Merge pull request #24 from graphcore-research/simplify-round

Simplify round, fix directed rounding

Author: awf

src/gfloat/round.py

@@ -40,7 +40,6 @@ def round_float(
     # Constants
     p = fi.precision
     bias = fi.expBias
-    t = p - 1
 
     if np.isnan(v):
         if fi.num_nans == 0:
@@ -56,59 +55,57 @@ def round_float(
     if np.isinf(vpos):
         result = np.inf
 
-    elif fi.has_subnormals and vpos < fi.smallest_subnormal / 2:
-        # Test against smallest_subnormal to avoid subnormals in frexp below
-        # Note that this restricts us to types narrower than float64
-        result = 0.0
+    elif vpos == 0:
+        result = 0
 
     else:
-        # Extract significand (mantissa) and exponent
-        fsignificand, expval = np.frexp(vpos)
-        assert fsignificand >= 0.5 and fsignificand < 1.0
-        # Bring significand into range [1.0, 2.0)
-        fsignificand *= 2
-        expval -= 1
+        # Extract exponent
+        expval = int(np.floor(np.log2(vpos)))
+
+        assert expval > -1024 + p  # not yet tested for float64 near-subnormals
 
         # Effective precision, accounting for right shift for subnormal values
-        biased_exp = expval + bias
         if fi.has_subnormals:
-            effective_precision = t + min(biased_exp - 1, 0)
-        else:
-            effective_precision = t
+            expval = max(expval, 1 - bias)
 
         # Lift to "integer * 2^e"
-        fsignificand *= 2.0**effective_precision
-        expval -= effective_precision
+        expval = expval - p + 1
+
+        fsignificand = vpos * 2.0**-expval
 
         # Round
         isignificand = math.floor(fsignificand)
-        if isignificand != fsignificand:
-            # Need to round
-            if rnd == RoundMode.TowardZero:
-                pass
-            elif rnd == RoundMode.TowardPositive:
-                isignificand += 1 if not sign else 0
-            elif rnd == RoundMode.TowardNegative:
-                isignificand += 1 if sign else 0
-            else:
-                # Round to nearest
-                d = fsignificand - isignificand
-                if d > 0.5:
-                    isignificand += 1
-                elif d == 0.5:
-                    # Tie
-                    if rnd == RoundMode.TiesToAway:
-                        isignificand += 1
-                    else:
-                        # All other modes tie to even
-                        if fi.precision == 1:
-                            # No significand bits
-                            assert (isignificand == 1) or (isignificand == 0)
-                            if _isodd(biased_exp):
-                                expval += 1
-                        else:
-                            if _isodd(isignificand):
-                                isignificand += 1
+        delta = fsignificand - isignificand
+        if (
+            (rnd == RoundMode.TowardPositive and not sign and delta > 0)
+            or (rnd == RoundMode.TowardNegative and sign and delta > 0)
+            or (rnd == RoundMode.TiesToAway and delta >= 0.5)
+            or (rnd == RoundMode.TiesToEven and delta > 0.5)
+            or (rnd == RoundMode.TiesToEven and delta == 0.5 and _isodd(isignificand))
+        ):
+            isignificand += 1
+
+        ## Special case for Precision=1, all-log format with zero.
+        if fi.precision == 1:
+            # The logic is simply duplicated for clarity of reading.
+            isignificand = math.floor(fsignificand)
+            code_is_odd = isignificand != 0 and _isodd(expval + bias)
+            if (
+                (rnd == RoundMode.TowardPositive and not sign and delta > 0)
+                or (rnd == RoundMode.TowardNegative and sign and delta > 0)
+                or (rnd == RoundMode.TiesToAway and delta >= 0.5)
+                or (rnd == RoundMode.TiesToEven and delta > 0.5)
+                or (rnd == RoundMode.TiesToEven and delta == 0.5 and code_is_odd)
+            ):
+                # Go to nextUp.
+                # Increment isignificand if zero,
+                # else increment exponent
+                if isignificand == 0:
+                    isignificand = 1
+                else:
+                    assert isignificand == 1
+                    expval += 1
+        ## End special case for Precision=1.
 
         result = isignificand * (2.0**expval)
 
@@ -119,9 +116,15 @@ def round_float(
             return 0.0
 
     # Overflow
-    if result > (-fi.min if sign else fi.max):
-        if sat:
-            result = fi.max
+    amax = -fi.min if sign else fi.max
+    if result > amax:
+        if (
+            sat
+            or (rnd == RoundMode.TowardNegative and not sign and np.isfinite(v))
+            or (rnd == RoundMode.TowardPositive and sign and np.isfinite(v))
+            or (rnd == RoundMode.TowardZero and np.isfinite(v))
+        ):
+            result = amax
         else:
             if fi.has_infs:
                 result = np.inf

src/gfloat/types.py

@@ -146,7 +146,7 @@ def bits(self) -> int:
     @property
     def eps(self) -> float:
         """
-        The difference between 1.0 and the next smallest representable float
+        The difference between 1.0 and the smallest representable float
         larger than 1.0. For example, for 64-bit binary floats in the IEEE-754
         standard, ``eps = 2**-52``, approximately 2.22e-16.
         """
@@ -156,7 +156,7 @@ def eps(self) -> float:
     @property
     def epsneg(self) -> float:
         """
-        The difference between 1.0 and the next smallest representable float
+        The difference between 1.0 and the largest representable float
         less than 1.0. For example, for 64-bit binary floats in the IEEE-754
         standard, ``epsneg = 2**-53``, approximately 1.11e-16.
         """