BUG: Fix time spent checking equality of floating point numbers.

The use of np.allclose introduced a severe performance penalty,
caused by the creation of two `np.array`s for each check.

Instead create and use a similar check which maintains tolerance
to floating point rounding, but operates only on scalars.

zipline/finance/risk.py

@@ -64,6 +64,7 @@ from dateutil.relativedelta import relativedelta
 
 import zipline.finance.trading as trading
 from zipline.utils.date_utils import epoch_now
+import zipline.utils.math_utils as zp_math
 
 import pandas as pd
 
@@ -94,7 +95,7 @@ def sharpe_ratio(algorithm_volatility, algorithm_return, treasury_return):
     Returns:
         float. The Sharpe ratio.
     """
-    if np.allclose(algorithm_volatility, 0):
+    if zp_math.tolerant_equals(algorithm_volatility, 0):
         return 0.0
 
     return (algorithm_return - treasury_return) / algorithm_volatility
@@ -121,7 +122,7 @@ def sortino_ratio(algorithm_returns, algorithm_period_return, mar):
     downside = (rets[rets < mar] - mar) ** 2
     dr = np.sqrt(downside.sum() / len(rets))
 
-    if np.allclose(dr, 0):
+    if zp_math.tolerant_equals(dr, 0):
         return 0.0
 
     return (algorithm_period_return - mar) / dr
@@ -144,7 +145,11 @@ def information_ratio(algorithm_returns, benchmark_returns):
 
     relative_deviation = relative_returns.std(ddof=1)
 
-    if np.allclose(relative_deviation, 0) or np.isnan(relative_deviation):
+    if (
+        zp_math.tolerant_equals(relative_deviation, 0)
+        or
+        np.isnan(relative_deviation)
+    ):
         return 0.0
 
     return np.mean(relative_returns) / relative_deviation

zipline/finance/slippage.py

@@ -18,8 +18,7 @@ import math
 from copy import copy
 from functools import partial
 from zipline.protocol import DATASOURCE_TYPE
-
-import numpy as np
+import zipline.utils.math_utils as zp_math
 
 from logbook import Processor
 
@@ -71,7 +70,11 @@ def transact_stub(slippage, commission, event, open_orders):
         transactions = slippage.simulate(event, open_orders)
 
         for transaction in transactions:
-            if transaction and not np.allclose(transaction.amount, 0):
+            if (
+                transaction
+                and not
+                zp_math.tolerant_equals(transaction.amount, 0)
+            ):
                 direction = math.copysign(1, transaction.amount)
                 per_share, total_commission = commission.calculate(transaction)
                 transaction.price = transaction.price + (per_share * direction)
@@ -138,7 +141,7 @@ class VolumeShareSlippage(object):
 
             open_amount = order.amount - order.filled
 
-            if np.allclose(open_amount, 0):
+            if zp_math.tolerant_equals(open_amount, 0):
                 continue
 
             # check price limits, continue if the
@@ -150,7 +153,11 @@ class VolumeShareSlippage(object):
             # price impact accounts for the total volume of transactions
             # created against the current minute bar
             remaining_volume = max_volume - total_volume
-            if remaining_volume <= 0 or np.allclose(remaining_volume, 0):
+            if (
+                remaining_volume <= 0
+                or
+                zp_math.tolerant_equals(remaining_volume, 0)
+            ):
                 # we can't fill any more transactions
                 return txns
 
@@ -209,7 +216,7 @@ class FixedSlippage(object):
             if not order.triggered:
                 continue
 
-            if np.allclose(order.amount, 0):
+            if zp_math.tolerant_equals(order.amount, 0):
                 return txns
 
             txn = create_transaction(

zipline/gens/tradesimulation.py

@@ -14,7 +14,6 @@
 # limitations under the License.
 import itertools
 import math
-import numpy as np
 import uuid
 
 from copy import copy
@@ -32,6 +31,7 @@ from zipline.finance.slippage import (
     check_order_triggers
 )
 from zipline.finance.commission import PerShare
+import zipline.utils.math_utils as zp_math
 
 log = Logger('Trade Simulation')
 
@@ -83,7 +83,7 @@ class Blotter(object):
             yield date, results
 
     def process_trade(self, trade_event):
-        if np.allclose(trade_event.volume, 0):
+        if zp_math.tolerant_equals(trade_event.volume, 0):
             # there are zero volume trade_events bc some stocks trade
             # less frequently than once per minute.
             return []

zipline/transforms/stddev.py

@@ -16,10 +16,9 @@
 from collections import defaultdict
 from math import sqrt
 
-import numpy as np
-
 from zipline.errors import WrongDataForTransform
 from zipline.transforms.utils import EventWindow, TransformMeta
+import zipline.utils.math_utils as zp_math
 
 
 class MovingStandardDev(object):
@@ -118,7 +117,7 @@ class MovingStandardDevWindow(EventWindow):
             s_squared = (self.sum_sqr - self.sum * average) \
                 / (len(self) - 1)
 
-            if np.allclose(0, s_squared):
+            if zp_math.tolerant_equals(0, s_squared):
                 return 0.0
             stddev = sqrt(s_squared)
         return stddev

zipline/utils/math_utils.py

@@ -0,0 +1,20 @@
+#
+# Copyright 2013 Quantopian, Inc.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import math
+
+
+def tolerant_equals(a, b, atol=10e-7, rtol=10e-7):
+    return math.fabs(a - b) <= (atol + rtol * math.fabs(b))