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 */
22 static const unsigned long long oddplterm[HiPOWERop] = {
23 	0x0000000000000000LL,
24 	0x0051a1cf08fca228LL,
25 	0x0000000071284ff7LL
26 };
27 
28 #define	HiPOWERon	2	/* odd poly, negative terms */
29 static const unsigned long long oddnegterm[HiPOWERon] = {
30 	0x1291a9a184244e80LL,
31 	0x0000583245819c21LL
32 };
33 
34 #define	HiPOWERep	2	/* even poly, positive terms */
35 static const unsigned long long evenplterm[HiPOWERep] = {
36 	0x0e848884b539e888LL,
37 	0x00003c7f18b887daLL
38 };
39 
40 #define	HiPOWERen	2	/* even poly, negative terms */
41 static const unsigned long long evennegterm[HiPOWERen] = {
42 	0xf1f0200fd51569ccLL,
43 	0x003afb46105c4432LL
44 };
45 
46 static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL;
47 
48 /*--- poly_tan() ------------------------------------------------------------+
49  |                                                                           |
50  +---------------------------------------------------------------------------*/
poly_tan(FPU_REG * st0_ptr)51 void 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 }
214