llvm-project

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from math import *
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"""
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This script is used to generate a table used by
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libc/src/__support/high_precision_decimal.h.
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For the ith entry in the table there are two values (indexed starting at 0).
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The first value is the number of digits longer the second value would be if
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multiplied by 2^i.
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The second value is the smallest number that would create that number of
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additional digits (which in base ten is always 5^i). Anything less creates one
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fewer digit.
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As an example, the 3rd entry in the table is {1, "125"}. This means that if
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125 is multiplied by 2^3 = 8, it will have exactly one more digit.
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Multiplying it out we get 125 * 8 = 1000. 125 is the smallest number that gives
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that extra digit, for example 124 * 8 = 992, and all larger 3 digit numbers
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also give only one extra digit when multiplied by 8, for example 8 * 999 = 7992.
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This makes sense because 5^3 * 2^3 = 10^3, the smallest 4 digit number.
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For numbers with more digits we can ignore the digits past what's in the second
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value, since the most significant digits determine how many extra digits there
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will be. Looking at the previous example, if we have 1000, and we look at just
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the first 3 digits (since 125 has 3 digits), we see that 100 < 125, so we get
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one fewer than 1 extra digits, which is 0.
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Multiplying it out we get 1000 * 8 = 8000, which fits the expectation.
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Another few quick examples:
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For 1255, 125 !< 125, so 1 digit more: 1255 * 8 = 10040
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For 9999, 999 !< 125, so 1 digit more: 9999 * 8 = 79992
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Now let's try an example with the 10th entry: {4, "9765625"}. This one means
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that 9765625 * 2^10 will have 4 extra digits.
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Let's skip straight to the examples:
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For 1, 1 < 9765625, so 4-1=3 extra digits: 1 * 2^10 = 1024, 1 digit to 4 digits is a difference of 3.
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For 9765624, 9765624 < 9765625 so 3 extra digits: 9765624 * 1024 = 9999998976, 7 digits to 10 digits is a difference of 3.
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For 9765625, 9765625 !< 9765625 so 4 extra digits: 9765625 * 1024 = 10000000000, 7 digits to 11 digits is a difference of 4.
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For 9999999, 9999999 !< 9765625 so 4 extra digits: 9999999 * 1024 = 10239998976, 7 digits to 11 digits is a difference of 4.
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For 12345678, 1234567 < 9765625 so 3 extra digits: 12345678 * 1024 = 12641974272, 8 digits to 11 digits is a difference of 3.
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This is important when left shifting in the HPD class because it reads and
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writes the number backwards, and to shift in place it needs to know where the
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last digit should go. Since a binary left shift by i bits is the same as
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multiplying by 2^i we know that looking up the ith element in the table will
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tell us the number of additional digits. If the first digits of the number
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being shifted are greater than or equal to the digits of 5^i (the second value
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of each entry) then it is just the first value in the entry, else it is one
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fewer.
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"""
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# Generate Left Shift Table
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outStr = ""
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for i in range(61):
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    tenToTheI = 10**i
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    fiveToTheI = 5**i
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    outStr += "{"
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    # The number of new digits that would be created by multiplying 5**i by 2**i
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    outStr += str(ceil(log10(tenToTheI) - log10(fiveToTheI)))
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    outStr += ', "'
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    if not i == 0:
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        outStr += str(fiveToTheI)
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    outStr += '"},\n'
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print(outStr)
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