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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 | /*---------------------------------------------------------------------------+ | poly_l2.c | | | | Compute the base 2 log of a FPU_REG, using a polynomial approximation. | | | | Copyright (C) 1992,1993,1994,1997 | | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia | | E-mail billm@suburbia.net | | | | | +---------------------------------------------------------------------------*/ #include "exception.h" #include "reg_constant.h" #include "fpu_emu.h" #include "fpu_system.h" #include "control_w.h" #include "poly.h" static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result, long int *expon); /*--- poly_l2() -------------------------------------------------------------+ | Base 2 logarithm by a polynomial approximation. | +---------------------------------------------------------------------------*/ void poly_l2(FPU_REG *st0_ptr, FPU_REG *st1_ptr, u_char st1_sign) { long int exponent, expon, expon_expon; Xsig accumulator, expon_accum, yaccum; u_char sign, argsign; FPU_REG x; int tag; exponent = exponent16(st0_ptr); /* From st0_ptr, make a number > sqrt(2)/2 and < sqrt(2) */ if ( st0_ptr->sigh > (unsigned)0xb504f334 ) { /* Treat as sqrt(2)/2 < st0_ptr < 1 */ significand(&x) = - significand(st0_ptr); setexponent16(&x, -1); exponent++; argsign = SIGN_NEG; } else { /* Treat as 1 <= st0_ptr < sqrt(2) */ x.sigh = st0_ptr->sigh - 0x80000000; x.sigl = st0_ptr->sigl; setexponent16(&x, 0); argsign = SIGN_POS; } tag = FPU_normalize_nuo(&x); if ( tag == TAG_Zero ) { expon = 0; accumulator.msw = accumulator.midw = accumulator.lsw = 0; } else { log2_kernel(&x, argsign, &accumulator, &expon); } if ( exponent < 0 ) { sign = SIGN_NEG; exponent = -exponent; } else sign = SIGN_POS; expon_accum.msw = exponent; expon_accum.midw = expon_accum.lsw = 0; if ( exponent ) { expon_expon = 31 + norm_Xsig(&expon_accum); shr_Xsig(&accumulator, expon_expon - expon); if ( sign ^ argsign ) negate_Xsig(&accumulator); add_Xsig_Xsig(&accumulator, &expon_accum); } else { expon_expon = expon; sign = argsign; } yaccum.lsw = 0; XSIG_LL(yaccum) = significand(st1_ptr); mul_Xsig_Xsig(&accumulator, &yaccum); expon_expon += round_Xsig(&accumulator); if ( accumulator.msw == 0 ) { FPU_copy_to_reg1(&CONST_Z, TAG_Zero); return; } significand(st1_ptr) = XSIG_LL(accumulator); setexponent16(st1_ptr, expon_expon + exponent16(st1_ptr) + 1); tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign ^ st1_sign); FPU_settagi(1, tag); set_precision_flag_up(); /* 80486 appears to always do this */ return; } /*--- poly_l2p1() -----------------------------------------------------------+ | Base 2 logarithm by a polynomial approximation. | | log2(x+1) | +---------------------------------------------------------------------------*/ int poly_l2p1(u_char sign0, u_char sign1, FPU_REG *st0_ptr, FPU_REG *st1_ptr, FPU_REG *dest) { u_char tag; long int exponent; Xsig accumulator, yaccum; if ( exponent16(st0_ptr) < 0 ) { log2_kernel(st0_ptr, sign0, &accumulator, &exponent); yaccum.lsw = 0; XSIG_LL(yaccum) = significand(st1_ptr); mul_Xsig_Xsig(&accumulator, &yaccum); exponent += round_Xsig(&accumulator); exponent += exponent16(st1_ptr) + 1; if ( exponent < EXP_WAY_UNDER ) exponent = EXP_WAY_UNDER; significand(dest) = XSIG_LL(accumulator); setexponent16(dest, exponent); tag = FPU_round(dest, 1, 0, FULL_PRECISION, sign0 ^ sign1); FPU_settagi(1, tag); if ( tag == TAG_Valid ) set_precision_flag_up(); /* 80486 appears to always do this */ } else { /* The magnitude of st0_ptr is far too large. */ if ( sign0 != SIGN_POS ) { /* Trying to get the log of a negative number. */ #ifdef PECULIAR_486 /* Stupid 80486 doesn't worry about log(negative). */ changesign(st1_ptr); #else if ( arith_invalid(1) < 0 ) return 1; #endif /* PECULIAR_486 */ } /* 80486 appears to do this */ if ( sign0 == SIGN_NEG ) set_precision_flag_down(); else set_precision_flag_up(); } if ( exponent(dest) <= EXP_UNDER ) EXCEPTION(EX_Underflow); return 0; } #undef HIPOWER #define HIPOWER 10 static const unsigned long long logterms[HIPOWER] = { 0x2a8eca5705fc2ef0LL, 0xf6384ee1d01febceLL, 0x093bb62877cdf642LL, 0x006985d8a9ec439bLL, 0x0005212c4f55a9c8LL, 0x00004326a16927f0LL, 0x0000038d1d80a0e7LL, 0x0000003141cc80c6LL, 0x00000002b1668c9fLL, 0x000000002c7a46aaLL }; static const unsigned long leadterm = 0xb8000000; /*--- log2_kernel() ---------------------------------------------------------+ | Base 2 logarithm by a polynomial approximation. | | log2(x+1) | +---------------------------------------------------------------------------*/ static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result, long int *expon) { long int exponent, adj; unsigned long long Xsq; Xsig accumulator, Numer, Denom, argSignif, arg_signif; exponent = exponent16(arg); Numer.lsw = Denom.lsw = 0; XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg); if ( argsign == SIGN_POS ) { shr_Xsig(&Denom, 2 - (1 + exponent)); Denom.msw |= 0x80000000; div_Xsig(&Numer, &Denom, &argSignif); } else { shr_Xsig(&Denom, 1 - (1 + exponent)); negate_Xsig(&Denom); if ( Denom.msw & 0x80000000 ) { div_Xsig(&Numer, &Denom, &argSignif); exponent ++; } else { /* Denom must be 1.0 */ argSignif.lsw = Numer.lsw; argSignif.midw = Numer.midw; argSignif.msw = Numer.msw; } } #ifndef PECULIAR_486 /* Should check here that |local_arg| is within the valid range */ if ( exponent >= -2 ) { if ( (exponent > -2) || (argSignif.msw > (unsigned)0xafb0ccc0) ) { /* The argument is too large */ } } #endif /* PECULIAR_486 */ arg_signif.lsw = argSignif.lsw; XSIG_LL(arg_signif) = XSIG_LL(argSignif); adj = norm_Xsig(&argSignif); accumulator.lsw = argSignif.lsw; XSIG_LL(accumulator) = XSIG_LL(argSignif); mul_Xsig_Xsig(&accumulator, &accumulator); shr_Xsig(&accumulator, 2*(-1 - (1 + exponent + adj))); Xsq = XSIG_LL(accumulator); if ( accumulator.lsw & 0x80000000 ) Xsq++; accumulator.msw = accumulator.midw = accumulator.lsw = 0; /* Do the basic fixed point polynomial evaluation */ polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER-1); mul_Xsig_Xsig(&accumulator, &argSignif); shr_Xsig(&accumulator, 6 - adj); mul32_Xsig(&arg_signif, leadterm); add_two_Xsig(&accumulator, &arg_signif, &exponent); *expon = exponent + 1; accum_result->lsw = accumulator.lsw; accum_result->midw = accumulator.midw; accum_result->msw = accumulator.msw; } |