## Feature #9834

### Float#{next_float,prev_float}

**Description**

I'd like to add Float#next_float and Float#prev_float which

returns next representable floating-point number and

previous representable floating-point number.

p 3.0.next_float #=> 3.0000000000000004 p 3.0.prev_float #=> 2.9999999999999996

These methods can be useful to examine the behavior of floating-point numbers.

For example, they can be used to examine floating-point error in 0.1 + 0.1 + ... + 0.1.

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

The methods are implemented using nextafter() function described in

IEEE 754 (Appendix), C99 and POSIX.

It seems the function is pretty portable on Unix variants.

However I implemented missing/nextafter.c for environments which don't have the function.

Any idea?

**Files**

#### Updated by phasis68 (Heesob Park) over 6 years ago

Here is a pure ruby implementation of `Float#{next_float,prev_float}`

(adopted from http://golang.org/src/pkg/math/nextafter.go)

```
class Float
def dbl2num(dbl)
[dbl].pack('d').unpack('Q')[0]
end
def num2dbl(num)
[num].pack('Q').unpack('d')[0]
end
def nextafter(y)
y = y.to_f
if (self.nan? || y.nan?)
Float::NAN
elsif self == y
y
elsif self == 0
num2dbl(1) * (y<=>0.0)
elsif (y > self) == (self > 0)
num2dbl(dbl2num(self) + 1)
else
num2dbl(dbl2num(self) - 1)
end
end
def prev_float
nextafter(-Float::INFINITY)
end
def next_float
nextafter(Float::INFINITY)
end
end
```

#### Updated by akr (Akira Tanaka) over 6 years ago

Thank you for an interesting implementation.

Heesob Park wrote:

if (self==Float::NAN || y==Float::NAN)

This doesn't work. Float#nan? should be used.

elsif self == y r = self

This should be "r = y" to to follow C99's nextafter() behavior.

(It doesn't affect `next_float`

and `prev_float`

, though.)

#### Updated by marcandre (Marc-Andre Lafortune) over 6 years ago

Float#next or Float#next_float?

Yukihiro Matsumoto wrote:

Accepted.

Matz.

#### Updated by matz (Yukihiro Matsumoto) over 6 years ago

**Assignee**set to*akr (Akira Tanaka)*

Float#next_float definitely. Float#next is too short and too simple for this method.

Matz.

#### Updated by akr (Akira Tanaka) over 6 years ago

**Status**changed from*Open*to*Closed***% Done**changed from*0*to*100*

Applied in changeset r45982.

configure.in: Check nextafter() availability.

include/ruby/missing.h (nextafter): New optional declaration.

missing/nextafter.c: New file.

numeric.c: Float#next_float and Float#prev_float implemented.

[ruby-core:62562] [Feature #9834]