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1da177e4 LT |
1 | /*---------------------------------------------------------------------------+ |
2 | | poly_atan.c | | |
3 | | | | |
4 | | Compute the arctan of a FPU_REG, using a polynomial approximation. | | |
5 | | | | |
6 | | Copyright (C) 1992,1993,1994,1997 | | |
7 | | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia | | |
8 | | E-mail billm@suburbia.net | | |
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 "status_w.h" | |
18 | #include "control_w.h" | |
19 | #include "poly.h" | |
20 | ||
21 | ||
22 | #define HIPOWERon 6 /* odd poly, negative terms */ | |
23 | static const unsigned long long oddnegterms[HIPOWERon] = | |
24 | { | |
25 | 0x0000000000000000LL, /* Dummy (not for - 1.0) */ | |
26 | 0x015328437f756467LL, | |
27 | 0x0005dda27b73dec6LL, | |
28 | 0x0000226bf2bfb91aLL, | |
29 | 0x000000ccc439c5f7LL, | |
30 | 0x0000000355438407LL | |
31 | } ; | |
32 | ||
33 | #define HIPOWERop 6 /* odd poly, positive terms */ | |
34 | static const unsigned long long oddplterms[HIPOWERop] = | |
35 | { | |
36 | /* 0xaaaaaaaaaaaaaaabLL, transferred to fixedpterm[] */ | |
37 | 0x0db55a71875c9ac2LL, | |
38 | 0x0029fce2d67880b0LL, | |
39 | 0x0000dfd3908b4596LL, | |
40 | 0x00000550fd61dab4LL, | |
41 | 0x0000001c9422b3f9LL, | |
42 | 0x000000003e3301e1LL | |
43 | }; | |
44 | ||
45 | static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL; | |
46 | ||
47 | static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa); | |
48 | ||
49 | static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b); | |
50 | ||
51 | ||
52 | /*--- poly_atan() -----------------------------------------------------------+ | |
53 | | | | |
54 | +---------------------------------------------------------------------------*/ | |
55 | void poly_atan(FPU_REG *st0_ptr, u_char st0_tag, | |
56 | FPU_REG *st1_ptr, u_char st1_tag) | |
57 | { | |
58 | u_char transformed, inverted, | |
59 | sign1, sign2; | |
60 | int exponent; | |
61 | long int dummy_exp; | |
62 | Xsig accumulator, Numer, Denom, accumulatore, argSignif, | |
63 | argSq, argSqSq; | |
64 | u_char tag; | |
65 | ||
66 | sign1 = getsign(st0_ptr); | |
67 | sign2 = getsign(st1_ptr); | |
68 | if ( st0_tag == TAG_Valid ) | |
69 | { | |
70 | exponent = exponent(st0_ptr); | |
71 | } | |
72 | else | |
73 | { | |
74 | /* This gives non-compatible stack contents... */ | |
75 | FPU_to_exp16(st0_ptr, st0_ptr); | |
76 | exponent = exponent16(st0_ptr); | |
77 | } | |
78 | if ( st1_tag == TAG_Valid ) | |
79 | { | |
80 | exponent -= exponent(st1_ptr); | |
81 | } | |
82 | else | |
83 | { | |
84 | /* This gives non-compatible stack contents... */ | |
85 | FPU_to_exp16(st1_ptr, st1_ptr); | |
86 | exponent -= exponent16(st1_ptr); | |
87 | } | |
88 | ||
89 | if ( (exponent < 0) || ((exponent == 0) && | |
90 | ((st0_ptr->sigh < st1_ptr->sigh) || | |
91 | ((st0_ptr->sigh == st1_ptr->sigh) && | |
92 | (st0_ptr->sigl < st1_ptr->sigl))) ) ) | |
93 | { | |
94 | inverted = 1; | |
95 | Numer.lsw = Denom.lsw = 0; | |
96 | XSIG_LL(Numer) = significand(st0_ptr); | |
97 | XSIG_LL(Denom) = significand(st1_ptr); | |
98 | } | |
99 | else | |
100 | { | |
101 | inverted = 0; | |
102 | exponent = -exponent; | |
103 | Numer.lsw = Denom.lsw = 0; | |
104 | XSIG_LL(Numer) = significand(st1_ptr); | |
105 | XSIG_LL(Denom) = significand(st0_ptr); | |
106 | } | |
107 | div_Xsig(&Numer, &Denom, &argSignif); | |
108 | exponent += norm_Xsig(&argSignif); | |
109 | ||
110 | if ( (exponent >= -1) | |
111 | || ((exponent == -2) && (argSignif.msw > 0xd413ccd0)) ) | |
112 | { | |
113 | /* The argument is greater than sqrt(2)-1 (=0.414213562...) */ | |
114 | /* Convert the argument by an identity for atan */ | |
115 | transformed = 1; | |
116 | ||
