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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 | | | srem_mod.sa 3.1 12/10/90 | | The entry point sMOD computes the floating point MOD of the | input values X and Y. The entry point sREM computes the floating | point (IEEE) REM of the input values X and Y. | | INPUT | ----- | Double-extended value Y is pointed to by address in register | A0. Double-extended value X is located in -12(A0). The values | of X and Y are both nonzero and finite; although either or both | of them can be denormalized. The special cases of zeros, NaNs, | and infinities are handled elsewhere. | | OUTPUT | ------ | FREM(X,Y) or FMOD(X,Y), depending on entry point. | | ALGORITHM | --------- | | Step 1. Save and strip signs of X and Y: signX := sign(X), | signY := sign(Y), X := |X|, Y := |Y|, | signQ := signX EOR signY. Record whether MOD or REM | is requested. | | Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0. | If (L < 0) then | R := X, go to Step 4. | else | R := 2^(-L)X, j := L. | endif | | Step 3. Perform MOD(X,Y) | 3.1 If R = Y, go to Step 9. | 3.2 If R > Y, then { R := R - Y, Q := Q + 1} | 3.3 If j = 0, go to Step 4. | 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to | Step 3.1. | | Step 4. At this point, R = X - QY = MOD(X,Y). Set | Last_Subtract := false (used in Step 7 below). If | MOD is requested, go to Step 6. | | Step 5. R = MOD(X,Y), but REM(X,Y) is requested. | 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to | Step 6. | 5.2 If R > Y/2, then { set Last_Subtract := true, | Q := Q + 1, Y := signY*Y }. Go to Step 6. | 5.3 This is the tricky case of R = Y/2. If Q is odd, | then { Q := Q + 1, signX := -signX }. | | Step 6. R := signX*R. | | Step 7. If Last_Subtract = true, R := R - Y. | | Step 8. Return signQ, last 7 bits of Q, and R as required. | | Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus, | X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1), | R := 0. Return signQ, last 7 bits of Q, and R. | | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | The copyright notice above does not evidence any | actual or intended publication of such source code. SREM_MOD: |idnt 2,1 | Motorola 040 Floating Point Software Package |section 8 .include "fpsp.h" .set Mod_Flag,L_SCR3 .set SignY,FP_SCR3+4 .set SignX,FP_SCR3+8 .set SignQ,FP_SCR3+12 .set Sc_Flag,FP_SCR4 .set Y,FP_SCR1 .set Y_Hi,Y+4 .set Y_Lo,Y+8 .set R,FP_SCR2 .set R_Hi,R+4 .set R_Lo,R+8 Scale: .long 0x00010000,0x80000000,0x00000000,0x00000000 |xref t_avoid_unsupp .global smod smod: movel #0,Mod_Flag(%a6) bras Mod_Rem .global srem srem: movel #1,Mod_Flag(%a6) Mod_Rem: |..Save sign of X and Y moveml %d2-%d7,-(%a7) | ...save data registers movew (%a0),%d3 movew %d3,SignY(%a6) andil #0x00007FFF,%d3 | ...Y := |Y| | movel 4(%a0),%d4 movel 8(%a0),%d5 | ...(D3,D4,D5) is |Y| tstl %d3 bnes Y_Normal movel #0x00003FFE,%d3 | ...$3FFD + 1 tstl %d4 bnes HiY_not0 HiY_0: movel %d5,%d4 clrl %d5 subil #32,%d3 clrl %d6 bfffo %d4{#0:#32},%d6 lsll %d6,%d4 subl %d6,%d3 | ...(D3,D4,D5) is normalized | ...with bias $7FFD bras Chk_X HiY_not0: clrl %d6 bfffo %d4{#0:#32},%d6 subl %d6,%d3 lsll %d6,%d4 movel %d5,%d7 | ...a copy of D5 lsll %d6,%d5 negl %d6 addil #32,%d6 lsrl %d6,%d7 orl %d7,%d4 | ...(D3,D4,D5) normalized | ...with bias $7FFD bras Chk_X Y_Normal: addil #0x00003FFE,%d3 | ...(D3,D4,D5) normalized | ...with bias $7FFD Chk_X: movew -12(%a0),%d0 movew %d0,SignX(%a6) movew SignY(%a6),%d1 eorl %d0,%d1 andil #0x00008000,%d1 movew %d1,SignQ(%a6) | ...sign(Q) obtained andil #0x00007FFF,%d0 movel -8(%a0),%d1 movel -4(%a0),%d2 | ...(D0,D1,D2) is |X| tstl %d0 bnes X_Normal movel #0x00003FFE,%d0 tstl %d1 bnes HiX_not0 HiX_0: movel %d2,%d1 clrl %d2 subil #32,%d0 clrl %d6 bfffo %d1{#0:#32},%d6 lsll %d6,%d1 subl %d6,%d0 | ...(D0,D1,D2) is normalized | ...with bias $7FFD bras Init HiX_not0: clrl %d6 bfffo %d1{#0:#32},%d6 subl %d6,%d0 lsll %d6,%d1 movel %d2,%d7 | ...a copy of D2 lsll %d6,%d2 negl %d6 addil #32,%d6 lsrl %d6,%d7 orl %d7,%d1 | ...