[ruby-core:115385] [Ruby master Bug#17037] rounding of Rational#to_f

Issue #17037 has been updated by JesseJohnson (Jesse Johnson).


Test case:

```
  def test_rational_with_large_integer_components_to_f
    r = 450359962737049649/450359962737049600r
    assert_equal(1.0, r.to_f)
  end
```

The issue is that large integers, abs > 2 ** 53 - 1, are truncated when converting to double precision floating point and this affects which floating point value is closest after division. This can be fixed by using BigDecimal but I'm not sure that is an appropriate dependency for Rational.

----------------------------------------
Bug #17037: rounding of Rational#to_f
https://bugs.ruby-lang.org/issues/17037#change-105321

* Author: akr (Akira Tanaka)
* Status: Open
* Priority: Normal
* Backport: 2.5: UNKNOWN, 2.6: UNKNOWN, 2.7: UNKNOWN
----------------------------------------
I found a doubtful rounding behavior of Rational#to_f.

```
% ./ruby -ve '
a = 1r
e = Float::EPSILON.to_r
puts "e=#{e}"
n = 100
(0..n).each {|i|
  r = a + e * i / n
  f = r.to_f
  p [i, f, r]
}
'
ruby 2.8.0dev (2020-07-20T06:39:31Z master 935d0b3d05) [x86_64-linux]
e=1/4503599627370496
[0, 1.0, (1/1)]
[1, 1.0, (450359962737049601/450359962737049600)]
[2, 1.0, (225179981368524801/225179981368524800)]
[3, 1.0, (450359962737049603/450359962737049600)]
[4, 1.0, (112589990684262401/112589990684262400)]
[5, 1.0, (90071992547409921/90071992547409920)]
[6, 1.0, (225179981368524803/225179981368524800)]
[7, 1.0, (450359962737049607/450359962737049600)]
[8, 1.0, (56294995342131201/56294995342131200)]
[9, 1.0, (450359962737049609/450359962737049600)]
[10, 1.0, (45035996273704961/45035996273704960)]
[11, 1.0, (450359962737049611/450359962737049600)]
[12, 1.0, (112589990684262403/112589990684262400)]
[13, 1.0, (450359962737049613/450359962737049600)]
[14, 1.0, (225179981368524807/225179981368524800)]
[15, 1.0, (90071992547409923/90071992547409920)]
[16, 1.0, (28147497671065601/28147497671065600)]
[17, 1.0, (450359962737049617/450359962737049600)]
[18, 1.0, (225179981368524809/225179981368524800)]
[19, 1.0, (450359962737049619/450359962737049600)]
[20, 1.0, (22517998136852481/22517998136852480)]
[21, 1.0, (450359962737049621/450359962737049600)]
[22, 1.0, (225179981368524811/225179981368524800)]
[23, 1.0, (450359962737049623/450359962737049600)]
[24, 1.0, (56294995342131203/56294995342131200)]
[25, 1.0, (18014398509481985/18014398509481984)]
[26, 1.0, (225179981368524813/225179981368524800)]
[27, 1.0, (450359962737049627/450359962737049600)]
[28, 1.0, (112589990684262407/112589990684262400)]
[29, 1.0, (450359962737049629/450359962737049600)]
[30, 1.0, (45035996273704963/45035996273704960)]
[31, 1.0, (450359962737049631/450359962737049600)]
[32, 1.0, (14073748835532801/14073748835532800)]
[33, 1.0000000000000002, (450359962737049633/450359962737049600)]
[34, 1.0000000000000002, (225179981368524817/225179981368524800)]
[35, 1.0, (90071992547409927/90071992547409920)]
[36, 1.0000000000000002, (112589990684262409/112589990684262400)]
[37, 1.0000000000000002, (450359962737049637/450359962737049600)]
[38, 1.0000000000000002, (225179981368524819/225179981368524800)]
[39, 1.0000000000000002, (450359962737049639/450359962737049600)]
[40, 1.0, (11258999068426241/11258999068426240)]
[41, 1.0000000000000002, (450359962737049641/450359962737049600)]
[42, 1.0000000000000002, (225179981368524821/225179981368524800)]
[43, 1.0000000000000002, (450359962737049643/450359962737049600)]
[44, 1.0000000000000002, (112589990684262411/112589990684262400)]
[45, 1.0000000000000002, (90071992547409929/90071992547409920)]
[46, 1.0000000000000002, (225179981368524823/225179981368524800)]
[47, 1.0000000000000002, (450359962737049647/450359962737049600)]
[48, 1.0000000000000002, (28147497671065603/28147497671065600)]
[49, 1.0000000000000002, (450359962737049649/450359962737049600)]
[50, 1.0, (9007199254740993/9007199254740992)]
[51, 1.0000000000000002, (450359962737049651/450359962737049600)]
