1: /* Copyright (c) Stichting Mathematisch Centrum, Amsterdam, 1985. */
   2: 
   3: /*
   4:   $Header: b1num.h,v 1.4 85/08/22 16:41:53 timo Exp $
   5: */
   6: 
   7: /************************************************************************/
   8: /* Full numeric package: private definitions                            */
   9: /*                                                                      */
  10: /* A number is modelled as one of zero, unbounded integer,              */
  11: /*        unbounded rational or approximate.                            */
  12: /*     Zero has a 'length' field of zero, and nothing else.             */
  13: /*     A length field of +n means the number is an n digit integer,     */
  14: /*        (with digits to some large base).                             */
  15: /*     A length of -1 means there follow two floating point numbers,    */
  16: /*        one the fraction (zero or .5 <= frac <= 1), one the exponent  */
  17: /*        with respect to base 2 (should be an integral value).         */
  18: /*        (This is so when EXT_RANGE is defined.  Otherwise, there is   */
  19: /*        only one field, frac, which is not normalized.  This saves    */
  20: /*        code and data space on e.g. the IBM PC, where the natural     */
  21: /*        range of double's is sufficient (~1E307).)                    */
  22: /*     A length of -2 means there follow two values, pointers to two    */
  23: /*        unbounded integers, ie a rational number.                     */
  24: /*     A length of -n, n>2, means it is a rational with a print width   */
  25: /*        of n-2.                                                       */
  26: /*                                                                      */
  27: /************************************************************************/
  28: 
  29: /*************** Definitions exported for integers *****************/
  30: 
  31: typedef int digit;
  32: 
  33: typedef struct integer {
  34:     HEADER;
  35:     digit   dig[1];
  36: } *integer;
  37: 
  38: #define FreezeSmallInt(v, vv) \
  39:     (IsSmallInt(v) && (Freeze1(v, vv), Freeze2(v, vv)))
  40: #define Freeze1(v, vv) ((vv).type= Num, (vv).refcnt= Maxrefcnt)
  41: #define Freeze2(v, vv) \
  42:     ((vv).len= (v) != 0, (vv).dig[0]= SmallIntVal(v), (v)= &(vv))
  43: 
  44: integer int_gadd();
  45: integer int_canon();
  46: integer int_prod();
  47: integer int_quot();
  48: integer int_gcd();
  49: integer mk_int();
  50: integer int1mul();
  51: integer int_tento();
  52: integer int_half();
  53: integer int_mod();
  54: digit int_ldiv();
  55: 
  56: #define int_0 ((integer) MkSmallInt(0))
  57: #define int_1 ((integer) MkSmallInt(1))
  58: #define int_2 ((integer) MkSmallInt(2))
  59: #define int_10 ((integer) MkSmallInt(10))
  60: 
  61: #define int_sum(v, w) int_gadd(v, w, 1)
  62: #define int_diff(v, w) int_gadd(v, w, -1)
  63: #define int_neg(v) int_gadd(int_0, v, -1)
  64: 
  65: #define Integral(v) (IsSmallInt(v) || Length(v)>=0)
  66: #define Modulo(a,b) (((a)%(b)+(b))%(b))
  67: #define Digit(v,n) ((v)->dig[n])
  68: #define Msd(v) (IsSmallInt(v) ? SmallIntVal(v) : Digit(v,Length(v)-1))
  69: #define Lsd(v) (IsSmallInt(v) ? SmallIntVal(v) : Digit(v,0))
  70: 
  71: #define Odd(x) ((x)&1)
  72: #define Even(x) (!Odd(x))
  73: 
  74: /* Provisional definitions */
  75: 
  76: value copy();
  77: #define Copy(x) copy((value)(x))
  78: 
  79: /***************** Definitions exported for rationals *****************/
  80: 
  81: typedef struct {
  82:     HEADER;
  83:     integer num, den;
  84: } *rational;
  85: 
  86: 
  87: #define Numerator(a) ((a)->num)
  88: #define Denominator(a) ((a)->den)
  89: #define Rational(a) (!IsSmallInt(a) && Length(a)<-1)
  90: #define Roundsize(a) (-2-Length(a))
  91: 
  92: rational mk_rat();
  93: rational rat_sum();
  94: rational rat_diff();
  95: rational rat_neg();
  96: rational rat_prod();
  97: rational rat_quot();
  98: rational rat_power();
  99: 
 100: extern rational rat_zero;
 101: extern rational rat_half;
 102: 
 103: value tento();
 104: value mk_exact();
 105: 
 106: /***************** Definitions exported for approximate numbers *************/
 107: 
 108: #ifdef vax
 109: #define EXT_RANGE
 110: #endif
 111: 
 112: typedef struct real {
 113:     HEADER;
 114:     double  frac;
 115: #ifdef EXT_RANGE
 116:     double  expo;
 117: #endif EXT_RANGE
 118: } *real;
 119: 
 120: #define Frac(v) ((v)->frac)
 121: #ifdef EXT_RANGE
 122: #define Expo(v) ((v)->expo)
 123: #else
 124: #define Expo(v) 0.0
 125: #endif
 126: 
 127: #define Approximate(v) (!IsSmallInt(v) && Length(v)==-1)
 128: #define Exact(v) (!Approximate(v))
 129: 
 130: extern real app_0;
 131: 
 132: real mk_approx();
 133: 
 134: real app_sum();
 135: real app_diff();
 136: real app_prod();
 137: real app_quot();
 138: real app_neg();
 139: 
 140: real app_exp();
 141: real app_log();
 142: real app_power();
 143: 
 144: value app_floor();
 145: 
 146: 
 147: /* Numeric constants. */
 148: /* (Source: Knuth, The Art of Computer Programming, Vol. 1, Appendix B-1.) */
 149: 
 150: #define logtwo 0.6931471805599453094172321214581765680755
 151: #define invlogtwo 1.4426950408889634073599246810018921374266
 152: #define logten 2.3025850929940456840179914546843642076011
 153: #define logBASE (logten*tenlogBASE)
 154: #define twologBASE (logBASE*invlogtwo)

Defined struct's

integer defined in line 33; used 16 times
real defined in line 112; used 4 times

Defined typedef's

real defined in line 118; used 88 times

Defined macros

Approximate defined in line 127; used 10 times
Even defined in line 72; used 8 times
Exact defined in line 128; used 7 times
Freeze1 defined in line 40; used 1 times
  • in line 39
Freeze2 defined in line 41; used 1 times
  • in line 39
Odd defined in line 71; used 2 times
int_10 defined in line 59; used 2 times
invlogtwo defined in line 151; used 1 times
logBASE defined in line 153; used 1 times
logten defined in line 152; used 1 times
twologBASE defined in line 154; used 1 times

Usage of this include

Last modified: 1985-08-27
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