xref: /linux/arch/m68k/math-emu/multi_arith.h (revision be239684b18e1cdcafcf8c7face4a2f562c745ad)
1 /* SPDX-License-Identifier: GPL-2.0-or-later */
2 /* multi_arith.h: multi-precision integer arithmetic functions, needed
3    to do extended-precision floating point.
4 
5    (c) 1998 David Huggins-Daines.
6 
7    Somewhat based on arch/alpha/math-emu/ieee-math.c, which is (c)
8    David Mosberger-Tang.
9 
10  */
11 
12 /* Note:
13 
14    These are not general multi-precision math routines.  Rather, they
15    implement the subset of integer arithmetic that we need in order to
16    multiply, divide, and normalize 128-bit unsigned mantissae.  */
17 
18 #ifndef _MULTI_ARITH_H
19 #define _MULTI_ARITH_H
20 
21 #include "fp_emu.h"
22 
23 static inline void fp_denormalize(struct fp_ext *reg, unsigned int cnt)
24 {
25 	reg->exp += cnt;
26 
27 	switch (cnt) {
28 	case 0 ... 8:
29 		reg->lowmant = reg->mant.m32[1] << (8 - cnt);
30 		reg->mant.m32[1] = (reg->mant.m32[1] >> cnt) |
31 				   (reg->mant.m32[0] << (32 - cnt));
32 		reg->mant.m32[0] = reg->mant.m32[0] >> cnt;
33 		break;
34 	case 9 ... 32:
35 		reg->lowmant = reg->mant.m32[1] >> (cnt - 8);
36 		if (reg->mant.m32[1] << (40 - cnt))
37 			reg->lowmant |= 1;
38 		reg->mant.m32[1] = (reg->mant.m32[1] >> cnt) |
39 				   (reg->mant.m32[0] << (32 - cnt));
40 		reg->mant.m32[0] = reg->mant.m32[0] >> cnt;
41 		break;
42 	case 33 ... 39:
43 		asm volatile ("bfextu %1{%2,#8},%0" : "=d" (reg->lowmant)
44 			: "m" (reg->mant.m32[0]), "d" (64 - cnt));
45 		if (reg->mant.m32[1] << (40 - cnt))
46 			reg->lowmant |= 1;
47 		reg->mant.m32[1] = reg->mant.m32[0] >> (cnt - 32);
48 		reg->mant.m32[0] = 0;
49 		break;
50 	case 40 ... 71:
51 		reg->lowmant = reg->mant.m32[0] >> (cnt - 40);
52 		if ((reg->mant.m32[0] << (72 - cnt)) || reg->mant.m32[1])
53 			reg->lowmant |= 1;
54 		reg->mant.m32[1] = reg->mant.m32[0] >> (cnt - 32);
55 		reg->mant.m32[0] = 0;
56 		break;
57 	default:
58 		reg->lowmant = reg->mant.m32[0] || reg->mant.m32[1];
59 		reg->mant.m32[0] = 0;
60 		reg->mant.m32[1] = 0;
61 		break;
62 	}
63 }
64 
65 static inline int fp_overnormalize(struct fp_ext *reg)
66 {
67 	int shift;
68 
69 	if (reg->mant.m32[0]) {
70 		asm ("bfffo %1{#0,#32},%0" : "=d" (shift) : "dm" (reg->mant.m32[0]));
71 		reg->mant.m32[0] = (reg->mant.m32[0] << shift) | (reg->mant.m32[1] >> (32 - shift));
72 		reg->mant.m32[1] = (reg->mant.m32[1] << shift);
73 	} else {
74 		asm ("bfffo %1{#0,#32},%0" : "=d" (shift) : "dm" (reg->mant.m32[1]));
75 		reg->mant.m32[0] = (reg->mant.m32[1] << shift);
76 		reg->mant.m32[1] = 0;
77 		shift += 32;
78 	}
79 
80 	return shift;
81 }
82 
83 static inline int fp_addmant(struct fp_ext *dest, struct fp_ext *src)
84 {
85 	int carry;
86 
87 	/* we assume here, gcc only insert move and a clr instr */
88 	asm volatile ("add.b %1,%0" : "=d,g" (dest->lowmant)
89 		: "g,d" (src->lowmant), "0,0" (dest->lowmant));
90 	asm volatile ("addx.l %1,%0" : "=d" (dest->mant.m32[1])
91 		: "d" (src->mant.m32[1]), "0" (dest->mant.m32[1]));
92 	asm volatile ("addx.l %1,%0" : "=d" (dest->mant.m32[0])
93 		: "d" (src->mant.m32[0]), "0" (dest->mant.m32[0]));
94 	asm volatile ("addx.l %0,%0" : "=d" (carry) : "0" (0));
95 
96 	return carry;
97 }
98 
99 static inline int fp_addcarry(struct fp_ext *reg)
100 {
101 	if (++reg->exp == 0x7fff) {
102 		if (reg->mant.m64)
