1 // SPDX-License-Identifier: GPL-2.0
2 /*---------------------------------------------------------------------------+
3  |  poly_atan.c                                                              |
4  |                                                                           |
5  | Compute the arctan of a FPU_REG, using a polynomial approximation.        |
6  |                                                                           |
7  | Copyright (C) 1992,1993,1994,1997                                         |
8  |                  W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
9  |                  E-mail   billm@suburbia.net                              |
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 "status_w.h"
19 #include "control_w.h"
20 #include "poly.h"
21 
22 #define	HIPOWERon	6	/* odd poly, negative terms */
23 static const unsigned long long oddnegterms[HIPOWERon] = {
24 	0x0000000000000000LL,	/* Dummy (not for - 1.0) */
25 	0x015328437f756467LL,
26 	0x0005dda27b73dec6LL,
27 	0x0000226bf2bfb91aLL,
28 	0x000000ccc439c5f7LL,
29 	0x0000000355438407LL
30 };
31 
32 #define	HIPOWERop	6	/* odd poly, positive terms */
33 static const unsigned long long oddplterms[HIPOWERop] = {
34 /*  0xaaaaaaaaaaaaaaabLL,  transferred to fixedpterm[] */
35 	0x0db55a71875c9ac2LL,
36 	0x0029fce2d67880b0LL,
37 	0x0000dfd3908b4596LL,
38 	0x00000550fd61dab4LL,
39 	0x0000001c9422b3f9LL,
40 	0x000000003e3301e1LL
41 };
42 
43 static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL;
44 
45 static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa);
46 
47 static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b);
48 
49 /*--- poly_atan() -----------------------------------------------------------+
50  |                                                                           |
51  +---------------------------------------------------------------------------*/
poly_atan(FPU_REG * st0_ptr,u_char st0_tag,FPU_REG * st1_ptr,u_char st1_tag)52 void poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
53 	       FPU_REG *st1_ptr, u_char st1_tag)
54 {
55 	u_char transformed, inverted, sign1, sign2;
56 	int exponent;
57 	long int dummy_exp;
58 	Xsig accumulator, Numer, Denom, accumulatore, argSignif, argSq, argSqSq;
59 	u_char tag;
60 
61 	sign1 = getsign(st0_ptr);
62 	sign2 = getsign(st1_ptr);
63 	if (st0_tag == TAG_Valid) {
64 		exponent = exponent(st0_ptr);
65 	} else {
66 		/* This gives non-compatible stack contents... */
67 		FPU_to_exp16(st0_ptr, st0_ptr);
68 		exponent = exponent16(st0_ptr);
69 	}
70 	if (st1_tag == TAG_Valid) {
71 		exponent -= exponent(st1_ptr);
72 	} else {
73 		/* This gives non-compatible stack contents... */
74 		FPU_to_exp16(st1_ptr, st1_ptr);
75 		exponent -= exponent16(st1_ptr);
76 	}
77 
78 	if ((exponent < 0) || ((exponent == 0) &&
79 			       ((st0_ptr->sigh < st1_ptr->sigh) ||
80 				((st0_ptr->sigh == st1_ptr->sigh) &&
81 				 (st0_ptr->sigl < st1_ptr->sigl))))) {
82 		inverted = 1;
83 		Numer.lsw = Denom.lsw = 0;
84 		XSIG_LL(Numer) = significand(st0_ptr);
85 		XSIG_LL(Denom) = significand(st1_ptr);
86 	} else {
87 		inverted = 0;
88 		exponent = -exponent;
89 		Numer.lsw = Denom.lsw = 0;
90 		XSIG_LL(Numer) = significand(st1_ptr);
91 		XSIG_LL(Denom) = significand(st0_ptr);
92 	}
93 	div_Xsig(&Numer, &Denom, &argSignif);
94 	exponent += norm_Xsig(&argSignif);
95 
96 	if ((exponent >= -1)
97 	    || ((exponent == -2) && (argSignif.msw > 0xd413ccd0))) {
