32-Bit Floats

Description

R comes with a suite of utilities for linear algebra with "numeric" (double precision) vectors/matrices. However, sometimes single precision (or less!) is more than enough for a particular task. This package extends R's linear algebra facilities to include 32-bit float (single precision) data. Float vectors/matrices have half the precision of their "numeric"-type counterparts but are generally faster to numerically operate on, for a performance vs accuracy trade-off. The internal representation is an S4 class, which allows us to keep the syntax identical to that of base R's. Interaction between floats and base types for binary operators is generally possible; in these cases, type promotion always defaults to the higher precision. The package ships with copies of the single precision 'BLAS' and 'LAPACK', which are automatically built in the event they are not available on the system.

Author(s)

Drew Schmidt

Machine_float

Description

Numerical characteristics of the machine for floats. Contains analogues of much of the double precision details of .Machine.

Usage

Machine_float

Format

A list containing:

• float.eps epsilon

• float.xmin smallest non-zero float

• float.xmax largest non-inf float

• float.base radix

• float.digits the number of bits for the sign+significand

• float.exponent number of bits for the exponent

• float.min.exp "largest negative" (smallest) integer for the exponent that generates a normalized floating-point number

• float.max.exp largest integer for the exponent that generates a normalized floating-point number

Details

Values are taken directly from float.h.

NA_float_

Description

32-bit float NA

Usage

NA_float_

Format

A 32-bit float.

NaNf

Description

32-bit float NaN

Usage

NaNf

Format

A 32-bit float.

arithmetic

Description

Binary arithmetic numeric/float matrices.

Usage

## S4 method for signature 'float32,float32'
e1 + e2

## S4 method for signature 'float32,float32'
e1 * e2

## S4 method for signature 'float32,float32'
e1 - e2

## S4 method for signature 'float32,float32'
e1 / e2

## S4 method for signature 'float32,float32'
e1 ^ e2

## S4 method for signature 'float32,BaseLinAlg'
e1 + e2

## S4 method for signature 'float32,BaseLinAlg'
e1 * e2

## S4 method for signature 'float32,BaseLinAlg'
e1 - e2

## S4 method for signature 'float32,BaseLinAlg'
e1 / e2

## S4 method for signature 'float32,BaseLinAlg'
e1 ^ e2

## S4 method for signature 'BaseLinAlg,float32'
e1 + e2

## S4 method for signature 'BaseLinAlg,float32'
e1 * e2

## S4 method for signature 'BaseLinAlg,float32'
e1 - e2

## S4 method for signature 'BaseLinAlg,float32'
e1 / e2

## S4 method for signature 'BaseLinAlg,float32'
e1 ^ e2

## S4 method for signature 'float32,float32'
e1 < e2

## S4 method for signature 'float32,float32'
e1 <= e2

## S4 method for signature 'float32,float32'
e1 == e2

## S4 method for signature 'float32,float32'
e1 > e2

## S4 method for signature 'float32,float32'
e1 >= e2

## S4 method for signature 'float32,BaseLinAlg'
e1 < e2

## S4 method for signature 'float32,BaseLinAlg'
e1 <= e2

## S4 method for signature 'float32,BaseLinAlg'
e1 == e2

## S4 method for signature 'float32,BaseLinAlg'
e1 > e2

## S4 method for signature 'float32,BaseLinAlg'
e1 >= e2

## S4 method for signature 'BaseLinAlg,float32'
e1 < e2

## S4 method for signature 'BaseLinAlg,float32'
e1 <= e2

## S4 method for signature 'BaseLinAlg,float32'
e1 == e2

## S4 method for signature 'BaseLinAlg,float32'
e1 > e2

## S4 method for signature 'BaseLinAlg,float32'
e1 >= e2

Arguments

Value

A matrix of the same type as the highest precision input.

