Avoid precision loss when converting between units. Fixes #330

4 files changed, 36 insertions, 10 deletions

diff --git a/scss/cssdefs.py b/scss/cssdefs.py
index 5d9b7eb..79be7b4 100644
--- a/scss/cssdefs.py
+++ b/scss/cssdefs.py
@@ -1,6 +1,7 @@
 """Constants and functions defined by the CSS specification, not specific to
 Sass.
 """
+from fractions import Fraction
 from math import pi
 import re
 
@@ -166,15 +167,15 @@ BASE_UNIT_CONVERSIONS = {
     # Lengths
     'mm': (1, 'mm'),
     'cm': (10, 'mm'),
-    'in': (25.4, 'mm'),
-    'px': (25.4 / 96, 'mm'),
-    'pt': (25.4 / 72, 'mm'),
-    'pc': (25.4 / 6, 'mm'),
+    'in': (Fraction(254, 10), 'mm'),
+    'px': (Fraction(254, 960), 'mm'),
+    'pt': (Fraction(254, 720), 'mm'),
+    'pc': (Fraction(254, 60), 'mm'),
 
     # Angles
-    'deg': (1 / 360, 'turn'),
-    'grad': (1 / 400, 'turn'),
-    'rad': (pi / 2, 'turn'),
+    'deg': (Fraction(1, 360), 'turn'),
+    'grad': (Fraction(1, 400), 'turn'),
+    'rad': (Fraction.from_float(pi / 2), 'turn'),
     'turn': (1, 'turn'),
 
     # Times
@@ -187,7 +188,7 @@ BASE_UNIT_CONVERSIONS = {
 
     # Resolutions
     'dpi': (1, 'dpi'),
-    'dpcm': (2.54, 'dpi'),
+    'dpcm': (Fraction(254 / 100), 'dpi'),
     'dppx': (96, 'dpi'),
 }
 
@@ -252,7 +253,7 @@ def cancel_base_units(units, to_remove):
     # Copy the dict since we're about to mutate it
     to_remove = to_remove.copy()
     remaining_units = []
-    total_factor = 1
+    total_factor = Fraction(1)
 
     for unit in units:
         factor, base_unit = get_conversion_factor(unit)
diff --git a/scss/tests/files/bugs/unit-float-precision.css b/scss/tests/files/bugs/unit-float-precision.css
new file mode 100644
index 0000000..16e9d86
--- /dev/null
+++ b/scss/tests/files/bugs/unit-float-precision.css
@@ -0,0 +1,3 @@
+a {
+  width: 702px;
+}
diff --git a/scss/tests/files/bugs/unit-float-precision.scss b/scss/tests/files/bugs/unit-float-precision.scss
new file mode 100644
index 0000000..a57b294
--- /dev/null
+++ b/scss/tests/files/bugs/unit-float-precision.scss
@@ -0,0 +1,7 @@
+// A number of pixels is actually stored internally as millimeters, which
+// causes some slight precision issues in corner cases.  In this case, the
+// answer came out as 701px rather than 702px, because the subtraction yielded
+// 701.99999999px.
+a {
+    width: floor(742px - 40px);
+}
diff --git a/scss/types.py b/scss/types.py
index e733377..c35905a 100644
--- a/scss/types.py
+++ b/scss/types.py
@@ -5,6 +5,7 @@ from __future__ import unicode_literals
 
 from collections import Iterable
 import colorsys
+from fractions import Fraction
 import operator
 import re
 import string
@@ -255,7 +256,21 @@ class Number(Value):
             self.unit_denom = amount.unit_denom
             return
 
-        if not isinstance(amount, (int, float)):
+        # Numbers with units are stored internally as a "base" unit, which can
+        # involve float division, which can lead to precision errors in obscure
+        # cases.  Storing the original units would only partially solve this
+        # problem, because there'd still be a possible loss of precision when
+        # converting in Sass-land.  Almost all of the conversion factors are
+        # simple ratios of small whole numbers, so using Fraction across the
+        # board preserves as much precision as possible.
+        # TODO in fact, i wouldn't mind parsing Sass values as fractions of a
+        # power of ten!
+        # TODO this slowed the test suite down by about 10%, ha
+        if isinstance(amount, (int, float)):
+            amount = Fraction.from_float(amount)
+        elif isinstance(amount, Fraction):
+            pass
+        else:
             raise TypeError("Expected number, got %r" % (amount,))
 
         if unit is not None: