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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 | .file "reg_round.S" /*---------------------------------------------------------------------------+ | reg_round.S | | | | Rounding/truncation/etc for FPU basic arithmetic functions. | | | | Copyright (C) 1993,1995,1997 | | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, | | Australia. E-mail billm@suburbia.net | | | | This code has four possible entry points. | | The following must be entered by a jmp instruction: | | fpu_reg_round, fpu_reg_round_sqrt, and fpu_Arith_exit. | | | | The FPU_round entry point is intended to be used by C code. | | From C, call as: | | int FPU_round(FPU_REG *arg, unsigned int extent, unsigned int control_w) | | | | Return value is the tag of the answer, or-ed with FPU_Exception if | | one was raised, or -1 on internal error. | | | | For correct "up" and "down" rounding, the argument must have the correct | | sign. | | | +---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------+ | Four entry points. | | | | Needed by both the fpu_reg_round and fpu_reg_round_sqrt entry points: | | %eax:%ebx 64 bit significand | | %edx 32 bit extension of the significand | | %edi pointer to an FPU_REG for the result to be stored | | stack calling function must have set up a C stack frame and | | pushed %esi, %edi, and %ebx | | | | Needed just for the fpu_reg_round_sqrt entry point: | | %cx A control word in the same format as the FPU control word. | | Otherwise, PARAM4 must give such a value. | | | | | | The significand and its extension are assumed to be exact in the | | following sense: | | If the significand by itself is the exact result then the significand | | extension (%edx) must contain 0, otherwise the significand extension | | must be non-zero. | | If the significand extension is non-zero then the significand is | | smaller than the magnitude of the correct exact result by an amount | | greater than zero and less than one ls bit of the significand. | | The significand extension is only required to have three possible | | non-zero values: | | less than 0x80000000 <=> the significand is less than 1/2 an ls | | bit smaller than the magnitude of the | | true exact result. | | exactly 0x80000000 <=> the significand is exactly 1/2 an ls bit | | smaller than the magnitude of the true | | exact result. | | greater than 0x80000000 <=> the significand is more than 1/2 an ls | | bit smaller than the magnitude of the | | true exact result. | | | +---------------------------------------------------------------------------*/ /*---------------------------------------------------------------------------+ | The code in this module has become quite complex, but it should handle | | all of the FPU flags which are set at this stage of the basic arithmetic | | computations. | | There are a few rare cases where the results are not set identically to | | a real FPU. These require a bit more thought because at this stage the | | results of the code here appear to be more consistent... | | This may be changed in a future version. | +---------------------------------------------------------------------------*/ #include "fpu_emu.h" #include "exception.h" #include "control_w.h" /* Flags for FPU_bits_lost */ #define LOST_DOWN $1 #define LOST_UP $2 /* Flags for FPU_denormal */ #define DENORMAL $1 #define UNMASKED_UNDERFLOW $2 #ifndef NON_REENTRANT_FPU /* Make the code re-entrant by putting local storage on the stack: */ #define FPU_bits_lost (%esp) #define FPU_denormal 1(%esp) #else /* Not re-entrant, so we can gain speed by putting local storage in a static area: */ .data .align 4,0 FPU_bits_lost: .byte 0 FPU_denormal: .byte 0 #endif NON_REENTRANT_FPU .text .globl fpu_reg_round .globl fpu_reg_round_sqrt .globl fpu_Arith_exit /* Entry point when