1/*---------------------------------------------------------------------------+ 2 | poly_tan.c | 3 | | 4 | Compute the tan of a FPU_REG, using a polynomial approximation. | 5 | | 6 | Copyright (C) 1992,1993,1994,1997,1999 | 7 | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, | 8 | Australia. E-mail billm@melbpc.org.au | 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#define HiPOWERop 3 /* odd poly, positive terms */ 21static const unsigned long long oddplterm[HiPOWERop] = { 22 0x0000000000000000LL, 23 0x0051a1cf08fca228LL, 24 0x0000000071284ff7LL 25}; 26 27#define HiPOWERon 2 /* odd poly, negative terms */ 28static const unsigned long long oddnegterm[HiPOWERon] = { 29 0x1291a9a184244e80LL, 30 0x0000583245819c21LL 31}; 32 33#define HiPOWERep 2 /* even poly, positive terms */ 34static const unsigned long long evenplterm[HiPOWERep] = { 35 0x0e848884b539e888LL, 36 0x00003c7f18b887daLL 37}; 38 39#define HiPOWERen 2 /* even poly, negative terms */ 40static const unsigned long long evennegterm[HiPOWERen] = { 41 0xf1f0200fd51569ccLL, 42 0x003afb46105c4432LL 43}; 44 45static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL; 46 47/*--- poly_tan() ------------------------------------------------------------+ 48 | | 49 +---------------------------------------------------------------------------*/ 50void poly_tan(FPU_REG *st0_ptr) 51{ 52 long int exponent; 53 int invert; 54 Xsig argSq, argSqSq, accumulatoro, accumulatore, accum, 55 argSignif, fix_up; 56 unsigned long adj; 57 58 exponent = exponent(st0_ptr); 59 60#ifdef PARANOID 61 if (signnegative(st0_ptr)) { /* Can't hack a number < 0.0 */ 62 arith_invalid(0); 63 return; 64 } /* Need a positive number */ 65#endif /* PARANOID */ 66 67 /* Split the problem into two domains, smaller and larger than pi/4 */ 68 if ((exponent == 0) 69 || ((exponent == -1) && (st0_ptr->sigh > 0xc90fdaa2))) { 70 /* The argument is greater than (approx) pi/4 */ 71 invert = 1; 72 accum.lsw = 0; 73 XSIG_LL(accum) = significand(st0_ptr); 74 75 if (exponent == 0) { 76 /* The argument is >= 1.0 */ 77 /* Put the binary point at the left. */ 78 XSIG_LL(accum) <<= 1; 79 } 80 /* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */ 81 XSIG_LL(accum) = 0x921fb54442d18469LL - XSIG_LL(accum); 82 /* This is a special case which arises due to rounding. */ 83 if (XSIG_LL(accum) == 0xffffffffffffffffLL) { 84 FPU_settag0(TAG_Valid); 85 significand(st0_ptr) = 0x8a51e04daabda360LL; 86 setexponent16(st0_ptr, 87 (0x41 + EXTENDED_Ebias) | SIGN_Negative); 88 return; 89 } 90 91 argSignif.lsw = accum.lsw; 92 XSIG_LL(argSignif) = XSIG_LL(accum); 93 exponent = -1 + norm_Xsig(&argSignif); 94 } else { 95 invert = 0; 96 argSignif.lsw = 0; 97 XSIG_LL(accum) = XSIG_LL(argSignif) = significand(st0_ptr); 98 99 if (exponent < -1) { 100 /* shift the argument right by the required places */ 101 if (FPU_shrx(&XSIG_LL(accum), -1 - exponent) >= 102 0x80000000U) 103 XSIG_LL(accum)++; /* round up */ 104 } 105 } 106 107 XSIG_LL(argSq) = XSIG_LL(accum); 108 argSq.lsw = accum.lsw; 109 mul_Xsig_Xsig(&argSq, &argSq); 110 XSIG_LL(argSqSq) = XSIG_LL(argSq); 111 argSqSq.lsw = argSq.lsw; 112 mul_Xsig_Xsig(&argSqSq, &argSqSq); 113 114 /* Compute the negative terms for the numerator polynomial */ 115 accumulatoro.msw = accumulatoro.midw = accumulatoro.lsw = 0; 116 polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddnegterm, 117 HiPOWERon - 1); 118 mul_Xsig_Xsig(&accumulatoro, &argSq); 119 negate_Xsig(&accumulatoro); 120 /* Add the positive terms */ 121 polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddplterm, 122 HiPOWERop - 1); 123 124 /* Compute the positive terms for the denominator polynomial */ 125 accumulatore.msw = accumulatore.midw = accumulatore.lsw = 0; 126 polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evenplterm, 127 HiPOWERep - 1); 128 mul_Xsig_Xsig(&accumulatore, &argSq); 129 negate_Xsig(&accumulatore); 130 /* Add the negative terms */ 131 polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evennegterm, 132 HiPOWERen - 1); 133 /* Multiply by arg^2 */ 134 mul64_Xsig(&accumulatore, &XSIG_LL(argSignif)); 135 mul64_Xsig(&accumulatore, &XSIG_LL(argSignif)); 136 /* de-normalize and divide by 2 */ 137 shr_Xsig(&accumulatore, -2 * (1 + exponent) + 1); 138 negate_Xsig(&accumulatore); /* This does 1 - accumulator */ 139 140 /* Now find the ratio. */ 141 if (accumulatore.msw == 0) { 142 /* accumulatoro must contain 1.0 here, (actually, 0) but it 143 really doesn't matter what value we use because it will 144 have negligible effect in later calculations 145 */ 146 XSIG_LL(accum) = 0x8000000000000000LL; 147 accum.lsw = 0; 148 } else { 149 div_Xsig(&accumulatoro, &accumulatore, &accum); 150 } 151 152 /* Multiply by 1/3 * arg^3 */ 153 mul64_Xsig(&accum, &XSIG_LL(argSignif)); 154 mul64_Xsig(&accum, &XSIG_LL(argSignif)); 155 mul64_Xsig(&accum, &XSIG_LL(argSignif)); 156 mul64_Xsig(&accum, &twothirds); 157 shr_Xsig(&accum, -2 * (exponent + 1)); 158 159 /* tan(arg) = arg + accum */ 160 add_two_Xsig(&accum, &argSignif, &exponent); 161 162 if (invert) { 163 /* We now have the value of tan(pi_2 - arg) where pi_2 is an 164 approximation for pi/2 165 */ 166 /* The next step is to fix the answer to compensate for the 167 error due to the approximation used for pi/2 168 */ 169 170 /* This is (approx) delta, the error in our approx for pi/2 171 (see above). It has an exponent of -65 172 */ 173 XSIG_LL(fix_up) = 0x898cc51701b839a2LL; 174 fix_up.lsw = 0; 175 176 if (exponent == 0) 177 adj = 0xffffffff; /* We want approx 1.0 here, but 178 this is close enough. */ 179 else if (exponent > -30) { 180 adj = accum.msw >> -(exponent + 1); /* tan */ 181 adj = mul_32_32(adj, adj); /* tan^2 */ 182 } else 183 adj = 0; 184 adj = mul_32_32(0x898cc517, adj); /* delta * tan^2 */ 185 186 fix_up.msw += adj; 187 if (!(fix_up.msw & 0x80000000)) { /* did fix_up overflow ? */ 188 /* Yes, we need to add an msb */ 189 shr_Xsig(&fix_up, 1); 190 fix_up.msw |= 0x80000000; 191 shr_Xsig(&fix_up, 64 + exponent); 192 } else 193 shr_Xsig(&fix_up, 65 + exponent); 194 195 add_two_Xsig(&accum, &fix_up, &exponent); 196 197 /* accum now contains tan(pi/2 - arg). 198 Use tan(arg) = 1.0 / tan(pi/2 - arg) 199 */ 200 accumulatoro.lsw = accumulatoro.midw = 0; 201 accumulatoro.msw = 0x80000000; 202 div_Xsig(&accumulatoro, &accum, &accum); 203 exponent = -exponent - 1; 204 } 205 206 /* Transfer the result */ 207 round_Xsig(&accum); 208 FPU_settag0(TAG_Valid); 209 significand(st0_ptr) = XSIG_LL(accum); 210 setexponent16(st0_ptr, exponent + EXTENDED_Ebias); /* Result is positive. */ 211 212} 213