## Bug #14635

closed### Float#round(n) returns a wrong result when n is big

**Description**

**First of all, don't confuse that this is a usual floating-point error issue.**

The following looks inconsistent:

```
3.0e-31 #=> 3.0e-31
3.0e-31.round(31) #=> 3.0000000000000003e-31
```

## What it should be¶

A Float value is actually a range.

`3.0e-31`

represents a range of `0.299999999999999959315060e-30`

.. `0.300000000000000003105637e-30`

(the bounds are approximate). I call this range "A".

`3.0000000000000003e-31`

represents a range of `0.300000000000000003105637e-30`

.. `0.300000000000000046896214e-30`

. I call this range "B".

`x.round(31)`

should (1) multiple x with `10**31`

, (2) round it as an integer, and (3) divide it with `10**31`

.

In this case:

(1) `3.0e-31 * 10**31`

is a range of `2.99999999999999959315060`

.. `3.00000000000000003105637`

.

(2) The rounded result is 3, whichever value is chosen from the range above.

(3) `3.0 / 10**31`

is within the range "A", not within the range "B", so the result should be `3.0e-31`

, not `3.0000000000000003e-31`

.

## How the bug occurs¶

The reason why `3.0e-31.round(31)`

returns `3.0000000000000003e-31`

, is the implementation issue of `Float#round`

. It does the following:

(1) `f = pow(10, b)`

(2) `x = round(x * f)`

as an integer

(3) return `x / f`

However, a double variable `f`

cannot represent `pow(10, 31)`

precisely. In other words, the `10**31`

must be handled as an integer, but the implementation handles it as an inexact floating-point value. This is the issue.

## How to fix¶

The issue is simple, but it might be very difficult to fix. `strtod`

handles a string `"3.0e-31"`

correctly. So, by doing the same as `strtod`

, this issue would be fixed. However, the strtod implementation looks very difficult, at least to me. Contribution from mathematician is welcome.

(Honestly, I don't want to see such a complication in the source code. Another simpler approach would be more preferable.)

## References¶

This issue has been already reported in #5273 by marcandre. But the status of the ticket looks unclear; I cannot see how many issues remains. So, I created this ticket for just one bug that I could confirm.

#### Updated by mame (Yusuke Endoh) about 6 years ago

**Related to***Bug #5273: Float#round returns the wrong floats for higher precision*added

#### Updated by mame (Yusuke Endoh) about 6 years ago

**Subject**changed from*Float#round sometimes returns a wrong result*to*Float#round(n) returns a wrong result when n is big*

#### Updated by mame (Yusuke Endoh) about 6 years ago

I've found a much simpler solution: when `n`

is big, it should first translate the float to a rational, then call `Rational#round`

, and finally translate the resulting rational to a float. It is slow, only when n >= 23 for `Float#round(n)`

.

Currently, `Rational#to_f`

has the same inaccuracy issue, which can be fixed by #14637. The following patch includes the hunk for #14637.

```
diff --git a/bignum.c b/bignum.c
index b4c7560034..fd5f385cac 100644
--- a/bignum.c
+++ b/bignum.c
@@ -6178,9 +6178,7 @@ rb_big_fdiv_double(VALUE x, VALUE y)
return big_fdiv_int(x, rb_int2big(FIX2LONG(y)));
}
else if (RB_BIGNUM_TYPE_P(y)) {
- dy = rb_big2dbl(y);
- if (isinf(dx) || isinf(dy))
- return big_fdiv_int(x, y);
+ return big_fdiv_int(x, y);
}
else if (RB_FLOAT_TYPE_P(y)) {
dy = RFLOAT_VALUE(y);
diff --git a/internal.h b/internal.h
index 9b6a213151..0bf20b19b0 100644
--- a/internal.h
+++ b/internal.h
@@ -1689,6 +1689,7 @@ VALUE rb_cstr_to_rat(const char *, int);
VALUE rb_rational_abs(VALUE self);
VALUE rb_rational_cmp(VALUE self, VALUE other);
VALUE rb_numeric_quo(VALUE x, VALUE y);
+VALUE rb_flo_round_by_rational(int argc, VALUE *argv, VALUE num);
/* re.c */
VALUE rb_reg_compile(VALUE str, int options, const char *sourcefile, int sourceline);
diff --git a/numeric.c b/numeric.c
index 01856c7f20..15b27e9132 100644
--- a/numeric.c
+++ b/numeric.c
@@ -2239,6 +2239,10 @@ flo_round(int argc, VALUE *argv, VALUE num)
frexp(number, &binexp);
if (float_round_overflow(ndigits, binexp)) return num;
if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0);
+ if (ndigits > DBL_MANT_DIG * log(2.0) / log(5.0)) {
+ /* In this case, pow(10, ndigits) cannot 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);
diff --git a/rational.c b/rational.c
index d88f50f886..01bb88d1ae 100644
--- a/rational.c
+++ b/rational.c
@@ -1533,6 +1533,13 @@ nurat_round_n(int argc, VALUE *argv, VALUE self)
return f_round_common(argc, argv, self, round_func);
}
+static VALUE float_to_r(VALUE self);
+VALUE
+rb_flo_round_by_rational(int argc, VALUE *argv, VALUE num)
+{
+ return nurat_to_f(nurat_round_n(argc, argv, float_to_r(num)));
+}
+
static double
nurat_to_double(VALUE self)
{
@@ -2016,7 +2023,6 @@ integer_denominator(VALUE self)
return INT2FIX(1);
}
-static VALUE float_to_r(VALUE self);
/*
* call-seq:
* flo.numerator -> integer
```

#### Updated by marcandre (Marc-Andre Lafortune) over 3 years ago

**Has duplicate***Bug #17183: Float round working weirdly*added

#### Updated by marcandre (Marc-Andre Lafortune) over 3 years ago

**Has duplicate**deleted (*Bug #17183: Float round working weirdly*)

#### Updated by marcandre (Marc-Andre Lafortune) over 3 years ago

**Related to***Bug #17183: Float round working weirdly*added

#### Updated by jeremyevans0 (Jeremy Evans) almost 3 years ago

This issue still exists in the master branch. I've submitted a pull request that uses a modified version of @mame's patch to fix this issue: https://github.com/ruby/ruby/pull/4682

#### Updated by jeremyevans (Jeremy Evans) almost 3 years ago

**Status**changed from*Feedback*to*Closed*

Applied in changeset git|d16b68cb2204eeb5af8bd39149202b630374c67f.

Use Rational for Float#round with ndigits > 14

ndigits higher than 14 can result in values that are slightly too

large due to floating point limitations. Converting to rational

for the calculation and then back to float fixes these issues.

Fixes [Bug #14635]

Fixes [Bug #17183]

Co-authored by: Yusuke Endoh mame@ruby-lang.org