root/arch/m68k/math-emu/multi_arith.h

INCLUDED FROM

DEFINITIONS

1. fp_denormalize
2. fp_overnormalize
3. fp_addmant
4. fp_addcarry
5. fp_submant
6. fp_multiplymant
7. fp_dividemant
8. fp_putmant128

   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 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 
  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 
  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 
  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 
 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 
 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 
 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 
 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 */