103 			fp_set_sr(FPSR_EXC_INEX2);
104 		reg->mant.m64 = 0;
105 		fp_set_sr(FPSR_EXC_OVFL);
106 		return 0;
107 	}
108 	reg->lowmant = (reg->mant.m32[1] << 7) | (reg->lowmant ? 1 : 0);
109 	reg->mant.m32[1] = (reg->mant.m32[1] >> 1) |
110 			   (reg->mant.m32[0] << 31);
111 	reg->mant.m32[0] = (reg->mant.m32[0] >> 1) | 0x80000000;
112 
113 	return 1;
114 }
115 
116 static inline void fp_submant(struct fp_ext *dest, struct fp_ext *src1,
117 			      struct fp_ext *src2)
118 {
119 	/* we assume here, gcc only insert move and a clr instr */
120 	asm volatile ("sub.b %1,%0" : "=d,g" (dest->lowmant)
121 		: "g,d" (src2->lowmant), "0,0" (src1->lowmant));
122 	asm volatile ("subx.l %1,%0" : "=d" (dest->mant.m32[1])
123 		: "d" (src2->mant.m32[1]), "0" (src1->mant.m32[1]));
124 	asm volatile ("subx.l %1,%0" : "=d" (dest->mant.m32[0])
125 		: "d" (src2->mant.m32[0]), "0" (src1->mant.m32[0]));
126 }
127 
128 #define fp_mul64(desth, destl, src1, src2) ({				\
129 	asm ("mulu.l %2,%1:%0" : "=d" (destl), "=d" (desth)		\
130 		: "dm" (src1), "0" (src2));				\
131 })
132 #define fp_div64(quot, rem, srch, srcl, div)				\
133 	asm ("divu.l %2,%1:%0" : "=d" (quot), "=d" (rem)		\
134 		: "dm" (div), "1" (srch), "0" (srcl))
135 #define fp_add64(dest1, dest2, src1, src2) ({				\
136 	asm ("add.l %1,%0" : "=d,dm" (dest2)				\
137 		: "dm,d" (src2), "0,0" (dest2));			\
138 	asm ("addx.l %1,%0" : "=d" (dest1)				\
139 		: "d" (src1), "0" (dest1));				\
140 })
141 #define fp_addx96(dest, src) ({						\
142 	/* we assume here, gcc only insert move and a clr instr */	\
143 	asm volatile ("add.l %1,%0" : "=d,g" (dest->m32[2])		\
144 		: "g,d" (temp.m32[1]), "0,0" (dest->m32[2]));		\
145 	asm volatile ("addx.l %1,%0" : "=d" (dest->m32[1])		\
146 		: "d" (temp.m32[0]), "0" (dest->m32[1]));		\
147 	asm volatile ("addx.l %1,%0" : "=d" (dest->m32[0])		\
148 		: "d" (0), "0" (dest->m32[0]));				\
149 })
150 #define fp_sub64(dest, src) ({						\
151 	asm ("sub.l %1,%0" : "=d,dm" (dest.m32[1])			\
152 		: "dm,d" (src.m32[1]), "0,0" (dest.m32[1]));		\
153 	asm ("subx.l %1,%0" : "=d" (dest.m32[0])			\
154 		: "d" (src.m32[0]), "0" (dest.m32[0]));			\
155 })
156 #define fp_sub96c(dest, srch, srcm, srcl) ({				\
157 	char carry;							\
158 	asm ("sub.l %1,%0" : "=d,dm" (dest.m32[2])			\
159 		: "dm,d" (srcl), "0,0" (dest.m32[2]));			\
160 	asm ("subx.l %1,%0" : "=d" (dest.m32[1])			\
161 		: "d" (srcm), "0" (dest.m32[1]));			\
162 	asm ("subx.l %2,%1; scs %0" : "=d" (carry), "=d" (dest.m32[0])	\
163 		: "d" (srch), "1" (dest.m32[0]));			\
164 	carry;								\
165 })
166 
167 static inline void fp_multiplymant(union fp_mant128 *dest, struct fp_ext *src1,
168 				   struct fp_ext *src2)
169 {
170 	union fp_mant64 temp;
171 
172 	fp_mul64(dest->m32[0], dest->m32[1], src1->mant.m32[0], src2->mant.m32[0]);
173 	fp_mul64(dest->m32[2], dest->m32[3], src1->mant.m32[1], src2->mant.m32[1]);
174 
175 	fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[0], src2->mant.m32[1]);
176 	fp_addx96(dest, temp);
177 
178 	fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[1], src2->mant.m32[0]);
179 	fp_addx96(dest, temp);
180 }
181 
182 static inline void fp_dividemant(union fp_mant128 *dest, struct fp_ext *src,
183 				 struct fp_ext *div)
184 {
185 	union fp_mant128 tmp;
186 	union fp_mant64 tmp64;
187 	unsigned long *mantp = dest->m32;
188 	unsigned long fix, rem, first, dummy;
