| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 1 | /* multi_arith.h: multi-precision integer arithmetic functions, needed | 
|  | 2 | to do extended-precision floating point. | 
|  | 3 |  | 
|  | 4 | (c) 1998 David Huggins-Daines. | 
|  | 5 |  | 
|  | 6 | Somewhat based on arch/alpha/math-emu/ieee-math.c, which is (c) | 
|  | 7 | David Mosberger-Tang. | 
|  | 8 |  | 
|  | 9 | You may copy, modify, and redistribute this file under the terms of | 
|  | 10 | the GNU General Public License, version 2, or any later version, at | 
|  | 11 | your convenience. */ | 
|  | 12 |  | 
|  | 13 | /* Note: | 
|  | 14 |  | 
|  | 15 | These are not general multi-precision math routines.  Rather, they | 
|  | 16 | implement the subset of integer arithmetic that we need in order to | 
|  | 17 | multiply, divide, and normalize 128-bit unsigned mantissae.  */ | 
|  | 18 |  | 
|  | 19 | #ifndef MULTI_ARITH_H | 
|  | 20 | #define MULTI_ARITH_H | 
|  | 21 |  | 
|  | 22 | #if 0	/* old code... */ | 
|  | 23 |  | 
|  | 24 | /* Unsigned only, because we don't need signs to multiply and divide. */ | 
|  | 25 | typedef unsigned int int128[4]; | 
|  | 26 |  | 
|  | 27 | /* Word order */ | 
|  | 28 | enum { | 
|  | 29 | MSW128, | 
|  | 30 | NMSW128, | 
|  | 31 | NLSW128, | 
|  | 32 | LSW128 | 
|  | 33 | }; | 
|  | 34 |  | 
|  | 35 | /* big-endian */ | 
|  | 36 | #define LO_WORD(ll) (((unsigned int *) &ll)[1]) | 
|  | 37 | #define HI_WORD(ll) (((unsigned int *) &ll)[0]) | 
|  | 38 |  | 
|  | 39 | /* Convenience functions to stuff various integer values into int128s */ | 
|  | 40 |  | 
|  | 41 | static inline void zero128(int128 a) | 
|  | 42 | { | 
|  | 43 | a[LSW128] = a[NLSW128] = a[NMSW128] = a[MSW128] = 0; | 
|  | 44 | } | 
|  | 45 |  | 
|  | 46 | /* Human-readable word order in the arguments */ | 
|  | 47 | static inline void set128(unsigned int i3, unsigned int i2, unsigned int i1, | 
|  | 48 | unsigned int i0, int128 a) | 
|  | 49 | { | 
|  | 50 | a[LSW128] = i0; | 
|  | 51 | a[NLSW128] = i1; | 
|  | 52 | a[NMSW128] = i2; | 
|  | 53 | a[MSW128] = i3; | 
|  | 54 | } | 
|  | 55 |  | 
|  | 56 | /* Convenience functions (for testing as well) */ | 
|  | 57 | static inline void int64_to_128(unsigned long long src, int128 dest) | 
|  | 58 | { | 
|  | 59 | dest[LSW128] = (unsigned int) src; | 
|  | 60 | dest[NLSW128] = src >> 32; | 
|  | 61 | dest[NMSW128] = dest[MSW128] = 0; | 
|  | 62 | } | 
|  | 63 |  | 
|  | 64 | static inline void int128_to_64(const int128 src, unsigned long long *dest) | 
|  | 65 | { | 
|  | 66 | *dest = src[LSW128] | (long long) src[NLSW128] << 32; | 
|  | 67 | } | 
|  | 68 |  | 
|  | 69 | static inline void put_i128(const int128 a) | 
|  | 70 | { | 
|  | 71 | printk("%08x %08x %08x %08x\n", a[MSW128], a[NMSW128], | 
|  | 72 | a[NLSW128], a[LSW128]); | 
|  | 73 | } | 
|  | 74 |  | 
|  | 75 | /* Internal shifters: | 
|  | 76 |  | 
|  | 77 | Note that these are only good for 0 < count < 32. | 
|  | 78 | */ | 
|  | 79 |  | 
|  | 80 | static inline void _lsl128(unsigned int count, int128 a) | 
|  | 81 | { | 
|  | 82 | a[MSW128] = (a[MSW128] << count) | (a[NMSW128] >> (32 - count)); | 
|  | 83 | a[NMSW128] = (a[NMSW128] << count) | (a[NLSW128] >> (32 - count)); | 
|  | 84 | a[NLSW128] = (a[NLSW128] << count) | (a[LSW128] >> (32 - count)); | 
|  | 85 | a[LSW128] <<= count; | 
|  | 86 | } | 
|  | 87 |  | 
|  | 88 | static inline void _lsr128(unsigned int count, int128 a) | 
|  | 89 | { | 
|  | 90 | a[LSW128] = (a[LSW128] >> count) | (a[NLSW128] << (32 - count)); | 
|  | 91 | a[NLSW128] = (a[NLSW128] >> count) | (a[NMSW128] << (32 - count)); | 
|  | 92 | a[NMSW128] = (a[NMSW128] >> count) | (a[MSW128] << (32 - count)); | 
|  | 93 | a[MSW128] >>= count; | 
|  | 94 | } | 
|  | 95 |  | 
|  | 96 | /* Should be faster, one would hope */ | 
|  | 97 |  | 
|  | 98 | static inline void lslone128(int128 a) | 
|  | 99 | { | 
|  | 100 | asm volatile ("lsl.l #1,%0\n" | 
|  | 101 | "roxl.l #1,%1\n" | 
|  | 102 | "roxl.l #1,%2\n" | 
|  | 103 | "roxl.l #1,%3\n" | 
|  | 104 | : | 
