1 // SPDX-License-Identifier: GPL-2.0
2 /*---------------------------------------------------------------------------+
3  |  poly_l2.c                                                                |
4  |                                                                           |
5  | Compute the base 2 log 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 "control_w.h"
19 #include "poly.h"
20 
21 static void log2_kernel(FPU_REG const *arg, u_char argsign,
22 			Xsig * accum_result, long int *expon);
23 
24 /*--- poly_l2() -------------------------------------------------------------+
25  |   Base 2 logarithm by a polynomial approximation.                         |
26  +---------------------------------------------------------------------------*/
poly_l2(FPU_REG * st0_ptr,FPU_REG * st1_ptr,u_char st1_sign)27 void poly_l2(FPU_REG *st0_ptr, FPU_REG *st1_ptr, u_char st1_sign)
28 {
29 	long int exponent, expon, expon_expon;
30 	Xsig accumulator, expon_accum, yaccum;
31 	u_char sign, argsign;
32 	FPU_REG x;
33 	int tag;
34 
35 	exponent = exponent16(st0_ptr);
36 
37 	/* From st0_ptr, make a number > sqrt(2)/2 and < sqrt(2) */
38 	if (st0_ptr->sigh > (unsigned)0xb504f334) {
39 		/* Treat as  sqrt(2)/2 < st0_ptr < 1 */
40 		significand(&x) = -significand(st0_ptr);
41 		setexponent16(&x, -1);
42 		exponent++;
43 		argsign = SIGN_NEG;
44 	} else {
45 		/* Treat as  1 <= st0_ptr < sqrt(2) */
46 		x.sigh = st0_ptr->sigh - 0x80000000;
47 		x.sigl = st0_ptr->sigl;
48 		setexponent16(&x, 0);
49 		argsign = SIGN_POS;
50 	}
51 	tag = FPU_normalize_nuo(&x);
52 
53 	if (tag == TAG_Zero) {
54 		expon = 0;
55 		accumulator.msw = accumulator.midw = accumulator.lsw = 0;
56 	} else {
57 		log2_kernel(&x, argsign, &accumulator, &expon);
58 	}
59 
60 	if (exponent < 0) {
61 		sign = SIGN_NEG;
62 		exponent = -exponent;
63 	} else
64 		sign = SIGN_POS;
65 	expon_accum.msw = exponent;
66 	expon_accum.midw = expon_accum.lsw = 0;
67 	if (exponent) {
68 		expon_expon = 31 + norm_Xsig(&expon_accum);
69 		shr_Xsig(&accumulator, expon_expon - expon);
70 
71 		if (sign ^ argsign)
72 			negate_Xsig(&accumulator);
73 		add_Xsig_Xsig(&accumulator, &expon_accum);
74 	} else {
75 		expon_expon = expon;
76 		sign = argsign;
77 	}
78 
79 	yaccum.lsw = 0;
80 	XSIG_LL(yaccum) = significand(st1_ptr);
81 	mul_Xsig_Xsig(&accumulator, &yaccum);
82 
83 	expon_expon += round_Xsig(&accumulator);
84 
85 	if (accumulator.msw == 0) {
86 		FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
87 		return;
88 	}
89 
90 	significand(st1_ptr) = XSIG_LL(accumulator);
91 	setexponent16(st1_ptr, expon_expon + exponent16(st1_ptr) + 1);
92 
93 	tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign ^ st1_sign);
94 	FPU_settagi(1, tag);
95 
96 	set_precision_flag_up();	/* 80486 appears to always do this */
97 
98 	return;
99 
100 }
101 
102 /*--- poly_l2p1() -----------------------------------------------------------+
103  |   Base 2 logarithm by a polynomial approximation.                         |
104  |   log2(x+1)                                                               |
105  +---------------------------------------------------------------------------*/
poly_l2p1(u_char sign0,u_char sign1,FPU_REG * st0_ptr,FPU_REG * st1_ptr,FPU_REG * dest)106 int poly_l2p1(u_char sign0, u_char sign1,
107 	      FPU_REG * st0_ptr, FPU_REG * st1_ptr, FPU_REG * dest)
108 {
109 	u_char tag;
110 	long int exponent;
111 	Xsig accumulator, yaccum;
112 
113 	if (exponent16(st0_ptr) < 0) {
114 		log2_kernel(st0_ptr, sign0, &accumulator, &exponent);
115 
116 		yaccum.lsw = 0;
117 		XSIG_LL(yaccum) = significand(st1_ptr);
118 		mul_Xsig_Xsig(&accumulator, &yaccum);
119 
120 		exponent += round_Xsig(&accumulator);
121 
122 		exponent += exponent16(st1_ptr) + 1;
123 		if (exponent < EXP_WAY_UNDER)
124 			exponent = EXP_WAY_UNDER;
125 
126 		significand(dest) = XSIG_LL(accumulator);
