From fde3b696562a12dc3ec99fcb85004a6a40e040f0 Mon Sep 17 00:00:00 2001
From: Nicolas Martinelli <nim@odoo.com>
Date: Wed, 7 Aug 2019 07:28:57 +0000
Subject: [PATCH] [FIX] tools: epsilon magnitude
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The following rounding is incorrect:
```
>>> float_round(6.6 * 0.175, precision_digits=2)
1.15
```

Indeed, 6.6 * 0.175 = 1.155 ≈ 1.16.

In this specific case, the `epsilon` computed is not sufficient. A
precision of 53 gives:
normalized_value = 115.49999999999997
epsilon = 1.2823075934420547e-14
=> new normalized_value = 115.49999999999999

Bad luck, this is just not enough to tip the value in the right
direction.

However, a precision of 52 is sufficient:
normalized_value = 115.49999999999997
epsilon = 2.5646151868841094e-14
=> new normalized_value = 115.5

The value of 53 was chosen from the `binary64` number format precision.
In case of Python, the corresponding machine epsilon is 2^-52 [1].
Therefore, using 52 instead of 53 does make sense.

It is worth noting that the value of the machine epsilon
2^-52 = 2.2204460492503131e-16, which is still 2 orders of magnitude
below our dynamic estimation.

[1] https://en.wikipedia.org/wiki/Machine_epsilon
[2] `numpy.finfo(float).eps = 2.2204460492503131e-16`

opw-2047368

closes odoo/odoo#35521

Signed-off-by: Nicolas Martinelli (nim) <nim@odoo.com>
---
 addons/web/static/src/js/core/utils.js | 2 +-
 odoo/addons/base/tests/test_float.py   | 2 ++
 odoo/tools/float_utils.py              | 2 +-
 3 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/addons/web/static/src/js/core/utils.js b/addons/web/static/src/js/core/utils.js
index a21c4241864..231ad97d202 100644
--- a/addons/web/static/src/js/core/utils.js
+++ b/addons/web/static/src/js/core/utils.js
@@ -309,7 +309,7 @@ var utils = {
         }
         var normalized_value = value / precision;
         var epsilon_magnitude = Math.log(Math.abs(normalized_value))/Math.log(2);
-        var epsilon = Math.pow(2, epsilon_magnitude - 53);
+        var epsilon = Math.pow(2, epsilon_magnitude - 52);
         normalized_value += normalized_value >= 0 ? epsilon : -epsilon;
 
         /**
diff --git a/odoo/addons/base/tests/test_float.py b/odoo/addons/base/tests/test_float.py
index a5f91982303..641c9c2d9e7 100644
--- a/odoo/addons/base/tests/test_float.py
+++ b/odoo/addons/base/tests/test_float.py
@@ -27,6 +27,8 @@ class TestFloatPrecision(TransactionCase):
         try_round(0.0049,'0.00')   # 0.0049 is closer to 0 than to 0.01, so should round down
         try_round(0.005,'0.01')   # the rule is to round half away from zero
         try_round(-0.005,'-0.01') # the rule is to round half away from zero
+        try_round(6.6 * 0.175, '1.16') # 6.6 * 0.175 is rounded to 1.15 with epsilon = 53
+        try_round(-6.6 * 0.175, '-1.16')
 
         def try_zero(amount, expected):
             self.assertEqual(currency.is_zero(amount), expected,
diff --git a/odoo/tools/float_utils.py b/odoo/tools/float_utils.py
index 041a87cabbe..eb3c0b4bd01 100644
--- a/odoo/tools/float_utils.py
+++ b/odoo/tools/float_utils.py
@@ -73,7 +73,7 @@ def float_round(value, precision_digits=None, precision_rounding=None, rounding_
     normalized_value = value / rounding_factor # normalize
     sign = math.copysign(1.0, normalized_value)
     epsilon_magnitude = math.log(abs(normalized_value), 2)
-    epsilon = 2**(epsilon_magnitude-53)
+    epsilon = 2**(epsilon_magnitude-52)
 
     # TIE-BREAKING: UP/DOWN (for ceiling[resp. flooring] operations)
     # When rounding the value up[resp. down], we instead subtract[resp. add] the epsilon value