Numerical Characteristics of the Machine (original) (raw)
| .Machine {base} | R Documentation |
|---|
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 numberx such that 1 + x != 1. It equalsdouble.base ^ ulp.digits if either double.base is 2 ordouble.rounding is 0; otherwise, it is(double.base ^ double.ulp.digits) / 2. Normally2.220446e-16. |
|---|---|
| double.neg.eps | a small positive floating-point number xsuch that 1 - x != 1. It equalsdouble.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. Normally1.110223e-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 of0 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 isuch 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 thatdouble.base ^ i is positive and normalized. Normally -1022. |
| double.max.exp | the smallest positive power of double.base that overflows. Normally1024. |
| 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 usually8. |
| 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 possibly12 (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 SEXPtype. 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_ttype: 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. Whencapabilities("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](../../base/help/capabilities.html)("long.double") is true, R uses the ‘long double’ C type in quite a few places internally for accumulators in e.g. [sum](../../base/help/sum.html), reading non-integer numeric constants into (binary) double precision numbers, or arithmetic such as x %% y; also, ‘long double’ can be read by[readBin](../../base/help/readBin.html).
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](../../base/help/capabilities.html)("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](../../base/help/.Platform.html) for details of the platform.
Examples
.Machine
## or for a neat printout
noquote(unlist(format(.Machine)))
[Package _base_ version 4.6.0 Index]