0            # => true
    2.0 > Rational(1, 2) # => true
    2.0 > 2.0            # => false

`Float::NAN > Float::NAN` returns an implementation-dependent value.

self >= other → true or false
Source

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

        a = RFLOAT_VALUE(x);
        if (RB_TYPE_P(y, T_FIXNUM) || RB_BIGNUM_TYPE_P(y)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return RBOOL(-FIX2LONG(rel) >= 0);
            return Qfalse;
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            b = RFLOAT_VALUE(y);
    #if MSC_VERSION_BEFORE(1300)
            if (isnan(b)) return Qfalse;
    #endif
        }
        else {
            return rb_num_coerce_relop(x, y, idGE);
        }
    #if MSC_VERSION_BEFORE(1300)
        if (isnan(a)) return Qfalse;
    #endif
        return RBOOL(a >= b);
    }

Returns `true` if `self` is numerically greater than or equal to `other`:

    2.0 >= 1              # => true
    2.0 >= 1.0            # => true
    2.0 >= Rational(1, 2) # => true
    2.0 >= 2.0            # => true
    2.0 >= 2.1            # => false

`Float::NAN >= Float::NAN` returns an implementation-dependent value.

abs → float
Source

    # File numeric.rb, line 368
    def abs
      Primitive.attr! :leaf
      Primitive.cexpr! 'rb_float_abs(self)'
    end

Returns the absolute value of `self`:

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

Also aliased as: magnitude
angle
Alias for: arg
arg → 0 or Math::PI
Source

    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);
    }

Returns 0 if `self` is positive, Math::PI otherwise.

Also aliased as: angle, phase
ceil(ndigits = 0) → float or integer
Source

    static VALUE
    flo_ceil(int argc, VALUE *argv, VALUE num)
    {
        int ndigits = flo_ndigits(argc, argv);
        return rb_float_ceil(num, ndigits);
    }

Returns a numeric that is a “ceiling” value for `self`, as specified by the given `ndigits`, which must be an integer-convertible object.

When `ndigits` is positive, returns a `Float` with `ndigits` decimal digits after the decimal point (as available, but no fewer than 1):

    f = 12345.6789
    f.ceil(1) # => 12345.7
    f.ceil(3) # => 12345.679
    f.ceil(30) # => 12345.6789
    f = -12345.6789
    f.ceil(1) # => -12345.6
    f.ceil(3) # => -12345.678
    f.ceil(30) # => -12345.6789
    f = 0.0
    f.ceil(1)   # => 0.0
    f.ceil(100) # => 0.0

When `ndigits` is non-positive, returns an `Integer` based on a computed granularity:

- The granularity is `10 ** ndigits.abs`.

- The returned value is the largest multiple of the granularity that is less than or equal to `self`.

Examples with positive `self`:

ndigits | Granularity | 12345.6789.ceil(ndigits)
--- | --- | ---
0 | 1 | 12346
-1 | 10 | 12350
-2 | 100 | 12400
-3 | 1000 | 13000
-4 | 10000 | 20000
-5 | 100000 | 100000

Examples with negative `self`:

ndigits | Granularity | -12345.6789.ceil(ndigits)
--- | --- | ---
0 | 1 | -12345
-1 | 10 | -12340
-2 | 100 | -12300
-3 | 1000 | -12000
-4 | 10000 | -10000
-5 | 100000 | 0

When `self` is zero and `ndigits` is non-positive, returns `Integer` zero:

    0.0.ceil(0)  # => 0
    0.0.ceil(-1) # => 0
    0.0.ceil(-2) # => 0

Note that the limited precision of floating-point arithmetic may lead to surprising results:

    (2.1 / 0.7).ceil  #=> 4 # Not 3 (because 2.1 / 0.7 # => 3.0000000000000004, not 3.0)

Related: `Float#floor`.

coerce(other) → array
Source

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

Returns a 2-element array containing `other` converted to a Float and `self`:

    f = 3.14                 # => 3.14
    f.coerce(2)              # => [2.0, 3.14]
    f.coerce(2.0)            # => [2.0, 3.14]
    f.coerce(Rational(1, 2)) # => [0.5, 3.14]
    f.coerce(Complex(1, 0))  # => [1.0, 3.14]

Raises an exception if a type conversion fails.

denominator → integer
Source

    VALUE
    rb_float_denominator(VALUE self)
    {
        double d = RFLOAT_VALUE(self);
        VALUE r;
        if (!isfinite(d))
            return INT2FIX(1);
        r = float_to_r(self);
        return nurat_denominator(r);
    }

