Package float. August 6, 2018

Transcription

1 Type Package Title 32-Bit Floats Version Package float August 6, 2018 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 etends 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 synta 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. License BSD 2-clause License + file LICENSE Copyright The copyright for the single precision BLAS/LAPACK distribution located in src/lapack is given in the file src/lapack/license. Depends R (>= 3.1.0), methods Imports utils, tools ByteCompile yes URL BugReports Maintainer Drew Schmidt <wrathematics@gmail.com> RoygenNote NeedsCompilation yes Author Drew Schmidt [aut, cre, cph], Wei-Chen Chen [ctb] (win32 fies), Dmitriy Selivanov [ctb] (improvements in eternal package linking), ORNL [cph] 1

2 2 R topics documented: Repository CRAN Date/Publication :00:13 UTC R topics documented: float-package Machine_float arithmetic backsolve bind bracket c chol chol2inv colsums comparison converters crossprod diag dims eigen etremes float float float32-class hyperbolic is.float issymmetric log mathis matmult miscmath na names norm print-float qr rand rcond rep round scale solve specialmath sum svd sweep

3 float-package 3 trig pose Inde 41 float-package 32-Bit Floats 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 etends 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 synta 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 Numerical characteristics of the machine for floats. A global variable containing the float (single precision) analogues of much of the double precision details of.machine..machine Details.Machine_float s are taken directly from float.h.

4 4 arithmetic A list containing: float.eps epsilon float.min smallest non-zero float float.ma largest non-inf float float.base radi float.digits the number of bits for the sign+significand float.eponent number of bits for the eponent float.min.ep "largest negative" (smallest) integer for the eponent that generates a normalized floating-point number float.ma.ep largest integer for the eponent that generates a normalized floating-point number arithmetic arithmetic Binary arithmetic numeric/float matrices. ## 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'

5 arithmetic 5 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'

6 6 arithmetic 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 e1, e2 Numeric/float vectors/matrices. A matri of the same type as the highest precision input. s1 = flrunif(5, 5) s2 = flrunif(5, 5) = matri(1:25, 5) s1 + s2 # float typeof() # integer + s2 # float storage.mode() = "double" + s2 # double

7 backsolve 7 backsolve backsolve Solve a triangular system. ## S4 method for signature 'float32,float32' backsolve(r,, k = ncol(r), upper.tri = TRUE, transpose = FALSE) ## S4 method for signature 'float32,baselinalg' backsolve(r,, k = ncol(r), upper.tri = TRUE, transpose = FALSE) ## S4 method for signature 'BaseLinAlg,float32' backsolve(r,, k = ncol(r), upper.tri = TRUE, transpose = FALSE) ## S4 method for signature 'float32,float32' forwardsolve(l,, k = ncol(l), upper.tri = FALSE, transpose = FALSE) ## S4 method for signature 'float32,baselinalg' forwardsolve(l,, k = ncol(l), upper.tri = FALSE, transpose = FALSE) ## S4 method for signature 'BaseLinAlg,float32' forwardsolve(l,, k = ncol(l), upper.tri = FALSE, transpose = FALSE) r, l A triangular coefficients matri. k upper.tri transpose The right hand sides. The number of equations (columns of r + rows of ) to use. Should the upper triangle be used? (if not the lower is) Should the transposed coefficients matri be used? More efficient than manually transposing with t().

8 8 bind s = flrunif(10, 3) cp = crossprod(s) y = fl(1:3) backsolve(cp, y) bind rbind rbind() and cbind() for floats. ## S3 method for class 'float32' rbind(..., deparse.level = 1) ## S3 method for class 'float32' cbind(..., deparse.level = 1)... vectors or matrices (numeric or float) deparse.level ignored A matri of the same type as the highest precision input. = fl(matri(1:10, 5)) rbind(, ) cbind(, )

9 bracket 9 bracket Etract Etract subsets of a float vector/matri. [i, j, drop = TRUE] ## S4 replacement method for signature 'float32' [i, j,...] <- value A float vector/matri. i, j,... The indices. Most combinations of integer/double/logical values will be treated the same as R does. One major difference is that NA values will not be tolerated. drop value Logical. If TRUE, single column matrices will be treated as one-dimensional vectors. The replacement value. A float vector/matri. ## Not run: s = flrunif(10, 3) s[, -1] s[c(1, 3, 5, 7), 1:2] ## End(Not run)

10 10 chol c c Combine float/numeric vector(s)/matri[ ces]. c(,...) A float matri.... Additional elements (numeric/float vectors/matrices) to sum. A matri of the same type as the highest precision input. = flrunif(10, 3) c(, NA, 1L) chol chol Cholesky factorization for a float vector/matri. chol() A float vector/matri.

