src/float/cl_F.h

   1 // cl_F internals
   2
   3 #ifndef _CL_F_H
   4 #define _CL_F_H
   5
   6 #include "cl_number.h"
   7 #include "cl_macros.h"
   8 #include "cl_float.h"
   9
  10
  11 nonreturning_function(extern, cl_error_floating_point_overflow, (void));
  12 nonreturning_function(extern, cl_error_floating_point_underflow, (void));
  13
  14 #define underflow_allowed()  (! cl_inhibit_floating_point_underflow)
  15
  16
  17 // For all floating-point formats:
  18 // Sign s, Exponent e, Mantissa mk-1,...,m0
  19 // represents the number (-1)^s * 2^(e-_EXP_MID) * [0 . 1 mk-1 ... m0]
  20 // e=0 represents the number 0, always with sign s=0 (and mantissa =0).
  21 // _exp_low and _exp_high are (inclusive) bounds for e.
  22 // Bits for   Sign s    Exponent e    Mantissa m (= k)
  23 // SF           1           8             16
  24 // FF           1           8             23
  25 // DF           1          11             52
  26 // LF           1          32         intDsize*n >= 53
  27
  28
  29 // Konversionen ohne Rundung:
  30
  31 // cl_SF_to_FF(x) wandelt ein Short-Float x in ein Single-Float um.
  32 extern const cl_FF cl_SF_to_FF (const cl_SF& x);
  33
  34 // cl_SF_to_DF(x) wandelt ein Short-Float x in ein Double-Float um.
  35 extern const cl_DF cl_SF_to_DF (const cl_SF& x);
  36
  37 // cl_SF_to_LF(x,len) wandelt ein Short-Float x in ein Long-Float mit len Digits um.
  38 // > uintC len: gewünschte Anzahl Digits, >=LF_minlen
  39 extern const cl_LF cl_SF_to_LF (const cl_SF& x, uintC len);
  40
  41 // cl_FF_to_DF(x) wandelt ein Single-Float x in ein Double-Float um.
  42 extern const cl_DF cl_FF_to_DF (const cl_FF& x);
  43
  44 // cl_FF_to_LF(x,len) wandelt ein Single-Float x in ein Long-Float mit len Digits um.
  45 // > uintC len: gewünschte Anzahl Digits, >=LF_minlen
  46 extern const cl_LF cl_FF_to_LF (const cl_FF& x, uintC len);
  47
  48 // cl_DF_to_LF(x,len) wandelt ein Double-Float x in ein Long-Float mit len Digits um.
  49 // > uintC len: gewünschte Anzahl Digits, >=LF_minlen
  50 extern const cl_LF cl_DF_to_LF (const cl_DF& x, uintC len);
  51
  52
  53 // Konversionen mit Rundung:
  54
  55 // cl_FF_to_SF(x) wandelt ein Single-Float x in ein Short-Float um.
  56 extern const cl_SF cl_FF_to_SF (const cl_FF& x);
  57
  58 // cl_DF_to_SF(x) wandelt ein Double-Float x in ein Short-Float um.
  59 extern const cl_SF cl_DF_to_SF (const cl_DF& x);
  60
  61 // cl_LF_to_SF(x) wandelt ein Long-Float x in ein Short-Float um.
  62 extern const cl_SF cl_LF_to_SF (const cl_LF& x);
  63
  64 // cl_DF_to_FF(x) wandelt ein Double-Float x in ein Single-Float um.
  65 extern const cl_FF cl_DF_to_FF (const cl_DF& x);
  66
  67 // cl_LF_to_FF(x) wandelt ein Long-Float x in ein Single-Float um.
  68 extern const cl_FF cl_LF_to_FF (const cl_LF& x);
  69
  70 // cl_LF_to_DF(x) wandelt ein Long-Float x in ein Double-Float um.
  71 extern const cl_DF cl_LF_to_DF (const cl_LF& x);
  72
  73
  74 // Fehlermeldung wegen NaN
  75 nonreturning_function(extern, cl_error_floating_point_nan, (void));
  76
  77
  78 // Runtime typing support.
  79 extern cl_class cl_class_ffloat;
  80 extern cl_class cl_class_dfloat;
  81 extern cl_class cl_class_lfloat;
  82
  83 // Type test.