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

See also `Float#numerator`.

divmod(other) → array
Source

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

        if (FIXNUM_P(y)) {
            fy = (double)FIX2LONG(y);
        }
        else if (RB_BIGNUM_TYPE_P(y)) {
            fy = rb_big2dbl(y);
        }
        else if (RB_FLOAT_TYPE_P(y)) {
            fy = RFLOAT_VALUE(y);
        }
        else {
            return rb_num_coerce_bin(x, y, id_divmod);
        }
        flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
        a = dbl2ival(div);
        b = DBL2NUM(mod);
        return rb_assoc_new(a, b);
    }

Returns a 2-element array `[q, r]`, where

    q = (self/other).floor      # Quotient
    r = self % other            # Remainder

Examples:

    11.0.divmod(4)              # => [2, 3.0]
    11.0.divmod(-4)             # => [-3, -1.0]
    -11.0.divmod(4)             # => [-3, 1.0]
    -11.0.divmod(-4)            # => [2, -3.0]

    12.0.divmod(4)              # => [3, 0.0]
    12.0.divmod(-4)             # => [-3, 0.0]
    -12.0.divmod(4)             # => [-3, -0.0]
    -12.0.divmod(-4)            # => [3, -0.0]

    13.0.divmod(4.0)            # => [3, 1.0]
    13.0.divmod(Rational(4, 1)) # => [3, 1.0]

eql?(other) → true or false
Source

    VALUE
    rb_float_eql(VALUE x, VALUE y)
    {
        if (RB_FLOAT_TYPE_P(y)) {
            double a = RFLOAT_VALUE(x);
            double b = RFLOAT_VALUE(y);
    #if MSC_VERSION_BEFORE(1300)
            if (isnan(a) || isnan(b)) return Qfalse;
    #endif
        return RBOOL(a == b);
        }
        return Qfalse;
    }

Returns `true` if `other` is a Float with the same value as `self`, `false` otherwise:

    2.0.eql?(2.0)            # => true
    2.0.eql?(1.0)            # => false
    2.0.eql?(1)              # => false
    2.0.eql?(Rational(2, 1)) # => false
    2.0.eql?(Complex(2, 0))  # => false

`Float::NAN.eql?(Float::NAN)` returns an implementation-dependent value.

Related: `Float#==` (performs type conversions).

fdiv
Alias for: quo
finite? → true or false
Source

    VALUE
    rb_flo_is_finite_p(VALUE num)
    {
        double value = RFLOAT_VALUE(num);

        return RBOOL(isfinite(value));
    }

Returns `true` if `self` is not `Infinity`, `-Infinity`, or `NaN`, `false` otherwise:

    f = 2.0      # => 2.0
    f.finite?    # => true
    f = 1.0/0.0  # => Infinity
    f.finite?    # => false
    f = -1.0/0.0 # => -Infinity
    f.finite?    # => false
    f = 0.0/0.0  # => NaN
    f.finite?    # => false

floor(ndigits = 0) → float or integer
Source

    static VALUE
    flo_floor(int argc, VALUE *argv, VALUE num)
    {
        int ndigits = flo_ndigits(argc, argv);
        return rb_float_floor(num, ndigits);
    }

Returns a float or integer that is a “floor” value for `self`, as specified by `ndigits`, which must be an integer-convertible object.

When `self` is zero, returns a zero value: a float if `ndigits` is positive, an integer otherwise:

    f = 0.0      # => 0.0
    f.floor(20)  # => 0.0
    f.floor(0)   # => 0
    f.floor(-20) # => 0

When `self` is non-zero and `ndigits` is positive, returns a float with `ndigits` digits after the decimal point (as available):

    f = 12345.6789
    f.floor(1)  # => 12345.6
    f.floor(3)  # => 12345.678
    f.floor(30) # => 12345.6789
    f = -12345.6789
    f.floor(1)  # => -12345.7
    f.floor(3)  # => -12345.679
    f.floor(30) # => -12345.6789

When `self` is non-zero and `ndigits` is non-positive, returns an integer value based on a computed granularity:

- The granularity is `10 ** ndigits.abs`.

- The returned value is the largest multiple of the granularity that is less than or equal to `self`.

