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)))

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