[52, 1.0000000000000002, (112589990684262413/112589990684262400)]
[53, 1.0000000000000002, (450359962737049653/450359962737049600)]
[54, 1.0000000000000002, (225179981368524827/225179981368524800)]
[55, 1.0000000000000002, (90071992547409931/90071992547409920)]
[56, 1.0000000000000002, (56294995342131207/56294995342131200)]
[57, 1.0000000000000002, (450359962737049657/450359962737049600)]
[58, 1.0000000000000002, (225179981368524829/225179981368524800)]
[59, 1.0000000000000002, (450359962737049659/450359962737049600)]
[60, 1.0000000000000002, (22517998136852483/22517998136852480)]
[61, 1.0000000000000002, (450359962737049661/450359962737049600)]
[62, 1.0000000000000002, (225179981368524831/225179981368524800)]
[63, 1.0000000000000002, (450359962737049663/450359962737049600)]
[64, 1.0000000000000002, (7036874417766401/7036874417766400)]
[65, 1.0000000000000002, (90071992547409933/90071992547409920)]
[66, 1.0000000000000002, (225179981368524833/225179981368524800)]
[67, 1.0000000000000002, (450359962737049667/450359962737049600)]
[68, 1.0000000000000002, (112589990684262417/112589990684262400)]
[69, 1.0000000000000002, (450359962737049669/450359962737049600)]
[70, 1.0000000000000002, (45035996273704967/45035996273704960)]
[71, 1.0000000000000002, (450359962737049671/450359962737049600)]
[72, 1.0000000000000002, (56294995342131209/56294995342131200)]
[73, 1.0000000000000002, (450359962737049673/450359962737049600)]
[74, 1.0000000000000002, (225179981368524837/225179981368524800)]
[75, 1.0000000000000002, (18014398509481987/18014398509481984)]
[76, 1.0000000000000002, (112589990684262419/112589990684262400)]
[77, 1.0000000000000002, (450359962737049677/450359962737049600)]
[78, 1.0000000000000002, (225179981368524839/225179981368524800)]
[79, 1.0000000000000002, (450359962737049679/450359962737049600)]
[80, 1.0000000000000002, (5629499534213121/5629499534213120)]
[81, 1.0000000000000002, (450359962737049681/450359962737049600)]
[82, 1.0000000000000002, (225179981368524841/225179981368524800)]
[83, 1.0000000000000002, (450359962737049683/450359962737049600)]
[84, 1.0000000000000002, (112589990684262421/112589990684262400)]
[85, 1.0000000000000002, (90071992547409937/90071992547409920)]
[86, 1.0000000000000002, (225179981368524843/225179981368524800)]
[87, 1.0000000000000002, (450359962737049687/450359962737049600)]
[88, 1.0000000000000002, (56294995342131211/56294995342131200)]
[89, 1.0000000000000002, (450359962737049689/450359962737049600)]
[90, 1.0000000000000002, (45035996273704969/45035996273704960)]
[91, 1.0000000000000002, (450359962737049691/450359962737049600)]
[92, 1.0000000000000002, (112589990684262423/112589990684262400)]
[93, 1.0000000000000002, (450359962737049693/450359962737049600)]
[94, 1.0000000000000002, (225179981368524847/225179981368524800)]
[95, 1.0000000000000002, (90071992547409939/90071992547409920)]
[96, 1.0000000000000002, (14073748835532803/14073748835532800)]
[97, 1.0000000000000002, (450359962737049697/450359962737049600)]
[98, 1.0000000000000002, (225179981368524849/225179981368524800)]
[99, 1.0000000000000002, (450359962737049699/450359962737049600)]
[100, 1.0000000000000002, (4503599627370497/4503599627370496)]
```

This sample program tries to convert rationals between
1.0 and 1.0 + Float::EPSILON to float.
Since there is no representable float values between them
(except 1.0 and 1.0 + Float::EPSILON),
I expect that
r.to_f returns 1.0 for r < X and
1.0 + Float::EPSILON for r > X
for some X.

But my expectation is not valid:

```
[34, 1.0000000000000002, (225179981368524817/225179981368524800)]
[35, 1.0, (90071992547409927/90071992547409920)]
```

I.e.

`1 + Float::EPSILON.to_r * 34 / 100 <
1 + Float::EPSILON.to_r * 35 / 100`

but

`(1 + Float::EPSILON.to_r * 34 / 100).to_f >
(1 + Float::EPSILON.to_r * 35 / 100).to_f`

I guess Rational#to_f should round the rational value to a nearest representable float value.




-- 
https://bugs.ruby-lang.org/
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