class Float - RDoc Documentation

# class Float

`Float` objects represent inexact real numbers 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#floats_imprecise

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

### 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

float % other → float click to toggle source

Returns the modulo after division of `float` by `other`.

    6543.21.modulo(137)      #=> 104.21000000000004
    6543.21.modulo(137.24)   #=> 92.92999999999961

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

        if (RB_TYPE_P(y, T_FIXNUM)) {
            fy = (double)FIX2LONG(y);
        }
        else if (RB_TYPE_P(y, T_BIGNUM)) {
            fy = rb_big2dbl(y);
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            fy = RFLOAT_VALUE(y);
        }
        else {
            return rb_num_coerce_bin(x, y, '%');
        }
        return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
    }

Also aliased as: modulo
float * other → float click to toggle source

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

    VALUE
    rb_float_mul(VALUE x, VALUE y)
    {
        if (RB_TYPE_P(y, T_FIXNUM)) {
            return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
        }
        else if (RB_TYPE_P(y, T_BIGNUM)) {
            return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
        }
        else {
            return rb_num_coerce_bin(x, y, '*');
        }
    }

float ** other → float click to toggle source

Raises `float` to the power of `other`.

    2.0**3   #=> 8.0

    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 (RB_TYPE_P(y, T_FIXNUM)) {
            dx = RFLOAT_VALUE(x);
            dy = (double)FIX2LONG(y);
        }
        else if (RB_TYPE_P(y, T_BIGNUM)) {
            dx = RFLOAT_VALUE(x);
            dy = rb_big2dbl(y);
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            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));
    }

float + other → float click to toggle source

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

    VALUE
    rb_float_plus(VALUE x, VALUE y)
    {
        if (RB_TYPE_P(y, T_FIXNUM)) {
            return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
        }
        else if (RB_TYPE_P(y, T_BIGNUM)) {
            return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
        }
        else {
            return rb_num_coerce_bin(x, y, '+');
        }
    }

float - other → float click to toggle source

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

    VALUE
    rb_float_minus(VALUE x, VALUE y)
    {
        if (RB_TYPE_P(y, T_FIXNUM)) {
            return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
        }
        else if (RB_TYPE_P(y, T_BIGNUM)) {
            return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
        }
        else {
            return rb_num_coerce_bin(x, y, '-');
        }
    }

-float → float click to toggle source

Returns `float`, negated.

    VALUE
    rb_float_uminus(VALUE flt)
    {
        return DBL2NUM(-RFLOAT_VALUE(flt));
    }

float / other → float click to toggle source

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

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

        if (RB_TYPE_P(y, T_FIXNUM)) {
            den = FIX2LONG(y);
        }
        else if (RB_TYPE_P(y, T_BIGNUM)) {
            den = rb_big2dbl(y);
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            den = RFLOAT_VALUE(y);
        }
        else {
            return rb_num_coerce_bin(x, y, '/');
        }

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

float < real → true or false click to toggle source

Returns `true` if `float` is less than `real`.

The result of `NaN < NaN` is undefined, so an implementation-dependent value is returned.

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

        a = RFLOAT_VALUE(x);
        if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return -FIX2LONG(rel) < 0 ? Qtrue : Qfalse;
            return Qfalse;
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            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 (a < b)?Qtrue:Qfalse;
    }

float <= real → true or false click to toggle source

Returns `true` if `float` is less than or equal to `real`.

The result of `NaN <= NaN` is undefined, so an implementation-dependent value is returned.

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

        a = RFLOAT_VALUE(x);
        if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return -FIX2LONG(rel) <= 0 ? Qtrue : Qfalse;
            return Qfalse;
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            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 (a <= b)?Qtrue:Qfalse;
    }

float <=> real → -1, 0, +1, or nil click to toggle source

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

The result of `NaN <=> NaN` is undefined, so an implementation-dependent value is returned.

`nil` is returned if the two values are incomparable.

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

        a = RFLOAT_VALUE(x);
        if (isnan(a)) return Qnil;
        if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return LONG2FIX(-FIX2LONG(rel));
            return rel;
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            b = RFLOAT_VALUE(y);
        }
        else {
            if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) {
                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);
    }

float == obj → true or false click to toggle source

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

    1.0 == 1   #=> true

The result of `NaN == NaN` is undefined, so an implementation-dependent value is returned.

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

        if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
            return rb_integer_float_eq(y, x);
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            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 (a == b)?Qtrue:Qfalse;
    }

Also aliased as: ===

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

    1.0 == 1   #=> true

The result of `NaN == NaN` is undefined, so an implementation-dependent value is returned.

