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1da177e4 LT |
1 | /*---------------------------------------------------------------------------+ |
2 | | poly_l2.c | | |
3 | | | | |
4 | | Compute the base 2 log 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 | ||
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 | ||
22 | static void log2_kernel(FPU_REG const *arg, u_char argsign, | |
23 | Xsig *accum_result, long int *expon); | |
24 | ||
25 | ||
26 | /*--- poly_l2() -------------------------------------------------------------+ | |
27 | | Base 2 logarithm by a polynomial approximation. | | |
28 | +---------------------------------------------------------------------------*/ | |
29 | void poly_l2(FPU_REG *st0_ptr, FPU_REG *st1_ptr, u_char st1_sign) | |
30 | { | |
31 | long int exponent, expon, expon_expon; | |
32 | Xsig accumulator, expon_accum, yaccum; | |
33 | u_char sign, argsign; | |
34 | FPU_REG x; | |
35 | int tag; | |
36 | ||
37 | exponent = exponent16(st0_ptr); | |
38 | ||
39 | /* From st0_ptr, make a number > sqrt(2)/2 and < sqrt(2) */ | |
40 | if ( st0_ptr->sigh > (unsigned)0xb504f334 ) | |
41 | { | |
42 | /* Treat as sqrt(2)/2 < st0_ptr < 1 */ | |
43 | significand(&x) = - significand(st0_ptr); | |
44 | setexponent16(&x, -1); | |
45 | exponent++; | |
46 | argsign = SIGN_NEG; | |
47 | } | |
48 | else | |
49 | { | |
50 | /* Treat as 1 <= st0_ptr < sqrt(2) */ | |
51 | x.sigh = st0_ptr->sigh - 0x80000000; | |
52 | x.sigl = st0_ptr->sigl; | |
53 | setexponent16(&x, 0); | |
54 | argsign = SIGN_POS; | |
55 | } | |
56 | tag = FPU_normalize_nuo(&x); | |
57 | ||
58 | if ( tag == TAG_Zero ) | |
59 | { | |
60 | expon = 0; | |
61 | accumulator.msw = accumulator.midw = accumulator.lsw = 0; | |
62 | } | |
63 | else | |
64 | { | |
65 | log2_kernel(&x, argsign, &accumulator, &expon); | |
66 | } | |
67 | ||
68 | if ( exponent < 0 ) | |
69 | { | |
70 | sign = SIGN_NEG; | |
71 | exponent = -exponent; | |
72 | } | |
73 | else | |
74 | sign = SIGN_POS; | |
75 | expon_accum.msw = exponent; expon_accum.midw = expon_accum.lsw = 0; | |
76 | if ( exponent ) | |
77 | { | |
78 | expon_expon = 31 + norm_Xsig(&expon_accum); | |
79 | shr_Xsig(&accumulator, expon_expon - expon); | |
80 | ||
81 | if ( sign ^ argsign ) | |
82 | negate_Xsig(&accumulator); | |
83 | add_Xsig_Xsig(&accumulator, &expon_accum); | |
84 | } | |
85 | else | |
86 | { | |
87 | expon_expon = expon; | |
88 | sign = argsign; | |
89 | } | |
90 | ||
91 | yaccum.lsw = 0; XSIG_LL(yaccum) = significand(st1_ptr); | |
92 | mul_Xsig_Xsig(&accumulator, &yaccum); | |
93 | ||
94 | expon_expon += round_Xsig(&accumulator); | |
95 | ||
96 | if ( accumulator.msw == 0 ) | |
97 | { | |
98 | FPU_copy_to_reg1(&CONST_Z, TAG_Zero); | |
99 | return; | |
100 | } | |
101 | ||
102 | significand(st1_ptr) = XSIG_LL(accumulator); | |
103 | setexponent16(st1_ptr, expon_expon + exponent16(st1_ptr) + 1); | |
104 | ||
105 | tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign ^ st1_sign); | |
106 | FPU_settagi(1, tag); | |
107 | ||
108 | set_precision_flag_up(); /* 80486 appears to always do this */ | |
109 | ||
110 | return; | |
111 | ||
112 | } | |
113 | ||
114 | ||
115 | /*--- poly_l2p1() -----------------------------------------------------------+ | |
116 | | Base 2 logarithm by a polynomial approximation. | | |
117 | | log2(x+1) | | |
118 | +---------------------------------------------------------------------------*/ | |
119 | int poly_l2p1(u_char sign0, u_char sign1, | |
120 | FPU_REG *st0_ptr, FPU_REG *st1_ptr, FPU_REG *dest) | |
121 | { | |
122 | u_char tag; | |
123 | long int exponent; | |
124 | Xsig accumulator, yaccum; | |
125 | ||
126 | if ( exponent16(st0_ptr) < 0 ) | |
127 | { | |
128 | log2_kernel(st0_ptr, sign0, &accumulator, &exponent); | |
129 | ||
130 | yaccum.lsw = 0; | |
131 | XSIG_LL(yaccum) = significand(st1_ptr); | |
132 | mul_Xsig_Xsig(&accumulator, &yaccum); | |
133 | ||
134 | exponent += round_Xsig(&accumulator); | |
135 | ||
136 | exponent += exponent16(st1_ptr) + 1; | |
137 | if ( exponent < EXP_WAY_UNDER ) exponent = EXP_WAY_UNDER; | |
138 | ||
139 | significand(dest) = XSIG_LL(accumulator); | |
140 | setexponent16(dest, exponent); | |
141 | ||
142 | tag = FPU_round(dest, 1, 0, FULL_PRECISION, sign0 ^ sign1); | |