(D0,D1,D2) normalized | ...with bias $7FFD bras Init X_Normal: addil #0x00003FFE,%d0 | ...(D0,D1,D2) normalized | ...with bias $7FFD Init: | movel %d3,L_SCR1(%a6) | ...save biased expo(Y) movel %d0,L_SCR2(%a6) |save d0 subl %d3,%d0 | ...L := expo(X)-expo(Y) | Move.L D0,L ...D0 is j clrl %d6 | ...D6 := carry <- 0 clrl %d3 | ...D3 is Q moveal #0,%a1 | ...A1 is k; j+k=L, Q=0 |..(Carry,D1,D2) is R tstl %d0 bges Mod_Loop |..expo(X) < expo(Y). Thus X = mod(X,Y) | movel L_SCR2(%a6),%d0 |restore d0 bra Get_Mod |..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L Mod_Loop: tstl %d6 | ...test carry bit bgts R_GT_Y |..At this point carry = 0, R = (D1,D2), Y = (D4,D5) cmpl %d4,%d1 | ...compare hi(R) and hi(Y) bnes R_NE_Y cmpl %d5,%d2 | ...compare lo(R) and lo(Y) bnes R_NE_Y |..At this point, R = Y bra Rem_is_0 R_NE_Y: |..use the borrow of the previous compare bcss R_LT_Y | ...borrow is set iff R < Y R_GT_Y: |..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0 |..and Y < (D1,D2) < 2Y. Either way, perform R - Y subl %d5,%d2 | ...lo(R) - lo(Y) subxl %d4,%d1 | ...hi(R) - hi(Y) clrl %d6 | ...clear carry addql #1,%d3 | ...Q := Q + 1 R_LT_Y: |..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0. tstl %d0 | ...see if j = 0. beqs PostLoop addl %d3,%d3 | ...Q := 2Q addl %d2,%d2 | ...lo(R) = 2lo(R) roxll #1,%d1 | ...hi(R) = 2hi(R) + carry scs %d6 | ...set Carry if 2(R) overflows addql #1,%a1 | ...k := k+1 subql #1,%d0 | ...j := j - 1 |..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y. bras Mod_Loop PostLoop: |..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y. |..normalize R. movel L_SCR1(%a6),%d0 | ...new biased expo of R tstl %d1 bnes HiR_not0 HiR_0: movel %d2,%d1 clrl %d2 subil #32,%d0 clrl %d6 bfffo %d1{#0:#32},%d6 lsll %d6,%d1 subl %d6,%d0 | ...(D0,D1,D2) is normalized | ...with bias $7FFD bras Get_Mod HiR_not0: clrl %d6 bfffo %d1{#0:#32},%d6 bmis Get_Mod | ...already normalized subl %d6,%d0 lsll %d6,%d1 movel %d2,%d7 | ...a copy of D2 lsll %d6,%d2 negl %d6 addil #32,%d6 lsrl %d6,%d7 orl %d7,%d1 | ...(D0,D1,D2) normalized | Get_Mod: cmpil #0x000041FE,%d0 bges No_Scale Do_Scale: movew %d0,R(%a6) clrw R+2(%a6) movel %d1,R_Hi(%a6) movel %d2,R_Lo(%a6) movel L_SCR1(%a6),%d6 movew %d6,Y(%a6) clrw Y+2(%a6) movel %d4,Y_Hi(%a6) movel %d5,Y_Lo(%a6) fmovex R(%a6),%fp0 | ...no exception movel #1,Sc_Flag(%a6) bras ModOrRem No_Scale: movel %d1,R_Hi(%a6) movel %d2,R_Lo(%a6) subil #0x3FFE,%d0 movew %d0,R(%a6) clrw R+2(%a6) movel L_SCR1(%a6),%d6 subil #0x3FFE,%d6 movel %d6,L_SCR1(%a6) fmovex R(%a6),%fp0 movew %d6,Y(%a6) movel %d4,Y_Hi(%a6) movel %d5,Y_Lo(%a6) movel #0,Sc_Flag(%a6) | ModOrRem: movel Mod_Flag(%a6),%d6 beqs Fix_Sign movel L_SCR1(%a6),%d6 | ...new biased expo(Y) subql #1,%d6 | ...biased expo(Y/2) cmpl %d6,%d0 blts Fix_Sign bgts Last_Sub cmpl %d4,%d1 bnes Not_EQ cmpl %d5,%d2 bnes Not_EQ bra Tie_Case Not_EQ: bcss Fix_Sign Last_Sub: | fsubx Y(%a6),%fp0 | ...no exceptions addql #1,%d3 | ...Q := Q + 1 | Fix_Sign: |..Get sign of X movew SignX(%a6),%d6 bges Get_Q fnegx %fp0 |..Get Q | Get_Q: clrl %d6 movew SignQ(%a6),%d6 | ...D6 is sign(Q) movel #8,%d7 lsrl %d7,%d6 andil #0x0000007F,%d3 | ...7 bits of Q orl %d6,%d3 | ...sign and bits of Q swap %d3 fmovel %fpsr,%d6 andil #0xFF00FFFF,%d6 orl %d3,%d6 fmovel %d6,%fpsr | ...put Q in fpsr | Restore: moveml (%a7)+,%d2-%d7 fmovel USER_FPCR(%a6),%fpcr movel Sc_Flag(%a6),%d0 beqs Finish fmulx Scale(%pc),%fp0 | ...may cause underflow bra t_avoid_unsupp |check for denorm as a | ;result of the scaling Finish: fmovex %fp0,%fp0 |capture exceptions & round rts Rem_is_0: |..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1) addql #1,%d3 cmpil #8,%d0 | ...D0 is j bges Q_Big lsll %d0,%d3 bras Set_R_0 Q_Big: clrl %d3 Set_R_0: fmoves #0x00000000,%fp0 movel #0,Sc_Flag(%a6) bra Fix_Sign Tie_Case: |..Check parity of Q movel %d3,%d6 andil #0x00000001,%d6 tstl %d6 beq Fix_Sign | ...Q is even |..Q is odd, Q := Q + 1, signX := -signX addql #1,%d3 movew SignX(%a6),%d6 eoril #0x00008000,%d6 movew %d6,SignX(%a6) bra Fix_Sign |end |