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/arch/i386/math-emu/poly_2xm1.c

https://bitbucket.org/evzijst/gittest
C | 156 lines | 104 code | 23 blank | 29 comment | 15 complexity | 41d716aa234f64f8ec35e6a7f58dea81 MD5 | raw file
  1/*---------------------------------------------------------------------------+
  2 |  poly_2xm1.c                                                              |
  3 |                                                                           |
  4 | Function to compute 2^x-1 by a polynomial approximation.                  |
  5 |                                                                           |
  6 | Copyright (C) 1992,1993,1994,1997                                         |
  7 |                  W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
  8 |                  E-mail   billm@suburbia.net                              |
  9 |                                                                           |
 10 |                                                                           |
 11 +---------------------------------------------------------------------------*/
 12
 13#include "exception.h"
 14#include "reg_constant.h"
 15#include "fpu_emu.h"
 16#include "fpu_system.h"
 17#include "control_w.h"
 18#include "poly.h"
 19
 20
 21#define	HIPOWER	11
 22static const unsigned long long lterms[HIPOWER] =
 23{
 24  0x0000000000000000LL,  /* This term done separately as 12 bytes */
 25  0xf5fdeffc162c7543LL,
 26  0x1c6b08d704a0bfa6LL,
 27  0x0276556df749cc21LL,
 28  0x002bb0ffcf14f6b8LL,
 29  0x0002861225ef751cLL,
 30  0x00001ffcbfcd5422LL,
 31  0x00000162c005d5f1LL,
 32  0x0000000da96ccb1bLL,
 33  0x0000000078d1b897LL,
 34  0x000000000422b029LL
 35};
 36
 37static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
 38
 39/* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
 40   These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
 41 */
 42static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
 43static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
 44static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
 45static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
 46
 47static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
 48				     &shiftterm2, &shiftterm3 };
 49
 50
 51/*--- poly_2xm1() -----------------------------------------------------------+
 52 | Requires st(0) which is TAG_Valid and < 1.                                |
 53 +---------------------------------------------------------------------------*/
 54int	poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
 55{
 56  long int              exponent, shift;
 57  unsigned long long    Xll;
 58  Xsig                  accumulator, Denom, argSignif;
 59  u_char                tag;
 60
 61  exponent = exponent16(arg);
 62
 63#ifdef PARANOID
 64  if ( exponent >= 0 )    	/* Don't want a |number| >= 1.0 */
 65    {
 66      /* Number negative, too large, or not Valid. */
 67      EXCEPTION(EX_INTERNAL|0x127);
 68      return 1;
 69    }
 70#endif /* PARANOID */
 71
 72  argSignif.lsw = 0;
 73  XSIG_LL(argSignif) = Xll = significand(arg);
 74
 75  if ( exponent == -1 )
 76    {
 77      shift = (argSignif.msw & 0x40000000) ? 3 : 2;
 78      /* subtract 0.5 or 0.75 */
 79      exponent -= 2;
 80      XSIG_LL(argSignif) <<= 2;
 81      Xll <<= 2;
 82    }
 83  else if ( exponent == -2 )
 84    {
 85      shift = 1;
 86      /* subtract 0.25 */
 87      exponent--;
 88      XSIG_LL(argSignif) <<= 1;
 89      Xll <<= 1;
 90    }
 91  else
 92    shift = 0;
 93
 94  if ( exponent < -2 )
 95    {
 96      /* Shift the argument right by the required places. */
 97      if ( FPU_shrx(&Xll, -2-exponent) >= 0x80000000U )
 98	Xll++;	/* round up */
 99    }
100
101  accumulator.lsw = accumulator.midw = accumulator.msw = 0;
102  polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER-1);
103  mul_Xsig_Xsig(&accumulator, &argSignif);
104  shr_Xsig(&accumulator, 3);
105
106  mul_Xsig_Xsig(&argSignif, &hiterm);   /* The leading term */
107  add_two_Xsig(&accumulator, &argSignif, &exponent);
108
109  if ( shift )
110    {
111      /* The argument is large, use the identity:
112	 f(x+a) = f(a) * (f(x) + 1) - 1;
113	 */
114      shr_Xsig(&accumulator, - exponent);
115      accumulator.msw |= 0x80000000;      /* add 1.0 */
116      mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
117      accumulator.msw &= 0x3fffffff;      /* subtract 1.0 */
118      exponent = 1;
119    }
120
121  if ( sign != SIGN_POS )
122    {
123      /* The argument is negative, use the identity:
124	     f(-x) = -f(x) / (1 + f(x))
125	 */
126      Denom.lsw = accumulator.lsw;
127      XSIG_LL(Denom) = XSIG_LL(accumulator);
128      if ( exponent < 0 )
129	shr_Xsig(&Denom, - exponent);
130      else if ( exponent > 0 )
131	{
132	  /* exponent must be 1 here */
133	  XSIG_LL(Denom) <<= 1;
134	  if ( Denom.lsw & 0x80000000 )
135	    XSIG_LL(Denom) |= 1;
136	  (Denom.lsw) <<= 1;
137	}
138      Denom.msw |= 0x80000000;      /* add 1.0 */
139      div_Xsig(&accumulator, &Denom, &accumulator);
140    }
141
142  /* Convert to 64 bit signed-compatible */
143  exponent += round_Xsig(&accumulator);
144
145  result = &st(0);
146  significand(result) = XSIG_LL(accumulator);
147  setexponent16(result, exponent);
148
149  tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
150
151  setsign(result, sign);
152  FPU_settag0(tag);
153
154  return 0;
155
156}