|  | 105 | "=d" (a[LSW128]), | 
|  | 106 | "=d"(a[NLSW128]), | 
|  | 107 | "=d"(a[NMSW128]), | 
|  | 108 | "=d"(a[MSW128]) | 
|  | 109 | : | 
|  | 110 | "0"(a[LSW128]), | 
|  | 111 | "1"(a[NLSW128]), | 
|  | 112 | "2"(a[NMSW128]), | 
|  | 113 | "3"(a[MSW128])); | 
|  | 114 | } | 
|  | 115 |  | 
|  | 116 | static inline void lsrone128(int128 a) | 
|  | 117 | { | 
|  | 118 | asm volatile ("lsr.l #1,%0\n" | 
|  | 119 | "roxr.l #1,%1\n" | 
|  | 120 | "roxr.l #1,%2\n" | 
|  | 121 | "roxr.l #1,%3\n" | 
|  | 122 | : | 
|  | 123 | "=d" (a[MSW128]), | 
|  | 124 | "=d"(a[NMSW128]), | 
|  | 125 | "=d"(a[NLSW128]), | 
|  | 126 | "=d"(a[LSW128]) | 
|  | 127 | : | 
|  | 128 | "0"(a[MSW128]), | 
|  | 129 | "1"(a[NMSW128]), | 
|  | 130 | "2"(a[NLSW128]), | 
|  | 131 | "3"(a[LSW128])); | 
|  | 132 | } | 
|  | 133 |  | 
|  | 134 | /* Generalized 128-bit shifters: | 
|  | 135 |  | 
|  | 136 | These bit-shift to a multiple of 32, then move whole longwords.  */ | 
|  | 137 |  | 
|  | 138 | static inline void lsl128(unsigned int count, int128 a) | 
|  | 139 | { | 
|  | 140 | int wordcount, i; | 
|  | 141 |  | 
|  | 142 | if (count % 32) | 
|  | 143 | _lsl128(count % 32, a); | 
|  | 144 |  | 
|  | 145 | if (0 == (wordcount = count / 32)) | 
|  | 146 | return; | 
|  | 147 |  | 
|  | 148 | /* argh, gak, endian-sensitive */ | 
|  | 149 | for (i = 0; i < 4 - wordcount; i++) { | 
|  | 150 | a[i] = a[i + wordcount]; | 
|  | 151 | } | 
|  | 152 | for (i = 3; i >= 4 - wordcount; --i) { | 
|  | 153 | a[i] = 0; | 
|  | 154 | } | 
|  | 155 | } | 
|  | 156 |  | 
|  | 157 | static inline void lsr128(unsigned int count, int128 a) | 
|  | 158 | { | 
|  | 159 | int wordcount, i; | 
|  | 160 |  | 
|  | 161 | if (count % 32) | 
|  | 162 | _lsr128(count % 32, a); | 
|  | 163 |  | 
|  | 164 | if (0 == (wordcount = count / 32)) | 
|  | 165 | return; | 
|  | 166 |  | 
|  | 167 | for (i = 3; i >= wordcount; --i) { | 
|  | 168 | a[i] = a[i - wordcount]; | 
|  | 169 | } | 
|  | 170 | for (i = 0; i < wordcount; i++) { | 
|  | 171 | a[i] = 0; | 
|  | 172 | } | 
|  | 173 | } | 
|  | 174 |  | 
|  | 175 | static inline int orl128(int a, int128 b) | 
|  | 176 | { | 
|  | 177 | b[LSW128] |= a; | 
|  | 178 | } | 
|  | 179 |  | 
|  | 180 | static inline int btsthi128(const int128 a) | 
|  | 181 | { | 
|  | 182 | return a[MSW128] & 0x80000000; | 
|  | 183 | } | 
|  | 184 |  | 
|  | 185 | /* test bits (numbered from 0 = LSB) up to and including "top" */ | 
|  | 186 | static inline int bftestlo128(int top, const int128 a) | 
|  | 187 | { | 
|  | 188 | int r = 0; | 
|  | 189 |  | 
|  | 190 | if (top > 31) | 
|  | 191 | r |= a[LSW128]; | 
|  | 192 | if (top > 63) | 
|  | 193 | r |= a[NLSW128]; | 
|  | 194 | if (top > 95) | 
|  | 195 | r |= a[NMSW128]; | 
|  | 196 |  | 
|  | 197 | r |= a[3 - (top / 32)] & ((1 << (top % 32 + 1)) - 1); | 
|  | 198 |  | 
|  | 199 | return (r != 0); | 
|  | 200 | } | 
|  | 201 |  | 
|  | 202 | /* Aargh.  We need these because GCC is broken */ | 
|  | 203 | /* FIXME: do them in assembly, for goodness' sake! */ | 
|  | 204 | static inline void mask64(int pos, unsigned long long *mask) | 
|  | 205 | { | 
|  | 206 | *mask = 0; | 
|  | 207 |  | 
|  | 208 | if (pos < 32) { | 
|  | 209 | LO_WORD(*mask) = (1 << pos) - 1; | 
|  | 210 | return; | 
|  | 211 | } | 
|  | 212 | LO_WORD(*mask) = -1; | 
|  | 213 | HI_WORD(*mask) = (1 << (pos - 32)) - 1; | 
|  | 214 | } | 
|  | 215 |  | 
|  | 216 | static inline void bset64(int pos, unsigned long long *dest) | 
|  | 217 | { | 
|  | 218 | /* This conditional will be optimized away.  Thanks, GCC! */ | 
|  | 219 | if (pos < 32) | 
|  | 220 | asm volatile ("bset %1,%0":"=m" | 
|  | 221 | (LO_WORD(*dest)):"id"(pos)); | 
|  | 222 | else | 
|  | 223 | asm volatile ("bset %1,%0":"=m" | 
|  | 224 | (HI_WORD(*dest)):"id"(pos - 32)); | 
|  | 225 | } | 
|  | 226 |  | 
|  | 227 | static inline int btst64(int pos, unsigned long long dest) | 
|  | 228 | { | 
|  | 229 | if (pos < 32) | 
|  | 230 | return (0 != (LO_WORD(dest) & (1 << pos))); | 
|  | 231 | else | 
