R: Machine Characteristics

Machine Characteristics

Usage

Machine()
.Machine

Description

Machine() returns information on numeric characteristics of the machine R is running on, such as the largest double or integer and the machine's precision.

.Machine is a variable holding this information.

The algorithm is based on Cody's subroutine MACHAR (see the reference below).

Value

Machine() returns a list with components (for simplicity, the prefix ``double'' is omitted in the explanations)

`double.eps`	the smallest positive floating-point number `x` such that `1 + x != 1`. It equals `base^ulp.digits` if either `base` is 2 or `rounding` is 0; otherwise, it is `(base^ulp.digits) / 2`.
`double.neg.eps`	a small positive floating-point number `x` such that `1 - x != 1`. It equals `base^neg.ulp.digits` if `base` is 2 or `round` is 0; otherwise, it is `(base^neg.ulp.digits) / 2`. As `neg.ulp.digits` is bounded below by `-(digits + 3)`, `neg.eps` may not be the smallest number that can alter 1 by subtraction.
`double.xmin`	the smallest non-vanishing normalized floating-point power of the radix, i.e., `base^min.exp`.
`double.xmax`	the largest finite floating-point number. Typically, it is equal to `(1 - neg.eps) * base^max.exp`, but on some machines it is only the second, or perhaps third, largest number, being too small by 1 or 2 units in the last digit of the significand.
`double.base`	the radix for the floating-point representation
`double.digits`	the number of base digits in the floating-point significand
`double.rounding`	the rounding action. 0 if floating-point addition chops; 1 if floating-point addition rounds, but not in the IEEE style; 2 if floating-point addition rounds in the IEEE style; 3 if floating-point addition chops, and there is partial underflow; 4 if floating-point addition rounds, but not in the IEEE style, and there is partial underflow; 5 if floating-point addition rounds in the IEEE style, and there is partial underflow
`double.guard`	the number of guard digits for multiplication with truncating arithmetic. It is 1 if floating-point arithmetic truncates and more than `digits` base `base` digits participate in the post-normalization shift of the floating-point significand in multiplication, and 0 otherwise.
`double.ulp.digits`	the largest negative integer `i` such that `1 + base^i != 1`, except that it is bounded below by `-(digits + 3)`.
`double.neg.ulp.digits`	the largest negative integer `i` such that `1 - base^i != 1`, except that it is bounded below by `-(digits + 3)`.
`double.exponent`	the number of bits (decimal places if `base` is 10) reserved for the representation of the exponent (including the bias or sign) of a floating-point number
`double.min.exp`	the largest in magnitude negative integer `i` such that `base ^ i` is positive and normalized.
`double.max.exp`	the smallest positive power of `base` that overflows.
`integer.max`	the largest integer which can be represented.

References

W. J. Cody (1988), MACHAR: A Subroutine to Dynamically Determine Machine Parameters. Transactions on Mathematical Software, 14, 4, 303-311.

Examples

str(Machine())
1 +     .Machine$double.eps != 1
1 + .5* .Machine$double.eps == 1