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 */
21 static const unsigned long long oddplterm[HiPOWERop] = {
22 0x0000000000000000LL,
23 0x0051a1cf08fca228LL,
24 0x0000000071284ff7LL
25 };
26
27 #define HiPOWERon 2 /* odd poly, negative terms */
28 static const unsigned long long oddnegterm[HiPOWERon] = {
29 0x1291a9a184244e80LL,
30 0x0000583245819c21LL
31 };
32
33 #define HiPOWERep 2 /* even poly, positive terms */
34 static const unsigned long long evenplterm[HiPOWERep] = {
35 0x0e848884b539e888LL,
36 0x00003c7f18b887daLL
37 };
38
39 #define HiPOWERen 2 /* even poly, negative terms */
40 static const unsigned long long evennegterm[HiPOWERen] = {
41 0xf1f0200fd51569ccLL,
42 0x003afb46105c4432LL
43 };
44
45 static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL;
46
47 /*--- poly_tan() ------------------------------------------------------------+
48 | |
49 +---------------------------------------------------------------------------*/
50 void 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
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