Examples

library(float)

s1 = flrunif(5, 5)
s2 = flrunif(5, 5)
x = matrix(1:25, 5)

s1 + s2 # float

typeof(x) # integer
x + s2 # float

storage.mode(x) = "double"
x + s2 # double

backsolve

Description

Solve a triangular system.

Usage

## S4 method for signature 'float32,float32'
backsolve(r, x, k = ncol(r), upper.tri = TRUE, transpose = FALSE)

## S4 method for signature 'float32,BaseLinAlg'
backsolve(r, x, k = ncol(r), upper.tri = TRUE, transpose = FALSE)

## S4 method for signature 'BaseLinAlg,float32'
backsolve(r, x, k = ncol(r), upper.tri = TRUE, transpose = FALSE)

## S4 method for signature 'float32,float32'
forwardsolve(l, x, k = ncol(l), upper.tri = FALSE, transpose = FALSE)

## S4 method for signature 'float32,BaseLinAlg'
forwardsolve(l, x, k = ncol(l), upper.tri = FALSE, transpose = FALSE)

## S4 method for signature 'BaseLinAlg,float32'
forwardsolve(l, x, k = ncol(l), upper.tri = FALSE, transpose = FALSE)

Arguments

Examples

library(float)

s = flrunif(10, 3)
cp = crossprod(s)
y = fl(1:3)
backsolve(cp, y)

rbind

Description

rbind() and cbind() for floats.

Usage

## S3 method for class 'float32'
rbind(..., deparse.level = 1)

## S3 method for class 'float32'
cbind(..., deparse.level = 1)

Arguments

Value

A matrix of the same type as the highest precision input.

Examples

library(float)
x = fl(matrix(1:10, 5))

rbind(x, x)
cbind(x, x)

Extract

Description

Extract subsets of a float vector/matrix.

Usage

## S4 method for signature 'float32'
x[i, j, drop = TRUE]

## S4 replacement method for signature 'float32'
x[i, j, ...] <- value

Arguments

Value

A float vector/matrix.

Examples

## Not run: 
library(float)

s = flrunif(10, 3)
s[, -1]
s[c(1, 3, 5, 7), 1:2]

## End(Not run)

c

Description

Combine float/numeric vector(s)/matri[x|ces].

Usage

## S4 method for signature 'float32'
c(x, ...)

Arguments

Value

A matrix of the same type as the highest precision input.

Examples

library(float)
x = flrunif(10, 3)

c(x, NA, 1L)

chol

Description

Cholesky factorization for a float vector/matrix.

Usage

## S4 method for signature 'float32'
chol(x)

Arguments

Value

A float vector/matrix.

Examples

library(float)

s = flrunif(10, 3)
cp = crossprod(s)
chol(cp)

chol2inv

Description

Return the inverse of the original matrix using the Cholesky factorization of a float vector/matrix.

Usage

## S4 method for signature 'float32'
chol2inv(x, size = NCOL(x), LINPACK = FALSE)

Arguments

Value

A float vector/matrix.

Examples

library(float)

s = flrunif(10, 3)
cp = crossprod(s)
cp %*% chol2inv(chol(cp))

colSums

Description

Row and columns sums/means.

Usage

## S4 method for signature 'float32'
colSums(x, na.rm = FALSE, dims = 1)

## S4 method for signature 'float32'
rowSums(x, na.rm = FALSE, dims = 1)

## S4 method for signature 'float32'
colMeans(x, na.rm = FALSE, dims = 1)

## S4 method for signature 'float32'
rowMeans(x, na.rm = FALSE, dims = 1)

Arguments

Value

A matrix of the same type as the highest precision input.

Examples

library(float)

s = flrunif(5, 3)

rowSums(s)
colSums(s)

comparison

Description

Binary comparison operators for numeric/float matrices.

Arguments

Value

A vector/matrix of logicals.

Examples

## Not run: 
library(float)
s = flrunif(5, 5)
x = matrix(1:25, 5)

s > x
s <= 0

## End(Not run)

converters

Description

Convert between a numeric vector/matrix and a float vector/matrix.