|  | 232 | return (0 != (HI_WORD(dest) & (1 << (pos - 32)))); | 
|  | 233 | } | 
|  | 234 |  | 
|  | 235 | static inline void lsl64(int count, unsigned long long *dest) | 
|  | 236 | { | 
|  | 237 | if (count < 32) { | 
|  | 238 | HI_WORD(*dest) = (HI_WORD(*dest) << count) | 
|  | 239 | | (LO_WORD(*dest) >> count); | 
|  | 240 | LO_WORD(*dest) <<= count; | 
|  | 241 | return; | 
|  | 242 | } | 
|  | 243 | count -= 32; | 
|  | 244 | HI_WORD(*dest) = LO_WORD(*dest) << count; | 
|  | 245 | LO_WORD(*dest) = 0; | 
|  | 246 | } | 
|  | 247 |  | 
|  | 248 | static inline void lsr64(int count, unsigned long long *dest) | 
|  | 249 | { | 
|  | 250 | if (count < 32) { | 
|  | 251 | LO_WORD(*dest) = (LO_WORD(*dest) >> count) | 
|  | 252 | | (HI_WORD(*dest) << (32 - count)); | 
|  | 253 | HI_WORD(*dest) >>= count; | 
|  | 254 | return; | 
|  | 255 | } | 
|  | 256 | count -= 32; | 
|  | 257 | LO_WORD(*dest) = HI_WORD(*dest) >> count; | 
|  | 258 | HI_WORD(*dest) = 0; | 
|  | 259 | } | 
|  | 260 | #endif | 
|  | 261 |  | 
|  | 262 | static inline void fp_denormalize(struct fp_ext *reg, unsigned int cnt) | 
|  | 263 | { | 
|  | 264 | reg->exp += cnt; | 
|  | 265 |  | 
|  | 266 | switch (cnt) { | 
|  | 267 | case 0 ... 8: | 
|  | 268 | reg->lowmant = reg->mant.m32[1] << (8 - cnt); | 
|  | 269 | reg->mant.m32[1] = (reg->mant.m32[1] >> cnt) | | 
|  | 270 | (reg->mant.m32[0] << (32 - cnt)); | 
|  | 271 | reg->mant.m32[0] = reg->mant.m32[0] >> cnt; | 
|  | 272 | break; | 
|  | 273 | case 9 ... 32: | 
|  | 274 | reg->lowmant = reg->mant.m32[1] >> (cnt - 8); | 
|  | 275 | if (reg->mant.m32[1] << (40 - cnt)) | 
|  | 276 | reg->lowmant |= 1; | 
|  | 277 | reg->mant.m32[1] = (reg->mant.m32[1] >> cnt) | | 
|  | 278 | (reg->mant.m32[0] << (32 - cnt)); | 
|  | 279 | reg->mant.m32[0] = reg->mant.m32[0] >> cnt; | 
|  | 280 | break; | 
|  | 281 | case 33 ... 39: | 
|  | 282 | asm volatile ("bfextu %1{%2,#8},%0" : "=d" (reg->lowmant) | 
|  | 283 | : "m" (reg->mant.m32[0]), "d" (64 - cnt)); | 
|  | 284 | if (reg->mant.m32[1] << (40 - cnt)) | 
|  | 285 | reg->lowmant |= 1; | 
|  | 286 | reg->mant.m32[1] = reg->mant.m32[0] >> (cnt - 32); | 
|  | 287 | reg->mant.m32[0] = 0; | 
|  | 288 | break; | 
|  | 289 | case 40 ... 71: | 
|  | 290 | reg->lowmant = reg->mant.m32[0] >> (cnt - 40); | 
|  | 291 | if ((reg->mant.m32[0] << (72 - cnt)) || reg->mant.m32[1]) | 
|  | 292 | reg->lowmant |= 1; | 
|  | 293 | reg->mant.m32[1] = reg->mant.m32[0] >> (cnt - 32); | 
|  | 294 | reg->mant.m32[0] = 0; | 
|  | 295 | break; | 
|  | 296 | default: | 
|  | 297 | reg->lowmant = reg->mant.m32[0] || reg->mant.m32[1]; | 
|  | 298 | reg->mant.m32[0] = 0; | 
|  | 299 | reg->mant.m32[1] = 0; | 
|  | 300 | break; | 
|  | 301 | } | 
|  | 302 | } | 
|  | 303 |  | 
|  | 304 | static inline int fp_overnormalize(struct fp_ext *reg) | 
|  | 305 | { | 
|  | 306 | int shift; | 
|  | 307 |  | 
|  | 308 | if (reg->mant.m32[0]) { | 
|  | 309 | asm ("bfffo %1{#0,#32},%0" : "=d" (shift) : "dm" (reg->mant.m32[0])); | 
|  | 310 | reg->mant.m32[0] = (reg->mant.m32[0] << shift) | (reg->mant.m32[1] >> (32 - shift)); | 
|  | 311 | reg->mant.m32[1] = (reg->mant.m32[1] << shift); | 
|  | 312 | } else { | 
|  | 313 | asm ("bfffo %1{#0,#32},%0" : "=d" (shift) : "dm" (reg->mant.m32[1])); | 
|  | 314 | reg->mant.m32[0] = (reg->mant.m32[1] << shift); | 
|  | 315 | reg->mant.m32[1] = 0; | 
|  | 316 | shift += 32; | 
|  | 317 | } | 
|  | 318 |  | 
|  | 319 | return shift; | 
|  | 320 | } | 
|  | 321 |  | 
|  | 322 | static inline int fp_addmant(struct fp_ext *dest, struct fp_ext *src) | 
|  | 323 | { | 
|  | 324 | int carry; | 
|  | 325 |  | 
|  | 326 | /* we assume here, gcc only insert move and a clr instr */ | 
|  | 327 | asm volatile ("add.b %1,%0" : "=d,g" (dest->lowmant) | 
|  | 328 | : "g,d" (src->lowmant), "0,0" (dest->lowmant)); | 
|  | 329 | asm volatile ("addx.l %1,%0" : "=d" (dest->mant.m32[1]) | 
|  | 330 | : "d" (src->mant.m32[1]), "0" (dest->mant.m32[1])); | 
|  | 331 | asm volatile ("addx.l %1,%0" : "=d" (dest->mant.m32[0]) | 
