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-#!/usr/bin/env python
-#
-# Copyright 2018 Developers of the Rand project.
-# Copyright 2013 The Rust Project Developers.
-#
-# Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-# https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-# <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
-# option. This file may not be copied, modified, or distributed
-# except according to those terms.
-
-# This creates the tables used for distributions implemented using the
-# ziggurat algorithm in `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']
-
-# 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)
- for i in range(TABLE_LEN+1):
- fvec[i] = f(xvec[i])
-
- return xvec, fvec
-
-# 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 2018 Developers of the Rand project.
-// Copyright 2013 The Rust Project Developers.
-//
-// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
-// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
-// <LICENSE-MIT or https://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))