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Since a DNA molecule has two strands, a gene in the genome rearrangement studies is usually denoted by a signed integer, with sign indicating the DNA strand to which the gene belongs, and a chromosome by a series of integers corresponding to those genes on the chromosome.
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Given bits for the significand, the encoding of can be computed by multiplying it by (left-shifting it bits), rounding to the nearest integer (or truncating toward minus infinity--as implemented by the floor function), and encoding the -bit result as a binary (signed) integer.
PHP stores whole numbers in a platform-dependent range, either a 64-bit or 32-bit signed integer equivalent to the C-language long type.
Signed integer addition with overflow checking.
Signed integer addition *without* overflow checking.
Signed integer subtraction with overflow checking.
Signed integer subtraction *without* overflow checking.
These data are in the same 16bit signed integer format used for the GTopo30.
Unfortunately, dealing with multiplication of Dedekind cuts is a time-consuming case-by-case process similar to the addition of signed integers.
The size of the datasets is limited by memory and by the maximal value of 32-bit signed long integers (2 147 483 647) used for internal indexing.
We have to multiply that by an integer to get another integer.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com