Rmpfr: formatMpfr – R documentation

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formatMpfr

Formatting MPFR (multiprecision) Numbers

Description

Flexible formatting of “multiprecision numbers”, i.e., objects of class mpfr. formatMpfr() is also the mpfr method of the generic format function.

The formatN() methods for mpfr numbers renders them differently than their double precision equivalents, by appending "_M".

Function .mpfr2str() is the low level work horse for formatMpfr() and hence all print()ing of "mpfr" objects.

Usage

formatMpfr(x, digits = NULL, trim = FALSE, scientific = NA,
           maybe.full = !is.null(digits) && is.na(scientific),
	   base = 10, showNeg0 = TRUE, max.digits = Inf,
	   big.mark = "", big.interval = 3L,
	   small.mark = "", small.interval = 5L,
           decimal.mark = ".",
           exponent.char = if(base <= 14) "e" else if(base <= 36) "E" else "|e",
           exponent.plus = TRUE,
           zero.print = NULL, drop0trailing = FALSE, ...)

## S3 method for class 'mpfr'
formatN(x, drop0trailing = TRUE, ...)

.mpfr2str(x, digits = NULL, maybe.full = !is.null(digits), base = 10L)

Arguments

`x`	an MPFR number (vector or array).
`digits`	how many significant digits (in the `base` chosen!) are to be used in the result. The default, `NULL`, uses enough digits to represent the full precision, often one or two digits more than “you” would expect. For `base`s 2,4,8,16, or 32, MPFR requires `digits` at least 2. For such bases, `digits = 1` is changed into `2`, with a message.
`trim`	logical; if `FALSE`, numbers are right-justified to a common width: if `TRUE` the leading blanks for justification are suppressed.
`scientific`	either a logical specifying whether MPFR numbers should be encoded in scientific format (“exponential representation”), or an integer penalty (see `options("scipen")`). Missing values correspond to the current default penalty.
`maybe.full`	`logical`, passed to `.mpfr2str()`.
`base`	an integer in 2,3,..,62; the base (“basis”) in which the numbers should be represented. Apart from the default base 10, binary (`base = 2`) or hexadecimal (`base = 16`) are particularly interesting.
`showNeg0`	logical indicating if “negative” zeros should be shown with a `"-"`. The default, `TRUE` is intentially different from `format(<numeric>)`.
`exponent.char`	the “exponent” character to be used in scientific notation. The default takes into account that for `base` B >= 15, `"e"` is part of the (mantissa) digits and the same is true for `"E"` when B >= 37.
`exponent.plus`	`logical` indicating if `"+"` should be for positive exponents in exponential (aka “scientific”) representation. This used to be hardcoded to `FALSE`; the new default is compatible to R's `format()`ing of numbers and helps to note visually when exponents are in use.
`max.digits`	a (large) positive number to limit the number of (mantissa) digits, notably when `digits` is `NULL` (as by default). Otherwise, a numeric `digits` is preferred to setting `max.digits` (which should not be smaller than `digits`).
`big.mark, big.interval, small.mark, small.interval, decimal.mark, zero.print, drop0trailing`	used for prettying decimal sequences, these are passed to `prettyNum` and that help page explains the details.
`...`	further arguments passed to or from other methods.

Value

a character vector or array, say cx, of the same length as x. Since Rmpfr version 0.5-3 (2013-09), if x is an mpfrArray, then cx is a character array with the same dim and dimnames as x.

Note that in scientific notation, the integer exponent is always in decimal, i.e., base 10 (even when base is not 10), but of course meaning base powers, e.g., in base 32, "u.giE3"is the same as "ugi0" which is 32^3 times "u.gi". This is in contrast, e.g., with sprintf("%a", x) where the powers after "p" are powers of 2.

Author(s)

Martin Maechler

References

The MPFR manual's description of mpfr_get_str() which is the C-internal workhorse for .mpfr2str() (on which formatMpfr() builds).

Examples

## Printing of MPFR numbers  uses formatMpfr() internally.
 ## Note how each components uses the "necessary" number of digits:
 ( x3 <- c(Const("pi", 168), mpfr(pi, 140), 3.14) )
 format(x3[3], 15)
 format(x3[3], 15, drop0 = TRUE)# "3.14" .. dropping the trailing zeros
 x3[4] <- 2^30
 x3[4] # automatically drops trailing zeros
 format(x3[1], dig = 41, small.mark = "'") # (41 - 1 = ) 40 digits after "."

 rbind(formatN(           x3,  digits = 15),
       formatN(as.numeric(x3), digits = 15))

 (Zero <- mpfr(c(0,1/-Inf), 20)) # 0 and "-0"
 xx <- c(Zero, 1:2, Const("pi", 120), -100*pi, -.00987)
 format(xx, digits = 2)
 format(xx, digits = 1, showNeg0 = FALSE)# "-0" no longer shown

## Output in other bases :
formatMpfr(mpfr(10^6, 40), base=32, drop0trailing=TRUE)
## "ugi0"
mpfr("ugi0", base=32) #-> 1'000'000


i32 <- mpfr(1:32, precBits = 64)
format(i32,   base=  2, drop0trailing=TRUE)
format(i32,   base= 16, drop0trailing=TRUE)
format(1/i32, base=  2, drop0trailing=TRUE)# using scientific notation for [17..32]
format(1/i32, base= 32)
format(1/i32, base= 62, drop0trailing=TRUE)
format(mpfr(2, 64)^-(1:16), base=16, drop0trailing=TRUE)

Rmpfr

R MPFR - Multiple Precision Floating-Point Reliable

v0.8-4

GPL (>= 2)

Authors

Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Richard M. Heiberger [ctb] (formatHex(), *Bin, *Dec), John C. Nash [ctb] (hjkMpfr(), origin of unirootR()), Hans W. Borchers [ctb] (optimizeR(*, "GoldenRatio"); origin of hjkMpfr())

Initial release

2021-04-08