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*/
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 |
7 | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
8 | Australia. E-mail billm@vaxc.cc.monash.edu.au |
9 | |
10 | |
11 +---------------------------------------------------------------------------*/
12
13
14 #include "exception.h"
15 #include "reg_constant.h"
16 #include "fpu_emu.h"
17 #include "control_w.h"
18
19
20
21 #define HIPOWER 9
22 static unsigned short const lterms[HIPOWER][4] =
23 {
24 /* Ideal computation with these coeffs gives about
25 64.6 bit rel accuracy. */
26 { 0xe177, 0xb82f, 0x7652, 0x7154 },
27 { 0xee0f, 0xe80f, 0x2770, 0x7b1c },
28 { 0x0fc0, 0xbe87, 0xb143, 0x49dd },
29 { 0x78b9, 0xdadd, 0xec54, 0x34c2 },
30 { 0x003a, 0x5de9, 0x628b, 0x2909 },
31 { 0x5588, 0xed16, 0x4abf, 0x2193 },
32 { 0xb461, 0x85f7, 0x347a, 0x1c6a },
33 { 0x0975, 0x87b3, 0xd5bf, 0x1876 },
34 { 0xe85c, 0xcec9, 0x84e7, 0x187d }
35 };
36
37
38
39
40 /*--- poly_l2() -------------------------------------------------------------+
41 | Base 2 logarithm by a polynomial approximation. |
42 +---------------------------------------------------------------------------*/
43 void poly_l2(FPU_REG const *arg, FPU_REG *result)
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*/
44 {
45 short exponent;
46 char zero; /* flag for an Xx == 0 */
47 unsigned short bits, shift;
48 unsigned long long Xsq;
49 FPU_REG accum, denom, num, Xx;
50
51
52 exponent = arg->exp - EXP_BIAS;
53
54 accum.tag = TW_Valid; /* set the tags to Valid */
55
56 if ( arg->sigh > (unsigned)0xb504f334 )
57 {
58 /* This is good enough for the computation of the polynomial
59 sum, but actually results in a loss of precision for
60 the computation of Xx. This will matter only if exponent
61 becomes zero. */
62 exponent++;
63 accum.sign = 1; /* sign to negative */
64 num.exp = EXP_BIAS; /* needed to prevent errors in div routine */
65 reg_u_div(&CONST_1, arg, &num, FULL_PRECISION);
66 }
67 else
68 {
69 accum.sign = 0; /* set the sign to positive */
70 num.sigl = arg->sigl; /* copy the mantissa */
71 num.sigh = arg->sigh;
72 }
73
74
75 /* shift num left, lose the ms bit */
76 num.sigh <<= 1;
77 if ( num.sigl & 0x80000000 ) num.sigh |= 1;
78 num.sigl <<= 1;
79
80 denom.sigl = num.sigl;
81 denom.sigh = num.sigh;
82 poly_div4(&significand(&denom));
83 denom.sigh += 0x80000000; /* set the msb */
84 Xx.exp = EXP_BIAS; /* needed to prevent errors in div routine */
85 reg_u_div(&num, &denom, &Xx, FULL_PRECISION);
86
87 zero = !(Xx.sigh | Xx.sigl);
88
89 mul64(&significand(&Xx), &significand(&Xx), &Xsq);
90 poly_div16(&Xsq);
91
92 accum.exp = -1; /* exponent of accum */
93
94 /* Do the basic fixed point polynomial evaluation */
95 polynomial((unsigned *)&accum.sigl, (unsigned *)&Xsq, lterms, HIPOWER-1);
96
97 if ( !exponent )
98 {
99 /* If the exponent is zero, then we would lose precision by
100 sticking to fixed point computation here */
101 /* We need to re-compute Xx because of loss of precision. */
102 FPU_REG lXx;
103 char sign;
104
105 sign = accum.sign;
106 accum.sign = 0;
107
108 /* make accum compatible and normalize */
109 accum.exp = EXP_BIAS + accum.exp;
110 normalize(&accum);
111
112 if ( zero )
113 {
114 reg_move(&CONST_Z, result);
115 }
116 else
117 {
118 /* we need to re-compute lXx to better accuracy */
119 num.tag = TW_Valid; /* set the tags to Vaild */
120 num.sign = 0; /* set the sign to positive */
121 num.exp = EXP_BIAS - 1;
122 if ( sign )
123 {
124 /* The argument is of the form 1-x */
125 /* Use 1-1/(1-x) = x/(1-x) */
126 significand(&num) = - significand(arg);
127 normalize(&num);
128 reg_div(&num, arg, &num, FULL_PRECISION);
129 }
130 else
131 {
132 normalize(&num);
133 }
134
135 denom.tag = TW_Valid; /* set the tags to Valid */
136 denom.sign = SIGN_POS; /* set the sign to positive */
137 denom.exp = EXP_BIAS;