11 chol2inv 11 A float vector/matri. s = flrunif(10, 3) cp = crossprod(s) chol(cp) chol2inv chol2inv Return the inverse of the original matri using the Cholesky factorization of a float vector/matri. chol2inv(, size = NCOL(), LINPACK = FALSE) size LINPACK A float vector/matri. The number of columns to use. Ignored. A float vector/matri. s = flrunif(10, 3) cp = crossprod(s) cp %*% chol2inv(chol(cp))

12 12 colsums colsums colsums Row and columns sums/means. colsums(, na.rm = FALSE, dims = 1) rowsums(, na.rm = FALSE, dims = 1) colmeans(, na.rm = FALSE, dims = 1) rowmeans(, na.rm = FALSE, dims = 1) na.rm dims A float vector/matri. Should missing values be removed? Ignored. Be honest, you ve never even used this argument before, have you? A matri of the same type as the highest precision input. s = flrunif(5, 3) rowsums(s) colsums(s)

13 comparison 13 comparison comparison Binary comparison operators for numeric/float matrices. e1, e2 Numeric/float vectors/matrices. A vector/matri of logicals. ## Not run: s = flrunif(5, 5) = matri(1:25, 5) s > s <= 0 ## End(Not run) converters converters Convert between a numeric vector/matri and a float vector/matri. fl(, strict = FALSE) dbl(, strict = FALSE) int(, strict = FALSE) as.float(, strict = FALSE) ## S3 method for class 'float32' as.double(,...)

14 14 converters ## S3 method for class 'float32' as.integer(,...) as.numeric(,...) ## S3 method for class 'float32' as.vector(, mode = "any") ## S3 method for class 'float32' as.matri(,...) typeof() storage.mode() strict mode,... A numeric or float vector/matri. Should the function error if given the wrong kind of input? Otherwise it just silently returns the input. Ignored. Details fl(), int(), and dbl() are shorthand for as.float(), as.integer(), and as.double(), respectively. The data stored in the type of whatever was asked for (the opposite of the input). = matri(1:30, 10, 3) s = fl() y = dbl(s) all.equal(, y)

15 crossprod 15 crossprod crossprod Croddproducts. ## S4 method for signature 'Mat' crossprod(, y = NULL) ## S4 method for signature 'Mat' tcrossprod(, y = NULL) y A float vector/matri. Either NULL, or a numeric/float matri. Details If y is a numeric matri, then will be promoted to a numeric matri, and the return will therefore be numeric (not float). A float matri (unless y is numeric; see details section). s = flrunif(10, 3) crossprod(s) tcrossprod(s)

16 16 dims diag diag Methods for getting the diagonal of a float matri, or constructing a float matri given a float vector. diag( = 1, nrow, ncol) nrow, ncol A float vector (create a diagonal matri) or matri (get its diagonal). As in base R s diag(). A float vector or matri, depending on the input. s = flrunif(10, 3) s diag(s) diag(diag(s)) dims dim Dimension information for a float vector/matri. nrow() ncol()

17 eigen 17 NROW() NCOL() dim() length() ## S4 replacement method for signature 'float32' dim() <- value value A float vector/matri. The right hand side for the "setter" (dim<-). The requested integer values. s = flrunif(10, 3) dim(s) nrow(s) ncol(s) eigen eigen Solve a system of equations or invert a float matri. eigen(, symmetric, only.values = FALSE, EISPACK = FALSE)

18 18 etremes symmetric only.values EISPACK A float vector/matri. Is the matri symmetric? If not, it will be tested for symmetry with issymmetric(). Note that only symmetric matrices are supported at this time. Should only the values (and not the vectors) be returned? Ignored. A list containing the values and optionally vectors, each stored as floats. s = flrunif(10, 3) cp = crossprod(s) eigen(cp) etremes etremes Min/ma values for any combination of float/numeric vector(s)/matri[ ces]. min(,..., na.rm = FALSE) ma(,..., na.rm = FALSE) which.min() which.ma() A float matri.... Additional elements (numeric/float vectors/matrices) to sum. na.rm should NA s be removed?

