gcc/ada/urealp.ads

   1 ------------------------------------------------------------------------------
   2 --                                                                          --
   3 --                         GNAT COMPILER COMPONENTS                         --
   4 --                                                                          --
   5 --                               U R E A L P                                --
   6 --                                                                          --
   7 --                                 S p e c                                  --
   8 --                                                                          --
   9 --                                                                          --
  10 --          Copyright (C) 1992-2002 Free Software Foundation, Inc.          --
  11 --                                                                          --
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  21 -- MA 02111-1307, USA.                                                      --
  22 --                                                                          --
  23 -- As a special exception,  if other files  instantiate  generics from this --
  24 -- unit, or you link  this unit with other files  to produce an executable, --
  25 -- this  unit  does not  by itself cause  the resulting  executable  to  be --
  26 -- covered  by the  GNU  General  Public  License.  This exception does not --
  27 -- however invalidate  any other reasons why  the executable file  might be --
  28 -- covered by the  GNU Public License.                                      --
  29 --                                                                          --
  30 -- GNAT was originally developed  by the GNAT team at  New York University. --
  31 -- It is now maintained by Ada Core Technologies Inc (http://www.gnat.com). --
  32 --                                                                          --
  33 ------------------------------------------------------------------------------
  34
  35 --  Support for universal real arithmetic
  36
  37 with Types; use Types;
  38 with Uintp; use Uintp;
  39
  40 package Urealp is
  41
  42    ---------------------------------------
  43    -- Representation of Universal Reals --
  44    ---------------------------------------
  45
  46    --  A universal real value is represented by a single value (which is
  47    --  an index into an internal table). These values are not hashed, so
  48    --  the equality operator should not be used on Ureal values (instead
  49    --  use the UR_Eq function).
  50
  51    --  A Ureal value represents an arbitrary precision universal real value,
  52    --  stored internally using four components
  53
  54    --    the numerator (Uint, always non-negative)
  55    --    the denominator (Uint, always non-zero, always positive if base = 0)
  56    --    a real base (Nat, either zero, or in the range 2 .. 16)
  57    --    a sign flag (Boolean), set if negative
  58
  59    --  If the base is zero, then the absolute value of the Ureal is simply
  60    --  numerator/denominator. If the base is non-zero, then the absolute
  61    --  value is num / (rbase ** den).
  62
  63    --  Negative numbers are represented by the sign of the numerator being
  64    --  negative. The denominator is always positive.
  65
  66    --  A normalized Ureal value has base = 0, and numerator/denominator
  67    --  reduced to lowest terms, with zero itself being represented as 0/1.
  68    --  This is a canonical format, so that for normalized Ureal values it
  69    --  is the case that two equal values always have the same denominator
  70    --  and numerator values.
  71
  72    --  Note: a value of minus zero is legitimate, and the operations in
  73    --  Urealp preserve the handling of signed zeroes in accordance with
  74    --  the rules of IEEE P754 ("IEEE floating point").
  75
  76    ------------------------------
  77    -- Types for Urealp Package --
  78    ------------------------------
  79
  80    type Ureal is private;
  81    --  Type used for representation of universal reals
  82
  83    No_Ureal : constant Ureal;
  84    --  Constant used to indicate missing or unset Ureal value
  85
  86    ---------------------
  87    -- Ureal Constants --
  88    ---------------------
  89
  90    function Ureal_0 return Ureal;
  91    --  Returns value 0.0
  92
  93    function Ureal_M_0 return Ureal;
  94    --  Returns value -0.0
  95
  96    function Ureal_Tenth return Ureal;
  97    --  Returns value 0.1
  98
  99    function Ureal_Half return Ureal;
 100    --  Returns value 0.5
 101
 102    function Ureal_1 return Ureal;
 103    --  Returns value 1.0
 104
 105    function Ureal_2 return Ureal;
 106    --  Returns value 2.0
 107
 108    function Ureal_10 return Ureal;
 109    --  Returns value 10.0
 110
 111    function Ureal_100 return Ureal;
 112    --  Returns value 100.0
 113
 114    function Ureal_2_128 return Ureal;
 115    --  Returns value 2.0 ** 128
 116
 117    function Ureal_2_M_128 return Ureal;
 118    --  Returns value 2.0 ** (-128)
 119
 120    -----------------
 121    -- Subprograms --
 122    -----------------
 123
 124    procedure Initialize;
 125    --  Initialize Ureal tables. Note that Initialize must not be called if
 126    --  Tree_Read is used. Note also that there is no Lock routine in this
 127    --  unit. These tables are among the few tables that can be expanded
 128    --  during Gigi processing.
 129
 130    procedure Tree_Read;
 131    --  Initializes internal tables from current tree file using Tree_Read.
 132    --  Note that Initialize should not be called if Tree_Read is used.
 133    --  Tree_Read includes all necessary initialization.