138
139 reg_div(&num, &denom, &lXx, FULL_PRECISION);
140
141 reg_u_mul(&lXx, &accum, &accum, FULL_PRECISION);
142
143 reg_u_add(&lXx, &accum, result, FULL_PRECISION);
144
145 normalize(result);
146 }
147
148 result->sign = sign;
149 return;
150 }
151
152 mul64(&significand(&accum),
153 &significand(&Xx), &significand(&accum));
154
155 significand(&accum) += significand(&Xx);
156
157 if ( Xx.sigh > accum.sigh )
158 {
159 /* There was an overflow */
160
161 poly_div2(&significand(&accum));
162 accum.sigh |= 0x80000000;
163 accum.exp++;
164 }
165
166 /* When we add the exponent to the accum result later, we will
167 require that their signs are the same. Here we ensure that
168 this is so. */
169 if ( exponent && ((exponent < 0) ^ (accum.sign)) )
170 {
171 /* signs are different */
172
173 accum.sign = !accum.sign;
174
175 /* An exceptional case is when accum is zero */
176 if ( accum.sigl | accum.sigh )
177 {
178 /* find 1-accum */
179 /* Shift to get exponent == 0 */
180 if ( accum.exp < 0 )
181 {
182 poly_div2(&significand(&accum));
183 accum.exp++;
184 }
185 /* Just negate, but throw away the sign */
186 significand(&accum) = - significand(&accum);
187 if ( exponent < 0 )
188 exponent++;
189 else
190 exponent--;
191 }
192 }
193
194 shift = exponent >= 0 ? exponent : -exponent ;
195 bits = 0;
196 if ( shift )
197 {
198 if ( accum.exp )
199 {
200 accum.exp++;
201 poly_div2(&significand(&accum));
202 }
203 while ( shift )
204 {
205 poly_div2(&significand(&accum));
206 if ( shift & 1)
207 accum.sigh |= 0x80000000;
208 shift >>= 1;
209 bits++;
210 }
211 }
212
213 /* Convert to 64 bit signed-compatible */
214 accum.exp += bits + EXP_BIAS - 1;
215
216 reg_move(&accum, result);
217 normalize(result);
218
219 return;
220 }
221
222
223 /*--- poly_l2p1() -----------------------------------------------------------+
224 | Base 2 logarithm by a polynomial approximation. |
225 | log2(x+1) |
226 +---------------------------------------------------------------------------*/
227 int poly_l2p1(FPU_REG const *arg, FPU_REG *result)
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228 {
229 char sign = 0;
230 unsigned long long Xsq;
231 FPU_REG arg_pl1, denom, accum, local_arg, poly_arg;
232
233
234 sign = arg->sign;
235
236 reg_add(arg, &CONST_1, &arg_pl1, FULL_PRECISION);
237
238 if ( (arg_pl1.sign) | (arg_pl1.tag) )
239 { /* We need a valid positive number! */
240 return 1;
241 }
242
243 reg_add(&CONST_1, &arg_pl1, &denom, FULL_PRECISION);
244 reg_div(arg, &denom, &local_arg, FULL_PRECISION);
245 local_arg.sign = 0; /* Make the sign positive */
246
247 /* Now we need to check that |local_arg| is less than
248 3-2*sqrt(2) = 0.17157.. = .0xafb0ccc0 * 2^-2 */
249
250 if ( local_arg.exp >= EXP_BIAS - 3 )
251 {
252 if ( (local_arg.exp > EXP_BIAS - 3) ||
253 (local_arg.sigh > (unsigned)0xafb0ccc0) )
254 {
255 /* The argument is large */
256 poly_l2(&arg_pl1, result); return 0;
257 }
258 }
259
260 /* Make a copy of local_arg */
261 reg_move(&local_arg, &poly_arg);
262
263 /* Get poly_arg bits aligned as required */
264 shrx((unsigned *)&(poly_arg.sigl), -(poly_arg.exp - EXP_BIAS + 3));
265
266 mul64(&significand(&poly_arg), &significand(&poly_arg), &Xsq);
267 poly_div16(&Xsq);
268
269 /* Do the basic fixed point polynomial evaluation */
270 polynomial(&(accum.sigl), (unsigned *)&Xsq, lterms, HIPOWER-1);
271
272 accum.tag = TW_Valid; /* set the tags to Valid */
273 accum.sign = SIGN_POS; /* and make accum positive */
274
275 /* make accum compatible and normalize */
276 accum.exp = EXP_BIAS - 1;
277 normalize(&accum);
278
279 reg_u_mul(&local_arg, &accum, &accum, FULL_PRECISION);
280
281 reg_u_add(&local_arg, &accum, result, FULL_PRECISION);
282
283 /* Multiply the result by 2 */
284 result->exp++;
285
286 result->sign = sign;
287
288 return 0;
289 }
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*/