Alias for: ==
float > real → true or false click to toggle source

Returns `true` if `float` is greater than `real`.

The result of `NaN > NaN` is undefined, so an implementation-dependent value is returned.

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

        a = RFLOAT_VALUE(x);
        if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return -FIX2LONG(rel) > 0 ? Qtrue : Qfalse;
            return Qfalse;
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            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 (a > b)?Qtrue:Qfalse;
    }

float >= real → true or false click to toggle source

Returns `true` if `float` is greater than or equal to `real`.

The result of `NaN >= NaN` is undefined, so an implementation-dependent value is returned.

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

        a = RFLOAT_VALUE(x);
        if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
            VALUE rel = rb_integer_float_cmp(y, x);
            if (FIXNUM_P(rel))
                return -FIX2LONG(rel) >= 0 ? Qtrue : Qfalse;
            return Qfalse;
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            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 (a >= b)?Qtrue:Qfalse;
    }

abs → float click to toggle source

Returns the absolute value of `float`.

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

`Float#magnitude` is an alias for `Float#abs`.

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

Also aliased as: magnitude
angle → 0 or float

Returns 0 if the value is positive, pi otherwise.

Alias for: arg
arg → 0 or float click to toggle source

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);
    }

Also aliased as: angle, phase
ceil([ndigits]) → integer or float click to toggle source

Returns the smallest number greater than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

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

    1.234567.ceil(2)   #=> 1.24
    1.234567.ceil(3)   #=> 1.235
    1.234567.ceil(4)   #=> 1.2346
    1.234567.ceil(5)   #=> 1.23457

    34567.89.ceil(-5)  #=> 100000
    34567.89.ceil(-4)  #=> 40000
    34567.89.ceil(-3)  #=> 35000
    34567.89.ceil(-2)  #=> 34600
    34567.89.ceil(-1)  #=> 34570
    34567.89.ceil(0)   #=> 34568
    34567.89.ceil(1)   #=> 34567.9
    34567.89.ceil(2)   #=> 34567.89
    34567.89.ceil(3)   #=> 34567.89

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

    (2.1 / 0.7).ceil  #=> 4 (!)

    static VALUE
    flo_ceil(int argc, VALUE *argv, VALUE num)
    {
        int ndigits = 0;

        if (rb_check_arity(argc, 0, 1)) {
            ndigits = NUM2INT(argv[0]);
        }
        return rb_float_ceil(num, ndigits);
    }

coerce(numeric) → array click to toggle source

Returns an array with both `numeric` and `float` represented as `Float` objects.

This is achieved by converting `numeric` to a `Float`.

    1.2.coerce(3)       #=> [3.0, 1.2]
    2.5.coerce(1.1)     #=> [1.1, 2.5]

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

denominator → integer click to toggle source

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

See also `Float#numerator`.

    VALUE
    rb_float_denominator(VALUE self)
    {
        double d = RFLOAT_VALUE(self);
        VALUE r;
        if (isinf(d) || isnan(d))
            return INT2FIX(1);
        r = float_to_r(self);
        return nurat_denominator(r);
    }

divmod(numeric) → array click to toggle source

See `Numeric#divmod`.

    42.0.divmod(6)   #=> [7, 0.0]
    42.0.divmod(5)   #=> [8, 2.0]

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

        if (RB_TYPE_P(y, T_FIXNUM)) {
            fy = (double)FIX2LONG(y);
        }
        else if (RB_TYPE_P(y, T_BIGNUM)) {
            fy = rb_big2dbl(y);
        }
        else if (RB_TYPE_P(y, T_FLOAT)) {
            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);
    }

eql?(obj) → true or false click to toggle source

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

    1.0.eql?(1)   #=> false

The result of `NaN.eql?(NaN)` is undefined, so an implementation-dependent value is returned.

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

fdiv(numeric) → float

Returns `float / numeric`, same as Float#/.

Alias for: quo
finite? → true or false click to toggle source

Returns `true` if `float` is a valid IEEE floating point number, i.e. it is not infinite and `Float#nan?` is `false`.