19 float 19 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. A single value. = flrunif(10, 3) min() min(, 1) float float An analogue to integer() and double() for preallocation. float(length = 0, nrow, ncol) length nrow, ncol Input data of type integer. Number of rows/columns if a matri return is desired. See details section for more information. Details If both of nrow and ncol are specified, then length is ignored, and the retor is a matri. If one (but not the other) of nrow or ncol is given, then the function errors. Otherwise, a vector of length length is returned. A float vector/matri of 0 s.

20 20 float32-class float(10) float(nrow=2, ncol=3) float32 float32 A float32 class constructor. For developers only. float32() Input data of type integer. 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(). A float32 class object. float32-class Class float32 An S4 container for 32-bit float vector/matri objects. Slots Data A vector or matri of integers.

21 hyperbolic 21 hyperbolic Hyperbolic functions Hyperbolic functions. sinh() cosh() tanh() asinh() acosh() atanh() A float vector/matri. A float vector/matri of the same dimensions as the input. ## Not run: = flrunif(10) sinh() ## End(Not run)

22 22 issymmetric is.float is.float Tests if argument is a float matri. is.float() An R object. Details is.float() and is.float() are different names for the same function. A logical value. = matri(0, 5, 5) s = flrunif(10, 3) is.float() is.float(s) issymmetric issymmetric Test if a float matri is symmetric. issymmetric(object,...)

23 log 23 object... Ignored. A logical value. s = flrunif(10, 3) issymmetric(s) cp = crossprod(s) issymmetric(s) A float vector/matri. log Logarithms and Eponentials ep/log functions. ep() epm1() log(, base = ep(1)) log10() log2() base A float vector/matri. The logarithm base.

24 24 mathis A float vector/matri of the same dimensions as the input. ## Not run: = flrunif(10) log() ## End(Not run) mathis Finite, infinite, and NaNs Finite, infinite, and NaNs. is.finite() is.infinite() is.nan() A float vector/matri. An integer vector/matri of the same dimensions as the input. ## Not run: = flrnorm(10) is.nan(sqrt()) ## End(Not run)

25 matmult 25 matmult matmult Matri multiplication for numeric/float matrices. ## S4 method for signature 'float32,float32' %*% y ## S4 method for signature 'float32,matri' %*% y ## S4 method for signature 'matri,float32' %*% y, y Numeric/float matrices. Details If a numeric matri is multiplied against a float matri, then if the "numeric" matri is integers, the integers are promoted to floats. Otherwise, the float matri is promoted to doubles. A matri of the same type as the highest precision input. s1 = flrunif(5, 5) s2 = flrunif(5, 2) = matri(1:25, 5) s1 %*% s2 # float storage.mode() # integer %*% s2 # float storage.mode() = "double" %*% s2 # double

26 26 na miscmath Miscellaneous mathematical functions Miscellaneous mathematical functions. abs() sqrt() A float vector/matri. A float vector/matri of the same dimensions as the input. ## Not run: = flrunif(10) sqrt() ## End(Not run) na NA NA utilities.

27 names 27 is.na() na.omit(object,...) na.eclude(object,...), object A float vector/matri.... Ignored. s = flrunif(10, 3) is.na(s) names names "name" setter/getters. names() ## S4 replacement method for signature 'float32' names() <- value rownames() ## S4 replacement method for signature 'float32' rownames() <- value colnames()

28 28 norm ## S4 replacement method for signature 'float32' colnames() <- value dimnames() ## S4 replacement method for signature 'float32' dimnames() <- value value A float vector/matri. Replacement value. norm norm Compute matri norm. ## S4 method for signature 'float32,any' norm(, type = c("o", "I", "F", "M", "2")) type A float vector/matri. "O"-ne, "I"-nfinity, "F"-robenius, "M"-a modulus, and "2" norms. A single float. s = flrunif(10, 3) norm(s, type="o")

