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