R Under development (unstable) (2024-11-15 r87338 ucrt) -- "Unsuffered Consequences"
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> require("Rmpfr")
Loading required package: Rmpfr
Loading required package: gmp

Attaching package: 'gmp'

The following objects are masked from 'package:base':

    %*%, apply, crossprod, matrix, tcrossprod

C code of R package 'Rmpfr': GMP using 64 bits per limb


Attaching package: 'Rmpfr'

The following object is masked from 'package:gmp':

    outer

The following objects are masked from 'package:stats':

    dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm

The following objects are masked from 'package:base':

    cbind, pmax, pmin, rbind

> 
> ### Simple basic examples of creation of   "mpfr"  objects
> 
> pi. <- Const("pi", prec = 260)
> pi. # nicely prints 80 digits [260 * log10(2) ~= 78.3 ~ 80]
1 'mpfr' number of precision  260   bits 
[1] 3.1415926535897932384626433832795028841971693993751058209749445923078164062862088
> 
> ## These both failed (in mpfr2str(.)) with a seg.fault:
> c(mpfr(1, prec=3), pi.)
2 'mpfr' numbers of precision  3 .. 260  bits 
[1]                                                                                 1
[2] 3.1415926535897932384626433832795028841971693993751058209749445923078164062862088
> m0 <- mpfr(numeric(), prec=64)
> ## print()ing / str() of 0-length mpfr
> stopifnot(
+     grepl("0 'mpfr' numbers", capture.output(    m0)),
+     grepl("0 'mpfr' numbers", capture.output(str(m0))))
> 
> c(m0,m0) # failed in Rmpfr <= 0.6-0
0 'mpfr' numbers 
> stopifnot(identical(c(m0,m0), m0),
+ 	  identical(c(m0,pi.), pi.),
+ 	  identical(c(pi.,m0), pi.))
> 
> ## This is TRUE for 0 and -0 :
> Zero <- mpfr(c(0,1/-Inf), 20)
> stopifnot(mpfrIs0(Zero), is.whole(Zero))
> stopifnot(mpfr.is.0(Zero))# deprecated but must work
Warning message:
In mpfr.is.0(Zero) : 'mpfr.is.0' is deprecated.
Use 'mpfrIs0' instead.
See help("Deprecated")
> stopifnot(mpfr.is.integer(Zero))# deprecated but must work
Warning message:
In mpfr.is.integer(Zero) : 'mpfr.is.integer' is deprecated.
Use '.mpfr.is.whole' instead.
See help("Deprecated")
> Zero # the "-0" should print correctly
2 'mpfr' numbers of precision  20   bits 
[1]  0 -0
> stopifnot(.getSign(Zero) == c(1,-1),
+           sign(Zero) == 0,
+ 	  identical(format(Zero, digits=1), c("0.", "-0.")))
> 
> ## testing 'recycling'
> b <- c(20,120,80, 60)
> (x <- mpfr(2^-(5:7), precBits = b))
4 'mpfr' numbers of precision  20 .. 120  bits 
[1]   0.03125  0.015625 0.0078125   0.03125
> 
> d.spec <- c(0,NA,NaN,Inf,-Inf)
> (spec <- mpfr(d.spec, 3))
5 'mpfr' numbers of precision  3   bits 
[1]    0  NaN  NaN  Inf -Inf
> stopifnot(length(x) == 4, x[1] == x[4], getPrec(x) == b,
+ 	  identical(is.na(spec), is.na(d.spec)),
+ 	  identical(is.finite(spec), is.finite(d.spec)),
+ 	  identical(is.infinite(spec), is.infinite(d.spec)),
+ 	  ## mpfr(<mpfr>, .) :
+ 	  identical(x,    mpfr(x,    getPrec(x))),
+ 	  identical(spec, mpfr(spec, getPrec(spec))),
+ 	  asNumeric(1/mpfr(x, 16)) == 2^c(5:7,5),
+ 	  identical(format(spec), c("0.", "NaN", "NaN", "Inf", "-Inf")),
+ 	  mpfr(0.2, prec = 5:15, rnd.mode = "D") < 0.2)
> 
> B.set <- setNames(2:62, paste0("B=",2:62))
> str(lapply(B.set, function(B) format(spec, base= B)))# "0.0" and "0.00" -- FIXME
List of 61
 $ B=2 : chr [1:5] "0.0" "NaN" "NaN" "Inf" ...
 $ B=3 : chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=4 : chr [1:5] "0.0" "NaN" "NaN" "Inf" ...
 $ B=5 : chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=6 : chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=7 : chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=8 : chr [1:5] "0.0" "NaN" "NaN" "Inf" ...
 $ B=9 : chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=10: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=11: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=12: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=13: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=14: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=15: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=16: chr [1:5] "0.0" "NaN" "NaN" "Inf" ...
 $ B=17: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=18: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=19: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=20: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=21: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=22: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=23: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=24: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=25: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=26: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=27: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=28: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=29: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=30: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=31: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=32: chr [1:5] "0.0" "NaN" "NaN" "Inf" ...
