.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."` 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.

### Source

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

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