Examples with positive `self`:

ndigits | Granularity | 12345.6789.floor(ndigits)
--- | --- | ---
0 | 1 | 12345
-1 | 10 | 12340
-2 | 100 | 12300
-3 | 1000 | 12000
-4 | 10000 | 10000
-5 | 100000 | 0

Examples with negative `self`:

ndigits | Granularity | -12345.6789.floor(ndigits)
--- | --- | ---
0 | 1 | -12346
-1 | 10 | -12350
-2 | 100 | -12400
-3 | 1000 | -13000
-4 | 10000 | -20000
-5 | 100000 | -100000
-6 | 1000000 | -1000000

Note that the limited precision of floating-point arithmetic may lead to surprising results:

    (0.3 / 0.1).floor  # => 2 # Not 3, (because (0.3 / 0.1) # => 2.9999999999999996, not 3.0)

Related: `Float#ceil`.

hash → integer
Source

    static VALUE
    flo_hash(VALUE num)
    {
        return rb_dbl_hash(RFLOAT_VALUE(num));
    }

Returns the integer hash value for `self`.

See also `Object#hash`.

infinite? → -1, 1, or nil
Source

    VALUE
    rb_flo_is_infinite_p(VALUE num)
    {
        double value = RFLOAT_VALUE(num);

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

        return Qnil;
    }

Returns:

- 1, if `self` is `Infinity`.

- -1 if `self` is `-Infinity`.

- `nil`, otherwise.

Examples:

    f = 1.0/0.0  # => Infinity
    f.infinite?  # => 1
    f = -1.0/0.0 # => -Infinity
    f.infinite?  # => -1
    f = 1.0      # => 1.0
    f.infinite?  # => nil
    f = 0.0/0.0  # => NaN
    f.infinite?  # => nil

inspect
Alias for: to_s
magnitude
Alias for: abs
modulo
Alias for: %
nan? → true or false
Source

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

        return RBOOL(isnan(value));
    }

Returns `true` if `self` is a NaN, `false` otherwise.

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

negative? → true or false
Source

    # File numeric.rb, line 407
    def negative?
      Primitive.attr! :leaf
      Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) < 0.0)'
    end

Returns `true` if `self` is less than 0, `false` otherwise.

next_float → float
Source

    static VALUE
    flo_next_float(VALUE vx)
    {
        return flo_nextafter(vx, HUGE_VAL);
    }

Returns the next-larger representable Float.

These examples show the internally stored values (64-bit hexadecimal) for each Float `f` and for the corresponding `f.next_float`:

    f = 0.0      # 0x0000000000000000
    f.next_float # 0x0000000000000001

    f = 0.01     # 0x3f847ae147ae147b
    f.next_float # 0x3f847ae147ae147c

In the remaining examples here, the output is shown in the usual way (result `to_s`):

    0.01.next_float    # => 0.010000000000000002
    1.0.next_float     # => 1.0000000000000002
    100.0.next_float   # => 100.00000000000001

    f = 0.01
    (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float }

Output:

     0 0x1.47ae147ae147bp-7 0.01
     1 0x1.47ae147ae147cp-7 0.010000000000000002
     2 0x1.47ae147ae147dp-7 0.010000000000000004
     3 0x1.47ae147ae147ep-7 0.010000000000000005

    f = 0.0; 100.times { f += 0.1 }
    f                           # => 9.99999999999998       # should be 10.0 in the ideal world.
    10-f                        # => 1.9539925233402755e-14 # the floating point error.
    10.0.next_float-10          # => 1.7763568394002505e-15 # 1 ulp (unit in the last place).
    (10-f)/(10.0.next_float-10) # => 11.0                   # the error is 11 ulp.
    (10-f)/(10*Float::EPSILON)  # => 8.8                    # approximation of the above.
    "%a" % 10                   # => "0x1.4p+3"
    "%a" % f                    # => "0x1.3fffffffffff5p+3" # the last hex digit is 5.  16 - 5 = 11 ulp.

Related: `Float#prev_float`

numerator → integer
Source

    VALUE
    rb_float_numerator(VALUE self)
    {
        double d = RFLOAT_VALUE(self);
        VALUE r;
        if (!isfinite(d))
            return self;
        r = float_to_r(self);
        return nurat_numerator(r);
    }

Returns the numerator. The result is machine dependent.

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

See also `Float#denominator`.

phase
Alias for: arg
positive? → true or false
Source

    # File numeric.rb, line 398
    def positive?
      Primitive.attr! :leaf
      Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) > 0.0)'
    end

Returns `true` if `self` is greater than 0, `false` otherwise.

prev_float → float
Source

    static VALUE
    flo_prev_float(VALUE vx)
    {
        return flo_nextafter(vx, -HUGE_VAL);
    }

Returns the next-smaller representable Float.

