.Machine {base} R Documentation

## Numerical Characteristics of the Machine

### Description

`.Machine` is a variable holding information on the numerical characteristics of the machine R is running on, such as the largest double or integer and the machine's precision.

### Usage

```.Machine
```

### Details

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

### Value

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. `sizeof.long` the number of bytes in a C `long` type. `sizeof.longlong` the number of bytes in a C `long long` type. Will be zero if there is no such type. `sizeof.longdouble` the number of bytes in a C `long double` type. Will be zero if there is no such type. `sizeof.pointer` the number of bytes in a C `SEXP` type.

### References

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

`.Platform` for details of the platform.
```.Machine