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 --          Copyright (C) 1992-2018, Free Software Foundation, Inc.         --
  10 --                                                                          --
  11 -- GNAT is free software;  you can  redistribute it  and/or modify it under --
  12 -- terms of the  GNU General Public License as published  by the Free Soft- --
  13 -- ware  Foundation;  either version 3,  or (at your option) any later ver- --
  14 -- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --
  15 -- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --
  16 -- or FITNESS FOR A PARTICULAR PURPOSE.                                     --
  17 --                                                                          --
  18 -- As a special exception under Section 7 of GPL version 3, you are granted --
  19 -- additional permissions described in the GCC Runtime Library Exception,   --
  20 -- version 3.1, as published by the Free Software Foundation.               --
  21 --                                                                          --
  22 -- You should have received a copy of the GNU General Public License and    --
  23 -- a copy of the GCC Runtime Library Exception along with this program;     --
  24 -- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --
  25 -- <http://www.gnu.org/licenses/>.                                          --
  26 --                                                                          --
  27 -- GNAT was originally developed  by the GNAT team at  New York University. --
  28 -- Extensive contributions were provided by Ada Core Technologies Inc.      --
  29 --                                                                          --
  30 ------------------------------------------------------------------------------
  31
  32 --  Support for universal real arithmetic
  33
  34 with Types; use Types;
  35 with Uintp; use Uintp;
  36
  37 package Urealp is
  38
  39    ---------------------------------------
  40    -- Representation of Universal Reals --
  41    ---------------------------------------
  42
  43    --  A universal real value is represented by a single value (which is
  44    --  an index into an internal table). These values are not hashed, so
  45    --  the equality operator should not be used on Ureal values (instead
  46    --  use the UR_Eq function).
  47
  48    --  A Ureal value represents an arbitrary precision universal real value,
  49    --  stored internally using four components:
  50
  51    --    the numerator (Uint, always non-negative)
  52    --    the denominator (Uint, always non-zero, always positive if base = 0)
  53    --    a real base (Nat, either zero, or in the range 2 .. 16)
  54    --    a sign flag (Boolean), set if negative
  55
  56    --  Negative numbers are represented by the sign flag being True.
  57
  58    --  If the base is zero, then the absolute value of the Ureal is simply
  59    --  numerator/denominator, where denominator is positive. If the base is
  60    --  non-zero, then the absolute value is numerator / (base ** denominator).
  61    --  In that case, since base is positive, (base ** denominator) is also
  62    --  positive, even when denominator is negative or null.
  63
  64    --  A normalized Ureal value has base = 0, and numerator/denominator
  65    --  reduced to lowest terms, with zero itself being represented as 0/1.
  66    --  This is a canonical format, so that for normalized Ureal values it
  67    --  is the case that two equal values always have the same denominator
  68    --  and numerator values.
  69
  70    --  Note: a value of minus zero is legitimate, and the operations in
  71    --  Urealp preserve the handling of signed zeroes in accordance with
  72    --  the rules of IEEE P754 ("IEEE floating point").