|  | 332 | : "d" (src->mant.m32[0]), "0" (dest->mant.m32[0])); | 
|  | 333 | asm volatile ("addx.l %0,%0" : "=d" (carry) : "0" (0)); | 
|  | 334 |  | 
|  | 335 | return carry; | 
|  | 336 | } | 
|  | 337 |  | 
|  | 338 | static inline int fp_addcarry(struct fp_ext *reg) | 
|  | 339 | { | 
|  | 340 | if (++reg->exp == 0x7fff) { | 
|  | 341 | if (reg->mant.m64) | 
|  | 342 | fp_set_sr(FPSR_EXC_INEX2); | 
|  | 343 | reg->mant.m64 = 0; | 
|  | 344 | fp_set_sr(FPSR_EXC_OVFL); | 
|  | 345 | return 0; | 
|  | 346 | } | 
|  | 347 | reg->lowmant = (reg->mant.m32[1] << 7) | (reg->lowmant ? 1 : 0); | 
|  | 348 | reg->mant.m32[1] = (reg->mant.m32[1] >> 1) | | 
|  | 349 | (reg->mant.m32[0] << 31); | 
|  | 350 | reg->mant.m32[0] = (reg->mant.m32[0] >> 1) | 0x80000000; | 
|  | 351 |  | 
|  | 352 | return 1; | 
|  | 353 | } | 
|  | 354 |  | 
|  | 355 | static inline void fp_submant(struct fp_ext *dest, struct fp_ext *src1, | 
|  | 356 | struct fp_ext *src2) | 
|  | 357 | { | 
|  | 358 | /* we assume here, gcc only insert move and a clr instr */ | 
|  | 359 | asm volatile ("sub.b %1,%0" : "=d,g" (dest->lowmant) | 
|  | 360 | : "g,d" (src2->lowmant), "0,0" (src1->lowmant)); | 
|  | 361 | asm volatile ("subx.l %1,%0" : "=d" (dest->mant.m32[1]) | 
|  | 362 | : "d" (src2->mant.m32[1]), "0" (src1->mant.m32[1])); | 
|  | 363 | asm volatile ("subx.l %1,%0" : "=d" (dest->mant.m32[0]) | 
|  | 364 | : "d" (src2->mant.m32[0]), "0" (src1->mant.m32[0])); | 
|  | 365 | } | 
|  | 366 |  | 
|  | 367 | #define fp_mul64(desth, destl, src1, src2) ({				\ | 
|  | 368 | asm ("mulu.l %2,%1:%0" : "=d" (destl), "=d" (desth)		\ | 
| Al Viro | 7f26333 | 2006-01-12 01:06:19 -0800 | [diff] [blame] | 369 | : "dm" (src1), "0" (src2));				\ | 
| Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 370 | }) | 
|  | 371 | #define fp_div64(quot, rem, srch, srcl, div)				\ | 
|  | 372 | asm ("divu.l %2,%1:%0" : "=d" (quot), "=d" (rem)		\ | 
|  | 373 | : "dm" (div), "1" (srch), "0" (srcl)) | 
|  | 374 | #define fp_add64(dest1, dest2, src1, src2) ({				\ | 
|  | 375 | asm ("add.l %1,%0" : "=d,dm" (dest2)				\ | 
|  | 376 | : "dm,d" (src2), "0,0" (dest2));			\ | 
|  | 377 | asm ("addx.l %1,%0" : "=d" (dest1)				\ | 
|  | 378 | : "d" (src1), "0" (dest1));				\ | 
|  | 379 | }) | 
|  | 380 | #define fp_addx96(dest, src) ({						\ | 
|  | 381 | /* we assume here, gcc only insert move and a clr instr */	\ | 
|  | 382 | asm volatile ("add.l %1,%0" : "=d,g" (dest->m32[2])		\ | 
|  | 383 | : "g,d" (temp.m32[1]), "0,0" (dest->m32[2]));		\ | 
|  | 384 | asm volatile ("addx.l %1,%0" : "=d" (dest->m32[1])		\ | 
|  | 385 | : "d" (temp.m32[0]), "0" (dest->m32[1]));		\ | 
|  | 386 | asm volatile ("addx.l %1,%0" : "=d" (dest->m32[0])		\ | 
|  | 387 | : "d" (0), "0" (dest->m32[0]));				\ | 
|  | 388 | }) | 
|  | 389 | #define fp_sub64(dest, src) ({						\ | 
|  | 390 | asm ("sub.l %1,%0" : "=d,dm" (dest.m32[1])			\ | 
|  | 391 | : "dm,d" (src.m32[1]), "0,0" (dest.m32[1]));		\ | 
|  | 392 | asm ("subx.l %1,%0" : "=d" (dest.m32[0])			\ | 
|  | 393 | : "d" (src.m32[0]), "0" (dest.m32[0]));			\ | 
|  | 394 | }) | 
|  | 395 | #define fp_sub96c(dest, srch, srcm, srcl) ({				\ | 
|  | 396 | char carry;							\ | 
|  | 397 | asm ("sub.l %1,%0" : "=d,dm" (dest.m32[2])			\ | 
|  | 398 | : "dm,d" (srcl), "0,0" (dest.m32[2]));			\ | 
|  | 399 | asm ("subx.l %1,%0" : "=d" (dest.m32[1])			\ | 
|  | 400 | : "d" (srcm), "0" (dest.m32[1]));			\ | 
|  | 401 | asm ("subx.l %2,%1; scs %0" : "=d" (carry), "=d" (dest.m32[0])	\ | 
|  | 402 | : "d" (srch), "1" (dest.m32[0]));			\ | 
|  | 403 | carry;								\ | 
|  | 404 | }) | 
|  | 405 |  | 
|  | 406 | static inline void fp_multiplymant(union fp_mant128 *dest, struct fp_ext *src1, | 
|  | 407 | struct fp_ext *src2) | 
|  | 408 | { | 
|  | 409 | union fp_mant64 temp; | 
|  | 410 |  | 
|  | 411 | fp_mul64(dest->m32[0], dest->m32[1], src1->mant.m32[0], src2->mant.m32[0]); | 
|  | 412 | fp_mul64(dest->m32[2], dest->m32[3], src1->mant.m32[1], src2->mant.m32[1]); | 
|  | 413 |  | 
