.Machine {base}

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), 16 (most 64-bit builds) or 8 (CPUs such as ARM where for most compilers ‘⁠long double⁠’ is identical to double).

sizeof.pointer

the number of bytes in the C SEXP type. Will be 4 on 32-bit builds and 8 on 64-bit builds of R.

sizeof.time_t

the number of bytes in the C time_t type: a 64-bit time_t (value 8) is much preferred these days. Note that this is the type used by code in R itself, not necessarily the system type if R was configured with --with-internal-tzcode as also used on Windows.

longdouble.eps, longdouble.neg.eps, longdouble.digits, ...

introduced in R 4.0.0. When capabilities("long.double") is true, there are 10 such "longdouble.kind" values, specifying the ‘⁠long double⁠’ property corresponding to its "double.*" counterpart. 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. There are other implementation of long double, usually in software for example on Sparc Solaris and AIX.

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 on versions of R prior to 4.0.4, .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)))