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1 #!/usr/bin/env python2
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2 #
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3 # Copyright 2011-2016 Google Inc.
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4 #
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5 # Licensed under the Apache License, Version 2.0 (the "License");
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6 # you may not use this file except in compliance with the License.
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7 # You may obtain a copy of the License at
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8 #
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9 # http://www.apache.org/licenses/LICENSE-2.0
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10 #
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11 # Unless required by applicable law or agreed to in writing, software
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12 # distributed under the License is distributed on an "AS IS" BASIS,
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13 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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14 # See the License for the specific language governing permissions and
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15 # limitations under the License.
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16 #
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17 # vim: sw=2 sts=2 et
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18
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19 from math import log, ceil
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20 import sys
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21
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22
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23 def find_largest_power(less_than, base):
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24 power = int(log(less_than) / log(base))
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25 return base ** power
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26
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27
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28 def divmod_iter(x, by, chunk=None):
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29 if x < by:
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30 return [x]
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31
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32 if hasattr(x, 'bit_length'):
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33 # crude log(2, x)
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34 divisions = x.bit_length() // by.bit_length()
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35 else:
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36 divisions = log(x) / log(by)
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37
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38 if divisions < 1024:
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39 return divmod_iter_basic(x, by, chunk)
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40 else:
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41 return divmod_iter_chunking(x, by, chunk)
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42
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43
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44 def divmod_iter_chunking(x, by, chunk=None):
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45 """Generate successive (x % by); x /= by, but faster.
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46
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47 If provided, |chunk| must be a power of |by| (otherwise it is determined
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48 automatically for 1024 per inner loop, based on analysis of bench_genmod.py)
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49 """
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50
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51 if by == 1:
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52 assert x == 0, x
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53 yield 0
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54 return
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55
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56 if chunk is None:
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57 digits_per_chunk = 1024
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58 chunk = by ** digits_per_chunk
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59 else:
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60 digits_per_chunk = int(round(log(chunk) / log(by)))
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61 if (by ** digits_per_chunk) != chunk:
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62 raise ValueError("Chunk=%d must be a power of by=%d" % (chunk, by))
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63
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64 assert digits_per_chunk > 0
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65
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66 while x:
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67 x, this_chunk = divmod(x, chunk)
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68 #this_chunk = int(this_chunk)
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69 for _ in range(digits_per_chunk):
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70 this_chunk, m = divmod(this_chunk, by)
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71 yield m
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72
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73 if this_chunk == 0 and x == 0:
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74 break
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75
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76
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77 def divmod_iter_basic(x, by, chunk=None):
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78 """Generate successive (x % by); x /= by, the obvious way.
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79
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80 Chunk is ignored.
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81 """
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82 while x:
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83 x, m = divmod(x, by)
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84 yield m
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85
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86 def powersum(x, low, high):
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87 # http://mikestoolbox.com/powersum.html
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88 xm1 = x - 1
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89 if xm1 == 0:
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90 return high - low + 1
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91 a = x ** (high + 1)
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92 b = x ** low
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93 return (a - b) // xm1
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