98 		/* The argument is greater than sqrt(2)-1 (=0.414213562...) */
99 		/* Convert the argument by an identity for atan */
100 		transformed = 1;
101 
102 		if (exponent >= 0) {
103 #ifdef PARANOID
104 			if (!((exponent == 0) &&
105 			      (argSignif.lsw == 0) && (argSignif.midw == 0) &&
106 			      (argSignif.msw == 0x80000000))) {
107 				EXCEPTION(EX_INTERNAL | 0x104);	/* There must be a logic error */
108 				return;
109 			}
110 #endif /* PARANOID */
111 			argSignif.msw = 0;	/* Make the transformed arg -> 0.0 */
112 		} else {
113 			Numer.lsw = Denom.lsw = argSignif.lsw;
114 			XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);
115 
116 			if (exponent < -1)
117 				shr_Xsig(&Numer, -1 - exponent);
118 			negate_Xsig(&Numer);
119 
120 			shr_Xsig(&Denom, -exponent);
121 			Denom.msw |= 0x80000000;
122 
123 			div_Xsig(&Numer, &Denom, &argSignif);
124 
125 			exponent = -1 + norm_Xsig(&argSignif);
126 		}
127 	} else {
128 		transformed = 0;
129 	}
130 
131 	argSq.lsw = argSignif.lsw;
132 	argSq.midw = argSignif.midw;
133 	argSq.msw = argSignif.msw;
134 	mul_Xsig_Xsig(&argSq, &argSq);
135 
136 	argSqSq.lsw = argSq.lsw;
137 	argSqSq.midw = argSq.midw;
138 	argSqSq.msw = argSq.msw;
139 	mul_Xsig_Xsig(&argSqSq, &argSqSq);
140 
141 	accumulatore.lsw = argSq.lsw;
142 	XSIG_LL(accumulatore) = XSIG_LL(argSq);
143 
144 	shr_Xsig(&argSq, 2 * (-1 - exponent - 1));
145 	shr_Xsig(&argSqSq, 4 * (-1 - exponent - 1));
146 
147 	/* Now have argSq etc with binary point at the left
148 	   .1xxxxxxxx */
149 
150 	/* Do the basic fixed point polynomial evaluation */
151 	accumulator.msw = accumulator.midw = accumulator.lsw = 0;
152 	polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
153 			oddplterms, HIPOWERop - 1);
154 	mul64_Xsig(&accumulator, &XSIG_LL(argSq));
155 	negate_Xsig(&accumulator);
156 	polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms,
157 			HIPOWERon - 1);
158 	negate_Xsig(&accumulator);
159 	add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);
160 
161 	mul64_Xsig(&accumulatore, &denomterm);
162 	shr_Xsig(&accumulatore, 1 + 2 * (-1 - exponent));
163 	accumulatore.msw |= 0x80000000;
164 
165 	div_Xsig(&accumulator, &accumulatore, &accumulator);
166 
167 	mul_Xsig_Xsig(&accumulator, &argSignif);
168 	mul_Xsig_Xsig(&accumulator, &argSq);
169 
170 	shr_Xsig(&accumulator, 3);
171 	negate_Xsig(&accumulator);
172 	add_Xsig_Xsig(&accumulator, &argSignif);
173 
174 	if (transformed) {
175 		/* compute pi/4 - accumulator */
176 		shr_Xsig(&accumulator, -1 - exponent);
177 		negate_Xsig(&accumulator);
178 		add_Xsig_Xsig(&accumulator, &pi_signif);
179 		exponent = -1;
180 	}
181 
182 	if (inverted) {
183 		/* compute pi/2 - accumulator */
184 		shr_Xsig(&accumulator, -exponent);
185 		negate_Xsig(&accumulator);
186 		add_Xsig_Xsig(&accumulator, &pi_signif);
187 		exponent = 0;
188 	}
189 
190 	if (sign1) {
191 		/* compute pi - accumulator */
192 		shr_Xsig(&accumulator, 1 - exponent);
193 		negate_Xsig(&accumulator);
194 		add_Xsig_Xsig(&accumulator, &pi_signif);
195 		exponent = 1;
196 	}
197 
198 	exponent += round_Xsig(&accumulator);
199 
200 	significand(st1_ptr) = XSIG_LL(accumulator);
201 	setexponent16(st1_ptr, exponent);
202 
203 	tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
204 	FPU_settagi(1, tag);
205 
206 	set_precision_flag_up();	/* We do not really know if up or down,
207 					   use this as the default. */
208 
209 }
210