 $ B=33: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=34: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=35: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=36: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=37: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=38: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=39: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=40: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=41: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=42: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=43: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=44: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=45: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=46: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=47: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=48: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=49: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=50: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=51: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=52: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=53: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=54: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=55: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=56: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=57: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=58: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=59: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=60: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=61: chr [1:5] "0." "NaN" "NaN" "Inf" ...
 $ B=62: chr [1:5] "0." "NaN" "NaN" "Inf" ...
> 
> t2 <- mpfr(2^10,3)
> ## digits = 1 used to crash: MPFR assertion failed: m >= 2 || ((((b) & ((b) - 1)) == 0) == 0 && m >= 1)
> ## ---------- (+ seg.fault) for 'base = 2' (and others, not for default base = 10),
> ## digits = NULL  should choose "enough" ... but does not
> str(r  <- lapply(B.set, function(B) .mpfr2str(t2, digits=1, base = B)))
base = 2, digits = 1 is increased to digits = 2
base = 4, digits = 1 is increased to digits = 2
base = 8, digits = 1 is increased to digits = 2
base = 16, digits = 1 is increased to digits = 2
base = 32, digits = 1 is increased to digits = 2
List of 61
 $ B=2 :List of 4
  ..$ str   : chr "10"
  ..$ exp   : int 11
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=3 :List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 7
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=4 :List of 4
  ..$ str   : chr "10"
  ..$ exp   : int 6
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=5 :List of 4
  ..$ str   : chr "2"
  ..$ exp   : int 5
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=6 :List of 4
  ..$ str   : chr "5"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=7 :List of 4
  ..$ str   : chr "3"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=8 :List of 4
  ..$ str   : chr "20"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=9 :List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=10:List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=11:List of 4
  ..$ str   : chr "8"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=12:List of 4
  ..$ str   : chr "7"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=13:List of 4
  ..$ str   : chr "6"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=14:List of 4
  ..$ str   : chr "5"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=15:List of 4
  ..$ str   : chr "5"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=16:List of 4
  ..$ str   : chr "40"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=17:List of 4
  ..$ str   : chr "4"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=18:List of 4
  ..$ str   : chr "3"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=19:List of 4
  ..$ str   : chr "3"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=20:List of 4
  ..$ str   : chr "3"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=21:List of 4
  ..$ str   : chr "2"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=22:List of 4
  ..$ str   : chr "2"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=23:List of 4
  ..$ str   : chr "2"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=24:List of 4
  ..$ str   : chr "2"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=25:List of 4
