Add-based SR (#44)

Previous implementation was based on comparison: x - floor(x) > rand
This changes to be based on add: x + rand >= floor(x) + 1

No behavioural change expected, but bias direction and rounding profiles are inverted

Author: awf

docs/source/03-value-tables.ipynb

@@ -230,9 +230,7 @@
     "        0xFF,\n",
     "    ):\n",
     "        print(\n",
-    "            str_tablerow(\n",
-    "                fi, decode_float(fi, i), show_b16_info=True, vs_width=8, vs_d=4\n",
-    "            )\n",
+    "            str_tablerow(fi, decode_float(fi, i), show_b16_info=True, vs_width=8, vs_d=4)\n",
     "        )"
    ]
   },
@@ -3266,7 +3264,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "gfloat-clean",
    "language": "python",
    "name": "python3"
   },

docs/source/05-stochastic-rounding.ipynb

@@ -31,7 +31,7 @@ dependencies = {file = ["requirements.txt"]}
 optional-dependencies = {dev = {file = ["requirements-dev.txt"]}}
 
 [tool.black]
-line-length = 88
+line-length = 90
 fast = true
 
 [tool.mypy]

pyproject.toml

@@ -5,9 +5,7 @@
 from .types import FormatInfo
 
 
-def decode_ndarray(
-    fi: FormatInfo, codes: np.ndarray, np: ModuleType = np
-) -> np.ndarray:
+def decode_ndarray(fi: FormatInfo, codes: np.ndarray, np: ModuleType = np) -> np.ndarray:
     r"""
     Vectorized version of :meth:`decode_float`
 

src/gfloat/decode_ndarray.py

@@ -102,7 +102,7 @@ def round_float(
             case RoundMode.TowardNegative:
                 should_round_away = sign and delta > 0
             case RoundMode.TiesToAway:
-                should_round_away = delta >= 0.5
+                should_round_away = delta + 0.5 >= 1.0
             case RoundMode.TiesToEven:
                 should_round_away = delta > 0.5 or (delta == 0.5 and code_is_odd)
             case RoundMode.Stochastic:
@@ -113,20 +113,20 @@ def round_float(
                     (d - floord > 0.5) or ((d - floord == 0.5) and _isodd(floord))
                 )
 
-                should_round_away = d > srbits
+                should_round_away = d + srbits >= 2.0**srnumbits
             case RoundMode.StochasticOdd:
                 ## RTNE delta to srbits
                 d = delta * 2.0**srnumbits
                 floord = np.floor(d).astype(np.int64)
                 d = floord + (
-                    (d - floord > 0.5) or ((d - floord == 0.5) and ~_isodd(floord))
+                    (d - floord > 0.5) or ((d - floord == 0.5) and not _isodd(floord))
                 )
 
-                should_round_away = d > srbits
+                should_round_away = d + srbits >= 2.0**srnumbits
             case RoundMode.StochasticFast:
-                should_round_away = delta > (0.5 + srbits) * 2.0**-srnumbits
+                should_round_away = delta + (0.5 + srbits) * 2.0**-srnumbits >= 1.0
             case RoundMode.StochasticFastest:
-                should_round_away = delta > srbits * 2.0**-srnumbits
+                should_round_away = delta + srbits * 2.0**-srnumbits >= 1.0
 
         if should_round_away:
             # This may increase isignificand to 2**p,

src/gfloat/round.py

@@ -78,14 +78,19 @@ def round_ndarray(
     match rnd:
         case RoundMode.TowardZero:
             should_round_away = np.zeros_like(delta, dtype=bool)
+
         case RoundMode.TowardPositive:
             should_round_away = ~is_negative & (delta > 0)
+
         case RoundMode.TowardNegative:
             should_round_away = is_negative & (delta > 0)
+
         case RoundMode.TiesToAway:
             should_round_away = delta >= 0.5
+
         case RoundMode.TiesToEven:
             should_round_away = (delta > 0.5) | ((delta == 0.5) & code_is_odd)
+
         case RoundMode.Stochastic:
             assert srbits is not None
             ## RTNE delta to srbits
@@ -94,7 +99,8 @@ def round_ndarray(
             dd = d - floord
             drnd = floord + (dd > 0.5) + ((dd == 0.5) & _isodd(floord))
 
-            should_round_away = drnd > srbits
+            should_round_away = drnd + srbits >= 2.0**srnumbits
+
         case RoundMode.StochasticOdd:
             assert srbits is not None
             ## RTNO delta to srbits
@@ -103,13 +109,15 @@ def round_ndarray(
             dd = d - floord
             drnd = floord + (dd > 0.5) + ((dd == 0.5) & ~_isodd(floord))
 
-            should_round_away = drnd > srbits
+            should_round_away = drnd + srbits >= 2.0**srnumbits
+
         case RoundMode.StochasticFast:
             assert srbits is not None
-            should_round_away = delta > (2 * srbits + 1) * 2.0 ** -(1 + srnumbits)
+            should_round_away = delta + (2 * srbits + 1) * 2.0 ** -(1 + srnumbits) >= 1.0
+
         case RoundMode.StochasticFastest:
             assert srbits is not None
-            should_round_away = delta > srbits * 2.0**-srnumbits
+            should_round_away = delta + srbits * 2.0**-srnumbits >= 1.0
 
     isignificand = np.where(should_round_away, isignificand + 1, isignificand)
 

src/gfloat/round_ndarray.py

@@ -222,9 +222,7 @@ def test_p3109_k8_specials(fi: FormatInfo) -> None:
     assert fi.code_of_neginf == 0xFF
 
 
-@pytest.mark.parametrize(
-    "k,p", [(8, 3), (8, 1), (6, 1), (6, 5), (3, 1), (3, 2), (11, 3)]
-)
+@pytest.mark.parametrize("k,p", [(8, 3), (8, 1), (6, 1), (6, 5), (3, 1), (3, 2), (11, 3)])
 def test_p3109_specials(k: int, p: int) -> None:
     fi = format_info_p3109(k, p)
     assert fi.code_of_nan == 2 ** (k - 1)