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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 | ||
1da177e4 | 21 | #define HIPOWERon 6 /* odd poly, negative terms */ |
3d0d14f9 IM |
22 | static const unsigned long long oddnegterms[HIPOWERon] = { |
23 | 0x0000000000000000LL, /* Dummy (not for - 1.0) */ | |
24 | 0x015328437f756467LL, | |
25 | 0x0005dda27b73dec6LL, | |
26 | 0x0000226bf2bfb91aLL, | |
27 | 0x000000ccc439c5f7LL, | |
28 | 0x0000000355438407LL | |
29 | }; | |
1da177e4 LT |
30 | |
31 | #define HIPOWERop 6 /* odd poly, positive terms */ | |
3d0d14f9 | 32 | static const unsigned long long oddplterms[HIPOWERop] = { |
1da177e4 | 33 | /* 0xaaaaaaaaaaaaaaabLL, transferred to fixedpterm[] */ |
3d0d14f9 IM |
34 | 0x0db55a71875c9ac2LL, |
35 | 0x0029fce2d67880b0LL, | |
36 | 0x0000dfd3908b4596LL, | |
37 | 0x00000550fd61dab4LL, | |
38 | 0x0000001c9422b3f9LL, | |
39 | 0x000000003e3301e1LL | |
1da177e4 LT |
40 | }; |
41 | ||
42 | static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL; | |
43 | ||
44 | static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa); | |
45 | ||
46 | static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b); | |
47 | ||
1da177e4 LT |
48 | /*--- poly_atan() -----------------------------------------------------------+ |
49 | | | | |
50 | +---------------------------------------------------------------------------*/ | |
3d0d14f9 IM |
51 | void poly_atan(FPU_REG * st0_ptr, u_char st0_tag, |
52 | FPU_REG * st1_ptr, u_char st1_tag) | |
1da177e4 | 53 | { |
3d0d14f9 IM |
54 | u_char transformed, inverted, sign1, sign2; |
55 | int exponent; | |
56 | long int dummy_exp; | |
57 | Xsig accumulator, Numer, Denom, accumulatore, argSignif, argSq, argSqSq; | |
58 | u_char tag; | |
59 | ||
60 | sign1 = getsign(st0_ptr); | |
61 | sign2 = getsign(st1_ptr); | |
62 | if (st0_tag == TAG_Valid) { | |
63 | exponent = exponent(st0_ptr); | |
64 | } else { | |
65 | /* This gives non-compatible stack contents... */ | |
66 | FPU_to_exp16(st0_ptr, st0_ptr); | |
67 | exponent = exponent16(st0_ptr); | |
68 | } | |
69 | if (st1_tag == TAG_Valid) { | |
70 | exponent -= exponent(st1_ptr); | |
71 | } else { | |
72 | /* This gives non-compatible stack contents... */ | |
73 | FPU_to_exp16(st1_ptr, st1_ptr); | |
74 | exponent -= exponent16(st1_ptr); | |
75 | } | |
76 | ||
77 | if ((exponent < 0) || ((exponent == 0) && | |
78 | ((st0_ptr->sigh < st1_ptr->sigh) || | |
79 | ((st0_ptr->sigh == st1_ptr->sigh) && | |
80 | (st0_ptr->sigl < st1_ptr->sigl))))) { | |
81 | inverted = 1; | |
82 | Numer.lsw = Denom.lsw = 0; | |
83 | XSIG_LL(Numer) = significand(st0_ptr); | |
84 | XSIG_LL(Denom) = significand(st1_ptr); | |
85 | } else { | |
86 | inverted = 0; | |
87 | exponent = -exponent; | |
88 | Numer.lsw = Denom.lsw = 0; | |
89 | XSIG_LL(Numer) = significand(st1_ptr); | |
90 | XSIG_LL(Denom) = significand(st0_ptr); | |
91 | } | |
92 | div_Xsig(&Numer, &Denom, &argSignif); | |
93 | exponent += norm_Xsig(&argSignif); | |
94 | ||
95 | if ((exponent >= -1) | |
96 | || ((exponent == -2) && (argSignif.msw > 0xd413ccd0))) { | |
97 | /* The argument is greater than sqrt(2)-1 (=0.414213562...) */ | |
98 | /* Convert the argument by an identity for atan */ | |
99 | transformed = 1; | |
100 | ||
101 | if (exponent >= 0) { | |
1da177e4 | 102 | #ifdef PARANOID |
3d0d14f9 IM |
103 | if (!((exponent == 0) && |
104 | (argSignif.lsw == 0) && (argSignif.midw == 0) && | |
105 | (argSignif.msw == 0x80000000))) { | |
106 | EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic error */ | |