  ..$ str   : chr "2"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=26:List of 4
  ..$ str   : chr "2"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=27:List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=28:List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=29:List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=30:List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=31:List of 4
  ..$ str   : chr "1"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=32:List of 4
  ..$ str   : chr "10"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=33:List of 4
  ..$ str   : chr "v"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=34:List of 4
  ..$ str   : chr "u"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=35:List of 4
  ..$ str   : chr "t"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=36:List of 4
  ..$ str   : chr "s"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=37:List of 4
  ..$ str   : chr "S"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=38:List of 4
  ..$ str   : chr "R"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=39:List of 4
  ..$ str   : chr "Q"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=40:List of 4
  ..$ str   : chr "Q"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=41:List of 4
  ..$ str   : chr "P"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=42:List of 4
  ..$ str   : chr "O"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=43:List of 4
  ..$ str   : chr "O"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=44:List of 4
  ..$ str   : chr "N"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=45:List of 4
  ..$ str   : chr "N"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=46:List of 4
  ..$ str   : chr "M"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=47:List of 4
  ..$ str   : chr "M"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=48:List of 4
  ..$ str   : chr "L"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=49:List of 4
  ..$ str   : chr "L"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=50:List of 4
  ..$ str   : chr "K"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=51:List of 4
  ..$ str   : chr "K"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=52:List of 4
  ..$ str   : chr "K"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=53:List of 4
  ..$ str   : chr "J"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=54:List of 4
  ..$ str   : chr "J"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=55:List of 4
  ..$ str   : chr "J"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=56:List of 4
  ..$ str   : chr "I"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=57:List of 4
  ..$ str   : chr "I"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=58:List of 4
  ..$ str   : chr "I"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=59:List of 4
  ..$ str   : chr "H"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=60:List of 4
  ..$ str   : chr "H"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=61:List of 4
  ..$ str   : chr "H"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=62:List of 4
  ..$ str   : chr "H"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
> str(r. <- lapply(B.set, function(B) .mpfr2str(t2,           base = B)))
List of 61
 $ B=2 :List of 4
  ..$ str   : chr "100"
  ..$ exp   : int 11
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=3 :List of 4
  ..$ str   : chr "111"
  ..$ exp   : int 7
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=4 :List of 4
  ..$ str   : chr "10"
  ..$ exp   : int 6
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=5 :List of 4
  ..$ str   : chr "131"
  ..$ exp   : int 5
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=6 :List of 4
  ..$ str   : chr "443"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=7 :List of 4
  ..$ str   : chr "266"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=8 :List of 4
  ..$ str   : chr "20"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=9 :List of 4
  ..$ str   : chr "14"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=10:List of 4
  ..$ str   : chr "10"
  ..$ exp   : int 4
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=11:List of 4
  ..$ str   : chr "85"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=12:List of 4
  ..$ str   : chr "71"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=13:List of 4
  ..$ str   : chr "61"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=14:List of 4
  ..$ str   : chr "53"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=15:List of 4
  ..$ str   : chr "48"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=16:List of 4