 134
 135    procedure Tree_Write;
 136    --  Writes out internal tables to current tree file using Tree_Write
 137
 138    function Rbase (Real : Ureal) return Nat;
 139    --  Return the base of the universal real.
 140
 141    function Denominator (Real : Ureal) return Uint;
 142    --  Return the denominator of the universal real.
 143
 144    function Numerator (Real : Ureal) return Uint;
 145    --  Return the numerator of the universal real.
 146
 147    function Norm_Den (Real : Ureal) return Uint;
 148    --  Return the denominator of the universal real after a normalization.
 149
 150    function Norm_Num (Real : Ureal) return Uint;
 151    --  Return the numerator of the universal real after a normalization.
 152
 153    function UR_From_Uint (UI : Uint) return Ureal;
 154    --  Returns real corresponding to universal integer value
 155
 156    function UR_To_Uint (Real : Ureal) return Uint;
 157    --  Return integer value obtained by accurate rounding of real value.
 158    --  The rounding of values half way between two integers is away from
 159    --  zero, as required by normal Ada 95 rounding semantics.
 160
 161    function UR_Trunc (Real : Ureal) return Uint;
 162    --  Return integer value obtained by a truncation of real towards zero
 163
 164    function UR_Ceiling (Real : Ureal) return Uint;
 165    --  Return value of smallest integer not less than the given value
 166
 167    function UR_Floor (Real : Ureal) return Uint;
 168    --  Return value of smallest integer not greater than the given value
 169
 170    --  Conversion table for above four functions
 171
 172    --    Input    To_Uint    Trunc    Ceiling    Floor
 173    --     1.0        1         1         1         1
 174    --     1.2        1         1         2         1
 175    --     1.5        2         1         2         1
 176    --     1.7        2         1         2         1
 177    --     2.0        2         2         2         2
 178    --    -1.0       -1        -1        -1        -1
 179    --    -1.2       -1        -1        -1        -2
 180    --    -1.5       -2        -1        -1        -2
 181    --    -1.7       -2        -1        -1        -2
 182    --    -2.0       -2        -2        -2        -2
 183
 184    function UR_From_Components
 185      (Num      : Uint;
 186       Den      : Uint;
 187       Rbase    : Nat := 0;
 188       Negative : Boolean := False)
 189       return     Ureal;
 190    --  Builds real value from given numerator, denominator and base. The
 191    --  value is negative if Negative is set to true, and otherwise is
 192    --  non-negative.
 193
 194    function UR_Add (Left : Ureal; Right : Ureal) return Ureal;
 195    function UR_Add (Left : Ureal; Right : Uint)  return Ureal;
 196    function UR_Add (Left : Uint;  Right : Ureal) return Ureal;
 197    --  Returns real sum of operands
 198
 199    function UR_Div (Left : Ureal; Right : Ureal) return Ureal;
 200    function UR_Div (Left : Uint;  Right : Ureal) return Ureal;
 201    function UR_Div (Left : Ureal; Right : Uint)  return Ureal;
 202    --  Returns real quotient of operands. Fatal error if Right is zero
 203
 204    function UR_Mul (Left : Ureal; Right : Ureal) return Ureal;
 205    function UR_Mul (Left : Uint;  Right : Ureal) return Ureal;
 206    function UR_Mul (Left : Ureal; Right : Uint)  return Ureal;
 207    --  Returns real product of operands
 208
 209    function UR_Sub (Left : Ureal; Right : Ureal) return Ureal;
 210    function UR_Sub (Left : Uint;  Right : Ureal) return Ureal;
 211    function UR_Sub (Left : Ureal; Right : Uint)  return Ureal;
 212    --  Returns real difference of operands
 213
 214    function UR_Exponentiate (Real  : Ureal; N : Uint) return  Ureal;
 215    --  Returns result of raising Ureal to Uint power.
 216    --  Fatal error if Left is 0 and Right is negative.
 217
 218    function UR_Abs (Real : Ureal) return Ureal;
 219    --  Returns abs function of real
 220
 221    function UR_Negate (Real : Ureal) return Ureal;
 222    --  Returns negative of real
 223
 224    function UR_Eq (Left, Right : Ureal) return Boolean;
 225    --  Compares reals for equality.
 226
 227    function UR_Max (Left, Right : Ureal) return Ureal;
 228    --  Returns the maximum of two reals
 229
 230    function UR_Min (Left, Right : Ureal) return Ureal;
 231    --  Returns the minimum of two reals
 232
 233    function UR_Ne (Left, Right : Ureal) return Boolean;
 234    --  Compares reals for inequality.
 235
 236    function UR_Lt (Left, Right : Ureal) return Boolean;
 237    --  Compares reals for less than.
 238
 239    function UR_Le (Left, Right : Ureal) return Boolean;
 240    --  Compares reals for less than or equal.
 241
 242    function UR_Gt (Left, Right : Ureal) return Boolean;
 243    --  Compares reals for greater than.
 244
 245    function UR_Ge (Left, Right : Ureal) return Boolean;
 246    --  Compares reals for greater than or equal.
