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Showing content from https://docs.ruby-lang.org/en/master/Digest/../syntax/../Float.html below:

class Float - Documentation for Ruby 3.5

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.

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

• 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.

• % (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.

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.

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              
10.0 % 3              
10.0 % 4              

10.0 % -2             
10.0 % -3             
10.0 % -4             

10.0 % 4.0            
10.0 % Rational(4, 1) 

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              
f * 2.0            
f * Rational(1, 2) 
f * Complex(2, 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 (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              
f ** -2             
f ** 2.1            
f ** Rational(2, 1) 
f ** Complex(2, 0)  

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                 
f + 1.0               
f + Rational(1, 1)    
f + Complex(1, 0)     

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                 
f - 1.0               
f - Rational(1, 1)    
f - Complex(1, 0)     

def -@
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_float_uminus(self)'
end

Returns self, negated.

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              
f / 2.0            
f / Rational(2, 1) 
f / Complex(2, 0)  

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              
2.0 < 3.0            
2.0 < Rational(3, 1) 
2.0 < 2.0            

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);
#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              
2.0 <= 3.0            
2.0 <= Rational(3, 1) 
2.0 <= 2.0            
2.0 <= 1.0            

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);
}

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

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

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

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              
2.0 == 2.0            
2.0 == Rational(2, 1) 
2.0 == Complex(2, 0)  

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);
#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              
2.0 > 1.0            
2.0 > Rational(1, 2) 
2.0 > 2.0            

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

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

def abs
  Primitive.attr! :leaf
  Primitive.cexpr! 'rb_float_abs(self)'
end

Returns the absolute value of self:

(-34.56).abs 
-34.56.abs   
34.56.abs    

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) 
f.ceil(3) 
f.ceil(30) 
f = -12345.6789
f.ceil(1) 
f.ceil(3) 
f.ceil(30) 
f = 0.0
f.ceil(1)   
f.ceil(100) 

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:

Examples with negative self:

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

0.0.ceil(0)  
0.0.ceil(-1) 
0.0.ceil(-2) 

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

(2.1 / 0.7).ceil  

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                 
f.coerce(2)              
f.coerce(2.0)            
f.coerce(Rational(1, 2)) 
f.coerce(Complex(1, 0))  

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      
r = self % other            

Examples:

11.0.divmod(4)              
11.0.divmod(-4)             
-11.0.divmod(4)             
-11.0.divmod(-4)            

12.0.divmod(4)              
12.0.divmod(-4)             
-12.0.divmod(4)             
-12.0.divmod(-4)            

13.0.divmod(4.0)            
13.0.divmod(Rational(4, 1)) 

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)            
2.0.eql?(1.0)            
2.0.eql?(1)              
2.0.eql?(Rational(2, 1)) 
2.0.eql?(Complex(2, 0))  

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      
f.finite?    
f = 1.0/0.0  
f.finite?    
f = -1.0/0.0 
f.finite?    
f = 0.0/0.0  
f.finite?    

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      
f.floor(20)  
f.floor(0)   
f.floor(-20) 

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)  
f.floor(3)  
f.floor(30) 
f = -12345.6789
f.floor(1)  
f.floor(3)  
f.floor(30) 

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:

Examples with negative self:

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

(0.3 / 0.1).floor  

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  
f.infinite?  
f = -1.0/0.0 
f.infinite?  
f = 1.0      
f.infinite?  
f = 0.0/0.0  
f.infinite?  

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     
f.nan?       
f = 0.0/0.0  
f.nan?       

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      
f.next_float 

f = 0.01     
f.next_float 

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

0.01.next_float    
1.0.next_float     
100.0.next_float   

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    
d = 0.3.denominator  
n.fdiv(d)            

See also Float#denominator.

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   
f.prev_float 

f = 0.01     
f.prev_float 

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

0.01.prev_float   
1.0.prev_float    
100.0.prev_float  

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)              
f.quo(-2)             
f.quo(Rational(2, 1)) 
f.quo(Complex(2, 0))  

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          
1.333.rationalize        
1.333.rationalize(0.01)  

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) 
f.round(3) 
f = -12345.6789
f.round(1) 
f.round(3) 

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

f = 12345.6789
f.round(0)  
f.round(-3) 
f = -12345.6789
f.round(0)  
f.round(-3) 

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)      
  3.5.round(half: :up)      
  (-2.5).round(half: :up)   
  

• :down: round toward zero:

  2.5.round(half: :down)    
  3.5.round(half: :down)    
  (-2.5).round(half: :down) 
  

• :even: round toward the candidate whose last nonzero digit is even:

  2.5.round(half: :even)    
  3.5.round(half: :even)    
  (-2.5).round(half: :even) 
  

Raises and exception if the value for half is invalid.

Related: Float#truncate.

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    
(-1.2).to_i 

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

(0.3 / 0.1).to_i  

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    
2.5.to_r    
-0.75.to_r  
0.0.to_r    
0.3.to_r    

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  
"0.3".to_r == 3/10r  

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         
  

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

  (10.1**50).to_s   
  

• ‘Infinity’.

  (10.1**500).to_s  
  

• ‘-Infinity’.

  (-10.1**500).to_s 
  

• ‘NaN’ (indicating not-a-number).

  (0.0/0.0).to_s    
  

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) 
f.truncate(3) 
f = -12345.6789
f.truncate(1) 
f.truncate(3) 

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

f = 12345.6789
f.truncate(0)  
f.truncate(-3) 
f = -12345.6789
f.truncate(0)  
f.truncate(-3) 

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

(0.3 / 0.1).truncate  

Related: Float#round.

def zero?
  Primitive.attr! :leaf
  Primitive.cexpr! 'RBOOL(FLOAT_ZERO_P(self))'
end

Returns true if self is 0.0, false otherwise.

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