Usage

fl(x, strict = FALSE)

dbl(x, strict = FALSE)

int(x, strict = FALSE)

as.float(x, strict = FALSE)

## S3 method for class 'float32'
as.double(x, ...)

## S3 method for class 'float32'
as.integer(x, ...)

## S4 method for signature 'float32'
as.numeric(x, ...)

## S3 method for class 'float32'
as.vector(x, mode = "any")

## S3 method for class 'float32'
as.matrix(x, ...)

## S3 method for class 'float32'
as.data.frame(x, ...)

## S4 method for signature 'float32'
typeof(x)

## S4 method for signature 'float32'
storage.mode(x)

Arguments

Details

fl(), int(), and dbl() are shorthand for as.float(), as.integer(), and as.double(), respectively.

Value

The data stored in the type of whatever was asked for (the opposite of the input).

Examples

library(float)

x = matrix(1:30, 10, 3)
s = fl(x)

y = dbl(s)

all.equal(x, y)

crossprod

Description

Croddproducts.

Usage

## S4 method for signature 'Mat'
crossprod(x, y = NULL)

## S4 method for signature 'Mat'
tcrossprod(x, y = NULL)

Arguments

Details

If y is a numeric matrix, then x will be promoted to a numeric matrix, and the return will therefore be numeric (not float).

Value

A float matrix (unless y is numeric; see details section).

Examples

library(float)

s = flrunif(10, 3)
crossprod(s)
tcrossprod(s)

diag

Description

Methods for getting the diagonal of a float matrix, or constructing a float matrix given a float vector.

Usage

## S4 method for signature 'float32'
diag(x = 1, nrow, ncol)

Arguments

Value

A float vector or matrix, depending on the input.

Examples

library(float)

s = flrunif(10, 3)
s
diag(s)
diag(diag(s))

dim

Description

Dimension information for a float vector/matrix.

Usage

## S4 method for signature 'float32'
nrow(x)

## S4 method for signature 'float32'
ncol(x)

## S4 method for signature 'float32'
NROW(x)

## S4 method for signature 'float32'
NCOL(x)

## S4 method for signature 'float32'
dim(x)

## S4 method for signature 'float32'
length(x)

## S4 replacement method for signature 'float32'
dim(x) <- value

Arguments

Value

The requested integer values.

Examples

library(float)

s = flrunif(10, 3)
dim(s)
nrow(s)
ncol(s)

eigen

Description

Solve a system of equations or invert a float matrix.

Usage

## S4 method for signature 'float32'
eigen(x, symmetric, only.values = FALSE, EISPACK = FALSE)

Arguments

Value

A list containing the values and optionally vectors, each stored as floats.

Examples

library(float)

s = flrunif(10, 3)
cp = crossprod(s)

eigen(cp)

extremes

Description

Min/max values for any combination of float/numeric vector(s)/matri[x|ces].

Usage

## S4 method for signature 'float32'
min(x, ..., na.rm = FALSE)

## S4 method for signature 'float32'
max(x, ..., na.rm = FALSE)

## S4 method for signature 'float32'
which.min(x)

## S4 method for signature 'float32'
which.max(x)

Arguments

Details

If there are any elements in ..., all elements in the list will first be summed in their native precision, then converted to double precision so they can be combined with base::sum(). The final result will be cast to single precision if ... contains only integer and/or float objects. Otherwise, the return will be double precision.

Value

A single value.

Examples

library(float)
x = flrunif(10, 3)

min(x)
min(x, 1)

float

Description

An analogue to integer() and double() for preallocation.

Usage

float(length = 0, nrow, ncol)

Arguments

Details

If both of nrow and ncol are specified, then length is ignored, and the retor is a matrix. If one (but not the other) of nrow or ncol is given, then the function errors. Otherwise, a vector of length length is returned.