  73
  74    ------------------------------
  75    -- Types for Urealp Package --
  76    ------------------------------
  77
  78    type Ureal is private;
  79    --  Type used for representation of universal reals
  80
  81    No_Ureal : constant Ureal;
  82    --  Constant used to indicate missing or unset Ureal value
  83
  84    ---------------------
  85    -- Ureal Constants --
  86    ---------------------
  87
  88    function Ureal_0 return Ureal;
  89    --  Returns value 0.0
  90
  91    function Ureal_M_0 return Ureal;
  92    --  Returns value -0.0
  93
  94    function Ureal_Tenth return Ureal;
  95    --  Returns value 0.1
  96
  97    function Ureal_Half return Ureal;
  98    --  Returns value 0.5
  99
 100    function Ureal_1 return Ureal;
 101    --  Returns value 1.0
 102
 103    function Ureal_2 return Ureal;
 104    --  Returns value 2.0
 105
 106    function Ureal_10 return Ureal;
 107    --  Returns value 10.0
 108
 109    function Ureal_100 return Ureal;
 110    --  Returns value 100.0
 111
 112    function Ureal_2_80 return Ureal;
 113    --  Returns value 2.0 ** 80
 114
 115    function Ureal_2_M_80 return Ureal;
 116    --  Returns value 2.0 ** (-80)
 117
 118    function Ureal_2_128 return Ureal;
 119    --  Returns value 2.0 ** 128
 120
 121    function Ureal_2_M_128 return Ureal;
 122    --  Returns value 2.0 ** (-128)
 123
 124    function Ureal_10_36 return Ureal;
 125    --  Returns value 10.0 ** 36
 126
 127    function Ureal_M_10_36 return Ureal;
 128    --  Returns value -10.0 ** 36
 129
 130    -----------------
 131    -- Subprograms --
 132    -----------------
 133
 134    procedure Initialize;
 135    --  Initialize Ureal tables. Note that Initialize must not be called if
 136    --  Tree_Read is used. Note also that there is no Lock routine in this
 137    --  unit. These tables are among the few tables that can be expanded
 138    --  during Gigi processing.
 139
 140    procedure Tree_Read;
 141    --  Initializes internal tables from current tree file using the relevant
 142    --  Table.Tree_Read routines. Note that Initialize should not be called if
 143    --  Tree_Read is used. Tree_Read includes all necessary initialization.
 144
 145    procedure Tree_Write;
 146    --  Writes out internal tables to current tree file using the relevant
 147    --  Table.Tree_Write routines.
 148
 149    function Rbase (Real : Ureal) return Nat;
 150    --  Return the base of the universal real
 151
 152    function Denominator (Real : Ureal) return Uint;
 153    --  Return the denominator of the universal real
 154
 155    function Numerator (Real : Ureal) return Uint;
 156    --  Return the numerator of the universal real
 157
 158    function Norm_Den (Real : Ureal) return Uint;
 159    --  Return the denominator of the universal real after a normalization
 160
 161    function Norm_Num (Real : Ureal) return Uint;
 162    --  Return the numerator of the universal real after a normalization
 163
 164    function UR_From_Uint (UI : Uint) return Ureal;
 165    --  Returns real corresponding to universal integer value
 166
 167    function UR_To_Uint (Real : Ureal) return Uint;
 168    --  Return integer value obtained by accurate rounding of real value.
 169    --  The rounding of values half way between two integers is away from
 170    --  zero, as required by normal Ada 95 rounding semantics.
 171
 172    function UR_Trunc (Real : Ureal) return Uint;
 173    --  Return integer value obtained by a truncation of real towards zero
 174
 175    function UR_Ceiling (Real : Ureal) return Uint;
 176    --  Return value of smallest integer not less than the given value
 177
 178    function UR_Floor (Real : Ureal) return Uint;
 179    --  Return value of smallest integer not greater than the given value
 180
 181    --  Conversion table for above four functions
 182
 183    --    Input    To_Uint    Trunc    Ceiling    Floor
 184    --     1.0        1         1         1         1
 185    --     1.2        1         1         2         1
 186    --     1.5        2         1         2         1
 187    --     1.7        2         1         2         1
 188    --     2.0        2         2         2         2
 189    --    -1.0       -1        -1        -1        -1
 190    --    -1.2       -1        -1        -1        -2
 191    --    -1.5       -2        -1        -1        -2
 192    --    -1.7       -2        -1        -1        -2
 193    --    -2.0       -2        -2        -2        -2
 194
 195    function UR_From_Components
 196      (Num      : Uint;
 197       Den      : Uint;
 198       Rbase    : Nat := 0;
 199       Negative : Boolean := False)
 200       return     Ureal;
 201    --  Builds real value from given numerator, denominator and base. The
 202    --  value is negative if Negative is set to true, and otherwise is
 203    --  non-negative.