|  | 414 | fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[0], src2->mant.m32[1]); | 
|  | 415 | fp_addx96(dest, temp); | 
|  | 416 |  | 
|  | 417 | fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[1], src2->mant.m32[0]); | 
|  | 418 | fp_addx96(dest, temp); | 
|  | 419 | } | 
|  | 420 |  | 
|  | 421 | static inline void fp_dividemant(union fp_mant128 *dest, struct fp_ext *src, | 
|  | 422 | struct fp_ext *div) | 
|  | 423 | { | 
|  | 424 | union fp_mant128 tmp; | 
|  | 425 | union fp_mant64 tmp64; | 
|  | 426 | unsigned long *mantp = dest->m32; | 
|  | 427 | unsigned long fix, rem, first, dummy; | 
|  | 428 | int i; | 
|  | 429 |  | 
|  | 430 | /* the algorithm below requires dest to be smaller than div, | 
|  | 431 | but both have the high bit set */ | 
|  | 432 | if (src->mant.m64 >= div->mant.m64) { | 
|  | 433 | fp_sub64(src->mant, div->mant); | 
|  | 434 | *mantp = 1; | 
|  | 435 | } else | 
|  | 436 | *mantp = 0; | 
|  | 437 | mantp++; | 
|  | 438 |  | 
|  | 439 | /* basic idea behind this algorithm: we can't divide two 64bit numbers | 
|  | 440 | (AB/CD) directly, but we can calculate AB/C0, but this means this | 
|  | 441 | quotient is off by C0/CD, so we have to multiply the first result | 
|  | 442 | to fix the result, after that we have nearly the correct result | 
|  | 443 | and only a few corrections are needed. */ | 
|  | 444 |  | 
|  | 445 | /* C0/CD can be precalculated, but it's an 64bit division again, but | 
|  | 446 | we can make it a bit easier, by dividing first through C so we get | 
|  | 447 | 10/1D and now only a single shift and the value fits into 32bit. */ | 
|  | 448 | fix = 0x80000000; | 
|  | 449 | dummy = div->mant.m32[1] / div->mant.m32[0] + 1; | 
|  | 450 | dummy = (dummy >> 1) | fix; | 
|  | 451 | fp_div64(fix, dummy, fix, 0, dummy); | 
|  | 452 | fix--; | 
|  | 453 |  | 
|  | 454 | for (i = 0; i < 3; i++, mantp++) { | 
|  | 455 | if (src->mant.m32[0] == div->mant.m32[0]) { | 
|  | 456 | fp_div64(first, rem, 0, src->mant.m32[1], div->mant.m32[0]); | 
|  | 457 |  | 
|  | 458 | fp_mul64(*mantp, dummy, first, fix); | 
|  | 459 | *mantp += fix; | 
|  | 460 | } else { | 
|  | 461 | fp_div64(first, rem, src->mant.m32[0], src->mant.m32[1], div->mant.m32[0]); | 
|  | 462 |  | 
|  | 463 | fp_mul64(*mantp, dummy, first, fix); | 
|  | 464 | } | 
|  | 465 |  | 
|  | 466 | fp_mul64(tmp.m32[0], tmp.m32[1], div->mant.m32[0], first - *mantp); | 
|  | 467 | fp_add64(tmp.m32[0], tmp.m32[1], 0, rem); | 
|  | 468 | tmp.m32[2] = 0; | 
|  | 469 |  | 
|  | 470 | fp_mul64(tmp64.m32[0], tmp64.m32[1], *mantp, div->mant.m32[1]); | 
|  | 471 | fp_sub96c(tmp, 0, tmp64.m32[0], tmp64.m32[1]); | 
|  | 472 |  | 
|  | 473 | src->mant.m32[0] = tmp.m32[1]; | 
|  | 474 | src->mant.m32[1] = tmp.m32[2]; | 
|  | 475 |  | 
|  | 476 | while (!fp_sub96c(tmp, 0, div->mant.m32[0], div->mant.m32[1])) { | 
|  | 477 | src->mant.m32[0] = tmp.m32[1]; | 
|  | 478 | src->mant.m32[1] = tmp.m32[2]; | 
|  | 479 | *mantp += 1; | 
|  | 480 | } | 
|  | 481 | } | 
|  | 482 | } | 
|  | 483 |  | 
|  | 484 | #if 0 | 
|  | 485 | static inline unsigned int fp_fls128(union fp_mant128 *src) | 
|  | 486 | { | 
|  | 487 | unsigned long data; | 
|  | 488 | unsigned int res, off; | 
|  | 489 |  | 
|  | 490 | if ((data = src->m32[0])) | 
|  | 491 | off = 0; | 
|  | 492 | else if ((data = src->m32[1])) | 
|  | 493 | off = 32; | 
|  | 494 | else if ((data = src->m32[2])) | 
|  | 495 | off = 64; | 
|  | 496 | else if ((data = src->m32[3])) | 
|  | 497 | off = 96; | 
|  | 498 | else | 
|  | 499 | return 128; | 
|  | 500 |  | 
|  | 501 | asm ("bfffo %1{#0,#32},%0" : "=d" (res) : "dm" (data)); | 
|  | 502 | return res + off; | 
|  | 503 | } | 
|  | 504 |  | 
|  | 505 | static inline void fp_shiftmant128(union fp_mant128 *src, int shift) | 
|  | 506 | { | 
|  | 507 | unsigned long sticky; | 
|  | 508 |  | 
|  | 509 | switch (shift) { | 
|  | 510 | case 0: | 
|  | 511 | return; | 
|  | 512 | case 1: | 
|  | 513 | asm volatile ("lsl.l #1,%0" | 
|  | 514 | : "=d" (src->m32[3]) : "0" (src->m32[3])); | 
