Machine {base} | R Documentation

## Machine Characteristics

### 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.

### Usage

    Machine()
    .Machine

### Details

The algorithm is based on Cody's (1988) subroutine MACHAR.

### 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

Cody, W. J. (1988) MACHAR: A subroutine to dynamically determine machine parameters. Transactions on Mathematical Software, 14, 4, 303–311.

### See Also

`machine` to determine the computer type which R is running on.

### Examples

    str(Machine())
    (Meps <- .Machine $ double.eps)

    ## All the following relations must hold :
    stopifnot(
     1 +     Meps != 1,
     1 + .5* Meps == 1,
     log2(.Machine$double.xmax) == .Machine$double.max.exp,
     log2(.Machine$double.xmin) == .Machine$double.min.exp,
     is.infinite(.Machine$double.base ^ .Machine$double.max.exp)
    )

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