 204
 205    function UR_Add (Left : Ureal; Right : Ureal) return Ureal;
 206    function UR_Add (Left : Ureal; Right : Uint)  return Ureal;
 207    function UR_Add (Left : Uint;  Right : Ureal) return Ureal;
 208    --  Returns real sum of operands
 209
 210    function UR_Div (Left : Ureal; Right : Ureal) return Ureal;
 211    function UR_Div (Left : Uint;  Right : Ureal) return Ureal;
 212    function UR_Div (Left : Ureal; Right : Uint)  return Ureal;
 213    --  Returns real quotient of operands. Fatal error if Right is zero
 214
 215    function UR_Mul (Left : Ureal; Right : Ureal) return Ureal;
 216    function UR_Mul (Left : Uint;  Right : Ureal) return Ureal;
 217    function UR_Mul (Left : Ureal; Right : Uint)  return Ureal;
 218    --  Returns real product of operands
 219
 220    function UR_Sub (Left : Ureal; Right : Ureal) return Ureal;
 221    function UR_Sub (Left : Uint;  Right : Ureal) return Ureal;
 222    function UR_Sub (Left : Ureal; Right : Uint)  return Ureal;
 223    --  Returns real difference of operands
 224
 225    function UR_Exponentiate (Real  : Ureal; N : Uint) return  Ureal;
 226    --  Returns result of raising Ureal to Uint power.
 227    --  Fatal error if Left is 0 and Right is negative.
 228
 229    function UR_Abs (Real : Ureal) return Ureal;
 230    --  Returns abs function of real
 231
 232    function UR_Negate (Real : Ureal) return Ureal;
 233    --  Returns negative of real
 234
 235    function UR_Eq (Left, Right : Ureal) return Boolean;
 236    --  Compares reals for equality
 237
 238    function UR_Max (Left, Right : Ureal) return Ureal;
 239    --  Returns the maximum of two reals
 240
 241    function UR_Min (Left, Right : Ureal) return Ureal;
 242    --  Returns the minimum of two reals
 243
 244    function UR_Ne (Left, Right : Ureal) return Boolean;
 245    --  Compares reals for inequality
 246
 247    function UR_Lt (Left, Right : Ureal) return Boolean;
 248    --  Compares reals for less than
 249
 250    function UR_Le (Left, Right : Ureal) return Boolean;
 251    --  Compares reals for less than or equal
 252
 253    function UR_Gt (Left, Right : Ureal) return Boolean;
 254    --  Compares reals for greater than
 255
 256    function UR_Ge (Left, Right : Ureal) return Boolean;
 257    --  Compares reals for greater than or equal
 258
 259    function UR_Is_Zero (Real : Ureal) return Boolean;
 260    --  Tests if real value is zero
 261
 262    function UR_Is_Negative (Real : Ureal) return Boolean;
 263    --  Tests if real value is negative, note that negative zero gives true
 264
 265    function UR_Is_Positive (Real : Ureal) return Boolean;
 266    --  Test if real value is greater than zero
 267
 268    procedure UR_Write (Real : Ureal; Brackets : Boolean := False);
 269    --  Writes value of Real to standard output. Used for debugging and
 270    --  tree/source output, and also for -gnatR representation output. If the
 271    --  result is easily representable as a standard Ada literal, it will be
 272    --  given that way, but as a result of evaluation of static expressions, it
 273    --  is possible to generate constants (e.g. 1/13) which have no such
 274    --  representation. In such cases (and in cases where it is too much work to
 275    --  figure out the Ada literal), the string that is output is of the form
 276    --  of some expression such as integer/integer, or integer*integer**integer.
 277    --  In the case where an expression is output, if Brackets is set to True,
 278    --  the expression is surrounded by square brackets.