29 print-float32 29 print-float32 print-float32 Print methods for float vector/matrices. print(,...) show(object), object A float vector/matri.... Ignored. s = flrunif(10, 3) print(s) s qr QR QR factorization and related functions. qr(, tol = 1e-07,...) ## S4 method for signature 'ANY' qr.q(qr, complete = FALSE, Dvec) ## S4 method for signature 'ANY' qr.r(qr, complete = FALSE)

30 30 rand ## S4 method for signature 'ANY' qr.qy(qr, y) ## S4 method for signature 'ANY' qr.qty(qr, y) tol A float matri.... Ignored. qr complete Dvec y Details The tolerance for determining numerical column rank. Output of qr(). Should the complete or truncated factor be returned? Vector of diagonals to use when re-constructing Q (default is 1 s). A vector/matri or right hand sides (int, float, or double). The factorization is performed by the LAPACK routine sgeqp3(). This should be similar to calling qr() on an ordinary R matri with the argument LAPACK=TRUE. Calling qr(, LAPACK=FALSE) on a double precision matri (the default) will not be comparable in performance (it is much slower) or numerics to calling qr(s) where s is single a float matri. = flrunif(10, 3) qr() rand Generators Random float vector/matri generators. flrunif() produces uniform random values. flrnorm() produces random normal values. flrand() will accept an arbitrary generator. See the details section for more information. flrunif(m, n, min = 0, ma = 1) flrnorm(m, n, mean = 0, sd = 1) flrand(generator, m, n,...)

31 rcond 31 Details m, n The dimensions of the matri/vector. m must be specified. If n is not, then the return is a vector. min, ma mean, sd generator Minimum and maimum values for the uniform generator. Mean and standard deviation values for the normal generator. A generating function, such as rnorm, or even something custom defined.... Additional arguments passed to the generator. For eample, if runif is passed as generator, then you might additionally pass ma=10. For flrunif() and flrnorm(), the data is produced without a double precision copy. That is, it is not (computationally) equivalent to fl(matri(runif(...))), though the operations are conceptually the same. For these, To produce a vector instead of a matri, leave argument n blank. Setting n=1 will produce an m1 matri. For flrand(), the data is generated in double precision in 4KiB batches and copied over to a preallocated 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. flrunif(10) # length 10 vector flrunif(10, 1) # 101 matri flrunif(10, min=10, ma=20) flrand(runif, 10) # conceptually the same as flrunif(10) mygen = function(n) sample(1:5, n, replace=true) flrand(mygen, 30) rcond rcond Compute matri norm. rcond(, norm = c("o", "I", "1"), triangular = FALSE,...)

32 32 rep norm triangular A float vector/matri. "O"-ne or "I"-nfinity norm. Should only the lower triangle be used?... Additional arguments. A single float. s = flrunif(10, 3) rcond(s) rep rep Replicate elements of a float vector/matri. ## S3 method for class 'float32' rep(,...) A float matri.... Additional arguments (passed to base::rep). A float vector. = fl(matri(1:6, 3, 2)) rep(, 5)

33 round 33 round Round Rounding functions. ceiling() floor() trunc(,...) round(, digits = 0) A float vector/matri.... ignored digits The number of digits to use in rounding. A float vector/matri of the same dimensions as the input. = flrnorm(10) floor()

34 34 solve scale scale Center/scale a float vector/matri. scale(, center = TRUE, scale = TRUE) center, scale A float vector/matri. Logical Details Only logical center and scale parameters are accepted at this time. A float matri. s = flrunif(10, 3) scale(s) solve solve Solve a system of equations or invert a float matri. solve(a, b,...)

35 specialmath 35 a, b A float vector/matri.... Ignored. A float matri if inverting. If solving a system, a float vector if given one "right hand side", and a float matri otherwise (just like R). s = flrunif(10, 3) cp = crossprod(s) solve(cp) y = fl(1:3) solve(cp, y) specialmath Special mathematical functions Special mathematical functions. gamma() lgamma() A float vector/matri. A float vector/matri of the same dimensions as the input.

