KVM: emulator: emulate AAM
[linux-3.10.git] / arch / x86 / math-emu / poly_tan.c
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 }