arch/x86/math-emu/poly_atan.c

   1 /*---------------------------------------------------------------------------+
   2  |  poly_atan.c                                                              |
   3  |                                                                           |
   4  | Compute the arctan 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 "status_w.h"
  18 #include "control_w.h"
  19 #include "poly.h"
  20
  21 #define HIPOWERon       6       /* odd poly, negative terms */
  22 static const unsigned long long oddnegterms[HIPOWERon] = {
  23         0x0000000000000000LL,   /* Dummy (not for - 1.0) */
  24         0x015328437f756467LL,
  25         0x0005dda27b73dec6LL,
  26         0x0000226bf2bfb91aLL,
  27         0x000000ccc439c5f7LL,
  28         0x0000000355438407LL
  29 };
  30
  31 #define HIPOWERop       6       /* odd poly, positive terms */
  32 static const unsigned long long oddplterms[HIPOWERop] = {
  33 /*  0xaaaaaaaaaaaaaaabLL,  transferred to fixedpterm[] */
  34         0x0db55a71875c9ac2LL,
  35         0x0029fce2d67880b0LL,
  36         0x0000dfd3908b4596LL,
  37         0x00000550fd61dab4LL,
  38         0x0000001c9422b3f9LL,
  39         0x000000003e3301e1LL
  40 };
  41
  42 static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL;
  43
  44 static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa);
  45
  46 static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b);
  47
  48 /*--- poly_atan() -----------------------------------------------------------+
  49  |                                                                           |
  50  +---------------------------------------------------------------------------*/
  51 void poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
  52                FPU_REG *st1_ptr, u_char st1_tag)
  53 {
  54         u_char transformed, inverted, sign1, sign2;
  55         int exponent;
  56         long int dummy_exp;
  57         Xsig accumulator, Numer, Denom, accumulatore, argSignif, argSq, argSqSq;
  58         u_char tag;
  59
  60         sign1 = getsign(st0_ptr);
  61         sign2 = getsign(st1_ptr);
  62         if (st0_tag == TAG_Valid) {
  63                 exponent = exponent(st0_ptr);
  64         } else {
  65                 /* This gives non-compatible stack contents... */
  66                 FPU_to_exp16(st0_ptr, st0_ptr);
  67                 exponent = exponent16(st0_ptr);
  68         }
  69         if (st1_tag == TAG_Valid) {
  70                 exponent -= exponent(st1_ptr);
  71         } else {
  72                 /* This gives non-compatible stack contents... */
  73                 FPU_to_exp16(st1_ptr, st1_ptr);
  74                 exponent -= exponent16(st1_ptr);
  75         }
  76
  77         if ((exponent < 0) || ((exponent == 0) &&
  78                                ((st0_ptr->sigh < st1_ptr->sigh) ||
  79                                 ((st0_ptr->sigh == st1_ptr->sigh) &&
  80                                  (st0_ptr->sigl < st1_ptr->sigl))))) {
  81                 inverted = 1;
  82                 Numer.lsw = Denom.lsw = 0;
  83                 XSIG_LL(Numer) = significand(st0_ptr);
  84                 XSIG_LL(Denom) = significand(st1_ptr);
  85         } else {
  86                 inverted = 0;
  87                 exponent = -exponent;
  88                 Numer.lsw = Denom.lsw = 0;
  89                 XSIG_LL(Numer) = significand(st1_ptr);
  90                 XSIG_LL(Denom) = significand(st0_ptr);
  91         }
  92         div_Xsig(&Numer, &Denom, &argSignif);
  93         exponent += norm_Xsig(&argSignif);
  94
  95         if ((exponent >= -1)
  96             || ((exponent == -2) && (argSignif.msw > 0xd413ccd0))) {
  97                 /* The argument is greater than sqrt(2)-1 (=0.414213562...) */
  98                 /* Convert the argument by an identity for atan */
  99                 transformed = 1;
 100
 101                 if (exponent >= 0) {
 102 #ifdef PARANOID
 103                         if (!((exponent == 0) &&
 104                               (argSignif.lsw == 0) && (argSignif.midw == 0) &&