These examples show the internally stored values (64-bit hexadecimal) for each Float `f` and for the corresponding `f.pev_float`:

    f = 5e-324   # 0x0000000000000001
    f.prev_float # 0x0000000000000000

    f = 0.01     # 0x3f847ae147ae147b
    f.prev_float # 0x3f847ae147ae147a

In the remaining examples here, the output is shown in the usual way (result `to_s`):

    0.01.prev_float   # => 0.009999999999999998
    1.0.prev_float    # => 0.9999999999999999
    100.0.prev_float  # => 99.99999999999999

    f = 0.01
    (0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.prev_float }

Output:

    0 0x1.47ae147ae147bp-7 0.01
    1 0x1.47ae147ae147ap-7 0.009999999999999998
    2 0x1.47ae147ae1479p-7 0.009999999999999997
    3 0x1.47ae147ae1478p-7 0.009999999999999995

Related: `Float#next_float`.

quo(other) → numeric
Source

    static VALUE
    flo_quo(VALUE x, VALUE y)
    {
        return num_funcall1(x, '/', y);
    }

Returns the quotient from dividing `self` by `other`:

    f = 3.14
    f.quo(2)              # => 1.57
    f.quo(-2)             # => -1.57
    f.quo(Rational(2, 1)) # => 1.57
    f.quo(Complex(2, 0))  # => (1.57+0.0i)

Also aliased as: fdiv
rationalize([eps]) → rational
Source

    static VALUE
    float_rationalize(int argc, VALUE *argv, VALUE self)
    {
        double d = RFLOAT_VALUE(self);
        VALUE rat;
        int neg = d < 0.0;
        if (neg) self = DBL2NUM(-d);

        if (rb_check_arity(argc, 0, 1)) {
            rat = rb_flt_rationalize_with_prec(self, argv[0]);
        }
        else {
            rat = rb_flt_rationalize(self);
        }
        if (neg) RATIONAL_SET_NUM(rat, rb_int_uminus(RRATIONAL(rat)->num));
        return rat;
    }

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

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

See also `Float#to_r`.

round(ndigits = 0, half: :up) → integer or float
Source

    static VALUE
    flo_round(int argc, VALUE *argv, VALUE num)
    {
        double number, f, x;
        VALUE nd, opt;
        int ndigits = 0;
        enum ruby_num_rounding_mode mode;

        if (rb_scan_args(argc, argv, "01:", &nd, &opt)) {
            ndigits = NUM2INT(nd);
        }
        mode = rb_num_get_rounding_option(opt);
        number = RFLOAT_VALUE(num);
        if (number == 0.0) {
            return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
        }
        if (ndigits < 0) {
            return rb_int_round(flo_to_i(num), ndigits, mode);
        }
        if (ndigits == 0) {
            x = ROUND_CALL(mode, round, (number, 1.0));
            return dbl2ival(x);
        }
        if (isfinite(number)) {
            int binexp;
            frexp(number, &binexp);
            if (float_round_overflow(ndigits, binexp)) return num;
            if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0);
            if (ndigits > 14) {
                /* In this case, pow(10, ndigits) may not be accurate. */
                return rb_flo_round_by_rational(argc, argv, num);
            }
            f = pow(10, ndigits);
            x = ROUND_CALL(mode, round, (number, f));
            return DBL2NUM(x / f);
        }
        return num;
    }

Returns `self` rounded to the nearest value with a precision of `ndigits` decimal digits.

When `ndigits` is non-negative, returns a float with `ndigits` after the decimal point (as available):

    f = 12345.6789
    f.round(1) # => 12345.7
    f.round(3) # => 12345.679
    f = -12345.6789
    f.round(1) # => -12345.7
    f.round(3) # => -12345.679

When `ndigits` is negative, returns an integer with at least `ndigits.abs` trailing zeros:

    f = 12345.6789
    f.round(0)  # => 12346
    f.round(-3) # => 12000
    f = -12345.6789
    f.round(0)  # => -12346
    f.round(-3) # => -12000

If keyword argument `half` is given, and `self` is equidistant from the two candidate values, the rounding is according to the given `half` value:

- `:up` or `nil`: round away from zero:

      2.5.round(half: :up)      # => 3
      3.5.round(half: :up)      # => 4
      (-2.5).round(half: :up)   # => -3

- `:down`: round toward zero:

      2.5.round(half: :down)    # => 2
      3.5.round(half: :down)    # => 3
      (-2.5).round(half: :down) # => -2

- `:even`: round toward the candidate whose last nonzero digit is even:

      2.5.round(half: :even)    # => 2
      3.5.round(half: :even)    # => 4
      (-2.5).round(half: :even) # => -2

Raises and exception if the value for `half` is invalid.