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

    #ifdef HAVE_ISFINITE
        if (!isfinite(value))
            return Qfalse;
    #else
        if (isinf(value) || isnan(value))
            return Qfalse;
    #endif

        return Qtrue;
    }

floor([ndigits]) → integer or float click to toggle source

Returns the largest number less than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

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

    1.234567.floor(2)   #=> 1.23
    1.234567.floor(3)   #=> 1.234
    1.234567.floor(4)   #=> 1.2345
    1.234567.floor(5)   #=> 1.23456

    34567.89.floor(-5)  #=> 0
    34567.89.floor(-4)  #=> 30000
    34567.89.floor(-3)  #=> 34000
    34567.89.floor(-2)  #=> 34500
    34567.89.floor(-1)  #=> 34560
    34567.89.floor(0)   #=> 34567
    34567.89.floor(1)   #=> 34567.8
    34567.89.floor(2)   #=> 34567.89
    34567.89.floor(3)   #=> 34567.89

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

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

    static VALUE
    flo_floor(int argc, VALUE *argv, VALUE num)
    {
        int ndigits = 0;
        if (rb_check_arity(argc, 0, 1)) {
            ndigits = NUM2INT(argv[0]);
        }
        return rb_float_floor(num, ndigits);
    }

hash → integer click to toggle source

Returns a hash code for this float.

See also `Object#hash`.

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

infinite? → -1, 1, or nil click to toggle source

Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, or `+Infinity`.

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

    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 a string containing a representation of `self`. As well as a fixed or exponential form of the `float`, the call may return `NaN`, `Infinity`, and `-Infinity`.

Alias for: to_s
magnitude → float

Returns the absolute value of `float`.

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

`Float#magnitude` is an alias for `Float#abs`.

Alias for: abs
modulo(other) → float

Returns the modulo after division of `float` by `other`.

    6543.21.modulo(137)      #=> 104.21000000000004
    6543.21.modulo(137.24)   #=> 92.92999999999961

Alias for: %
nan? → true or false click to toggle source

Returns `true` if `float` 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;
    }

negative? → true or false click to toggle source

Returns `true` if `float` is less than 0.

    static VALUE
    flo_negative_p(VALUE num)
    {
        double f = RFLOAT_VALUE(num);
        return f < 0.0 ? Qtrue : Qfalse;
    }

next_float → float click to toggle source

Returns the next representable floating point number.

Float::MAX.next_float and Float::INFINITY.next_float is `Float::INFINITY`.

Float::NAN.next_float is `Float::NAN`.

For example:

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

    0.01.next_float - 0.01     #=> 1.734723475976807e-18
    1.0.next_float - 1.0       #=> 2.220446049250313e-16
    100.0.next_float - 100.0   #=> 1.4210854715202004e-14

    f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float }
    #=> 0x1.47ae147ae147bp-7 0.01
    #   0x1.47ae147ae147cp-7 0.010000000000000002
    #   0x1.47ae147ae147dp-7 0.010000000000000004
    #   0x1.47ae147ae147ep-7 0.010000000000000005
    #   0x1.47ae147ae147fp-7 0.010000000000000007
    #   0x1.47ae147ae148p-7  0.010000000000000009
    #   0x1.47ae147ae1481p-7 0.01000000000000001
    #   0x1.47ae147ae1482p-7 0.010000000000000012
    #   0x1.47ae147ae1483p-7 0.010000000000000014
    #   0x1.47ae147ae1484p-7 0.010000000000000016
    #   0x1.47ae147ae1485p-7 0.010000000000000018
    #   0x1.47ae147ae1486p-7 0.01000000000000002
    #   0x1.47ae147ae1487p-7 0.010000000000000021
    #   0x1.47ae147ae1488p-7 0.010000000000000023
    #   0x1.47ae147ae1489p-7 0.010000000000000024
    #   0x1.47ae147ae148ap-7 0.010000000000000026
    #   0x1.47ae147ae148bp-7 0.010000000000000028
    #   0x1.47ae147ae148cp-7 0.01000000000000003
    #   0x1.47ae147ae148dp-7 0.010000000000000031
    #   0x1.47ae147ae148ep-7 0.010000000000000033

    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.

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

numerator → integer click to toggle source

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`.

    VALUE
    rb_float_numerator(VALUE self)
    {
        double d = RFLOAT_VALUE(self);
        VALUE r;
        if (isinf(d) || isnan(d))
            return self;
        r = float_to_r(self);
        return nurat_numerator(r);
    }

phase → 0 or float

Returns 0 if the value is positive, pi otherwise.

Alias for: arg
positive? → true or false click to toggle source

Returns `true` if `float` is greater than 0.

    static VALUE
    flo_positive_p(VALUE num)
    {
        double f = RFLOAT_VALUE(num);
        return f > 0.0 ? Qtrue : Qfalse;
    }

prev_float → float click to toggle source

Returns the previous representable floating point number.

(-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY.

Float::NAN.prev_float is `Float::NAN`.

