.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.

.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 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, ... introduced in R 4.0.0. When capabilities("long.double") is true, there are 10 such "longdouble." 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.