|  | 515 | asm volatile ("roxl.l #1,%0" | 
|  | 516 | : "=d" (src->m32[2]) : "0" (src->m32[2])); | 
|  | 517 | asm volatile ("roxl.l #1,%0" | 
|  | 518 | : "=d" (src->m32[1]) : "0" (src->m32[1])); | 
|  | 519 | asm volatile ("roxl.l #1,%0" | 
|  | 520 | : "=d" (src->m32[0]) : "0" (src->m32[0])); | 
|  | 521 | return; | 
|  | 522 | case 2 ... 31: | 
|  | 523 | src->m32[0] = (src->m32[0] << shift) | (src->m32[1] >> (32 - shift)); | 
|  | 524 | src->m32[1] = (src->m32[1] << shift) | (src->m32[2] >> (32 - shift)); | 
|  | 525 | src->m32[2] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift)); | 
|  | 526 | src->m32[3] = (src->m32[3] << shift); | 
|  | 527 | return; | 
|  | 528 | case 32 ... 63: | 
|  | 529 | shift -= 32; | 
|  | 530 | src->m32[0] = (src->m32[1] << shift) | (src->m32[2] >> (32 - shift)); | 
|  | 531 | src->m32[1] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift)); | 
|  | 532 | src->m32[2] = (src->m32[3] << shift); | 
|  | 533 | src->m32[3] = 0; | 
|  | 534 | return; | 
|  | 535 | case 64 ... 95: | 
|  | 536 | shift -= 64; | 
|  | 537 | src->m32[0] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift)); | 
|  | 538 | src->m32[1] = (src->m32[3] << shift); | 
|  | 539 | src->m32[2] = src->m32[3] = 0; | 
|  | 540 | return; | 
|  | 541 | case 96 ... 127: | 
|  | 542 | shift -= 96; | 
|  | 543 | src->m32[0] = (src->m32[3] << shift); | 
|  | 544 | src->m32[1] = src->m32[2] = src->m32[3] = 0; | 
|  | 545 | return; | 
|  | 546 | case -31 ... -1: | 
|  | 547 | shift = -shift; | 
|  | 548 | sticky = 0; | 
|  | 549 | if (src->m32[3] << (32 - shift)) | 
|  | 550 | sticky = 1; | 
|  | 551 | src->m32[3] = (src->m32[3] >> shift) | (src->m32[2] << (32 - shift)) | sticky; | 
|  | 552 | src->m32[2] = (src->m32[2] >> shift) | (src->m32[1] << (32 - shift)); | 
|  | 553 | src->m32[1] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift)); | 
|  | 554 | src->m32[0] = (src->m32[0] >> shift); | 
|  | 555 | return; | 
|  | 556 | case -63 ... -32: | 
|  | 557 | shift = -shift - 32; | 
|  | 558 | sticky = 0; | 
|  | 559 | if ((src->m32[2] << (32 - shift)) || src->m32[3]) | 
|  | 560 | sticky = 1; | 
|  | 561 | src->m32[3] = (src->m32[2] >> shift) | (src->m32[1] << (32 - shift)) | sticky; | 
|  | 562 | src->m32[2] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift)); | 
|  | 563 | src->m32[1] = (src->m32[0] >> shift); | 
|  | 564 | src->m32[0] = 0; | 
|  | 565 | return; | 
|  | 566 | case -95 ... -64: | 
|  | 567 | shift = -shift - 64; | 
|  | 568 | sticky = 0; | 
|  | 569 | if ((src->m32[1] << (32 - shift)) || src->m32[2] || src->m32[3]) | 
|  | 570 | sticky = 1; | 
|  | 571 | src->m32[3] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift)) | sticky; | 
|  | 572 | src->m32[2] = (src->m32[0] >> shift); | 
|  | 573 | src->m32[1] = src->m32[0] = 0; | 
|  | 574 | return; | 
|  | 575 | case -127 ... -96: | 
|  | 576 | shift = -shift - 96; | 
|  | 577 | sticky = 0; | 
|  | 578 | if ((src->m32[0] << (32 - shift)) || src->m32[1] || src->m32[2] || src->m32[3]) | 
|  | 579 | sticky = 1; | 
|  | 580 | src->m32[3] = (src->m32[0] >> shift) | sticky; | 
|  | 581 | src->m32[2] = src->m32[1] = src->m32[0] = 0; | 
|  | 582 | return; | 
|  | 583 | } | 
|  | 584 |  | 
|  | 585 | if (shift < 0 && (src->m32[0] || src->m32[1] || src->m32[2] || src->m32[3])) | 
|  | 586 | src->m32[3] = 1; | 
|  | 587 | else | 
|  | 588 | src->m32[3] = 0; | 
|  | 589 | src->m32[2] = 0; | 
|  | 590 | src->m32[1] = 0; | 
|  | 591 | src->m32[0] = 0; | 
|  | 592 | } | 
|  | 593 | #endif | 
|  | 594 |  | 
|  | 595 | static inline void fp_putmant128(struct fp_ext *dest, union fp_mant128 *src, | 
|  | 596 | int shift) | 
|  | 597 | { | 
|  | 598 | unsigned long tmp; | 
|  | 599 |  | 
|  | 600 | switch (shift) { | 
|  | 601 | case 0: | 
|  | 602 | dest->mant.m64 = src->m64[0]; | 
|  | 603 | dest->lowmant = src->m32[2] >> 24; | 
|  | 604 | if (src->m32[3] || (src->m32[2] << 8)) | 
|  | 605 | dest->lowmant |= 1; | 
|  | 606 | break; | 
|  | 607 | case 1: | 
|  | 608 | asm volatile ("lsl.l #1,%0" | 
