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