  84 inline cl_boolean longfloatp (const cl_F& x)
  85 {
  86         if (x.pointer_p())
  87                 if (x.pointer_type() == &cl_class_lfloat)
  88                         return cl_true;
  89         return cl_false;
  90 }
  91
  92 // Macro: verteilt je nach Float-Typ eines Floats x auf 4 Statements.
  93 // floattypecase(x, SF_statement,FF_statement,DF_statement,LF_statement);
  94 // x sollte eine Variable sein.
  95 #ifdef CL_WIDE_POINTERS
  96   #define floattypecase(x, SF_statement,FF_statement,DF_statement,LF_statement) \
  97     if (!(x).pointer_p())                                               \
  98       switch ((x).nonpointer_tag())                                     \
  99         { case cl_SF_tag: { SF_statement } break;                       \
 100           case cl_FF_tag: { FF_statement } break;                       \
 101           default: NOTREACHED                                           \
 102         }                                                               \
 103       else {                                                            \
 104         if ((x).pointer_type() == &cl_class_dfloat) { DF_statement }    \
 105         else if ((x).pointer_type() == &cl_class_lfloat) { LF_statement } \
 106         else NOTREACHED                                                 \
 107       }
 108 #else
 109   #define floattypecase(x, SF_statement,FF_statement,DF_statement,LF_statement) \
 110     if (!(x).pointer_p())                                               \
 111       switch ((x).nonpointer_tag())                                     \
 112         { case cl_SF_tag: { SF_statement } break;                       \
 113           default: NOTREACHED                                           \
 114         }                                                               \
 115       else {                                                            \
 116         if ((x).pointer_type() == &cl_class_ffloat) { FF_statement }    \
 117         else if ((x).pointer_type() == &cl_class_dfloat) { DF_statement } \
 118         else if ((x).pointer_type() == &cl_class_lfloat) { LF_statement } \
 119         else NOTREACHED                                                 \
 120       }
 121 #endif
 122
 123 // Macro: verteilt je nach Float-Typ eines Floats x auf 4 Statements,
 124 // die x vom jeweiligen Float-Typ benutzen dürfen.
 125 // floatcase(x, SF_statement,FF_statement,DF_statement,LF_statement);
 126 // x sollte eine Variable sein.
 127   #define floatcase(x, SF_statement,FF_statement,DF_statement,LF_statement) \
 128     floattypecase(x                                                        \
 129       , var cl_SF& __tmp = *(cl_SF*)&x; var cl_SF& x = __tmp; SF_statement \
 130       , var cl_FF& __tmp = *(cl_FF*)&x; var cl_FF& x = __tmp; FF_statement \
 131       , var cl_DF& __tmp = *(cl_DF*)&x; var cl_DF& x = __tmp; DF_statement \
 132       , var cl_LF& __tmp = *(cl_LF*)&x; var cl_LF& x = __tmp; LF_statement \
 133       )
 134
 135
 136 // GEN_F_OP1(arg1,F_OP,ergebnis_zuweisung)
 137 // generates the body of a float operation with one argument.
 138 // LF_OP is executed once the argument has been converted to its exact
 139 // float type.
 140 #define GEN_F_OP1(arg1,F_OP,ergebnis_zuweisung)  \
 141 {                                                                       \
 142         floatcase(arg1                                                  \
 143         , /* SF */      ergebnis_zuweisung F_OP(arg1);                  \
 144         , /* FF */      ergebnis_zuweisung F_OP(arg1);                  \
 145         , /* DF */      ergebnis_zuweisung F_OP(arg1);                  \
 146         , /* LF */      ergebnis_zuweisung F_OP(arg1);                  \
 147         );                                                              \
 148 }
 149
 150
 151 // GEN_F_OP2(arg1,arg2,F_OP,r,s,ergebnis_zuweisung)
 152 // generates the body of a float operation with two arguments.
 153 // F_OP is executed once both arguments have been converted to the same
 154 // float format (the longer one of arg1 and arg2). The r results are then
 155 // converted the shorter of the two float formats. (r = 0,1,2.)
 156 // s = 0,1. s=0 means the LF operation needs two long-floats of the same size.
 157 // s=1 means they may be of different sizes.
