Extreme numerical values in floating-point precision in R

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R uses IEEE 754 double-precision floating-point numbers.

Floating-point numbers are more dense near zero. This is a result of their being designed to compute accurately (the equivalent of about 16 significant decimal digits, as you have noticed) over a very wide range.

Perhaps you expected a fixed-point system with uniform absolute precision. In practice fixed-point is either wasteful or the ranges of each intermediate computation must be carefully estimated beforehand, with drastic consequences if they are wrong.

Positive floating-point numbers look like this, schematically:

+-+-+-+--+--+--+----+----+----+--------+--------+--------+--
0

The smallest positive normal double-precision number is 2 to the power of the minimal exponent. Near one, the double-precision floating-point numbers are already spread quite wide apart. There is a distance of 2-53 from one to the number below it, and a distance of 2-52 from one to the number above it.

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