189 	int i;
190 
191 	/* the algorithm below requires dest to be smaller than div,
192 	   but both have the high bit set */
193 	if (src->mant.m64 >= div->mant.m64) {
194 		fp_sub64(src->mant, div->mant);
195 		*mantp = 1;
196 	} else
197 		*mantp = 0;
198 	mantp++;
199 
200 	/* basic idea behind this algorithm: we can't divide two 64bit numbers
201 	   (AB/CD) directly, but we can calculate AB/C0, but this means this
202 	   quotient is off by C0/CD, so we have to multiply the first result
203 	   to fix the result, after that we have nearly the correct result
204 	   and only a few corrections are needed. */
205 
206 	/* C0/CD can be precalculated, but it's an 64bit division again, but
207 	   we can make it a bit easier, by dividing first through C so we get
208 	   10/1D and now only a single shift and the value fits into 32bit. */
209 	fix = 0x80000000;
210 	dummy = div->mant.m32[1] / div->mant.m32[0] + 1;
211 	dummy = (dummy >> 1) | fix;
212 	fp_div64(fix, dummy, fix, 0, dummy);
213 	fix--;
214 
215 	for (i = 0; i < 3; i++, mantp++) {
216 		if (src->mant.m32[0] == div->mant.m32[0]) {
217 			fp_div64(first, rem, 0, src->mant.m32[1], div->mant.m32[0]);
218 
219 			fp_mul64(*mantp, dummy, first, fix);
220 			*mantp += fix;
221 		} else {
222 			fp_div64(first, rem, src->mant.m32[0], src->mant.m32[1], div->mant.m32[0]);
223 
224 			fp_mul64(*mantp, dummy, first, fix);
225 		}
226 
227 		fp_mul64(tmp.m32[0], tmp.m32[1], div->mant.m32[0], first - *mantp);
228 		fp_add64(tmp.m32[0], tmp.m32[1], 0, rem);
229 		tmp.m32[2] = 0;
230 
231 		fp_mul64(tmp64.m32[0], tmp64.m32[1], *mantp, div->mant.m32[1]);
232 		fp_sub96c(tmp, 0, tmp64.m32[0], tmp64.m32[1]);
233 
234 		src->mant.m32[0] = tmp.m32[1];
235 		src->mant.m32[1] = tmp.m32[2];
236 
237 		while (!fp_sub96c(tmp, 0, div->mant.m32[0], div->mant.m32[1])) {
238 			src->mant.m32[0] = tmp.m32[1];
239 			src->mant.m32[1] = tmp.m32[2];
240 			*mantp += 1;
241 		}
242 	}
243 }
244 
245 static inline void fp_putmant128(struct fp_ext *dest, union fp_mant128 *src,
246 				 int shift)
247 {
248 	unsigned long tmp;
249 
250 	switch (shift) {
251 	case 0:
252 		dest->mant.m64 = src->m64[0];
253 		dest->lowmant = src->m32[2] >> 24;
254 		if (src->m32[3] || (src->m32[2] << 8))
255 			dest->lowmant |= 1;
256 		break;
257 	case 1:
258 		asm volatile ("lsl.l #1,%0"
259 			: "=d" (tmp) : "0" (src->m32[2]));
260 		asm volatile ("roxl.l #1,%0"
261 			: "=d" (dest->mant.m32[1]) : "0" (src->m32[1]));
262 		asm volatile ("roxl.l #1,%0"
263 			: "=d" (dest->mant.m32[0]) : "0" (src->m32[0]));
264 		dest->lowmant = tmp >> 24;
265 		if (src->m32[3] || (tmp << 8))
266 			dest->lowmant |= 1;
267 		break;
268 	case 31:
269 		asm volatile ("lsr.l #1,%1; roxr.l #1,%0"
270 			: "=d" (dest->mant.m32[0])
271 			: "d" (src->m32[0]), "0" (src->m32[1]));
272 		asm volatile ("roxr.l #1,%0"
273 			: "=d" (dest->mant.m32[1]) : "0" (src->m32[2]));
274 		asm volatile ("roxr.l #1,%0"
275 			: "=d" (tmp) : "0" (src->m32[3]));
276 		dest->lowmant = tmp >> 24;
277 		if (src->m32[3] << 7)
278 			dest->lowmant |= 1;
279 		break;
280 	case 32:
281 		dest->mant.m32[0] = src->m32[1];
282 		dest->mant.m32[1] = src->m32[2];
283 		dest->lowmant = src->m32[3] >> 24;
284 		if (src->m32[3] << 8)
285 			dest->lowmant |= 1;
286 		break;
287 	}
288 }
289 
290 #endif	/* _MULTI_ARITH_H */
291