Include module for desktop build

libs/pyutil/mathutil.py

@@ -0,0 +1,106 @@
+# Copyright (c) 2005-2010 Zooko Wilcox-O'Hearn
+#  This file is part of pyutil; see README.rst for licensing terms.
+
+"""
+A few commonly needed functions.
+"""
+
+import math
+
+def div_ceil(n, d):
+    """
+    The smallest integer k such that k*d >= n.
+    """
+    return (n/d) + (n%d != 0)
+
+def next_multiple(n, k):
+    """
+    The smallest multiple of k which is >= n.  Note that if n is 0 then the
+    answer is 0.
+    """
+    return div_ceil(n, k) * k
+
+def pad_size(n, k):
+    """
+    The smallest number that has to be added to n to equal a multiple of k.
+    """
+    if n%k:
+        return k - n%k
+    else:
+        return 0
+
+def is_power_of_k(n, k):
+    return k**int(math.log(n, k) + 0.5) == n
+
+def next_power_of_k(n, k):
+    p = 1
+    while p < n:
+        p *= k
+    return p
+
+def ave(l):
+    return sum(l) / len(l)
+
+def log_ceil(n, b):
+    """
+    The smallest integer k such that b^k >= n.
+
+    log_ceil(n, 2) is the number of bits needed to store any of n values, e.g.
+    the number of bits needed to store any of 128 possible values is 7.
+    """
+    p = 1
+    k = 0
+    while p < n:
+        p *= b
+        k += 1
+    return k
+
+def log_floor(n, b):
+    """
+    The largest integer k such that b^k <= n.
+    """
+    p = 1
+    k = 0
+    while p <= n:
+        p *= b
+        k += 1
+    return k - 1
+
+def linear_fit_slope(ps):
+    """
+    Single-independent-variable linear regression -- least squares method.
+
+    At least, I *think* this function computes that answer.  I no longer
+    remember where I learned this trick and at the moment I can't prove to 
+    myself that this is correct.
+
+    @param ps a sequence of tuples of (x, y)
+    """
+    avex = ave([x for (x, y) in ps])
+    avey = ave([y for (x, y) in ps])
+    sxy = sum([ (x - avex) * (y - avey) for (x, y) in ps ])
+    sxx = sum([ (x - avex) ** 2 for (x, y) in ps ])
+    if sxx == 0:
+        return None
+    return sxy / sxx
+
+def permute(l):
+    """
+    Return all possible permutations of l.
+
+    @type l: sequence
+    @rtype a set of sequences
+    """
+    if len(l) == 1:
+        return [l,]
+
+    res = []
+    for i in range(len(l)):
+        l2 = list(l[:])
+        x = l2.pop(i)
+        for l3 in permute(l2):
+            l3.append(x)
+            res.append(l3)
+
+    return res
+