Structure Real

(* Real -- SML Basis Library *)

type real = real

exception Div
and Overflow

val ~           : real -> real
val +           : real * real -> real
val -           : real * real -> real
val *           : real * real -> real
val /           : real * real -> real
val abs         : real -> real
val min         : real * real -> real
val max         : real * real -> real
val sign        : real -> int
val compare     : real * real -> order

val sameSign    : real * real -> bool
val toDefault   : real -> real
val fromDefault : real -> real
val fromInt     : int -> real

val floor       : real -> int
val ceil        : real -> int
val trunc       : real -> int
val round       : real -> int

val >           : real * real -> bool
val >=          : real * real -> bool
val <           : real * real -> bool
val <=          : real * real -> bool
val ==          : real * real -> bool
val !=          : real * real -> bool
val ?=          : real * real -> bool

val toString    : real -> string
val fromString  : string -> real option
val scan        : (char, 'a) StringCvt.reader -> (real, 'a) StringCvt.reader
val fmt         : StringCvt.realfmt -> real -> string

(* 
   [~]
   [*]
   [/]
   [+]
   [-]
   [>]
   [>=]
   [<]
   [<=] are the usual operations on defined reals (excluding NaN and Inf).

   [abs x] is x if x >= 0, and ~x if x < 0, that is, the absolute value of x.

   [min(x, y)] is the smaller of x and y.

   [max(x, y)] is the larger of x and y.

   [sign x] is ~1, 0, or 1, according as x is negative, zero, or positive.

   [compare(x, y)] returns LESS, EQUAL, or GREATER, according 
   as x is less than, equal to, or greater than y.

   [sameSign(x, y)] is true iff sign x = sign y.

   [toDefault x] is x.

   [fromDefault x] is x.

   [fromInt i] is the floating-point number representing integer i.

   [floor r] is the largest integer <= r (rounds towards minus infinity).
   May raise Overflow.

   [ceil r] is the smallest integer >= r (rounds towards plus infinity).
   May raise Overflow.

   [trunc r] is the numerically largest integer between r and zero
   (rounds towards zero).  May raise Overflow.

   [round r] is the integer nearest to r, using the default rounding
   mode.  May raise Overflow.

   [==(x, y)] is equivalent to x=y in Moscow ML (because of the
   absence of NaNs and Infs).

   [!=(x, y)] is equivalent to x<>y in Moscow ML (because of the
   absence of NaNs and Infs).

   [?=(x, y)] is false in Moscow ML (because of the absence of NaNs
   and Infs).

   [fmt spec r] returns a string representing r, in the format
   specified by spec (see below).  The requested number of digits must
   be >= 0 in the SCI and FIX formats and > 0 in the GEN format;
   otherwise Size is raised, even in a partial application fmt(spec).

      spec          description                            C printf 
      ---------------------------------------------------------------
      SCI NONE      scientific,   6 digits after point       %e
      SCI (SOME n)  scientific,   n digits after point       %.ne
      FIX NONE      fixed-point,  6 digits after point       %f
      FIX (SOME n)  fixed-point,  n digits after point       %.nf
      GEN NONE      auto choice, 12 significant digits       %.12g
      GEN (SOME n)  auto choice,  n significant digits       %.ng

   [toString r] returns a string representing r, with automatic choice
   of format according to the magnitude of r.  
   Equivalent to (fmt (GEN NONE) r).
   
   [fromString s] returns SOME(r) if a floating-point numeral can be
   scanned from a prefix of string s, ignoring any initial whitespace;
   returns NONE otherwise.  The valid forms of floating-point numerals
   are described by:
        [+~-]?(([0-9]+(\.[0-9]+)?)|(\.[0-9]+))([eE][+~-]?[0-9]+)?

   [scan getc charsrc] attempts to scan a floating-point number from
   the character source charsrc, using the accessor getc, and ignoring
   any initial whitespace.  If successful, it returns SOME(r, rest)
   where r is the number scanned, and rest is the unused part of the
   character source.  The valid forms of floating-point numerals
   are described by:
        [+~-]?(([0-9]+(\.[0-9]+)?)|(\.[0-9]+))([eE][+~-]?[0-9]+)?
*)