36 36 sum ## Not run: = flrunif(10) lgamma() ## End(Not run) sum sum Sums any combination of float/numeric vector(s)/matri[ ces]. sum(,..., na.rm = FALSE) Details A float matri.... Additional elements (numeric/float vectors/matrices) to sum. na.rm should NA s be removed? 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. A single value. = flrunif(10, 3) sum() sum(, 1)

37 svd 37 svd SVD SVD factorization. La.svd(, nu = min(n, p), nv = min(n, p)) svd(, nu = min(n, p), nv = min(n, p), LINPACK = FALSE) nu, nv LINPACK A float matri. The number of left/right singular vectors to return. Ignored Details The factorization is performed by the LAPACK routine sgesdd(). = flrunif(10, 3) svd() sweep sweep Sweep a vector through a float matri. sweep(, MARGIN, STATS, FUN = "-", check.margin = TRUE,...)

38 38 trig Details MARGIN STATS A float vector/matri. 1 (rows) or 2 (columns) Vector to sweep out. FUN Sweeping function; must be one of "+", "-", "*", or "/". check.margin Should /STATS margin lengths be checked?... Theoretically these are additional arguments passed to an arbitrary function. However, we only support basic arithmetic, so they are ignored. Note that if the length of STATS does not recycle eactly across MARGIN, the results here will differ slightly from the results of base R. A matri of the same type as the highest precision input. s = flrunif(10, 3) sweep(s, 2, fl(1)) trig Trigonometric functions Basic trig functions. sin() cos() tan() asin()

39 pose 39 acos() atan() A float vector/matri. A float vector/matri of the same dimensions as the input. ## Not run: = flrunif(10) sin() ## End(Not run) pose pose Transpose a float vector/matri. t() A float vector/matri. A float vector/matri.

40 40 pose s = flrunif(10, 3) dim(s) ts = t(s) dim(ts)

41 Inde Topic package float-package, 3 *,BaseLinAlg,float32-method (arithmetic), 4 *,float32,baselinalg-method (arithmetic), 4 *,float32,float32-method (arithmetic), 4 +,BaseLinAlg,float32-method (arithmetic), 4 +,float32,baselinalg-method (arithmetic), 4 +,float32,float32-method (arithmetic), 4 -,BaseLinAlg,float32-method (arithmetic), 4 -,float32,baselinalg-method (arithmetic), 4 -,float32,float32-method (arithmetic), 4.Machine_float, 3 /,BaseLinAlg,float32-method (arithmetic), 4 /,float32,baselinalg-method (arithmetic), 4 /,float32,float32-method (arithmetic), 4 <,BaseLinAlg,float32-method (arithmetic), 4 <,float32,baselinalg-method (arithmetic), 4 <,float32,float32-method (arithmetic), 4 <=,BaseLinAlg,float32-method (arithmetic), 4 <=,float32,baselinalg-method (arithmetic), 4 <=,float32,float32-method (arithmetic), 4 ==,BaseLinAlg,float32-method (arithmetic), 4 ==,float32,baselinalg-method (arithmetic), 4 ==,float32,float32-method (arithmetic), 4 >,BaseLinAlg,float32-method (arithmetic), 4 >,float32,baselinalg-method (arithmetic), 4 >,float32,float32-method (arithmetic), 4 >=,BaseLinAlg,float32-method (arithmetic), 4 >=,float32,baselinalg-method (arithmetic), 4 >=,float32,float32-method (arithmetic), 4 [,float32-method (bracket), 9 [<-,float32-method (bracket), 9 %*%,float32,float32-method (matmult), 25 %*%,float32,matri-method (matmult), 25 %*%,matri,float32-method (matmult), 25 ^,BaseLinAlg,float32-method (arithmetic), 4 ^,float32,baselinalg-method (arithmetic), 4 ^,float32,float32-method (arithmetic), 4 abs,float32-method (miscmath), 26 acos,float32-method (trig), 38 acosh,float32-method (hyperbolic), 21 arithmetic, 4 as.double.float32 (converters), 13 as.float (converters), 13 as.integer.float32 (converters), 13 as.matri.float32 (converters), 13 as.numeric,float32-method (converters), 13 as.vector.float32 (converters), 13 asin,float32-method (trig), 38 asinh,float32-method (hyperbolic), 21 atan,float32-method (trig), 38 atanh,float32-method (hyperbolic), 21 backsolve, 7 41