  ..$ str   : chr "40"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=17:List of 4
  ..$ str   : chr "39"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=18:List of 4
  ..$ str   : chr "33"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=19:List of 4
  ..$ str   : chr "2g"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=20:List of 4
  ..$ str   : chr "2b"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=21:List of 4
  ..$ str   : chr "27"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=22:List of 4
  ..$ str   : chr "23"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=23:List of 4
  ..$ str   : chr "1m"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=24:List of 4
  ..$ str   : chr "1j"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=25:List of 4
  ..$ str   : chr "1g"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=26:List of 4
  ..$ str   : chr "1d"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=27:List of 4
  ..$ str   : chr "1b"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=28:List of 4
  ..$ str   : chr "19"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=29:List of 4
  ..$ str   : chr "16"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=30:List of 4
  ..$ str   : chr "14"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=31:List of 4
  ..$ str   : chr "12"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=32:List of 4
  ..$ str   : chr "10"
  ..$ exp   : int 3
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=33:List of 4
  ..$ str   : chr "v1"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=34:List of 4
  ..$ str   : chr "u4"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=35:List of 4
  ..$ str   : chr "t9"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=36:List of 4
  ..$ str   : chr "sg"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=37:List of 4
  ..$ str   : chr "RP"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=38:List of 4
  ..$ str   : chr "Qa"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=39:List of 4
  ..$ str   : chr "QA"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=40:List of 4
  ..$ str   : chr "PO"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=41:List of 4
  ..$ str   : chr "Oe"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=42:List of 4
  ..$ str   : chr "OG"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=43:List of 4
  ..$ str   : chr "NZ"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=44:List of 4
  ..$ str   : chr "NC"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=45:List of 4
  ..$ str   : chr "MY"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=46:List of 4
  ..$ str   : chr "MC"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=47:List of 4
  ..$ str   : chr "Lb"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=48:List of 4
  ..$ str   : chr "LG"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=49:List of 4
  ..$ str   : chr "Ki"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=50:List of 4
  ..$ str   : chr "KO"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=51:List of 4
  ..$ str   : chr "K4"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=52:List of 4
  ..$ str   : chr "Ja"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=53:List of 4
  ..$ str   : chr "JH"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=54:List of 4
  ..$ str   : chr "Iq"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=55:List of 4
  ..$ str   : chr "IY"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=56:List of 4
  ..$ str   : chr "IG"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=57:List of 4
  ..$ str   : chr "Ht"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=58:List of 4
  ..$ str   : chr "Hc"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=59:List of 4
  ..$ str   : chr "HL"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=60:List of 4
  ..$ str   : chr "H4"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=61:List of 4
  ..$ str   : chr "Gm"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
 $ B=62:List of 4
  ..$ str   : chr "GW"
  ..$ exp   : int 2
  ..$ finite: logi TRUE
  ..$ is.0  : logi FALSE
> ## FIXME: still too short
> 
> x <- c(-12, 1:3 * pi)
> sss <- mpfr(x, 100)
> validObject(sss)
[1] TRUE
> sss
4 'mpfr' numbers of precision  100   bits 
[1]                               -12 3.1415926535897931159979634685442
[3] 6.2831853071795862319959269370884 9.4247779607693793479938904056326
> sss2 <- sss * sss
> stopifnot(identical(sss2, sss * x),
+           identical(sss2, x * sss),
+           sss ^ 2 == sss2)
> ## and go back {not sure if  identical() is guaranteed here, but it seems...}:
> stopifnot(identical(x, as(sss, "numeric")))
