Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 | |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 21 | #define HIPOWERon 6 /* odd poly, negative terms */ |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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 | }; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 30 | |
| 31 | #define HIPOWERop 6 /* odd poly, positive terms */ |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 32 | static const unsigned long long oddplterms[HIPOWERop] = { |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 33 | /* 0xaaaaaaaaaaaaaaabLL, transferred to fixedpterm[] */ |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 34 | 0x0db55a71875c9ac2LL, |
| 35 | 0x0029fce2d67880b0LL, |
| 36 | 0x0000dfd3908b4596LL, |
| 37 | 0x00000550fd61dab4LL, |
| 38 | 0x0000001c9422b3f9LL, |
| 39 | 0x000000003e3301e1LL |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 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 | |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 48 | /*--- poly_atan() -----------------------------------------------------------+ |
| 49 | | | |
| 50 | +---------------------------------------------------------------------------*/ |
Ingo Molnar | e8d591d | 2008-01-30 13:30:12 +0100 | [diff] [blame^] | 51 | void poly_atan(FPU_REG *st0_ptr, u_char st0_tag, |
| 52 | FPU_REG *st1_ptr, u_char st1_tag) |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 53 | { |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 59 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 76 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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); |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 94 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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) { |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 102 | #ifdef PARANOID |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 109 | #endif /* PARANOID */ |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 128 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 129 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 130 | argSq.lsw = argSignif.lsw; |
| 131 | argSq.midw = argSignif.midw; |
| 132 | argSq.msw = argSignif.msw; |
| 133 | mul_Xsig_Xsig(&argSq, &argSq); |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 134 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 179 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 180 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 188 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 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 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 196 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 197 | exponent += round_Xsig(&accumulator); |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 198 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 199 | significand(st1_ptr) = XSIG_LL(accumulator); |
| 200 | setexponent16(st1_ptr, exponent); |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 201 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 202 | tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2); |
| 203 | FPU_settagi(1, tag); |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 204 | |
Ingo Molnar | 3d0d14f | 2008-01-30 13:30:11 +0100 | [diff] [blame] | 205 | set_precision_flag_up(); /* We do not really know if up or down, |
| 206 | use this as the default. */ |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 207 | |
| 208 | } |