Add normal and exponential distributions to core::rand

src/etc/ziggurat_tables.py

@@ -0,0 +1,121 @@
+#!/usr/bin/env python
+# xfail-license
+
+# This creates the tables used for distributions implemented using the
+# ziggurat algorithm in `core::rand::distributions;`. They are
+# (basically) the tables as used in the ZIGNOR variant (Doornik 2005).
+# They are changed rarely, so the generated file should be checked in
+# to git.
+#
+# It creates 3 tables: X as in the paper, F which is f(x_i), and
+# F_DIFF which is f(x_i) - f(x_{i-1}). The latter two are just cached
+# values which is not done in that paper (but is done in other
+# variants). Note that the adZigR table is unnecessary because of
+# algebra.
+#
+# It is designed to be compatible with Python 2 and 3.
+
+from math import exp, sqrt, log, floor
+import random
+
+# The order should match the return value of `tables`
+TABLE_NAMES = ['X', 'F', 'F_DIFF']
+
+# The actual length of the table is 1 more, to stop
+# index-out-of-bounds errors. This should match the bitwise operation
+# to find `i` in `zigurrat` in `libstd/rand/mod.rs`. Also the *_R and
+# *_V constants below depend on this value.
+TABLE_LEN = 256
+
+# equivalent to `zigNorInit` in Doornik2005, but generalised to any
+# distribution. r = dR, v = dV, f = probability density function,
+# f_inv = inverse of f
+def tables(r, v, f, f_inv):
+    # compute the x_i
+    xvec = [0]*(TABLE_LEN+1)
+
+    xvec[0] = v / f(r)
+    xvec[1] = r
+
+    for i in range(2, TABLE_LEN):
+        last = xvec[i-1]
+        xvec[i] = f_inv(v / last + f(last))
+
+    # cache the f's
+    fvec = [0]*(TABLE_LEN+1)
+    fdiff = [0]*(TABLE_LEN+1)
+    for i in range(TABLE_LEN+1):
+        fvec[i] = f(xvec[i])
+        if i > 0:
+            fdiff[i] = fvec[i] - fvec[i-1]
+
+    return xvec, fvec, fdiff
+
+# Distributions
+# N(0, 1)
+def norm_f(x):
+    return exp(-x*x/2.0)
+def norm_f_inv(y):
+    return sqrt(-2.0*log(y))
+
+NORM_R = 3.6541528853610088
+NORM_V = 0.00492867323399
+
+NORM = tables(NORM_R, NORM_V,
+              norm_f, norm_f_inv)
+
+# Exp(1)
+def exp_f(x):
+    return exp(-x)
+def exp_f_inv(y):
+    return -log(y)
+
+EXP_R = 7.69711747013104972
+EXP_V = 0.0039496598225815571993
+
+EXP = tables(EXP_R, EXP_V,
+             exp_f, exp_f_inv)
+
+
+# Output the tables/constants/types
+
+def render_static(name, type, value):
+    # no space or
+    return 'pub static %s: %s =%s;\n' % (name, type, value)
+
+# static `name`: [`type`, .. `len(values)`] =
+#     [values[0], ..., values[3],
+#      values[4], ..., values[7],
+#      ... ];
+def render_table(name, values):
+    rows = []
+    # 4 values on each row
+    for i in range(0, len(values), 4):
+        row = values[i:i+4]
+        rows.append(', '.join('%.18f' % f for f in row))
+
+    rendered = '\n    [%s]' % ',\n     '.join(rows)
+    return render_static(name, '[f64, .. %d]' % len(values), rendered)
+
+
+with open('ziggurat_tables.rs', 'w') as f:
+    f.write('''// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+// Tables for distributions which are sampled using the ziggurat
+// algorithm. Autogenerated by `ziggurat_tables.py`.
+
+pub type ZigTable = &\'static [f64, .. %d];
+'''  % (TABLE_LEN + 1))
+    for name, tables, r in [('NORM', NORM, NORM_R),
+                            ('EXP', EXP, EXP_R)]:
+        f.write(render_static('ZIG_%s_R' % name, 'f64', ' %.18f' % r))
+        for (tabname, table) in zip(TABLE_NAMES, tables):
+            f.write(render_table('ZIG_%s_%s' % (name, tabname), table))