107 | return; | |
108 | } | |
1da177e4 | 109 | #endif /* PARANOID */ |
3d0d14f9 IM |
110 | argSignif.msw = 0; /* Make the transformed arg -> 0.0 */ |
111 | } else { | |
112 | Numer.lsw = Denom.lsw = argSignif.lsw; | |
113 | XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif); | |
114 | ||
115 | if (exponent < -1) | |
116 | shr_Xsig(&Numer, -1 - exponent); | |
117 | negate_Xsig(&Numer); | |
118 | ||
119 | shr_Xsig(&Denom, -exponent); | |
120 | Denom.msw |= 0x80000000; | |
121 | ||
122 | div_Xsig(&Numer, &Denom, &argSignif); | |
123 | ||
124 | exponent = -1 + norm_Xsig(&argSignif); | |
125 | } | |
126 | } else { | |
127 | transformed = 0; | |
128 | } | |
129 | ||
130 | argSq.lsw = argSignif.lsw; | |
131 | argSq.midw = argSignif.midw; | |
132 | argSq.msw = argSignif.msw; | |
133 | mul_Xsig_Xsig(&argSq, &argSq); | |
134 | ||
135 | argSqSq.lsw = argSq.lsw; | |
136 | argSqSq.midw = argSq.midw; | |
137 | argSqSq.msw = argSq.msw; | |
138 | mul_Xsig_Xsig(&argSqSq, &argSqSq); | |
139 | ||
140 | accumulatore.lsw = argSq.lsw; | |
141 | XSIG_LL(accumulatore) = XSIG_LL(argSq); | |
142 | ||
143 | shr_Xsig(&argSq, 2 * (-1 - exponent - 1)); | |
144 | shr_Xsig(&argSqSq, 4 * (-1 - exponent - 1)); | |
145 | ||
146 | /* Now have argSq etc with binary point at the left | |
147 | .1xxxxxxxx */ | |
148 | ||
149 | /* Do the basic fixed point polynomial evaluation */ | |
150 | accumulator.msw = accumulator.midw = accumulator.lsw = 0; | |
151 | polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), | |
152 | oddplterms, HIPOWERop - 1); | |
153 | mul64_Xsig(&accumulator, &XSIG_LL(argSq)); | |
154 | negate_Xsig(&accumulator); | |
155 | polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms, | |
156 | HIPOWERon - 1); | |
157 | negate_Xsig(&accumulator); | |
158 | add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp); | |
159 | ||
160 | mul64_Xsig(&accumulatore, &denomterm); | |
161 | shr_Xsig(&accumulatore, 1 + 2 * (-1 - exponent)); | |
162 | accumulatore.msw |= 0x80000000; | |
163 | ||
164 | div_Xsig(&accumulator, &accumulatore, &accumulator); | |
165 | ||
166 | mul_Xsig_Xsig(&accumulator, &argSignif); | |
167 | mul_Xsig_Xsig(&accumulator, &argSq); | |
168 | ||
169 | shr_Xsig(&accumulator, 3); | |
170 | negate_Xsig(&accumulator); | |
171 | add_Xsig_Xsig(&accumulator, &argSignif); | |
172 | ||
173 | if (transformed) { | |
174 | /* compute pi/4 - accumulator */ | |
175 | shr_Xsig(&accumulator, -1 - exponent); | |
176 | negate_Xsig(&accumulator); | |
177 | add_Xsig_Xsig(&accumulator, &pi_signif); | |
178 | exponent = -1; | |
179 | } | |
180 | ||
181 | if (inverted) { | |
182 | /* compute pi/2 - accumulator */ | |
183 | shr_Xsig(&accumulator, -exponent); | |
184 | negate_Xsig(&accumulator); | |
185 | add_Xsig_Xsig(&accumulator, &pi_signif); | |
186 | exponent = 0; | |
1da177e4 | 187 | } |
3d0d14f9 IM |
188 | |
189 | if (sign1) { | |
190 | /* compute pi - accumulator */ | |
191 | shr_Xsig(&accumulator, 1 - exponent); | |
192 | negate_Xsig(&accumulator); | |
193 | add_Xsig_Xsig(&accumulator, &pi_signif); | |
194 | exponent = 1; | |
1da177e4 | 195 | } |
3d0d14f9 IM |
196 | |
197 | exponent += round_Xsig(&accumulator); | |
198 | ||
199 | significand(st1_ptr) = XSIG_LL(accumulator); | |
200 | setexponent16(st1_ptr, exponent); | |
201 | ||
202 | tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2); | |
203 | FPU_settagi(1, tag); | |
204 | ||
205 | set_precision_flag_up(); /* We do not really know if up or down, | |
206 | use this as the default. */ | |
1da177e4 LT |
207 | |
208 | } |