1| 2| srem_mod.sa 3.1 12/10/90 3| 4| The entry point sMOD computes the floating point MOD of the 5| input values X and Y. The entry point sREM computes the floating 6| point (IEEE) REM of the input values X and Y. 7| 8| INPUT 9| ----- 10| Double-extended value Y is pointed to by address in register 11| A0. Double-extended value X is located in -12(A0). The values 12| of X and Y are both nonzero and finite; although either or both 13| of them can be denormalized. The special cases of zeros, NaNs, 14| and infinities are handled elsewhere. 15| 16| OUTPUT 17| ------ 18| FREM(X,Y) or FMOD(X,Y), depending on entry point. 19| 20| ALGORITHM 21| --------- 22| 23| Step 1. Save and strip signs of X and Y: signX := sign(X), 24| signY := sign(Y), X := |X|, Y := |Y|, 25| signQ := signX EOR signY. Record whether MOD or REM 26| is requested. 27| 28| Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0. 29| If (L < 0) then 30| R := X, go to Step 4. 31| else 32| R := 2^(-L)X, j := L. 33| endif 34| 35| Step 3. Perform MOD(X,Y) 36| 3.1 If R = Y, go to Step 9. 37| 3.2 If R > Y, then { R := R - Y, Q := Q + 1} 38| 3.3 If j = 0, go to Step 4. 39| 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to 40| Step 3.1. 41| 42| Step 4. At this point, R = X - QY = MOD(X,Y). Set 43| Last_Subtract := false (used in Step 7 below). If 44| MOD is requested, go to Step 6. 45| 46| Step 5. R = MOD(X,Y), but REM(X,Y) is requested. 47| 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to 48| Step 6. 49| 5.2 If R > Y/2, then { set Last_Subtract := true, 50| Q := Q + 1, Y := signY*Y }. Go to Step 6. 51| 5.3 This is the tricky case of R = Y/2. If Q is odd, 52| then { Q := Q + 1, signX := -signX }. 53| 54| Step 6. R := signX*R. 55| 56| Step 7. If Last_Subtract = true, R := R - Y. 57| 58| Step 8. Return signQ, last 7 bits of Q, and R as required. 59| 60| Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus, 61| X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1), 62| R := 0. Return signQ, last 7 bits of Q, and R. 63| 64| 65 66| Copyright (C) Motorola, Inc. 1990 67| All Rights Reserved 68| 69| For details on the license for this file, please see the 70| file, README, in this same directory. 71 72SREM_MOD: |idnt 2,1 | Motorola 040 Floating Point Software Package 73 74 |section 8 75 76#include "fpsp.h" 77 78 .set Mod_Flag,L_SCR3 79 .set SignY,FP_SCR3+4 80 .set SignX,FP_SCR3+8 81 .set SignQ,FP_SCR3+12 82 .set Sc_Flag,FP_SCR4 83 84 .set Y,FP_SCR1 85 .set Y_Hi,Y+4 86 .set Y_Lo,Y+8 87 88 .set R,FP_SCR2 89 .set R_Hi,R+4 90 .set R_Lo,R+8 91 92 93Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000 94 95 |xref t_avoid_unsupp 96 97 .global smod 98smod: 99 100 movel #0,Mod_Flag(%a6) 101 bras Mod_Rem 102 103 .global srem 104srem: 105 106 movel #1,Mod_Flag(%a6) 107 108Mod_Rem: 109|..Save sign of X and Y 110 moveml %d2-%d7,-(%a7) | ...save data registers 111 movew (%a0),%d3 112 movew %d3,SignY(%a6) 113 andil #0x00007FFF,%d3 | ...Y := |Y| 114 115| 116 movel 4(%a0),%d4 117 movel 8(%a0),%d5 | ...(D3,D4,D5) is |Y| 118 119 tstl %d3 120 bnes Y_Normal 121 122 movel #0x00003FFE,%d3 | ...