poly_tan.c (6947B)
1// SPDX-License-Identifier: GPL-2.0 2/*---------------------------------------------------------------------------+ 3 | poly_tan.c | 4 | | 5 | Compute the tan of a FPU_REG, using a polynomial approximation. | 6 | | 7 | Copyright (C) 1992,1993,1994,1997,1999 | 8 | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, | 9 | Australia. E-mail billm@melbpc.org.au | 10 | | 11 | | 12 +---------------------------------------------------------------------------*/ 13 14#include "exception.h" 15#include "reg_constant.h" 16#include "fpu_emu.h" 17#include "fpu_system.h" 18#include "control_w.h" 19#include "poly.h" 20 21#define HiPOWERop 3 /* odd poly, positive terms */ 22static const unsigned long long oddplterm[HiPOWERop] = { 23 0x0000000000000000LL, 24 0x0051a1cf08fca228LL, 25 0x0000000071284ff7LL 26}; 27 28#define HiPOWERon 2 /* odd poly, negative terms */ 29static const unsigned long long oddnegterm[HiPOWERon] = { 30 0x1291a9a184244e80LL, 31 0x0000583245819c21LL 32}; 33 34#define HiPOWERep 2 /* even poly, positive terms */ 35static const unsigned long long evenplterm[HiPOWERep] = { 36 0x0e848884b539e888LL, 37 0x00003c7f18b887daLL 38}; 39 40#define HiPOWERen 2 /* even poly, negative terms */ 41static const unsigned long long evennegterm[HiPOWERen] = { 42 0xf1f0200fd51569ccLL, 43 0x003afb46105c4432LL 44}; 45 46static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL; 47 48/*--- poly_tan() ------------------------------------------------------------+ 49 | | 50 +---------------------------------------------------------------------------*/ 51void poly_tan(FPU_REG *st0_ptr) 52{ 53 long int exponent; 54 int invert; 55 Xsig argSq, argSqSq, accumulatoro, accumulatore, accum, 56 argSignif, fix_up; 57 unsigned long adj; 58 59 exponent = exponent(st0_ptr); 60 61#ifdef PARANOID 62 if (signnegative(st0_ptr)) { /* Can't hack a number < 0.0 */ 63 arith_invalid(0); 64 return; 65 } /* Need a positive number */ 66#endif /* PARANOID */ 67 68 /* Split the problem into two domains, smaller and larger than pi/4 */ 69 if ((exponent == 0) 70 || ((exponent == -1) && (st0_ptr->sigh > 0xc90fdaa2))) { 71 /* The argument is greater than (approx) pi/4 */ 72 invert = 1; 73 accum.lsw = 0; 74 XSIG_LL(accum) = significand(st0_ptr); 75 76 if (exponent == 0) { 77 /* The argument is >= 1.0 */ 78 /* Put the binary point at the left. */ 79 XSIG_LL(accum) <<= 1; 80 } 81 /* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */ 82 XSIG_LL(accum) = 0x921fb54442d18469LL - XSIG_LL(accum); 83 /* This is a special case which arises due to rounding. */ 84 if (XSIG_LL(accum) == 0xffffffffffffffffLL) { 85 FPU_settag0(TAG_Valid); 86 significand(st0_ptr) = 0x8a51e04daabda360LL; 87 setexponent16(st0_ptr, 88 (0x41 + EXTENDED_Ebias) | SIGN_Negative); 89 return; 90 } 91 92 argSignif.lsw = accum.lsw; 93 XSIG_LL(argSignif) = XSIG_LL(accum); 94 exponent = -1 + norm_Xsig(&argSignif); 95 } else { 96 invert = 0; 97 argSignif.lsw = 0; 98 XSIG_LL(accum) = XSIG_LL(argSignif) = significand(st0_ptr); 99 100 if (exponent < -1) { 101 /* shift the argument right by the required places */ 102 if (FPU_shrx(&XSIG_LL(accum), -1 - exponent) >= 103 0x80000000U) 104 XSIG_LL(accum)++; /* round up */ 105 } 106 } 107 108 XSIG_LL(argSq) = XSIG_LL(accum); 109 argSq.lsw = accum.lsw; 110 mul_Xsig_Xsig(&argSq, &argSq); 111 XSIG_LL(argSqSq) = XSIG_LL(argSq); 112 argSqSq.lsw = argSq.lsw; 113 mul_Xsig_Xsig(&argSqSq, &argSqSq); 