|  | 609 | : "=d" (tmp) : "0" (src->m32[2])); | 
|  | 610 | asm volatile ("roxl.l #1,%0" | 
|  | 611 | : "=d" (dest->mant.m32[1]) : "0" (src->m32[1])); | 
|  | 612 | asm volatile ("roxl.l #1,%0" | 
|  | 613 | : "=d" (dest->mant.m32[0]) : "0" (src->m32[0])); | 
|  | 614 | dest->lowmant = tmp >> 24; | 
|  | 615 | if (src->m32[3] || (tmp << 8)) | 
|  | 616 | dest->lowmant |= 1; | 
|  | 617 | break; | 
|  | 618 | case 31: | 
|  | 619 | asm volatile ("lsr.l #1,%1; roxr.l #1,%0" | 
|  | 620 | : "=d" (dest->mant.m32[0]) | 
|  | 621 | : "d" (src->m32[0]), "0" (src->m32[1])); | 
|  | 622 | asm volatile ("roxr.l #1,%0" | 
|  | 623 | : "=d" (dest->mant.m32[1]) : "0" (src->m32[2])); | 
|  | 624 | asm volatile ("roxr.l #1,%0" | 
|  | 625 | : "=d" (tmp) : "0" (src->m32[3])); | 
|  | 626 | dest->lowmant = tmp >> 24; | 
|  | 627 | if (src->m32[3] << 7) | 
|  | 628 | dest->lowmant |= 1; | 
|  | 629 | break; | 
|  | 630 | case 32: | 
|  | 631 | dest->mant.m32[0] = src->m32[1]; | 
|  | 632 | dest->mant.m32[1] = src->m32[2]; | 
|  | 633 | dest->lowmant = src->m32[3] >> 24; | 
|  | 634 | if (src->m32[3] << 8) | 
|  | 635 | dest->lowmant |= 1; | 
|  | 636 | break; | 
|  | 637 | } | 
|  | 638 | } | 
|  | 639 |  | 
|  | 640 | #if 0 /* old code... */ | 
|  | 641 | static inline int fls(unsigned int a) | 
|  | 642 | { | 
|  | 643 | int r; | 
|  | 644 |  | 
|  | 645 | asm volatile ("bfffo %1{#0,#32},%0" | 
|  | 646 | : "=d" (r) : "md" (a)); | 
|  | 647 | return r; | 
|  | 648 | } | 
|  | 649 |  | 
|  | 650 | /* fls = "find last set" (cf. ffs(3)) */ | 
|  | 651 | static inline int fls128(const int128 a) | 
|  | 652 | { | 
|  | 653 | if (a[MSW128]) | 
|  | 654 | return fls(a[MSW128]); | 
|  | 655 | if (a[NMSW128]) | 
|  | 656 | return fls(a[NMSW128]) + 32; | 
|  | 657 | /* XXX: it probably never gets beyond this point in actual | 
|  | 658 | use, but that's indicative of a more general problem in the | 
|  | 659 | algorithm (i.e. as per the actual 68881 implementation, we | 
|  | 660 | really only need at most 67 bits of precision [plus | 
|  | 661 | overflow]) so I'm not going to fix it. */ | 
|  | 662 | if (a[NLSW128]) | 
|  | 663 | return fls(a[NLSW128]) + 64; | 
|  | 664 | if (a[LSW128]) | 
|  | 665 | return fls(a[LSW128]) + 96; | 
|  | 666 | else | 
|  | 667 | return -1; | 
|  | 668 | } | 
|  | 669 |  | 
|  | 670 | static inline int zerop128(const int128 a) | 
|  | 671 | { | 
|  | 672 | return !(a[LSW128] | a[NLSW128] | a[NMSW128] | a[MSW128]); | 
|  | 673 | } | 
|  | 674 |  | 
|  | 675 | static inline int nonzerop128(const int128 a) | 
|  | 676 | { | 
|  | 677 | return (a[LSW128] | a[NLSW128] | a[NMSW128] | a[MSW128]); | 
|  | 678 | } | 
|  | 679 |  | 
|  | 680 | /* Addition and subtraction */ | 
|  | 681 | /* Do these in "pure" assembly, because "extended" asm is unmanageable | 
|  | 682 | here */ | 
|  | 683 | static inline void add128(const int128 a, int128 b) | 
|  | 684 | { | 
|  | 685 | /* rotating carry flags */ | 
|  | 686 | unsigned int carry[2]; | 
|  | 687 |  | 
|  | 688 | carry[0] = a[LSW128] > (0xffffffff - b[LSW128]); | 
|  | 689 | b[LSW128] += a[LSW128]; | 
|  | 690 |  | 
|  | 691 | carry[1] = a[NLSW128] > (0xffffffff - b[NLSW128] - carry[0]); | 
|  | 692 | b[NLSW128] = a[NLSW128] + b[NLSW128] + carry[0]; | 
|  | 693 |  | 
|  | 694 | carry[0] = a[NMSW128] > (0xffffffff - b[NMSW128] - carry[1]); | 
|  | 695 | b[NMSW128] = a[NMSW128] + b[NMSW128] + carry[1]; | 
|  | 696 |  | 
|  | 697 | b[MSW128] = a[MSW128] + b[MSW128] + carry[0]; | 
|  | 698 | } | 
|  | 699 |  | 
|  | 700 | /* Note: assembler semantics: "b -= a" */ | 
|  | 701 | static inline void sub128(const int128 a, int128 b) | 
|  | 702 | { | 
|  | 703 | /* rotating borrow flags */ | 
|  | 704 | unsigned int borrow[2]; | 
|  | 705 |  | 
|  | 706 | borrow[0] = b[LSW128] < a[LSW128]; | 
|  | 707 | b[LSW128] -= a[LSW128]; | 
|  | 708 |  | 
|  | 709 | borrow[1] = b[NLSW128] < a[NLSW128] + borrow[0]; | 
|  | 710 | b[NLSW128] = b[NLSW128] - a[NLSW128] - borrow[0]; | 
|  | 711 |  | 