> 
> (cs <- as(sss, "character"))
[1] "-12"                               "3.1415926535897931159979634685442"
[3] "6.2831853071795862319959269370884" "9.4247779607693793479938904056326"
> 
> y <- c(0, 100,-10, 1.25, -2.5,
+        x * c(1,100,1e5,1e20),
+        x / 100^(1:4))
> (Y <- mpfr(y, 100))
13 'mpfr' numbers of precision  100   bits 
 [1]                                     0                                   100
 [3]                                   -10                                  1.25
 [5]                                  -2.5                                   -12
 [7]     314.15926535897932581065106205642     628318.53071795857977122068405151
 [9]                 942477796076937936896   -0.11999999999999999555910790149937
[11] 0.00031415926535897930899771113288921  6.2831853071795866542926731201923e-6
[13]  9.4247779607693799284994504768947e-8
> cbind(y, as.data.frame(.mpfr2str(Y, 20))[,c("exp","str")])
               y exp                   str
1   0.000000e+00   0  00000000000000000000
2   1.000000e+02   3  10000000000000000000
3  -1.000000e+01   2 -10000000000000000000
4   1.250000e+00   1  12500000000000000000
5  -2.500000e+00   1 -25000000000000000000
6  -1.200000e+01   2 -12000000000000000000
7   3.141593e+02   3  31415926535897932581
8   6.283185e+05   6  62831853071795857977
9   9.424778e+20  21  94247779607693793690
10 -1.200000e-01   0 -11999999999999999556
11  3.141593e-04  -3  31415926535897930900
12  6.283185e-06  -5  62831853071795866543
13  9.424778e-08  -7  94247779607693799285
> 
> s <- mpfr(43208,  14)# low precision
> eps8 <- 8 * .Machine$double.eps
> ## checking  mpfr -> character -> mpfr:
> i1..5f <- c("4.e+4", "4.3e+4", "4.32e+4", "43210.", "43208.")
> stopifnot(exprs = {
+     all.equal(y, as.numeric(format(Y, digits=20)), tol= eps8)
+     all.equal(Y, as(format(Y), "mpfr"), tol= eps8)
+     identical(sapply(1:5, formatMpfr, x=s), i1..5f)
+     identical(sapply(1:5, formatMpfr, x=s, exponent.plus=FALSE),
+               sub("e[+]", "e", i1..5f))
+ })
> 
> 
> ## More  character -> mpfr  checking :
> ## from   echo 'scale=200; 4*a(1)' | bc -l :
> cpi <- "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196"
> pi. <- Const("pi", prec=667)
> stopifnot(cpi == format(mpfr(cpi, prec=667), digits=201),
+           all.equal(pi., as(cpi, "mpfr")),
+           all.equal(pi., as(cpi, "mpfr"), tol = 1e-200))
> 
> set.seed(17)
> ## Check double -> mpfr -> character -> double :
> ##  Unfortunately,  format(<mpfr>, .) -> .mpfr2str() triggers a memory bug
> ##  that I think is an MPFR library "mis-feature"
> ## 2011-02-09 -- bug *no longer* triggered !
> rSign <- function(n) sample(c(-1,1), size = n, replace=TRUE)
> N <- function(x) as.numeric(x)
> ntry <- if(Sys.getenv("USER") == "maechler") 150 else 5
> for(n in 1:ntry) {
+     cat(if(n %% 10)"." else n)
+     x. <- rSign(100) * rlnorm(100)
+     prec <- rpois(1, 110); digs <- floor(0.95*(prec / log2(10)))
+     X. <- mpfr(x., precBits = prec)
+     stopifnot(all.equal(x., N(format(X., digits=digs)), tol = eps8)
+               , all.equal(x., N(log(exp(X.))), tol = 32*eps8)
+     )
+ }; cat("\n")
.....
> 
> stopifnot(identical(mpfr.is.0(X.),# deprecated but must work
+ 		    mpfrIs0  (X.)))
Warning message:
In mpfr.is.0(X.) : 'mpfr.is.0' is deprecated.
Use 'mpfrIs0' instead.
See help("Deprecated")
> X. <- X.[!mpfrIs0(X.)]
> stopifnot(all( X./X. == 1)) # TRUE
> 
> u <- mpfr(as.raw(0:100))
> z <- mpfr(1:12, 200)
> z[z > 100] <- 100 # nothing done  (but used to fail)
> z[] <- 0
> stopifnot(0:100 == u, is(z,"mpfr"), mpfrIs0(z),
+ 	  all.equal(u, mpfr(0:100, prec = 8), tol = 0),
+ 	  0:1 == mpfr(1:2 %% 2 == 0))
> z[3] <- Const("pi",200)
> ## z has length 12 -- now extend it:
> z[15:17] <- 1/mpfr(10:12, 100)
> stopifnot(all.equal(z[1:4], c(0,0,pi,0), tol = 1e-15), validObject(z),
+ 	  all.equal(z[13:17], c(NaN,NaN, 1/(10:12)), tol = 1e-15))
> 
> ## These seg.faulted (each via different R -> C interface) in the past:
> assertError <- tools::assertError
> assertError( pp <- Const("pi", prec   = 1e11) )
> assertError( mpfr("123.456",  precBits= 1e11) )
> assertError( mpfr(as.bigz(3), precBits= 1e11) )
> 
> stopifnot(identical(mpfr(NULL), mpfr(logical())))
> 
> ## mpfr --> bigInteger "bigz"
> Pi <- Const("pi", prec = 300)
> twoP <- mpfr(2, 100)^(-2:80)
> m <- Pi * twoP
> L <- mpfr(2, 256)^1000
> stopifnot(exprs = {
+     .mpfr2bigz(Pi) == 3
+     .mpfr2bigz(twoP) == as.bigz(c(0,0, 2^(0:80)))
+     .mpfr2bigz(m)       == floor(m)
+     .mpfr2bigz(m / L)   == 0
+     .mpfr2bigz(m * L)   == floor(m * L)   ## used to fail
+     .mpfr2bigz(m * L^8) == floor(m * L^8) ##   (ditto)
+ })
> 
> proc.time()
   user  system elapsed 
   1.35    0.12    1.46