For example:

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

    0.01 - 0.01.prev_float     #=> 1.734723475976807e-18
    1.0 - 1.0.prev_float       #=> 1.1102230246251565e-16
    100.0 - 100.0.prev_float   #=> 1.4210854715202004e-14

    f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float }
    #=> 0x1.47ae147ae147bp-7 0.01
    #   0x1.47ae147ae147ap-7 0.009999999999999998
    #   0x1.47ae147ae1479p-7 0.009999999999999997
    #   0x1.47ae147ae1478p-7 0.009999999999999995
    #   0x1.47ae147ae1477p-7 0.009999999999999993
    #   0x1.47ae147ae1476p-7 0.009999999999999992
    #   0x1.47ae147ae1475p-7 0.00999999999999999
    #   0x1.47ae147ae1474p-7 0.009999999999999988
    #   0x1.47ae147ae1473p-7 0.009999999999999986
    #   0x1.47ae147ae1472p-7 0.009999999999999985
    #   0x1.47ae147ae1471p-7 0.009999999999999983
    #   0x1.47ae147ae147p-7  0.009999999999999981
    #   0x1.47ae147ae146fp-7 0.00999999999999998
    #   0x1.47ae147ae146ep-7 0.009999999999999978
    #   0x1.47ae147ae146dp-7 0.009999999999999976
    #   0x1.47ae147ae146cp-7 0.009999999999999974
    #   0x1.47ae147ae146bp-7 0.009999999999999972
    #   0x1.47ae147ae146ap-7 0.00999999999999997
    #   0x1.47ae147ae1469p-7 0.009999999999999969
    #   0x1.47ae147ae1468p-7 0.009999999999999967

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

quo(numeric) → float click to toggle source

Returns `float / numeric`, same as Float#/.

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

Also aliased as: fdiv
rationalize([eps]) → rational click to toggle source

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`.

    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;
    }

round([ndigits] [, half: mode]) → integer or float click to toggle source

Returns `float` rounded to the nearest value with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

    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

If the optional `half` keyword argument is given, numbers that are half-way between two possible rounded values will be rounded according to the specified tie-breaking `mode`:

- `:up` or `nil`: round half away from zero (default)

- `:down`: round half toward zero

- `:even`: round half toward the nearest even number

      2.5.round(half: :up)      #=> 3
      2.5.round(half: :down)    #=> 2
      2.5.round(half: :even)    #=> 2
      3.5.round(half: :up)      #=> 4
      3.5.round(half: :down)    #=> 3
      3.5.round(half: :even)    #=> 4
      (-2.5).round(half: :up)   #=> -3
      (-2.5).round(half: :down) #=> -2
      (-2.5).round(half: :even) #=> -2

    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);
            f = pow(10, ndigits);
            x = ROUND_CALL(mode, round, (number, f));
            return DBL2NUM(x / f);
        }
        return num;
    }

to_d → bigdecimal click to toggle source
to_d(precision) → bigdecimal

Returns the value of `float` as a `BigDecimal`. The `precision` parameter is used to determine the number of significant digits for the result (the default is `Float::DIG`).

    require 'bigdecimal'
    require 'bigdecimal/util'

    0.5.to_d         # => 0.5e0
    1.234.to_d(2)    # => 0.12e1

See also `BigDecimal::new`.

    # File ext/bigdecimal/lib/bigdecimal/util.rb, line 46
    def to_d(precision=Float::DIG+1)
      BigDecimal(self, precision)
    end

to_f → self click to toggle source

Since `float` is already a `Float`, returns `self`.

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

to_i → integer click to toggle source

Returns the `float` truncated to an `Integer`.

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

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

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

`to_int` is an alias for `to_i`.

    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);
    }

Also aliased as: to_int

Returns the `float` truncated to an `Integer`.

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

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

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

`to_int` is an alias for `to_i`.

Alias for: to_i
to_r → rational click to toggle source

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`.

    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
    }

to_s → string click to toggle source

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

    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 + (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)) {
            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);
        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 <= 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;
    }

Also aliased as: inspect
truncate([ndigits]) → integer or float click to toggle source

Returns `float` truncated (toward zero) to a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

    2.8.truncate           #=> 2
    (-2.8).truncate        #=> -2
    1.234567.truncate(2)   #=> 1.23
    34567.89.truncate(-2)  #=> 34500

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

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

    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);
    }

zero? → true or false click to toggle source

Returns `true` if `float` is 0.0.

    static VALUE
    flo_zero_p(VALUE num)
    {
        return flo_iszero(num) ? Qtrue : Qfalse;
    }