R: Numerical Characteristics of the Machine

.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. As almost all current inplements of R use 32-bit integers and IEC 60059 floating-point (double precision) arithmetic, most of these values are the same for almost all R builds.

Note that on most platforms smaller positive values than .Machine$double.xmin can occur. On a typical R platform the smallest positive double is about 5e-324.

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`. Normally `2.220446e-16`.
`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`. Normally `1.110223e-16`. 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`. Normally `2.225074e-308`.
`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. Normally `1.797693e+308`.
`double.base`	the radix for the floating-point representation: normally `2`.
`double.digits`	the number of base digits in the floating-point significand: normally `53`.
`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. Normally `5`.
`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)`. Normally `-52`.
`double.neg.ulp.digits`	the largest negative integer `i` such that `1 - base^i != 1`, except that it is bounded below by `-(digits + 3)`. Normally `-53`.
`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. Normally `11`.
`double.min.exp`	the largest in magnitude negative integer `i` such that `base ^ i` is positive and normalized. Normally `-1022`.
`double.max.exp`	the smallest positive power of `base` that overflows. Normally `1024`.
`integer.max`	the largest integer which can be represented. Always `2147483647`.
`sizeof.long`	the number of bytes in a C `long` type: `4` or `8` (most 64-bit systems, but not Windows).
`sizeof.longlong`	the number of bytes in a C `long long` type. Will be zero if there is no such type, otherwise usually `8`.
`sizeof.longdouble`	the number of bytes in a C `long double` type. Will be zero if there is no such type, otherwise possibly `12` (Windows, 32-bit Linux/Solaris) or `16` (64-bit Linux/Solaris, Intel Mac OS X).
`sizeof.pointer`	the number of bytes in a C `SEXP` type. Will be `4` on 32-bit builds and `8` on 64-bit builds of R.

References

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

Examples

.Machine
## or for a neat printout
noquote(unlist(format(.Machine)))

[Package base version 2.9.0 ]