 158 #define GEN_F_OP2(arg1,arg2,F_OP,r,s,ergebnis_zuweisung)  \
 159 {                                                                       \
 160         floatcase(arg1                                                  \
 161         , /* arg1 SF */                                                 \
 162                 floatcase(arg2                                          \
 163                 , /* arg2 SF */                                         \
 164                         ergebnis_zuweisung CONCAT(NOMAP,r)(SF,          \
 165                         F_OP(arg1,arg2) );                              \
 166                 , /* arg2 FF */                                         \
 167                         ergebnis_zuweisung CONCAT(MAP,r)(FF,cl_FF_to_SF,\
 168                         F_OP(cl_SF_to_FF(arg1),arg2) );                 \
 169                 , /* arg2 DF */                                         \
 170                         ergebnis_zuweisung CONCAT(MAP,r)(DF,cl_DF_to_SF,\
 171                         F_OP(cl_SF_to_DF(arg1),arg2) );                 \
 172                 , /* arg2 LF */                                         \
 173                         ergebnis_zuweisung CONCAT(MAP,r)(LF,cl_LF_to_SF,\
 174                         F_OP(cl_SF_to_LF(arg1,CONCAT(LFlen,s)(arg2)),arg2) ); \
 175                 );                                                      \
 176         , /* arg1 FF */                                                 \
 177                 floatcase(arg2                                          \
 178                 , /* arg2 SF */                                         \
 179                         ergebnis_zuweisung CONCAT(MAP,r)(FF,cl_FF_to_SF,\
 180                         F_OP(arg1,cl_SF_to_FF(arg2)) );                 \
 181                 , /* arg2 FF */                                         \
 182                         ergebnis_zuweisung CONCAT(NOMAP,r)(FF,          \
 183                         F_OP(arg1,arg2) );                              \
 184                 , /* arg2 DF */                                         \
 185                         ergebnis_zuweisung CONCAT(MAP,r)(DF,cl_DF_to_FF,\
 186                         F_OP(cl_FF_to_DF(arg1),arg2) );                 \
 187                 , /* arg2 LF */                                         \
 188                         ergebnis_zuweisung CONCAT(MAP,r)(LF,cl_LF_to_FF,\
 189                         F_OP(cl_FF_to_LF(arg1,CONCAT(LFlen,s)(arg2)),arg2) ); \
 190                 );                                                      \
 191         , /* arg1 DF */                                                 \
 192                 floatcase(arg2                                          \
 193                 , /* arg2 SF */                                         \
 194                         ergebnis_zuweisung CONCAT(MAP,r)(DF,cl_DF_to_SF,\
 195                         F_OP(arg1,cl_SF_to_DF(arg2)) );                 \
 196                 , /* arg2 FF */                                         \
 197                         ergebnis_zuweisung CONCAT(MAP,r)(DF,cl_DF_to_FF,\
 198                         F_OP(arg1,cl_FF_to_DF(arg2)) );                 \
 199                 , /* arg2 DF */                                         \
 200                         ergebnis_zuweisung CONCAT(NOMAP,r)(DF,          \
 201                         F_OP(arg1,arg2) );                              \
 202                 , /* arg2 LF */                                         \
 203                         ergebnis_zuweisung CONCAT(MAP,r)(LF,cl_LF_to_DF,\
 204                         F_OP(cl_DF_to_LF(arg1,CONCAT(LFlen,s)(arg2)),arg2) ); \
 205                 );                                                      \
 206         , /* arg1 LF */                                                 \
 207                 floatcase(arg2                                          \
 208                 , /* arg2 SF */                                         \
 209                         ergebnis_zuweisung CONCAT(MAP,r)(LF,cl_LF_to_SF,\