Value

A float vector/matrix of 0's.

Examples

library(float)

float(10)
float(nrow=2, ncol=3)

float32

Description

A float32 class constructor. For developers only.

Usage

float32(x)

Arguments

Details

Wraps the integer-type data in the float32 S4 class, so that the data will be interpreted as 32-bit floats.

If instead you merely want to convert numeric/double data to float type, instead you should call fl(x).

Value

A float32 class object.

Class float32

Description

An S4 container for 32-bit float vector/matrix objects.

Slots

Data

A vector or matrix of integers.

Hyperbolic functions

Description

Hyperbolic functions.

Usage

## S4 method for signature 'float32'
sinh(x)

## S4 method for signature 'float32'
cosh(x)

## S4 method for signature 'float32'
tanh(x)

## S4 method for signature 'float32'
asinh(x)

## S4 method for signature 'float32'
acosh(x)

## S4 method for signature 'float32'
atanh(x)

Arguments

Value

A float vector/matrix of the same dimensions as the input.

Examples

## Not run: 
library(float)

x = flrunif(10)
sinh(x)

## End(Not run)

is.float

Description

Tests if argument is a float matrix.

Usage

is.float(x)

Arguments

Details

is.float() and is.float() are different names for the same function.

Value

A logical value.

Examples

library(float)

x = matrix(0, 5, 5)
s = flrunif(10, 3)
is.float(x)
is.float(s)

isSymmetric

Description

Test if a float matrix is symmetric.

Usage

## S4 method for signature 'float32'
isSymmetric(object, ...)

Arguments

Value

A logical value.

Examples

library(float)

s = flrunif(10, 3)
isSymmetric(s)

cp = crossprod(s)
isSymmetric(s)

Logarithms and Exponentials

Description

exp/log functions.

Usage

## S4 method for signature 'float32'
exp(x)

## S4 method for signature 'float32'
expm1(x)

## S4 method for signature 'float32'
log(x, base = exp(1))

## S4 method for signature 'float32'
log10(x)

## S4 method for signature 'float32'
log2(x)

Arguments

Value

A float vector/matrix of the same dimensions as the input.

Examples

## Not run: 
library(float)

x = flrunif(10)
log(x)

## End(Not run)

Finite, infinite, and NaNs

Description

Finite, infinite, and NaNs.

Usage

## S4 method for signature 'float32'
is.finite(x)

## S4 method for signature 'float32'
is.infinite(x)

## S4 method for signature 'float32'
is.nan(x)

Arguments

Value

An integer vector/matrix of the same dimensions as the input.

Examples

## Not run: 
library(float)

x = flrnorm(10)
is.nan(sqrt(x))

## End(Not run)

matmult

Description

Matrix multiplication for numeric/float matrices.

Usage

## S4 method for signature 'float32,float32'
x %*% y

## S4 method for signature 'float32,matrix'
x %*% y

## S4 method for signature 'matrix,float32'
x %*% y

Arguments

Details

If a numeric matrix is multiplied against a float matrix, then if the "numeric" matrix is integers, the integers are promoted to floats. Otherwise, the float matrix is promoted to doubles.

Value

A matrix of the same type as the highest precision input.

Examples

library(float)

s1 = flrunif(5, 5)
s2 = flrunif(5, 2)
x = matrix(1:25, 5)

s1 %*% s2 # float

storage.mode(x) # integer
x %*% s2 # float

storage.mode(x) = "double"
x %*% s2 # double

Miscellaneous mathematical functions

Description

Miscellaneous mathematical functions.

Usage

## S4 method for signature 'float32'
abs(x)

## S4 method for signature 'float32'
sqrt(x)

Arguments

Value

A float vector/matrix of the same dimensions as the input.

Examples

## Not run: 
library(float)

x = flrunif(10)
sqrt(x)

## End(Not run)

NA

Description

NA utilities.