114 115 /* Compute the negative terms for the numerator polynomial */ 116 accumulatoro.msw = accumulatoro.midw = accumulatoro.lsw = 0; 117 polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddnegterm, 118 HiPOWERon - 1); 119 mul_Xsig_Xsig(&accumulatoro, &argSq); 120 negate_Xsig(&accumulatoro); 121 /* Add the positive terms */ 122 polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddplterm, 123 HiPOWERop - 1); 124 125 /* Compute the positive terms for the denominator polynomial */ 126 accumulatore.msw = accumulatore.midw = accumulatore.lsw = 0; 127 polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evenplterm, 128 HiPOWERep - 1); 129 mul_Xsig_Xsig(&accumulatore, &argSq); 130 negate_Xsig(&accumulatore); 131 /* Add the negative terms */ 132 polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evennegterm, 133 HiPOWERen - 1); 134 /* Multiply by arg^2 */ 135 mul64_Xsig(&accumulatore, &XSIG_LL(argSignif)); 136 mul64_Xsig(&accumulatore, &XSIG_LL(argSignif)); 137 /* de-normalize and divide by 2 */ 138 shr_Xsig(&accumulatore, -2 * (1 + exponent) + 1); 139 negate_Xsig(&accumulatore); /* This does 1 - accumulator */ 140 141 /* Now find the ratio. */ 142 if (accumulatore.msw == 0) { 143 /* accumulatoro must contain 1.0 here, (actually, 0) but it 144 really doesn't matter what value we use because it will 145 have negligible effect in later calculations 146 */ 147 XSIG_LL(accum) = 0x8000000000000000LL; 148 accum.lsw = 0; 149 } else { 150 div_Xsig(&accumulatoro, &accumulatore, &accum); 151 } 152 153 /* Multiply by 1/3 * arg^3 */ 154 mul64_Xsig(&accum, &XSIG_LL(argSignif)); 155 mul64_Xsig(&accum, &XSIG_LL(argSignif)); 156 mul64_Xsig(&accum, &XSIG_LL(argSignif)); 157 mul64_Xsig(&accum, &twothirds); 158 shr_Xsig(&accum, -2 * (exponent + 1)); 159 160 /* tan(arg) = arg + accum */ 161 add_two_Xsig(&accum, &argSignif, &exponent); 162 163 if (invert) { 164 /* We now have the value of tan(pi_2 - arg) where pi_2 is an 165 approximation for pi/2 166 */ 167 /* The next step is to fix the answer to compensate for the 168 error due to the approximation used for pi/2 169 */ 170 171 /* This is (approx) delta, the error in our approx for pi/2 172 (see above). It has an exponent of -65 173 */ 174 XSIG_LL(fix_up) = 0x898cc51701b839a2LL; 175 fix_up.lsw = 0; 176 177 if (exponent == 0) 178 adj = 0xffffffff; /* We want approx 1.0 here, but 179 this is close enough. */ 180 else if (exponent > -30) { 181 adj = accum.msw >> -(exponent + 1); /* tan */ 182 adj = mul_32_32(adj, adj); /* tan^2 */ 183 } else 184 adj = 0; 185 adj = mul_32_32(0x898cc517, adj); /* delta * tan^2 */ 186 187 fix_up.msw += adj; 188 if (!(fix_up.msw & 0x80000000)) { /* did fix_up overflow ? */ 189 /* Yes, we need to add an msb */ 190 shr_Xsig(&fix_up, 1); 191 fix_up.msw |= 0x80000000; 192 shr_Xsig(&fix_up, 64 + exponent); 193 } else 194 shr_Xsig(&fix_up, 65 + exponent); 195 196 add_two_Xsig(&accum, &fix_up, &exponent); 197 198 /* accum now contains tan(pi/2 - arg). 199 Use tan(arg) = 1.0 / tan(pi/2 - arg) 200 */ 201 accumulatoro.lsw = accumulatoro.midw = 0; 202 accumulatoro.msw = 0x80000000; 203 div_Xsig(&accumulatoro, &accum, &accum); 204 exponent = -exponent - 1; 205 } 206 207 /* Transfer the result */ 208 round_Xsig(&accum); 209 FPU_settag0(TAG_Valid); 210 significand(st0_ptr) = XSIG_LL(accum); 211 setexponent16(st0_ptr, exponent + EXTENDED_Ebias); /* Result is positive. */ 212 213}