Bug #17037: rounding of Rational#to_f

• Status: Closed
• Assignee: -
• Target version: -
• Backport: 2.5: UNKNOWN, 2.6: UNKNOWN, 2.7: UNKNOWN

[akr (Akira Tanaka)]

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.

[akr (Akira Tanaka)]

Gauche scheme interpreter has same issue and Kawai-san (the author of Gauche) investigate it.

http://blog.practical-scheme.net/gauche/20200722-ratnum-flonum

[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.

[nobu (Nobuyoshi Nakada)]

• Status changed from Open to Closed

Applied in changeset git|8e93bf8e1fbac73b677c333b19a8b55ae9daddc3.

---

[Bug #17037] Improve accuracy of division near precision limits

When dividing near the precision limit of double, use Bignum
division to get rid of rounding errors.