Usage

## S4 method for signature 'float32'
is.na(x)

## S4 method for signature 'float32'
na.omit(object, ...)

## S4 method for signature 'float32'
na.exclude(object, ...)

Arguments

Examples

library(float)

s = flrunif(10, 3)
is.na(s)

names

Description

"name" setter/getters.

Usage

## S4 method for signature 'float32'
names(x)

## S4 replacement method for signature 'float32'
names(x) <- value

## S4 method for signature 'float32'
rownames(x)

## S4 replacement method for signature 'float32'
rownames(x) <- value

## S4 method for signature 'float32'
colnames(x)

## S4 replacement method for signature 'float32'
colnames(x) <- value

## S4 method for signature 'float32'
dimnames(x)

## S4 replacement method for signature 'float32'
dimnames(x) <- value

Arguments

norm

Description

Compute matrix norm.

Usage

## S4 method for signature 'float32,ANY'
norm(x, type = c("O", "I", "F", "M", "2"))

Arguments

Value

A single float.

Examples

library(float)

s = flrunif(10, 3)
norm(s, type="O")

print-float32

Description

Print methods for float vector/matrices.

Usage

## S4 method for signature 'float32'
print(x, ...)

## S4 method for signature 'float32'
show(object)

Arguments

Details

The printer works by

Examples

library(float)

s = flrunif(10, 3)
print(s)
s

QR

Description

QR factorization and related functions.

Usage

## S4 method for signature 'float32'
qr(x, tol = 1e-07, ...)

## S4 method for signature 'ANY'
qr.Q(qr, complete = FALSE, Dvec)

## S4 method for signature 'ANY'
qr.R(qr, complete = FALSE)

## S4 method for signature 'ANY'
qr.qy(qr, y)

## S4 method for signature 'ANY'
qr.qty(qr, y)

Arguments

Details

The factorization is performed by the LAPACK routine sgeqp3(). This should be similar to calling qr() on an ordinary R matrix with the argument LAPACK=TRUE. Calling qr(x, LAPACK=FALSE) on a double precision matrix 'x' (the default) will not be comparable in performance (it is much slower) or numerics to calling qr(s) where 's' is single a float matrix.

Examples

library(float)

x = flrunif(10, 3)
qr(x)

Generators

Description

Random float vector/matrix generators. flrunif() produces uniform random values. flrnorm() produces random normal values. flrand() will accept an arbitrary generator. See the details section for more information.

Usage

flrunif(m, n, min = 0, max = 1)

flrnorm(m, n, mean = 0, sd = 1)

flrand(generator, m, n, ...)

Arguments

Details

For flrunif() and flrnorm(), the data is produced without a double precision copy. That is, it is not (computationally) equivalent to fl(matrix(runif(...))), though the operations are conceptually the same. For these, To produce a vector instead of a matrix, leave argument n blank. Setting n=1 will produce an mx1 matrix.

For flrand(), the data is generated in double precision in 4KiB batches and copied over to a pre-allocated vector. This will be slower than generating all of the data up front and copying it, although it uses far less memory most of the time. So you can think of flrunif() and flrnorm() as highly optimized versions of flrand() for uniform and normal generators specifically.

Examples

library(float)

flrunif(10) # length 10 vector
flrunif(10, 1) # 10x1 matrix
flrunif(10, min=10, max=20)

flrand(runif, 10) # conceptually the same as flrunif(10)

mygen = function(n) sample(1:5, n, replace=TRUE)
flrand(mygen, 30)

rcond

Description

Compute matrix norm.

Usage

## S4 method for signature 'float32'
rcond(x, norm = c("O", "I", "1"), triangular = FALSE, ...)

Arguments

Value

A single float.

Examples

library(float)

s = flrunif(10, 3)
rcond(s)

rep

Description

Replicate elements of a float vector/matrix.

Usage

## S3 method for class 'float32'
rep(x, ...)

Arguments

Value

A float vector.

