A Float object stores a real number using the native architecture’s double-precision floating-point representation.
Some real numbers can be represented precisely as Float objects:
37.5 # => 37.5 98.75 # => 98.75 12.3125 # => 12.3125
Others cannot; among these are the transcendental numbers, including:
Pi, π: in mathematics, a number of infinite precision: 3.1415926535897932384626433… (to 25 places); in Ruby, it is of limited precision (in this case, to 16 decimal places):
Math::PI # => 3.141592653589793
Euler’s number, e: in mathematics, a number of infinite precision: 2.7182818284590452353602874… (to 25 places); in Ruby, it is of limited precision (in this case, to 15 decimal places):
Math::E # => 2.718281828459045
Some floating-point computations in Ruby give precise results:
1.0/2 # => 0.5 100.0/8 # => 12.5
Others do not:
In mathematics, 2/3 as a decimal number is an infinitely-repeating decimal: 0.666… (forever); in Ruby, 2.0/3 is of limited precision (in this case, to 16 decimal places):
2.0/3 # => 0.6666666666666666
In mathematics, the square root of 2 is an irrational number of infinite precision: 1.4142135623730950488016887… (to 25 decimal places); in Ruby, it is of limited precision (in this case, to 16 decimal places):
Math.sqrt(2.0) # => 1.4142135623730951
Even a simple computation can introduce imprecision:
x = 0.1 + 0.2 # => 0.30000000000000004 y = 0.3 # => 0.3 x == y # => false
See:
Note that precise storage and computation of rational numbers is possible using Rational objects.
You can create a Float object explicitly with:
You can convert certain objects to Floats with:
Method Float.
First, what’s elsewhere. Class Float:
Inherits from class Numeric and class Object.
Includes module Comparable.
Here, class Float provides methods for:
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).
<: 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.
*: 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.
The minimum number of significant decimal digits in a double-precision floating point.
Usually defaults to 15.
The difference between 1 and the smallest double-precision floating point number greater than 1.
Usually defaults to 2.2204460492503131e-16.
An expression representing positive infinity.
The number of base digits for the double data type.
Usually defaults to 53.
The largest possible integer in a double-precision floating point number.
Usually defaults to 1.7976931348623157e+308.
The largest positive exponent in a double-precision floating point where 10 raised to this power minus 1.
Usually defaults to 308.
The largest possible exponent value in a double-precision floating point.
Usually defaults to 1024.
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.
The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1.
Usually defaults to -307.
The smallest possible exponent value in a double-precision floating point.
Usually defaults to -1021.
An expression representing a value which is “not a number”.
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.
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
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 the numeric 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)
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));
} Returns self raised to the power exponent:
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)
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 the sum of self and other; the result may be inexact (see Float):
3.14 + 0 # => 3.14 3.14 + 1 # => 4.140000000000001 -3.14 + 0 # => -3.14 -3.14 + 1 # => -2.14 3.14 + -3.14 # => 0.0 -3.14 + -3.14 # => -6.28 3.14 + Complex(1, 0) # => (4.140000000000001+0i) 3.14 + Rational(1, 1) # => 4.140000000000001
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 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)
# File numeric.rb, line 389 def -@ Primitive.attr! :leaf Primitive.cexpr! 'rb_float_uminus(self)' end
Returns self, negated:
-3.14 # => -3.14 -(-3.14) # => 3.14 -0.0 # => -0.0
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 the quotient of self and 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)
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);
}
else {
return rb_num_coerce_relop(x, y, '<');
}
return RBOOL(a < b);
} Returns whether the value of self is less than the value of other; other must be numeric, but may not be Complex:
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.
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);
}
else {
return rb_num_coerce_relop(x, y, idLE);
}
return RBOOL(a <= b);
} Returns whether the value of self is less than or equal to the value of other; other must be numeric, but may not be Complex:
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.
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);
} Compares self and other.
Returns:
-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 <=> 2.1 # => -1 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 <=> 'foo' # => nil
Float::NAN <=> Float::NAN returns an implementation-dependent value.
Class Float includes module Comparable, each of whose methods uses Float#<=> for comparison.
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);
}
else {
return num_equal(x, y);
}
a = RFLOAT_VALUE(x);
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).
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);
}
else {
return rb_num_coerce_relop(x, y, '>');
}
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.
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);
}
else {
return rb_num_coerce_relop(x, y, idGE);
}
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.
# File numeric.rb, line 373 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
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.
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.
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.
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.
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]
VALUE
rb_float_eql(VALUE x, VALUE y)
{
if (RB_FLOAT_TYPE_P(y)) {
double a = RFLOAT_VALUE(x);
double b = RFLOAT_VALUE(y);
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).
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
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.
static VALUE
flo_hash(VALUE num)
{
return rb_dbl_hash(RFLOAT_VALUE(num));
} Returns the integer hash value for self.
See also Object#hash.
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
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
# File numeric.rb, line 416 def negative? Primitive.attr! :leaf Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) < 0.0)' end
Returns true if self is less than 0, false otherwise.
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
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.
# File numeric.rb, line 407 def positive? Primitive.attr! :leaf Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) > 0.0)' end
Returns true if self is greater than 0, false otherwise.
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.
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)
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.
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.
# File numeric.rb, line 360 def to_f self end
Returns self (which is already a Float).
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 (!)
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.
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"
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.
# File numeric.rb, line 398 def zero? Primitive.attr! :leaf Primitive.cexpr! 'RBOOL(FLOAT_ZERO_P(self))' end
Returns true if self is 0.0, false otherwise.
Ruby Core © 1993–2025 Yukihiro Matsumoto
Licensed under the Ruby License.
Ruby Standard Library © contributors
Licensed under their own licenses.