$3FFD + 1 123 tstl %d4 124 bnes HiY_not0 125 126HiY_0: 127 movel %d5,%d4 128 clrl %d5 129 subil #32,%d3 130 clrl %d6 131 bfffo %d4{#0:#32},%d6 132 lsll %d6,%d4 133 subl %d6,%d3 | ...(D3,D4,D5) is normalized 134| ...with bias $7FFD 135 bras Chk_X 136 137HiY_not0: 138 clrl %d6 139 bfffo %d4{#0:#32},%d6 140 subl %d6,%d3 141 lsll %d6,%d4 142 movel %d5,%d7 | ...a copy of D5 143 lsll %d6,%d5 144 negl %d6 145 addil #32,%d6 146 lsrl %d6,%d7 147 orl %d7,%d4 | ...(D3,D4,D5) normalized 148| ...with bias $7FFD 149 bras Chk_X 150 151Y_Normal: 152 addil #0x00003FFE,%d3 | ...(D3,D4,D5) normalized 153| ...with bias $7FFD 154 155Chk_X: 156 movew -12(%a0),%d0 157 movew %d0,SignX(%a6) 158 movew SignY(%a6),%d1 159 eorl %d0,%d1 160 andil #0x00008000,%d1 161 movew %d1,SignQ(%a6) | ...sign(Q) obtained 162 andil #0x00007FFF,%d0 163 movel -8(%a0),%d1 164 movel -4(%a0),%d2 | ...(D0,D1,D2) is |X| 165 tstl %d0 166 bnes X_Normal 167 movel #0x00003FFE,%d0 168 tstl %d1 169 bnes HiX_not0 170 171HiX_0: 172 movel %d2,%d1 173 clrl %d2 174 subil #32,%d0 175 clrl %d6 176 bfffo %d1{#0:#32},%d6 177 lsll %d6,%d1 178 subl %d6,%d0 | ...(D0,D1,D2) is normalized 179| ...with bias $7FFD 180 bras Init 181 182HiX_not0: 183 clrl %d6 184 bfffo %d1{#0:#32},%d6 185 subl %d6,%d0 186 lsll %d6,%d1 187 movel %d2,%d7 | ...a copy of D2 188 lsll %d6,%d2 189 negl %d6 190 addil #32,%d6 191 lsrl %d6,%d7 192 orl %d7,%d1 | ...(D0,D1,D2) normalized 193| ...with bias $7FFD 194 bras Init 195 196X_Normal: 197 addil #0x00003FFE,%d0 | ...(D0,D1,D2) normalized 198| ...with bias $7FFD 199 200Init: 201| 202 movel %d3,L_SCR1(%a6) | ...save biased expo(Y) 203 movel %d0,L_SCR2(%a6) |save d0 204 subl %d3,%d0 | ...L := expo(X)-expo(Y) 205| Move.L D0,L ...D0 is j 206 clrl %d6 | ...D6 := carry <- 0 207 clrl %d3 | ...D3 is Q 208 moveal #0,%a1 | ...A1 is k; j+k=L, Q=0 209 210|..(Carry,D1,D2) is R 211 tstl %d0 212 bges Mod_Loop 213 214|..expo(X) < expo(Y). Thus X = mod(X,Y) 215| 216 movel L_SCR2(%a6),%d0 |restore d0 217 bra Get_Mod 218 219|..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L 220 221 222Mod_Loop: 223 tstl %d6 | ...test carry bit 224 bgts R_GT_Y 225 226|..At this point carry = 0, R = (D1,D2), Y = (D4,D5) 227 cmpl %d4,%d1 | ...compare hi(R) and hi(Y) 228 bnes R_NE_Y 229 cmpl %d5,%d2 | ...compare lo(R) and lo(Y) 230 bnes R_NE_Y 231 232|..At this point, R = Y 233 bra Rem_is_0 234 235R_NE_Y: 236|..use the borrow of the previous compare 237 bcss R_LT_Y | ...borrow is set iff R < Y 238 239R_GT_Y: 240|..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0 241|..and Y < (D1,D2) < 2Y. Either way, perform R - Y 242 subl %d5,%d2 | ...lo(R) - lo(Y) 243 subxl %d4,%d1 | ...hi(R) - hi(Y) 244 clrl %d6 | ...clear carry 245 addql #1,%d3 | ...Q := Q + 1 246 247R_LT_Y: 248|..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0. 249 tstl %d0 | ...see if j = 0. 250 beqs PostLoop 251 252 addl %d3,%d3 | ...Q := 2Q 253 addl %d2,%d2 | ...lo(R) = 2lo(R) 254 roxll #1,%d1 | ...hi(R) = 2hi(R) + carry 255 scs %d6 | ...set Carry if 2(R) overflows 256 addql #1,%a1 | ...k := k+1 257 subql #1,%d0 | ...j := j - 1 258|..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y. 259 260 bras Mod_Loop 261 262PostLoop: 263|..