Decoded: OpenTTD (2003) v1.8 (2018)
Source file: math_func.cpp
Line-by-line code walkthrough by MaiZure

math_func.cpp defines several integer math function approximations

Original code:
https://github.com/MaiZure/OpenTTD-1.8/blob/master/src/core/math_func.cpp





1     COMMENT (*)
2     BLANK (-)
3     *
4     *
5     *
6     *
7     *
8     *
9     -
10    *
11    -
12    Include the OpenTTD platform-dependent header
13    Include the OpenTTD math function header
14    -
15    Include the OpenTTD safeguard header
16    -
17    *
18    *
19    *
20    *
21    *
22    *
23    *
24    *
25    *
26    Defines LeastCommonMultiple for two integers
27    BLOCK START - LeastCommonMultiple, two input LCM computation
28    If both inputs are zero, then zero is the only LCM
29    If one input is one or both are the same, then the only answer is the
      non-one
30    If one input is one, then the answer must be the other
31    -
32    Return the product of both inputs divded by the GCD
33    BLOCK END- LeastCommonMultiple
34    *
35    *
36    *
37    *
38    *
39    *
40    *
41    Defines GreatestCommonDivisor for two integers
42    BLOCK START - GreatestCommonDivisor, GCD a la Euclid
43    Loop while the second input has value
44    Store the second input as a temporary value
45    Update b with the modulus a mod b
46    Swap the old b to a
47    Loop until b has no value
48    Return the solution in a
49    -
50    BLOCK END - GreatestCommonDivisor
51    -
52    *
53    *
54    *
55    *
56    *
57    *
58    *
59    Defines DivideApprox with a dividend and a divisor
60    BLOCK START - DivideApprox, integer results that may be off by one
61    Initializes a 'random' number using the input
62    -
63    Calculates the remainder
64    -
65    Computers the integer answer
66    If the random number is less than the remainder (likely for large remainders)
67    Offset the answer by one in another 'random' direction
68    End check for offset
69    -
70    Return the answer that won't always be a simple truncation
71    BLOCK END - DivideApprox
72    -
73    *
74    *
75    *
76    *
77    *
78    *
79    Defines IntSqrt with one argument, the number to root
80    BLOCK START - IntSqrt
81    Initialize the result to 0
82    Compute a number with only the 31st bit high
83    *
84    *
85    Divide the base number of 4 until it is smaller than the input
86    -
87    While the base number is not zero...(gradually refine precision)
88    If the input is larger than the result...
89    Redeuce the result by the base number
90    Halve the result and add back the base number
91    Otherwise we've overshot the result..
92    Halve the result
93    End check for input number size
94    Cut the base number by another quarter
95    Repeat loop until the base number is zero
96    -
97    *
98    Add one is the input is larger (likely)
99    -
100   Return the result
101   BLOCK END - IntSqrt