 279
 280    procedure pr (Real : Ureal);
 281    pragma Export (Ada, pr);
 282    --  Writes value of Real to standard output with a terminating line return,
 283    --  using UR_Write as described above. This is for use from the debugger.
 284
 285    ------------------------
 286    -- Operator Renamings --
 287    ------------------------
 288
 289    function "+" (Left : Ureal; Right : Ureal) return Ureal renames UR_Add;
 290    function "+" (Left : Uint;  Right : Ureal) return Ureal renames UR_Add;
 291    function "+" (Left : Ureal; Right : Uint)  return Ureal renames UR_Add;
 292
 293    function "/" (Left : Ureal; Right : Ureal) return Ureal renames UR_Div;
 294    function "/" (Left : Uint;  Right : Ureal) return Ureal renames UR_Div;
 295    function "/" (Left : Ureal; Right : Uint)  return Ureal renames UR_Div;
 296
 297    function "*" (Left : Ureal; Right : Ureal) return Ureal renames UR_Mul;
 298    function "*" (Left : Uint;  Right : Ureal) return Ureal renames UR_Mul;
 299    function "*" (Left : Ureal; Right : Uint)  return Ureal renames UR_Mul;
 300
 301    function "-" (Left : Ureal; Right : Ureal) return Ureal renames UR_Sub;
 302    function "-" (Left : Uint;  Right : Ureal) return Ureal renames UR_Sub;
 303    function "-" (Left : Ureal; Right : Uint)  return Ureal renames UR_Sub;
 304
 305    function "**"  (Real  : Ureal; N : Uint) return Ureal
 306                                                      renames UR_Exponentiate;
 307
 308    function "abs" (Real : Ureal) return Ureal renames UR_Abs;
 309
 310    function "-"   (Real : Ureal) return Ureal renames UR_Negate;
 311
 312    function "="   (Left, Right : Ureal) return Boolean renames UR_Eq;
 313
 314    function "<"   (Left, Right : Ureal) return Boolean renames UR_Lt;
 315
 316    function "<="  (Left, Right : Ureal) return Boolean renames UR_Le;
 317
 318    function ">="  (Left, Right : Ureal) return Boolean renames UR_Ge;
 319
 320    function ">"   (Left, Right : Ureal) return Boolean renames UR_Gt;
 321
 322    -----------------------------
 323    -- Mark/Release Processing --
 324    -----------------------------
 325
 326    --  The space used by Ureal data is not automatically reclaimed. However,
 327    --  a mark-release regime is implemented which allows storage to be
 328    --  released back to a previously noted mark. This is used for example
 329    --  when doing comparisons, where only intermediate results get stored
 330    --  that do not need to be saved for future use.
 331
 332    type Save_Mark is private;
 333
 334    function Mark return Save_Mark;
 335    --  Note mark point for future release
 336
 337    procedure Release (M : Save_Mark);
 338    --  Release storage allocated since mark was noted
 339
 340    ------------------------------------
 341    -- Representation of Ureal Values --
 342    ------------------------------------
 343
 344 private
 345
 346    type Ureal is new Int range Ureal_Low_Bound .. Ureal_High_Bound;
 347    for Ureal'Size use 32;
 348
 349    No_Ureal : constant Ureal := Ureal'First;
 350
 351    type Save_Mark is new Int;
 352
 353    pragma Inline (Denominator);
 354    pragma Inline (Mark);
 355    pragma Inline (Norm_Num);
 356    pragma Inline (Norm_Den);
 357    pragma Inline (Numerator);
 358    pragma Inline (Rbase);
 359    pragma Inline (Release);
 360    pragma Inline (Ureal_0);
 361    pragma Inline (Ureal_M_0);
 362    pragma Inline (Ureal_Tenth);
 363    pragma Inline (Ureal_Half);
 364    pragma Inline (Ureal_1);
 365    pragma Inline (Ureal_2);
 366    pragma Inline (Ureal_10);
 367    pragma Inline (UR_From_Components);
 368
 369 end Urealp;