Related: `Float#truncate`.

to_f → self
Source

    # File numeric.rb, line 355
    def to_f
      self
    end

Returns `self` (which is already a Float).

to_i → integer
Source

    static VALUE
    flo_to_i(VALUE num)
    {
        double f = RFLOAT_VALUE(num);

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

        return dbl2ival(f);
    }

Returns `self` truncated to an `Integer`.

    1.2.to_i    # => 1
    (-1.2).to_i # => -1

Note that the limited precision of floating-point arithmetic may lead to surprising results:

    (0.3 / 0.1).to_i  # => 2 (!)

Also aliased as: to_int
to_int
Alias for: to_i
to_r → rational
Source

    static VALUE
    float_to_r(VALUE self)
    {
        VALUE f;
        int n;

        float_decode_internal(self, &f, &n);
    #if FLT_RADIX == 2
        if (n == 0)
            return rb_rational_new1(f);
        if (n > 0)
            return rb_rational_new1(rb_int_lshift(f, INT2FIX(n)));
        n = -n;
        return rb_rational_new2(f, rb_int_lshift(ONE, INT2FIX(n)));
    #else
        f = rb_int_mul(f, rb_int_pow(INT2FIX(FLT_RADIX), n));
        if (RB_TYPE_P(f, T_RATIONAL))
            return f;
        return rb_rational_new1(f);
    #endif
    }

Returns the value as a rational.

    2.0.to_r    #=> (2/1)
    2.5.to_r    #=> (5/2)
    -0.75.to_r  #=> (-3/4)
    0.0.to_r    #=> (0/1)
    0.3.to_r    #=> (5404319552844595/18014398509481984)

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.

    0.3.to_r   == 3/10r  #=> false
    "0.3".to_r == 3/10r  #=> true

See also `Float#rationalize`.

to_s → string
Source

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

        if (isinf(value)) {
            static const char minf[] = "-Infinity";
            const int pos = (value > 0); /* skip "-" */
            return rb_usascii_str_new(minf+pos, strlen(minf)-pos);
        }
        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);
        free(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 <= DBL_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 {
            goto exp;
        }
        return s;

      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;
    }

Returns a string containing a representation of `self`; depending of the value of `self`, the string representation may contain:

- A fixed-point number.

      3.14.to_s         # => "3.14"

- A number in “scientific notation” (containing an exponent).

      (10.1**50).to_s   # => "1.644631821843879e+50"

- ‘Infinity’.

      (10.1**500).to_s  # => "Infinity"

- ‘-Infinity’.

      (-10.1**500).to_s # => "-Infinity"

- ‘NaN’ (indicating not-a-number).

      (0.0/0.0).to_s    # => "NaN"

Also aliased as: inspect
truncate(ndigits = 0) → float or integer
Source

    static VALUE
    flo_truncate(int argc, VALUE *argv, VALUE num)
    {
        if (signbit(RFLOAT_VALUE(num)))
            return flo_ceil(argc, argv, num);
        else
            return flo_floor(argc, argv, num);
    }

Returns `self` truncated (toward zero) to a precision of `ndigits` decimal digits.

When `ndigits` is positive, returns a float with `ndigits` digits after the decimal point (as available):

    f = 12345.6789
    f.truncate(1) # => 12345.6
    f.truncate(3) # => 12345.678
    f = -12345.6789
    f.truncate(1) # => -12345.6
    f.truncate(3) # => -12345.678

When `ndigits` is negative, returns an integer with at least `ndigits.abs` trailing zeros:

    f = 12345.6789
    f.truncate(0)  # => 12345
    f.truncate(-3) # => 12000
    f = -12345.6789
    f.truncate(0)  # => -12345
    f.truncate(-3) # => -12000

Note that the limited precision of floating-point arithmetic may lead to surprising results:

    (0.3 / 0.1).truncate  #=> 2 (!)

Related: `Float#round`.

zero? → true or false
Source

    # File numeric.rb, line 389
    def zero?
      Primitive.attr! :leaf
      Primitive.cexpr! 'RBOOL(FLOAT_ZERO_P(self))'
    end

Returns `true` if `self` is 0.0, `false` otherwise.