117 | if ( exponent >= 0 ) | |
118 | { | |
119 | #ifdef PARANOID | |
120 | if ( !( (exponent == 0) && | |
121 | (argSignif.lsw == 0) && (argSignif.midw == 0) && | |
122 | (argSignif.msw == 0x80000000) ) ) | |
123 | { | |
124 | EXCEPTION(EX_INTERNAL|0x104); /* There must be a logic error */ | |
125 | return; | |
126 | } | |
127 | #endif /* PARANOID */ | |
128 | argSignif.msw = 0; /* Make the transformed arg -> 0.0 */ | |
129 | } | |
130 | else | |
131 | { | |
132 | Numer.lsw = Denom.lsw = argSignif.lsw; | |
133 | XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif); | |
134 | ||
135 | if ( exponent < -1 ) | |
136 | shr_Xsig(&Numer, -1-exponent); | |
137 | negate_Xsig(&Numer); | |
138 | ||
139 | shr_Xsig(&Denom, -exponent); | |
140 | Denom.msw |= 0x80000000; | |
141 | ||
142 | div_Xsig(&Numer, &Denom, &argSignif); | |
143 | ||
144 | exponent = -1 + norm_Xsig(&argSignif); | |
145 | } | |
146 | } | |
147 | else | |
148 | { | |
149 | transformed = 0; | |
150 | } | |
151 | ||
152 | argSq.lsw = argSignif.lsw; argSq.midw = argSignif.midw; | |
153 | argSq.msw = argSignif.msw; | |
154 | mul_Xsig_Xsig(&argSq, &argSq); | |
155 | ||
156 | argSqSq.lsw = argSq.lsw; argSqSq.midw = argSq.midw; argSqSq.msw = argSq.msw; | |
157 | mul_Xsig_Xsig(&argSqSq, &argSqSq); | |
158 | ||
159 | accumulatore.lsw = argSq.lsw; | |
160 | XSIG_LL(accumulatore) = XSIG_LL(argSq); | |
161 | ||
162 | shr_Xsig(&argSq, 2*(-1-exponent-1)); | |
163 | shr_Xsig(&argSqSq, 4*(-1-exponent-1)); | |
164 | ||
165 | /* Now have argSq etc with binary point at the left | |
166 | .1xxxxxxxx */ | |
167 | ||
168 | /* Do the basic fixed point polynomial evaluation */ | |
169 | accumulator.msw = accumulator.midw = accumulator.lsw = 0; | |
170 | polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), | |
171 | oddplterms, HIPOWERop-1); | |
172 | mul64_Xsig(&accumulator, &XSIG_LL(argSq)); | |
173 | negate_Xsig(&accumulator); | |
174 | polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms, HIPOWERon-1); | |
175 | negate_Xsig(&accumulator); | |
176 | add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp); | |
177 | ||
178 | mul64_Xsig(&accumulatore, &denomterm); | |
179 | shr_Xsig(&accumulatore, 1 + 2*(-1-exponent)); | |
180 | accumulatore.msw |= 0x80000000; | |
181 | ||
182 | div_Xsig(&accumulator, &accumulatore, &accumulator); | |
183 | ||
184 | mul_Xsig_Xsig(&accumulator, &argSignif); | |
185 | mul_Xsig_Xsig(&accumulator, &argSq); | |
186 | ||
187 | shr_Xsig(&accumulator, 3); | |
188 | negate_Xsig(&accumulator); | |
189 | add_Xsig_Xsig(&accumulator, &argSignif); | |
190 | ||
191 | if ( transformed ) | |
192 | { | |
193 | /* compute pi/4 - accumulator */ | |
194 | shr_Xsig(&accumulator, -1-exponent); | |
195 | negate_Xsig(&accumulator); | |
196 | add_Xsig_Xsig(&accumulator, &pi_signif); | |
197 | exponent = -1; | |
198 | } | |
199 | ||
200 | if ( inverted ) | |
201 | { | |
202 | /* compute pi/2 - accumulator */ | |
203 | shr_Xsig(&accumulator, -exponent); | |
204 | negate_Xsig(&accumulator); | |
205 | add_Xsig_Xsig(&accumulator, &pi_signif); | |
206 | exponent = 0; | |
207 | } | |
208 | ||
209 | if ( sign1 ) | |
210 | { | |
211 | /* compute pi - accumulator */ | |
212 | shr_Xsig(&accumulator, 1 - exponent); | |
213 | negate_Xsig(&accumulator); | |
214 | add_Xsig_Xsig(&accumulator, &pi_signif); | |
215 | exponent = 1; | |
216 | } | |
217 | ||
218 | exponent += round_Xsig(&accumulator); | |
219 | ||
220 | significand(st1_ptr) = XSIG_LL(accumulator); | |
221 | setexponent16(st1_ptr, exponent); | |
222 | ||
223 | tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2); | |
224 | FPU_settagi(1, tag); | |
225 | ||
226 | set_precision_flag_up(); /* We do not really know if up or down, | |
227 | use this as the default. */ | |
228 | ||
229 | } |