Examples

library(float)
x = fl(matrix(1:6, 3, 2))

rep(x, 5)

Round

Description

Rounding functions.

Usage

## S4 method for signature 'float32'
ceiling(x)

## S4 method for signature 'float32'
floor(x)

## S4 method for signature 'float32'
trunc(x, ...)

## S4 method for signature 'float32'
round(x, digits = 0)

Arguments

Value

A float vector/matrix of the same dimensions as the input.

Examples

library(float)

x = flrnorm(10)
floor(x)

scale

Description

Center/scale a float vector/matrix.

Usage

## S4 method for signature 'float32'
scale(x, center = TRUE, scale = TRUE)

Arguments

Details

Only logical center and scale parameters are accepted at this time.

Value

A float matrix.

Examples

library(float)

s = flrunif(10, 3)
scale(s)

sign

Description

Sign.

Usage

## S4 method for signature 'float32'
sign(x)

Arguments

Value

A float vector/matrix.

solve

Description

Solve a system of equations or invert a float matrix.

Usage

## S4 method for signature 'float32'
solve(a, b, ...)

Arguments

Value

A float matrix if inverting. If solving a system, a float vector if given one "right hand side", and a float matrix otherwise (just like R).

Examples

library(float)

s = flrunif(10, 3)
cp = crossprod(s)
solve(cp)

y = fl(1:3)
solve(cp, y)

Special mathematical functions

Description

Special mathematical functions.

Usage

## S4 method for signature 'float32'
gamma(x)

## S4 method for signature 'float32'
lgamma(x)

Arguments

Value

A float vector/matrix of the same dimensions as the input.

Examples

## Not run: 
library(float)

x = flrunif(10)
lgamma(x)

## End(Not run)

sum

Description

Sums any combination of float/numeric vector(s)/matri[x|ces].

Usage

## S4 method for signature 'float32'
sum(x, ..., na.rm = FALSE)

Arguments

Details

If there are any elements in ..., all elements in the list will first be summed in their native precision, then converted to double precision so they can be combined with base::sum(). The final result will be cast to single precision if ... contains only integer and/or float objects. Otherwise, the return will be double precision.

Value

A single value.

Examples

library(float)
x = flrunif(10, 3)

sum(x)
sum(x, 1)

SVD

Description

SVD factorization.

Usage

## S4 method for signature 'float32'
La.svd(x, nu = min(n, p), nv = min(n, p))

## S4 method for signature 'float32'
svd(x, nu = min(n, p), nv = min(n, p), LINPACK = FALSE)

Arguments

Details

The factorization is performed by the LAPACK routine sgesdd().

Examples

library(float)

x = flrunif(10, 3)
svd(x)

sweep

Description

Sweep a vector through a float matrix.

Usage

## S4 method for signature 'float32'
sweep(x, MARGIN, STATS, FUN = "-", check.margin = TRUE, ...)

Arguments

Details

Note that if the length of STATS does not recycle exactly across MARGIN, the results here will differ slightly from the results of base R.

Value

A matrix of the same type as the highest precision input.

Examples

library(float)

s = flrunif(10, 3)
sweep(s, 2, fl(1))

Trigonometric functions

Description

Basic trig functions.

Usage

## S4 method for signature 'float32'
sin(x)

## S4 method for signature 'float32'
cos(x)

## S4 method for signature 'float32'
tan(x)

## S4 method for signature 'float32'
asin(x)

## S4 method for signature 'float32'
acos(x)

## S4 method for signature 'float32'
atan(x)

Arguments

Value

A float vector/matrix of the same dimensions as the input.

Examples

## Not run: 
library(float)

x = flrunif(10)
sin(x)

## End(Not run)

xpose

Description

Transpose a float vector/matrix.

Usage

## S4 method for signature 'float32'
t(x)

Arguments

Value

A float vector/matrix.

Examples

library(float)

s = flrunif(10, 3)
dim(s)
ts = t(s)
dim(ts)