 247
 248    function UR_Is_Zero (Real : Ureal) return Boolean;
 249    --  Tests if real value is zero
 250
 251    function UR_Is_Negative (Real : Ureal) return Boolean;
 252    --  Tests if real value is negative, note that negative zero gives true
 253
 254    function UR_Is_Positive (Real : Ureal) return Boolean;
 255    --  Test if real value is greater than zero
 256
 257    procedure UR_Write (Real : Ureal);
 258    --  Writes value of Real to standard output. Used only for debugging and
 259    --  tree/source output. If the result is easily representable as a standard
 260    --  Ada literal, it will be given that way, but as a result of evaluation
 261    --  of static expressions, it is possible to generate constants (e.g. 1/13)
 262    --  which have no such representation. In such cases (and in cases where it
 263    --  is too much work to figure out the Ada literal), the string that is
 264    --  output is of the form [numerator/denominator].
 265
 266    procedure pr (Real : Ureal);
 267    pragma Export (Ada, pr);
 268    --  Writes value of Real to standard output with a terminating line return,
 269    --  using UR_Write as described above. This is for use from the debugger.
 270
 271    ------------------------
 272    -- Operator Renamings --
 273    ------------------------
 274
 275    function "+" (Left : Ureal; Right : Ureal) return Ureal renames UR_Add;
 276    function "+" (Left : Uint;  Right : Ureal) return Ureal renames UR_Add;
 277    function "+" (Left : Ureal; Right : Uint)  return Ureal renames UR_Add;
 278
 279    function "/" (Left : Ureal; Right : Ureal) return Ureal renames UR_Div;
 280    function "/" (Left : Uint;  Right : Ureal) return Ureal renames UR_Div;
 281    function "/" (Left : Ureal; Right : Uint)  return Ureal renames UR_Div;
 282
 283    function "*" (Left : Ureal; Right : Ureal) return Ureal renames UR_Mul;
 284    function "*" (Left : Uint;  Right : Ureal) return Ureal renames UR_Mul;
 285    function "*" (Left : Ureal; Right : Uint)  return Ureal renames UR_Mul;
 286
 287    function "-" (Left : Ureal; Right : Ureal) return Ureal renames UR_Sub;
 288    function "-" (Left : Uint;  Right : Ureal) return Ureal renames UR_Sub;
 289    function "-" (Left : Ureal; Right : Uint)  return Ureal renames UR_Sub;
 290
 291    function "**"  (Real  : Ureal; N : Uint) return Ureal
 292                                                      renames UR_Exponentiate;
 293
 294    function "abs" (Real : Ureal) return Ureal renames UR_Abs;
 295
 296    function "-"   (Real : Ureal) return Ureal renames UR_Negate;
 297
 298    function "="   (Left, Right : Ureal) return Boolean renames UR_Eq;
 299
 300    function "<"   (Left, Right : Ureal) return Boolean renames UR_Lt;
 301
 302    function "<="  (Left, Right : Ureal) return Boolean renames UR_Le;
 303
 304    function ">="  (Left, Right : Ureal) return Boolean renames UR_Ge;
 305
 306    function ">"   (Left, Right : Ureal) return Boolean renames UR_Gt;
 307
 308    -----------------------------
 309    -- Mark/Release Processing --
 310    -----------------------------
 311
 312    --  The space used by Ureal data is not automatically reclaimed. However,
 313    --  a mark-release regime is implemented which allows storage to be
 314    --  released back to a previously noted mark. This is used for example
 315    --  when doing comparisons, where only intermediate results get stored
 316    --  that do not need to be saved for future use.
 317
 318    type Save_Mark is private;
 319
 320    function Mark return Save_Mark;
 321    --  Note mark point for future release
 322
 323    procedure Release (M : Save_Mark);
 324    --  Release storage allocated since mark was noted
 325
 326    ------------------------------------
 327    -- Representation of Ureal Values --
 328    ------------------------------------
 329
 330 private
 331
 332    type Ureal is new Int range Ureal_Low_Bound .. Ureal_High_Bound;
 333    for Ureal'Size use 32;
 334
 335    No_Ureal : constant Ureal := Ureal'First;
 336
 337    type Save_Mark is new Int;
 338
 339    pragma Inline (Denominator);
 340    pragma Inline (Mark);
 341    pragma Inline (Norm_Num);
 342    pragma Inline (Norm_Den);
 343    pragma Inline (Numerator);
 344    pragma Inline (Rbase);
 345    pragma Inline (Release);
 346    pragma Inline (Ureal_0);
 347    pragma Inline (Ureal_M_0);
 348    pragma Inline (Ureal_Tenth);
 349    pragma Inline (Ureal_Half);
 350    pragma Inline (Ureal_1);
 351    pragma Inline (Ureal_2);
 352    pragma Inline (Ureal_10);
 353    pragma Inline (UR_From_Components);
 354
 355 end Urealp;