42 42 INDEX backsolve,baselinalg,float32-method (backsolve), 7 backsolve,float32,baselinalg-method (backsolve), 7 backsolve,float32,float32-method (backsolve), 7 bind, 8 bracket, 9 c, 10 c,float32-method (c), 10 cbind.float32 (bind), 8 ceiling,float32-method (round), 33 chol, 10 chol,float32-method (chol), 10 chol2inv, 11 chol2inv,float32-method (chol2inv), 11 colmeans,float32-method (colsums), 12 colnames,float32-method (names), 27 colnames<-,float32-method (names), 27 colsums, 12 colsums,float32-method (colsums), 12 comparison, 13 converters, 13 cos,float32-method (trig), 38 cosh,float32-method (hyperbolic), 21 crossprod, 15 crossprod,mat-method (crossprod), 15 dbl (converters), 13 diag, 16 diag,float32-method (diag), 16 dim,float32-method (dims), 16 dim<-,float32-method (dims), 16 dimnames,float32-method (names), 27 dimnames<-,float32-method (names), 27 dims, 16 eigen, 17 eigen,float32-method (eigen), 17 ep,float32-method (log), 23 epm1,float32-method (log), 23 etremes, 18 fl (converters), 13 float, 19 float-package, 3 float32, 20 float32-class, 20 floor,float32-method (round), 33 flrand (rand), 30 flrnorm (rand), 30 flrunif (rand), 30 forwardsolve,baselinalg,float32-method (backsolve), 7 forwardsolve,float32,baselinalg-method (backsolve), 7 forwardsolve,float32,float32-method (backsolve), 7 gamma,float32-method (specialmath), 35 hyperbolic, 21 int (converters), 13 is.finite,float32-method (mathis), 24 is.float, 22 is.infinite,float32-method (mathis), 24 is.na,float32-method (na), 26 is.nan,float32-method (mathis), 24 issymmetric, 22 issymmetric,float32-method (issymmetric), 22 La.svd,float32-method (svd), 37 length,float32-method (dims), 16 lgamma,float32-method (specialmath), 35 log, 23 log,float32-method (log), 23 log10,float32-method (log), 23 log2,float32-method (log), 23 mathis, 24 matmult, 25 ma,float32-method (etremes), 18 min,float32-method (etremes), 18 miscmath, 26 na, 26 names, 27 names,float32-method (names), 27 names<-,float32-method (names), 27 NCOL,float32-method (dims), 16 ncol,float32-method (dims), 16 norm, 28 norm,float32,any-method (norm), 28 NROW,float32-method (dims), 16 nrow,float32-method (dims), 16

43 INDEX 43 print,float32-method (print-float32), 29 print-float32, 29 qr, 29 qr,float32-method (qr), 29 qr.q,any-method (qr), 29 qr.qty,any-method (qr), 29 qr.qy,any-method (qr), 29 qr.r,any-method (qr), 29 which.min,float32-method (etremes), 18 pose, 39 rand, 30 rbind.float32 (bind), 8 rcond, 31 rcond,float32-method (rcond), 31 rep, 32 round, 33 round,float32-method (round), 33 rowmeans,float32-method (colsums), 12 rownames,float32-method (names), 27 rownames<-,float32-method (names), 27 rowsums,float32-method (colsums), 12 scale, 34 scale,float32-method (scale), 34 show,float32-method (print-float32), 29 sin,float32-method (trig), 38 sinh,float32-method (hyperbolic), 21 solve, 34 solve,float32-method (solve), 34 specialmath, 35 sqrt,float32-method (miscmath), 26 storage.mode,float32-method (converters), 13 sum, 36 sum,float32-method (sum), 36 svd, 37 svd,float32-method (svd), 37 sweep, 37 sweep,float32-method (sweep), 37 t,float32-method (pose), 39 tan,float32-method (trig), 38 tanh,float32-method (hyperbolic), 21 tcrossprod,mat-method (crossprod), 15 trig, 38 trunc,float32-method (round), 33 typeof,float32-method (converters), 13 which.ma,float32-method (etremes), 18