143 | FPU_settagi(1, tag); | |
144 | ||
145 | if ( tag == TAG_Valid ) | |
146 | set_precision_flag_up(); /* 80486 appears to always do this */ | |
147 | } | |
148 | else | |
149 | { | |
150 | /* The magnitude of st0_ptr is far too large. */ | |
151 | ||
152 | if ( sign0 != SIGN_POS ) | |
153 | { | |
154 | /* Trying to get the log of a negative number. */ | |
155 | #ifdef PECULIAR_486 /* Stupid 80486 doesn't worry about log(negative). */ | |
156 | changesign(st1_ptr); | |
157 | #else | |
158 | if ( arith_invalid(1) < 0 ) | |
159 | return 1; | |
160 | #endif /* PECULIAR_486 */ | |
161 | } | |
162 | ||
163 | /* 80486 appears to do this */ | |
164 | if ( sign0 == SIGN_NEG ) | |
165 | set_precision_flag_down(); | |
166 | else | |
167 | set_precision_flag_up(); | |
168 | } | |
169 | ||
170 | if ( exponent(dest) <= EXP_UNDER ) | |
171 | EXCEPTION(EX_Underflow); | |
172 | ||
173 | return 0; | |
174 | ||
175 | } | |
176 | ||
177 | ||
178 | ||
179 | ||
180 | #undef HIPOWER | |
181 | #define HIPOWER 10 | |
182 | static const unsigned long long logterms[HIPOWER] = | |
183 | { | |
184 | 0x2a8eca5705fc2ef0LL, | |
185 | 0xf6384ee1d01febceLL, | |
186 | 0x093bb62877cdf642LL, | |
187 | 0x006985d8a9ec439bLL, | |
188 | 0x0005212c4f55a9c8LL, | |
189 | 0x00004326a16927f0LL, | |
190 | 0x0000038d1d80a0e7LL, | |
191 | 0x0000003141cc80c6LL, | |
192 | 0x00000002b1668c9fLL, | |
193 | 0x000000002c7a46aaLL | |
194 | }; | |
195 | ||
196 | static const unsigned long leadterm = 0xb8000000; | |
197 | ||
198 | ||
199 | /*--- log2_kernel() ---------------------------------------------------------+ | |
200 | | Base 2 logarithm by a polynomial approximation. | | |
201 | | log2(x+1) | | |
202 | +---------------------------------------------------------------------------*/ | |
203 | static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result, | |
204 | long int *expon) | |
205 | { | |
206 | long int exponent, adj; | |
207 | unsigned long long Xsq; | |
208 | Xsig accumulator, Numer, Denom, argSignif, arg_signif; | |
209 | ||
210 | exponent = exponent16(arg); | |
211 | Numer.lsw = Denom.lsw = 0; | |
212 | XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg); | |
213 | if ( argsign == SIGN_POS ) | |
214 | { | |
215 | shr_Xsig(&Denom, 2 - (1 + exponent)); | |
216 | Denom.msw |= 0x80000000; | |
217 | div_Xsig(&Numer, &Denom, &argSignif); | |
218 | } | |
219 | else | |
220 | { | |
221 | shr_Xsig(&Denom, 1 - (1 + exponent)); | |
222 | negate_Xsig(&Denom); | |
223 | if ( Denom.msw & 0x80000000 ) | |
224 | { | |
225 | div_Xsig(&Numer, &Denom, &argSignif); | |
226 | exponent ++; | |
227 | } | |
228 | else | |
229 | { | |
230 | /* Denom must be 1.0 */ | |
231 | argSignif.lsw = Numer.lsw; argSignif.midw = Numer.midw; | |
232 | argSignif.msw = Numer.msw; | |
233 | } | |
234 | } | |
235 | ||
236 | #ifndef PECULIAR_486 | |
237 | /* Should check here that |local_arg| is within the valid range */ | |
238 | if ( exponent >= -2 ) | |
239 | { | |
240 | if ( (exponent > -2) || | |
241 | (argSignif.msw > (unsigned)0xafb0ccc0) ) | |
242 | { | |
243 | /* The argument is too large */ | |
244 | } | |
245 | } | |
246 | #endif /* PECULIAR_486 */ | |
247 | ||
248 | arg_signif.lsw = argSignif.lsw; XSIG_LL(arg_signif) = XSIG_LL(argSignif); | |
249 | adj = norm_Xsig(&argSignif); | |
250 | accumulator.lsw = argSignif.lsw; XSIG_LL(accumulator) = XSIG_LL(argSignif); | |
251 | mul_Xsig_Xsig(&accumulator, &accumulator); | |
252 | shr_Xsig(&accumulator, 2*(-1 - (1 + exponent + adj))); | |
253 | Xsq = XSIG_LL(accumulator); | |
254 | if ( accumulator.lsw & 0x80000000 ) | |
255 | Xsq++; | |
256 | ||
257 | accumulator.msw = accumulator.midw = accumulator.lsw = 0; | |
258 | /* Do the basic fixed point polynomial evaluation */ | |
259 | polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER-1); | |
260 | ||
261 | mul_Xsig_Xsig(&accumulator, &argSignif); | |
262 | shr_Xsig(&accumulator, 6 - adj); | |
263 | ||
264 | mul32_Xsig(&arg_signif, leadterm); | |
265 | add_two_Xsig(&accumulator, &arg_signif, &exponent); | |
266 | ||
267 | *expon = exponent + 1; | |
268 | accum_result->lsw = accumulator.lsw; | |
269 | accum_result->midw = accumulator.midw; | |
270 | accum_result->msw = accumulator.msw; | |
271 | ||
272 | } |