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y. 264 265|..normalize R. 266 movel L_SCR1(%a6),%d0 | ...new biased expo of R 267 tstl %d1 268 bnes HiR_not0 269 270HiR_0: 271 movel %d2,%d1 272 clrl %d2 273 subil #32,%d0 274 clrl %d6 275 bfffo %d1{#0:#32},%d6 276 lsll %d6,%d1 277 subl %d6,%d0 | ...(D0,D1,D2) is normalized 278| ...with bias $7FFD 279 bras Get_Mod 280 281HiR_not0: 282 clrl %d6 283 bfffo %d1{#0:#32},%d6 284 bmis Get_Mod | ...already normalized 285 subl %d6,%d0 286 lsll %d6,%d1 287 movel %d2,%d7 | ...a copy of D2 288 lsll %d6,%d2 289 negl %d6 290 addil #32,%d6 291 lsrl %d6,%d7 292 orl %d7,%d1 | ...(D0,D1,D2) normalized 293 294| 295Get_Mod: 296 cmpil #0x000041FE,%d0 297 bges No_Scale 298Do_Scale: 299 movew %d0,R(%a6) 300 clrw R+2(%a6) 301 movel %d1,R_Hi(%a6) 302 movel %d2,R_Lo(%a6) 303 movel L_SCR1(%a6),%d6 304 movew %d6,Y(%a6) 305 clrw Y+2(%a6) 306 movel %d4,Y_Hi(%a6) 307 movel %d5,Y_Lo(%a6) 308 fmovex R(%a6),%fp0 | ...no exception 309 movel #1,Sc_Flag(%a6) 310 bras ModOrRem 311No_Scale: 312 movel %d1,R_Hi(%a6) 313 movel %d2,R_Lo(%a6) 314 subil #0x3FFE,%d0 315 movew %d0,R(%a6) 316 clrw R+2(%a6) 317 movel L_SCR1(%a6),%d6 318 subil #0x3FFE,%d6 319 movel %d6,L_SCR1(%a6) 320 fmovex R(%a6),%fp0 321 movew %d6,Y(%a6) 322 movel %d4,Y_Hi(%a6) 323 movel %d5,Y_Lo(%a6) 324 movel #0,Sc_Flag(%a6) 325 326| 327 328 329ModOrRem: 330 movel Mod_Flag(%a6),%d6 331 beqs Fix_Sign 332 333 movel L_SCR1(%a6),%d6 | ...new biased expo(Y) 334 subql #1,%d6 | ...biased expo(Y/2) 335 cmpl %d6,%d0 336 blts Fix_Sign 337 bgts Last_Sub 338 339 cmpl %d4,%d1 340 bnes Not_EQ 341 cmpl %d5,%d2 342 bnes Not_EQ 343 bra Tie_Case 344 345Not_EQ: 346 bcss Fix_Sign 347 348Last_Sub: 349| 350 fsubx Y(%a6),%fp0 | ...no exceptions 351 addql #1,%d3 | ...Q := Q + 1 352 353| 354 355Fix_Sign: 356|..Get sign of X 357 movew SignX(%a6),%d6 358 bges Get_Q 359 fnegx %fp0 360 361|..Get Q 362| 363Get_Q: 364 clrl %d6 365 movew SignQ(%a6),%d6 | ...D6 is sign(Q) 366 movel #8,%d7 367 lsrl %d7,%d6 368 andil #0x0000007F,%d3 | ...7 bits of Q 369 orl %d6,%d3 | ...sign and bits of Q 370 swap %d3 371 fmovel %fpsr,%d6 372 andil #0xFF00FFFF,%d6 373 orl %d3,%d6 374 fmovel %d6,%fpsr | ...put Q in fpsr 375 376| 377Restore: 378 moveml (%a7)+,%d2-%d7 379 fmovel USER_FPCR(%a6),%fpcr 380 movel Sc_Flag(%a6),%d0 381 beqs Finish 382 fmulx Scale(%pc),%fp0 | ...may cause underflow 383 bra t_avoid_unsupp |check for denorm as a 384| ;result of the scaling 385 386Finish: 387 fmovex %fp0,%fp0 |capture exceptions & round 388 rts 389 390Rem_is_0: 391|..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1) 392 addql #1,%d3 393 cmpil #8,%d0 | ...D0 is j 394 bges Q_Big 395 396 lsll %d0,%d3 397 bras Set_R_0 398 399Q_Big: 400 clrl %d3 401 402Set_R_0: 403 fmoves #0x00000000,%fp0 404 movel #0,Sc_Flag(%a6) 405 bra Fix_Sign 406 407Tie_Case: 408|..Check parity of Q 409 movel %d3,%d6 410 andil #0x00000001,%d6 411 tstl %d6 412 beq Fix_Sign | ...Q is even 413 414|..Q is odd, Q := Q + 1, signX := -signX 415 addql #1,%d3 416 movew SignX(%a6),%d6 417 eoril #0x00008000,%d6 418 movew %d6,SignX(%a6) 419 bra Fix_Sign 420 421 |end 422