 105                               (argSignif.msw == 0x80000000))) {
 106                                 EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic error */
 107                                 return;
 108                         }
 109 #endif /* PARANOID */
 110                         argSignif.msw = 0;      /* Make the transformed arg -> 0.0 */
 111                 } else {
 112                         Numer.lsw = Denom.lsw = argSignif.lsw;
 113                         XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);
 114
 115                         if (exponent < -1)
 116                                 shr_Xsig(&Numer, -1 - exponent);
 117                         negate_Xsig(&Numer);
 118
 119                         shr_Xsig(&Denom, -exponent);
 120                         Denom.msw |= 0x80000000;
 121
 122                         div_Xsig(&Numer, &Denom, &argSignif);
 123
 124                         exponent = -1 + norm_Xsig(&argSignif);
 125                 }
 126         } else {
 127                 transformed = 0;
 128         }
 129
 130         argSq.lsw = argSignif.lsw;
 131         argSq.midw = argSignif.midw;
 132         argSq.msw = argSignif.msw;
 133         mul_Xsig_Xsig(&argSq, &argSq);
 134
 135         argSqSq.lsw = argSq.lsw;
 136         argSqSq.midw = argSq.midw;
 137         argSqSq.msw = argSq.msw;
 138         mul_Xsig_Xsig(&argSqSq, &argSqSq);
 139
 140         accumulatore.lsw = argSq.lsw;
 141         XSIG_LL(accumulatore) = XSIG_LL(argSq);
 142
 143         shr_Xsig(&argSq, 2 * (-1 - exponent - 1));
 144         shr_Xsig(&argSqSq, 4 * (-1 - exponent - 1));
 145
 146         /* Now have argSq etc with binary point at the left
 147            .1xxxxxxxx */
 148
 149         /* Do the basic fixed point polynomial evaluation */
 150         accumulator.msw = accumulator.midw = accumulator.lsw = 0;
 151         polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
 152                         oddplterms, HIPOWERop - 1);
 153         mul64_Xsig(&accumulator, &XSIG_LL(argSq));
 154         negate_Xsig(&accumulator);
 155         polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms,
 156                         HIPOWERon - 1);
 157         negate_Xsig(&accumulator);
 158         add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);
 159
 160         mul64_Xsig(&accumulatore, &denomterm);
 161         shr_Xsig(&accumulatore, 1 + 2 * (-1 - exponent));
 162         accumulatore.msw |= 0x80000000;
 163
 164         div_Xsig(&accumulator, &accumulatore, &accumulator);
 165
 166         mul_Xsig_Xsig(&accumulator, &argSignif);
 167         mul_Xsig_Xsig(&accumulator, &argSq);
 168
 169         shr_Xsig(&accumulator, 3);
 170         negate_Xsig(&accumulator);
 171         add_Xsig_Xsig(&accumulator, &argSignif);
 172
 173         if (transformed) {
 174                 /* compute pi/4 - accumulator */
 175                 shr_Xsig(&accumulator, -1 - exponent);
 176                 negate_Xsig(&accumulator);
 177                 add_Xsig_Xsig(&accumulator, &pi_signif);
 178                 exponent = -1;
 179         }
 180
 181         if (inverted) {
 182                 /* compute pi/2 - accumulator */
 183                 shr_Xsig(&accumulator, -exponent);
 184                 negate_Xsig(&accumulator);
 185                 add_Xsig_Xsig(&accumulator, &pi_signif);
 186                 exponent = 0;
 187         }
 188
 189         if (sign1) {
 190                 /* compute pi - accumulator */
 191                 shr_Xsig(&accumulator, 1 - exponent);
 192                 negate_Xsig(&accumulator);
 193                 add_Xsig_Xsig(&accumulator, &pi_signif);
 194                 exponent = 1;
 195         }
 196
 197         exponent += round_Xsig(&accumulator);
 198
 199         significand(st1_ptr) = XSIG_LL(accumulator);
 200         setexponent16(st1_ptr, exponent);
 201
 202         tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
 203         FPU_settagi(1, tag);
 204
 205         set_precision_flag_up();        /* We do not really know if up or down,
 206                                            use this as the default. */
 207
 208 }