127 		setexponent16(dest, exponent);
128 
129 		tag = FPU_round(dest, 1, 0, FULL_PRECISION, sign0 ^ sign1);
130 		FPU_settagi(1, tag);
131 
132 		if (tag == TAG_Valid)
133 			set_precision_flag_up();	/* 80486 appears to always do this */
134 	} else {
135 		/* The magnitude of st0_ptr is far too large. */
136 
137 		if (sign0 != SIGN_POS) {
138 			/* Trying to get the log of a negative number. */
139 #ifdef PECULIAR_486		/* Stupid 80486 doesn't worry about log(negative). */
140 			changesign(st1_ptr);
141 #else
142 			if (arith_invalid(1) < 0)
143 				return 1;
144 #endif /* PECULIAR_486 */
145 		}
146 
147 		/* 80486 appears to do this */
148 		if (sign0 == SIGN_NEG)
149 			set_precision_flag_down();
150 		else
151 			set_precision_flag_up();
152 	}
153 
154 	if (exponent(dest) <= EXP_UNDER)
155 		EXCEPTION(EX_Underflow);
156 
157 	return 0;
158 
159 }
160 
161 #undef HIPOWER
162 #define	HIPOWER	10
163 static const unsigned long long logterms[HIPOWER] = {
164 	0x2a8eca5705fc2ef0LL,
165 	0xf6384ee1d01febceLL,
166 	0x093bb62877cdf642LL,
167 	0x006985d8a9ec439bLL,
168 	0x0005212c4f55a9c8LL,
169 	0x00004326a16927f0LL,
170 	0x0000038d1d80a0e7LL,
171 	0x0000003141cc80c6LL,
172 	0x00000002b1668c9fLL,
173 	0x000000002c7a46aaLL
174 };
175 
176 static const unsigned long leadterm = 0xb8000000;
177 
178 /*--- log2_kernel() ---------------------------------------------------------+
179  |   Base 2 logarithm by a polynomial approximation.                         |
180  |   log2(x+1)                                                               |
181  +---------------------------------------------------------------------------*/
log2_kernel(FPU_REG const * arg,u_char argsign,Xsig * accum_result,long int * expon)182 static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result,
183 			long int *expon)
184 {
185 	long int exponent, adj;
186 	unsigned long long Xsq;
187 	Xsig accumulator, Numer, Denom, argSignif, arg_signif;
188 
189 	exponent = exponent16(arg);
190 	Numer.lsw = Denom.lsw = 0;
191 	XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg);
192 	if (argsign == SIGN_POS) {
193 		shr_Xsig(&Denom, 2 - (1 + exponent));
194 		Denom.msw |= 0x80000000;
195 		div_Xsig(&Numer, &Denom, &argSignif);
196 	} else {
197 		shr_Xsig(&Denom, 1 - (1 + exponent));
198 		negate_Xsig(&Denom);
199 		if (Denom.msw & 0x80000000) {
200 			div_Xsig(&Numer, &Denom, &argSignif);
201 			exponent++;
202 		} else {
203 			/* Denom must be 1.0 */
204 			argSignif.lsw = Numer.lsw;
205 			argSignif.midw = Numer.midw;
206 			argSignif.msw = Numer.msw;
207 		}
208 	}
209 
210 #ifndef PECULIAR_486
211 	/* Should check here that  |local_arg|  is within the valid range */
212 	if (exponent >= -2) {
213 		if ((exponent > -2) || (argSignif.msw > (unsigned)0xafb0ccc0)) {
214 			/* The argument is too large */
215 		}
216 	}
217 #endif /* PECULIAR_486 */
218 
219 	arg_signif.lsw = argSignif.lsw;
220 	XSIG_LL(arg_signif) = XSIG_LL(argSignif);
221 	adj = norm_Xsig(&argSignif);
222 	accumulator.lsw = argSignif.lsw;
223 	XSIG_LL(accumulator) = XSIG_LL(argSignif);
224 	mul_Xsig_Xsig(&accumulator, &accumulator);
225 	shr_Xsig(&accumulator, 2 * (-1 - (1 + exponent + adj)));
226 	Xsq = XSIG_LL(accumulator);
227 	if (accumulator.lsw & 0x80000000)
228 		Xsq++;
229 
230 	accumulator.msw = accumulator.midw = accumulator.lsw = 0;
231 	/* Do the basic fixed point polynomial evaluation */
232 	polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER - 1);
233 
234 	mul_Xsig_Xsig(&accumulator, &argSignif);
235 	shr_Xsig(&accumulator, 6 - adj);
236 
237 	mul32_Xsig(&arg_signif, leadterm);
238 	add_two_Xsig(&accumulator, &arg_signif, &exponent);
239 
240 	*expon = exponent + 1;
241 	accum_result->lsw = accumulator.lsw;
242 	accum_result->midw = accumulator.midw;
243 	accum_result->msw = accumulator.msw;
244 
245 }
246