]>
Commit | Line | Data |
---|---|---|
b2441318 | 1 | // SPDX-License-Identifier: GPL-2.0 |
1da177e4 LT |
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 | ||
1da177e4 | 22 | #define HIPOWERon 6 /* odd poly, negative terms */ |
3d0d14f9 IM |
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 | }; | |
1da177e4 LT |
31 | |
32 | #define HIPOWERop 6 /* odd poly, positive terms */ | |
3d0d14f9 | 33 | static const unsigned long long oddplterms[HIPOWERop] = { |
1da177e4 | 34 | /* 0xaaaaaaaaaaaaaaabLL, transferred to fixedpterm[] */ |
3d0d14f9 IM |
35 | 0x0db55a71875c9ac2LL, |
36 | 0x0029fce2d67880b0LL, | |
37 | 0x0000dfd3908b4596LL, | |
38 | 0x00000550fd61dab4LL, | |
39 | 0x0000001c9422b3f9LL, | |
40 | 0x000000003e3301e1LL | |
1da177e4 LT |
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 | ||
1da177e4 LT |
49 | /*--- poly_atan() -----------------------------------------------------------+ |
50 | | | | |
51 | +---------------------------------------------------------------------------*/ | |
e8d591dc IM |
52 | void poly_atan(FPU_REG *st0_ptr, u_char st0_tag, |
53 | FPU_REG *st1_ptr, u_char st1_tag) | |
1da177e4 | 54 | { |
3d0d14f9 IM |
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) { | |
1da177e4 | 103 | #ifdef PARANOID |
3d0d14f9 IM |
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 | } | |
1da177e4 | 110 | #endif /* PARANOID */ |
3d0d14f9 IM |
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; | |
1da177e4 | 188 | } |
3d0d14f9 IM |
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; | |
1da177e4 | 196 | } |
3d0d14f9 IM |
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. */ | |
1da177e4 LT |
208 | |
209 | } |