Calculate the number of grains of wheat on a chessboard given that the number on each square doubles.
There once was a wise servant who saved the life of a prince. The king promised to pay whatever the servant could dream up. Knowing that the king loved chess, the servant told the king he would like to have grains of wheat. One grain on the first square of a chess board, with the number of grains doubling on each successive square.
There are 64 squares on a chessboard (where square 1 has one grain, square 2 has two grains, and so on).
Write code that shows:
By default, numbers in awk
are represented as double-precision floating
point numbers. This provides 53 bits of precision (see Table
16.3 in the manual). Unfortunately, this is insufficient to
complete this exercise (spoiler alert, one test requires 63 bits of
precision).
"Insufficient precision" looks like this:
$ gawk 'BEGIN {
n = 2 ^ 54
if (n == n + 1)
print "not enough precision"
else
print "OK"
}'
not enough precision
GNU awk
has the capability to use arbitrary-precision numbers, if the
relevant libraries have been compiled into the awk
executable. Check
your awk version, and look for "GNU MPFR":
$ gawk --version
GNU Awk 5.0.1, API: 2.0 (GNU MPFR 4.0.2, GNU MP 6.2.0)
...
If it's present, enable the capability using the -M
option:
$ gawk -M 'BEGIN {
n = 2 ^ 54
if (n == n + 1)
print "not enough precision"
else
print "OK"
}'
OK
What if my awk
doesn't have -M
? You'll have to call out to an external
program that can do arbitrary precision arithmetic, like bc
. See the
section Using getline into a Variable from a Pipe for an
example how to do this.
Further reading: Arbitrary Precision Arithmetic
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