 210                         F_OP(arg1,cl_SF_to_LF(arg2,CONCAT(LFlen,s)(arg1))) ); \
 211                 , /* arg2 FF */                                         \
 212                         ergebnis_zuweisung CONCAT(MAP,r)(LF,cl_LF_to_FF,\
 213                         F_OP(arg1,cl_FF_to_LF(arg2,CONCAT(LFlen,s)(arg1))) ); \
 214                 , /* arg2 DF */                                         \
 215                         ergebnis_zuweisung CONCAT(MAP,r)(LF,cl_LF_to_DF,\
 216                         F_OP(arg1,cl_DF_to_LF(arg2,CONCAT(LFlen,s)(arg1))) ); \
 217                 , /* arg2 LF */                                         \
 218                         GEN_LF_OP2_AUX(arg1,arg2,F_OP,r,s,ergebnis_zuweisung) \
 219                 );                                                      \
 220         );                                                              \
 221 }
 222 #define GEN_LF_OP2_AUX(arg1,arg2,F_OP,r,s,ergebnis_zuweisung)  \
 223   CONCAT(GEN_LF_OP2_AUX,s)(arg1,arg2,F_OP,r,ergebnis_zuweisung)
 224 #define GEN_LF_OP2_AUX0(arg1,arg2,F_OP,r,ergebnis_zuweisung)  \
 225   var uintC len1 = TheLfloat(arg1)->len;                                \
 226   var uintC len2 = TheLfloat(arg2)->len;                                \
 227   if (len1 == len2) /* gleich -> direkt ausführen */                    \
 228     { ergebnis_zuweisung CONCAT(NOMAP,r) (LF, F_OP(arg1,arg2)); }       \
 229   elif (len1 > len2) /* -> arg2 auf die Länge von arg1 bringen */       \
 230     { ergebnis_zuweisung CONCAT(MAP,r) (LF, LF_shorten_len2,            \
 231       F_OP(arg1,extend(arg2,len1)) );                                   \
 232     }                                                                   \
 233   else /* (len1 < len2) -> arg1 auf die Länge von arg2 bringen */       \
 234     { ergebnis_zuweisung CONCAT(MAP,r) (LF, LF_shorten_len1,            \
 235       F_OP(extend(arg1,len2),arg2) );                                   \
 236     }
 237 #define LF_shorten_len1(arg)  shorten(arg,len1)
 238 #define LF_shorten_len2(arg)  shorten(arg,len2)
 239 #define GEN_LF_OP2_AUX1(arg1,arg2,F_OP,r,ergebnis_zuweisung)  \
 240   ergebnis_zuweisung CONCAT(NOMAP,r) (LF, F_OP(arg1,arg2));
 241
 242 #define NOMAP0(F,EXPR)  EXPR
 243 #define NOMAP1(F,EXPR)  EXPR
 244 #define MAP0(F,FN,EXPR)  EXPR
 245 #define MAP1(F,FN,EXPR)  FN(EXPR)
 246
 247 #define LFlen0(arg)  TheLfloat(arg)->len
 248 #define LFlen1(arg)  LF_minlen
 249
 250
 251 // cl_F_extendsqrt(x) erweitert die Genauigkeit eines Floats x um eine Stufe
 252 // SF -> FF -> DF -> LF(4) -> LF(5) -> LF(6) -> ...
 253 // Ein Float mit d Mantissenbits wird so zu einem Float mit
 254 // mindestens d+sqrt(d)+2 Mantissenbits.
 255 extern const cl_F cl_F_extendsqrt (const cl_F& x);
 256
 257 // cl_F_extendsqrtx(x) erweitert die Genauigkeit eines Floats x um eine Stufe
 258 // SF -> FF -> DF -> LF(4) -> LF(5) -> LF(6) -> ...
 259 // Ein Float mit d Mantissenbits und l Exponentenbits wird so zu einem Float
 260 // mit mindestens d+sqrt(d)+2+(l-1) Mantissenbits.
 261 extern const cl_F cl_F_extendsqrtx (const cl_F& x);
 262
 263 // cl_F_shortenrelative(x,y) tries to reduce the size of x, such that one
 264 // wouldn't notice it when adding x to y. y must be /= 0. More precisely,
 265 // this returns a float approximation of x, such that 1 ulp(x) < 1 ulp(y).
 266 extern const cl_F cl_F_shortenrelative (const cl_F& x, const cl_F& y);
 267
 268
 269 // Macro: dispatches according to a cl_float_format_t value.
 270 // floatformatcase(value, SF_statement,FF_statement,DF_statement,LF_statement)
 271 // LF_statement darf auf `len' zugreifen, die zu `value' korrespondierende
 272 // Mantissenlänge (gemessen in Digits).
 273   #define floatformatcase(value, SF_statement,FF_statement,DF_statement,LF_statement)  \
 274     { if ((value) <= cl_float_format_sfloat) { SF_statement }           \
 275       elif ((value) <= cl_float_format_ffloat) { FF_statement }         \
 276       elif ((value) <= cl_float_format_dfloat) { DF_statement }         \
 277       else { var uintL len = ceiling((uintL)(value),intDsize); LF_statement } \
 278     }
 279
 280
 281 #endif /* _CL_F_H */