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 all current implementations of R use 32-bit integers and use IEC 60559 floating-point (double precision) arithmetic, the `"integer"` and `"double"` related 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

`double.eps` | the smallest positive floating-point number `x` such that `1 + x != 1`. It equals `double.base ^ ulp.digits` if either `double.base` is 2 or `double.rounding` is 0; otherwise, it is `(double.base ^ double.ulp.digits) / 2`. Normally `2.220446e-16`.
`double.neg.eps` | a small positive floating-point number `x` such that `1 - x != 1`. It equals `double.base ^ double.neg.ulp.digits` if `double.base` is 2 or `double.rounding` is 0; otherwise, it is `(double.base ^ double.neg.ulp.digits) / 2`. Normally `1.110223e-16`. As `double.neg.ulp.digits` is bounded below by `-(double.digits + 3)`, `double.neg.eps` may not be the smallest number that can alter 1 by subtraction.
`double.xmin` | the smallest non-zero normalized floating-point number, a power of the radix, i.e., `double.base ^ double.min.exp`. Normally `2.225074e-308`.
`double.xmax` | the largest normalized floating-point number. Typically, it is equal to `(1 - double.neg.eps) * double.base ^ double.max.exp`, but on some machines it is only the second or third largest such number, being too small by 1 or 2 units in the last digit of the significand. Normally `1.797693e+308`. Note that larger unnormalized numbers can occur.
`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, one of 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 `double digits` base-`double.base` digits participate in the post-normalization shift of the floating-point significand in multiplication, and 0 otherwise. Normally `0`.
`double.ulp.digits` | the largest negative integer `i` such that `1 + double.base ^ i != 1`, except that it is bounded below by `-(double.digits + 3)`. Normally `-52`.
`double.neg.ulp.digits` | the largest negative integer `i` such that `1 - double.base ^ i != 1`, except that it is bounded below by `-(double.digits + 3)`. Normally `-53`.
`double.exponent` | the number of bits (decimal places if `double.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 `double.base ^ i` is positive and normalized. Normally `-1022`.
`double.max.exp` | the smallest positive power of `double.base` that overflows. Normally `1024`.
`integer.max` | the largest integer which can be represented. Always 2^31 - 1 = 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 (or its use was disabled when R was built), otherwise possibly `12` (most 32-bit builds) or `16` (most 64-bit builds).
`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.
`longdouble.eps, longdouble.neg.eps, longdouble.digits, ...` | when `capabilities("long.double")` is true, there are 10 such `"longdouble.<kind>"` values, specifying the `long double` property corresponding to its `"double.*"` counterpart, above, see also ‘Note’.

### Note

In the (typical) case where `capabilities("long.double")` is true, R uses the `long double` C type in quite a few places internally for accumulators in e.g. `sum`, reading non-integer numeric constants into (binary) double precision numbers, or arithmetic such as `x %% y`; also, `long double` can be read by `readBin`.
For this reason, in that case, `.Machine` contains ten further components, `longdouble.eps`, `*.neg.eps`, `*.digits`, `*.rounding` `*.guard`, `*.ulp.digits`, `*.neg.ulp.digits`, `*.exponent`, `*.min.exp`, and `*.max.exp`, computed entirely analogously to their `double.*` counterparts, see there.

`sizeof.longdouble` only tells you the amount of storage allocated for a long double. Often what is stored is the 80-bit extended double type of IEC 60559, padded to the double alignment used on the platform — this seems to be the case for the common R platforms using ix86 and x86_64 chips.

Note that it is legal for a platform to have a `long double` C type which is identical to the `double` type — this happens on ARM cpus. In that case `capabilities("long.double")` will be false but `.Machine` may contain `"longdouble.<kind>"` elements.

### Source

Uses a C translation of Fortran code in the reference, modified by the R Core Team to defeat over-optimization in modern compilers.

### References

Cody, W. J. (1988). MACHAR: A subroutine to dynamically determine machine parameters. Transactions on Mathematical Software, 14(4), 303–311. doi: 10.1145/50063.51907.

### See Also

`.Platform` for details of the platform.

### Examples

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

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