|  | 712 | borrow[0] = b[NMSW128] < a[NMSW128] + borrow[1]; | 
|  | 713 | b[NMSW128] = b[NMSW128] - a[NMSW128] - borrow[1]; | 
|  | 714 |  | 
|  | 715 | b[MSW128] = b[MSW128] - a[MSW128] - borrow[0]; | 
|  | 716 | } | 
|  | 717 |  | 
|  | 718 | /* Poor man's 64-bit expanding multiply */ | 
|  | 719 | static inline void mul64(unsigned long long a, unsigned long long b, int128 c) | 
|  | 720 | { | 
|  | 721 | unsigned long long acc; | 
|  | 722 | int128 acc128; | 
|  | 723 |  | 
|  | 724 | zero128(acc128); | 
|  | 725 | zero128(c); | 
|  | 726 |  | 
|  | 727 | /* first the low words */ | 
|  | 728 | if (LO_WORD(a) && LO_WORD(b)) { | 
|  | 729 | acc = (long long) LO_WORD(a) * LO_WORD(b); | 
|  | 730 | c[NLSW128] = HI_WORD(acc); | 
|  | 731 | c[LSW128] = LO_WORD(acc); | 
|  | 732 | } | 
|  | 733 | /* Next the high words */ | 
|  | 734 | if (HI_WORD(a) && HI_WORD(b)) { | 
|  | 735 | acc = (long long) HI_WORD(a) * HI_WORD(b); | 
|  | 736 | c[MSW128] = HI_WORD(acc); | 
|  | 737 | c[NMSW128] = LO_WORD(acc); | 
|  | 738 | } | 
|  | 739 | /* The middle words */ | 
|  | 740 | if (LO_WORD(a) && HI_WORD(b)) { | 
|  | 741 | acc = (long long) LO_WORD(a) * HI_WORD(b); | 
|  | 742 | acc128[NMSW128] = HI_WORD(acc); | 
|  | 743 | acc128[NLSW128] = LO_WORD(acc); | 
|  | 744 | add128(acc128, c); | 
|  | 745 | } | 
|  | 746 | /* The first and last words */ | 
|  | 747 | if (HI_WORD(a) && LO_WORD(b)) { | 
|  | 748 | acc = (long long) HI_WORD(a) * LO_WORD(b); | 
|  | 749 | acc128[NMSW128] = HI_WORD(acc); | 
|  | 750 | acc128[NLSW128] = LO_WORD(acc); | 
|  | 751 | add128(acc128, c); | 
|  | 752 | } | 
|  | 753 | } | 
|  | 754 |  | 
|  | 755 | /* Note: unsigned */ | 
|  | 756 | static inline int cmp128(int128 a, int128 b) | 
|  | 757 | { | 
|  | 758 | if (a[MSW128] < b[MSW128]) | 
|  | 759 | return -1; | 
|  | 760 | if (a[MSW128] > b[MSW128]) | 
|  | 761 | return 1; | 
|  | 762 | if (a[NMSW128] < b[NMSW128]) | 
|  | 763 | return -1; | 
|  | 764 | if (a[NMSW128] > b[NMSW128]) | 
|  | 765 | return 1; | 
|  | 766 | if (a[NLSW128] < b[NLSW128]) | 
|  | 767 | return -1; | 
|  | 768 | if (a[NLSW128] > b[NLSW128]) | 
|  | 769 | return 1; | 
|  | 770 |  | 
|  | 771 | return (signed) a[LSW128] - b[LSW128]; | 
|  | 772 | } | 
|  | 773 |  | 
|  | 774 | inline void div128(int128 a, int128 b, int128 c) | 
|  | 775 | { | 
|  | 776 | int128 mask; | 
|  | 777 |  | 
|  | 778 | /* Algorithm: | 
|  | 779 |  | 
|  | 780 | Shift the divisor until it's at least as big as the | 
|  | 781 | dividend, keeping track of the position to which we've | 
|  | 782 | shifted it, i.e. the power of 2 which we've multiplied it | 
|  | 783 | by. | 
|  | 784 |  | 
|  | 785 | Then, for this power of 2 (the mask), and every one smaller | 
|  | 786 | than it, subtract the mask from the dividend and add it to | 
|  | 787 | the quotient until the dividend is smaller than the raised | 
|  | 788 | divisor.  At this point, divide the dividend and the mask | 
|  | 789 | by 2 (i.e. shift one place to the right).  Lather, rinse, | 
|  | 790 | and repeat, until there are no more powers of 2 left. */ | 
|  | 791 |  | 
|  | 792 | /* FIXME: needless to say, there's room for improvement here too. */ | 
|  | 793 |  | 
|  | 794 | /* Shift up */ | 
|  | 795 | /* XXX: since it just has to be "at least as big", we can | 
|  | 796 | probably eliminate this horribly wasteful loop.  I will | 
|  | 797 | have to prove this first, though */ | 
|  | 798 | set128(0, 0, 0, 1, mask); | 
|  | 799 | while (cmp128(b, a) < 0 && !btsthi128(b)) { | 
|  | 800 | lslone128(b); | 
|  | 801 | lslone128(mask); | 
|  | 802 | } | 
|  | 803 |  | 
|  | 804 | /* Shift down */ | 
|  | 805 | zero128(c); | 
|  | 806 | do { | 
|  | 807 | if (cmp128(a, b) >= 0) { | 
|  | 808 | sub128(b, a); | 
|  | 809 | add128(mask, c); | 
|  | 810 | } | 
|  | 811 | lsrone128(mask); | 
|  | 812 | lsrone128(b); | 
|  | 813 | } while (nonzerop128(mask)); | 
|  | 814 |  | 
|  | 815 | /* The remainder is in a... */ | 
|  | 816 | } | 
|  | 817 | #endif | 
|  | 818 |  | 
|  | 819 | #endif	/* MULTI_ARITH_H */ |