kernel/arch/x86/math-emu/poly_l2.c

   1 /*---------------------------------------------------------------------------+
   2  |  poly_l2.c                                                                |
   3  |                                                                           |
   4  | Compute the base 2 log of a FPU_REG, using 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 static void log2_kernel(FPU_REG const *arg, u_char argsign,
  21                         Xsig * accum_result, long int *expon);
  22
  23 /*--- poly_l2() -------------------------------------------------------------+
  24  |   Base 2 logarithm by a polynomial approximation.                         |
  25  +---------------------------------------------------------------------------*/
  26 void poly_l2(FPU_REG *st0_ptr, FPU_REG *st1_ptr, u_char st1_sign)
  27 {
  28         long int exponent, expon, expon_expon;
  29         Xsig accumulator, expon_accum, yaccum;
  30         u_char sign, argsign;
  31         FPU_REG x;
  32         int tag;
  33
  34         exponent = exponent16(st0_ptr);
  35
  36         /* From st0_ptr, make a number > sqrt(2)/2 and < sqrt(2) */
  37         if (st0_ptr->sigh > (unsigned)0xb504f334) {
  38                 /* Treat as  sqrt(2)/2 < st0_ptr < 1 */
  39                 significand(&x) = -significand(st0_ptr);
  40                 setexponent16(&x, -1);
  41                 exponent++;
  42                 argsign = SIGN_NEG;
  43         } else {
  44                 /* Treat as  1 <= st0_ptr < sqrt(2) */
  45                 x.sigh = st0_ptr->sigh - 0x80000000;
  46                 x.sigl = st0_ptr->sigl;
  47                 setexponent16(&x, 0);
  48                 argsign = SIGN_POS;
  49         }
  50         tag = FPU_normalize_nuo(&x);
  51
  52         if (tag == TAG_Zero) {
  53                 expon = 0;
  54                 accumulator.msw = accumulator.midw = accumulator.lsw = 0;
  55         } else {
  56                 log2_kernel(&x, argsign, &accumulator, &expon);
  57         }
  58
  59         if (exponent < 0) {
  60                 sign = SIGN_NEG;
  61                 exponent = -exponent;
  62         } else
  63                 sign = SIGN_POS;
  64         expon_accum.msw = exponent;
  65         expon_accum.midw = expon_accum.lsw = 0;
  66         if (exponent) {
  67                 expon_expon = 31 + norm_Xsig(&expon_accum);
  68                 shr_Xsig(&accumulator, expon_expon - expon);
  69
  70                 if (sign ^ argsign)
  71                         negate_Xsig(&accumulator);
  72                 add_Xsig_Xsig(&accumulator, &expon_accum);
  73         } else {
  74                 expon_expon = expon;
  75                 sign = argsign;
  76         }
  77
  78         yaccum.lsw = 0;
  79         XSIG_LL(yaccum) = significand(st1_ptr);
  80         mul_Xsig_Xsig(&accumulator, &yaccum);
  81
  82         expon_expon += round_Xsig(&accumulator);
  83
  84         if (accumulator.msw == 0) {
  85                 FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
  86                 return;
  87         }
  88
  89         significand(st1_ptr) = XSIG_LL(accumulator);
  90         setexponent16(st1_ptr, expon_expon + exponent16(st1_ptr) + 1);
  91
  92         tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign ^ st1_sign);
  93         FPU_settagi(1, tag);
  94
  95         set_precision_flag_up();        /* 80486 appears to always do this */
  96
  97         return;
  98
  99 }
 100
 101 /*--- poly_l2p1() -----------------------------------------------------------+
 102  |   Base 2 logarithm by a polynomial approximation.                         |
 103  |   log2(x+1)                                                               |
 104  +---------------------------------------------------------------------------*/
 105 int poly_l2p1(u_char sign0, u_char sign1,
 106               FPU_REG * st0_ptr, FPU_REG * st1_ptr, FPU_REG * dest)
 107 {
 108         u_char tag;
 109         long int exponent;
 110         Xsig accumulator, yaccum;
 111
 112         if (exponent16(st0_ptr) < 0) {
 113                 log2_kernel(st0_ptr, sign0, &accumulator, &exponent);
 114
 115                 yaccum.lsw = 0;
 116                 XSIG_LL(yaccum) = significand(st1_ptr);
 117                 mul_Xsig_Xsig(&accumulator, &yaccum);
 118
 119                 exponent += round_Xsig(&accumulator);
 120
 121                 exponent += exponent16(st1_ptr) + 1;
 122                 if (exponent < EXP_WAY_UNDER)
 123                         exponent = EXP_WAY_UNDER;
 124
 125                 significand(dest) = XSIG_LL(accumulator);
 126                 setexponent16(dest, exponent);
 127
