formatMpfr: Formatting MPFR (multiprecision) Numbers

In Rmpfr: Interface R to MPFR - Multiple Precision Floating-Point Reliable

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)) || isFALSE(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 bases 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 \ge 15, "e" is part of the (mantissa) digits and the same is true for "E" when B \ge 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.

Note

Currently, formatMpfr(x, scientific = FALSE) does not work correctly, e.g., for x <- Const("pi", 128) * 2^c(-200,200), i.e., it uses the scientific / exponential-style format. This is considered bogous and hopefully will change.

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).

See Also

mpfr for creation and the mpfr class description with its many methods. The format generic, and the prettyNum utility on which formatMpfr is based as well. The S3 generic function formatN from package gmp.

.mpfr_formatinfo(x) provides the (cheap) non-string parts of .mpfr2str(x); the (base 2) exp exponents are also available via .mpfr2exp(x).

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


## This now works: The large number shows "as" large integer:
x <- Const("pi", 128) * 2^c(-200,200)
formatMpfr(x, scientific = FALSE) # was 1.955...e-60  5.048...e+60

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 documentation built on Aug. 8, 2025, 7:49 p.m.