 128                 tag = FPU_round(dest, 1, 0, FULL_PRECISION, sign0 ^ sign1);
 129                 FPU_settagi(1, tag);
 130
 131                 if (tag == TAG_Valid)
 132                         set_precision_flag_up();        /* 80486 appears to always do this */
 133         } else {
 134                 /* The magnitude of st0_ptr is far too large. */
 135
 136                 if (sign0 != SIGN_POS) {
 137                         /* Trying to get the log of a negative number. */
 138 #ifdef PECULIAR_486             /* Stupid 80486 doesn't worry about log(negative). */
 139                         changesign(st1_ptr);
 140 #else
 141                         if (arith_invalid(1) < 0)
 142                                 return 1;
 143 #endif /* PECULIAR_486 */
 144                 }
 145
 146                 /* 80486 appears to do this */
 147                 if (sign0 == SIGN_NEG)
 148                         set_precision_flag_down();
 149                 else
 150                         set_precision_flag_up();
 151         }
 152
 153         if (exponent(dest) <= EXP_UNDER)
 154                 EXCEPTION(EX_Underflow);
 155
 156         return 0;
 157
 158 }
 159
 160 #undef HIPOWER
 161 #define HIPOWER 10
 162 static const unsigned long long logterms[HIPOWER] = {
 163         0x2a8eca5705fc2ef0LL,
 164         0xf6384ee1d01febceLL,
 165         0x093bb62877cdf642LL,
 166         0x006985d8a9ec439bLL,
 167         0x0005212c4f55a9c8LL,
 168         0x00004326a16927f0LL,
 169         0x0000038d1d80a0e7LL,
 170         0x0000003141cc80c6LL,
 171         0x00000002b1668c9fLL,
 172         0x000000002c7a46aaLL
 173 };
 174
 175 static const unsigned long leadterm = 0xb8000000;
 176
 177 /*--- log2_kernel() ---------------------------------------------------------+
 178  |   Base 2 logarithm by a polynomial approximation.                         |
 179  |   log2(x+1)                                                               |
 180  +---------------------------------------------------------------------------*/
 181 static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result,
 182                         long int *expon)
 183 {
 184         long int exponent, adj;
 185         unsigned long long Xsq;
 186         Xsig accumulator, Numer, Denom, argSignif, arg_signif;
 187
 188         exponent = exponent16(arg);
 189         Numer.lsw = Denom.lsw = 0;
 190         XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg);
 191         if (argsign == SIGN_POS) {
 192                 shr_Xsig(&Denom, 2 - (1 + exponent));
 193                 Denom.msw |= 0x80000000;
 194                 div_Xsig(&Numer, &Denom, &argSignif);
 195         } else {
 196                 shr_Xsig(&Denom, 1 - (1 + exponent));
 197                 negate_Xsig(&Denom);
 198                 if (Denom.msw & 0x80000000) {
 199                         div_Xsig(&Numer, &Denom, &argSignif);
 200                         exponent++;
 201                 } else {
 202                         /* Denom must be 1.0 */
 203                         argSignif.lsw = Numer.lsw;
 204                         argSignif.midw = Numer.midw;
 205                         argSignif.msw = Numer.msw;
 206                 }
 207         }
 208
 209 #ifndef PECULIAR_486
 210         /* Should check here that  |local_arg|  is within the valid range */
 211         if (exponent >= -2) {
 212                 if ((exponent > -2) || (argSignif.msw > (unsigned)0xafb0ccc0)) {
 213                         /* The argument is too large */
 214                 }
 215         }
 216 #endif /* PECULIAR_486 */
 217
 218         arg_signif.lsw = argSignif.lsw;
 219         XSIG_LL(arg_signif) = XSIG_LL(argSignif);
 220         adj = norm_Xsig(&argSignif);
 221         accumulator.lsw = argSignif.lsw;
 222         XSIG_LL(accumulator) = XSIG_LL(argSignif);
 223         mul_Xsig_Xsig(&accumulator, &accumulator);
 224         shr_Xsig(&accumulator, 2 * (-1 - (1 + exponent + adj)));
 225         Xsq = XSIG_LL(accumulator);
 226         if (accumulator.lsw & 0x80000000)
 227                 Xsq++;
 228
 229         accumulator.msw = accumulator.midw = accumulator.lsw = 0;
 230         /* Do the basic fixed point polynomial evaluation */
 231         polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER - 1);
 232
 233         mul_Xsig_Xsig(&accumulator, &argSignif);
 234         shr_Xsig(&accumulator, 6 - adj);
 235
 236         mul32_Xsig(&arg_signif, leadterm);
 237         add_two_Xsig(&accumulator, &arg_signif, &exponent);
 238
 239         *expon = exponent + 1;
 240         accum_result->lsw = accumulator.lsw;
 241         accum_result->midw = accumulator.midw;
 242         accum_result->msw = accumulator.msw;
 243
 244 }