called from C */ ENTRY(FPU_round) pushl %ebp movl %esp,%ebp pushl %esi pushl %edi pushl %ebx movl PARAM1,%edi movl SIGH(%edi),%eax movl SIGL(%edi),%ebx movl PARAM2,%edx fpu_reg_round: /* Normal entry point */ movl PARAM4,%ecx #ifndef NON_REENTRANT_FPU pushl %ebx /* adjust the stack pointer */ #endif NON_REENTRANT_FPU #ifdef PARANOID /* Cannot use this here yet */ /* orl %eax,%eax */ /* jns L_entry_bugged */ #endif PARANOID cmpw EXP_UNDER,EXP(%edi) jle L_Make_denorm /* The number is a de-normal */ movb $0,FPU_denormal /* 0 -> not a de-normal */ Denorm_done: movb $0,FPU_bits_lost /* No bits yet lost in rounding */ movl %ecx,%esi andl CW_PC,%ecx cmpl PR_64_BITS,%ecx je LRound_To_64 cmpl PR_53_BITS,%ecx je LRound_To_53 cmpl PR_24_BITS,%ecx je LRound_To_24 #ifdef PECULIAR_486 /* With the precision control bits set to 01 "(reserved)", a real 80486 behaves as if the precision control bits were set to 11 "64 bits" */ cmpl PR_RESERVED_BITS,%ecx je LRound_To_64 #ifdef PARANOID jmp L_bugged_denorm_486 #endif PARANOID #else #ifdef PARANOID jmp L_bugged_denorm /* There is no bug, just a bad control word */ #endif PARANOID #endif PECULIAR_486 /* Round etc to 24 bit precision */ LRound_To_24: movl %esi,%ecx andl CW_RC,%ecx cmpl RC_RND,%ecx je LRound_nearest_24 cmpl RC_CHOP,%ecx je LCheck_truncate_24 cmpl RC_UP,%ecx /* Towards +infinity */ je LUp_24 cmpl RC_DOWN,%ecx /* Towards -infinity */ je LDown_24 #ifdef PARANOID jmp L_bugged_round24 #endif PARANOID LUp_24: cmpb SIGN_POS,PARAM5 jne LCheck_truncate_24 /* If negative then up==truncate */ jmp LCheck_24_round_up LDown_24: cmpb SIGN_POS,PARAM5 je LCheck_truncate_24 /* If positive then down==truncate */ LCheck_24_round_up: movl %eax,%ecx andl $0x000000ff,%ecx orl %ebx,%ecx orl %edx,%ecx jnz LDo_24_round_up jmp L_Re_normalise LRound_nearest_24: /* Do rounding of the 24th bit if needed (nearest or even) */ movl %eax,%ecx andl $0x000000ff,%ecx cmpl $0x00000080,%ecx jc LCheck_truncate_24 /* less than half, no increment needed */ jne LGreater_Half_24 /* greater than half, increment needed */ /* Possibly half, we need to check the ls bits */ orl %ebx,%ebx jnz LGreater_Half_24 /* greater than half, increment needed */ orl %edx,%edx jnz LGreater_Half_24 /* greater than half, increment needed */ /* Exactly half, increment only if 24th bit is 1 (round to even) */ testl $0x00000100,%eax jz LDo_truncate_24 LGreater_Half_24: /* Rounding: increment at the 24th bit */ LDo_24_round_up: andl $0xffffff00,%eax /* Truncate to 24 bits */ xorl %ebx,%ebx movb LOST_UP,FPU_bits_lost addl $0x00000100,%eax jmp LCheck_Round_Overflow LCheck_truncate_24: movl %eax,%ecx andl $0x000000ff,%ecx orl %ebx,%ecx orl %edx,%ecx jz L_Re_normalise /* No truncation needed */ LDo_truncate_24: andl $0xffffff00,%eax /* Truncate to 24 bits */ xorl %ebx,%ebx movb LOST_DOWN,FPU_bits_lost jmp L_Re_normalise /* Round etc to 53 bit precision */ LRound_To_53: movl %esi,%ecx andl CW_RC,%ecx cmpl RC_RND,%ecx je LRound_nearest_53 cmpl RC_CHOP,%ecx je LCheck_truncate_53 cmpl RC_UP,%ecx /* Towards +infinity */ je LUp_53 cmpl RC_DOWN,%ecx /* Towards -infinity */ je LDown_53 #ifdef PARANOID jmp L_bugged_round53 #endif PARANOID LUp_53: cmpb SIGN_POS,PARAM5 jne LCheck_truncate_53 /* If negative then up==truncate */ jmp LCheck_53_round_up LDown_53: cmpb SIGN_POS,PARAM5 je LCheck_truncate_53 /* If positive then down==truncate */ LCheck_53_round_up: movl %ebx,%ecx andl $0x000007ff,%ecx orl %edx,%ecx jnz LDo_53_round_up jmp L_Re_normalise LRound_nearest_53: /* Do rounding of the 53rd bit if needed (nearest or even) */ movl %ebx,%ecx andl $0x000007ff,%ecx cmpl $0x00000400,%ecx jc LCheck_truncate_53 /* less than half, no increment needed */ jnz LGreater_Half_53 /* greater than half, increment needed */ /* Possibly half, we need to check the ls bits */ orl %edx,%edx jnz LGreater_Half_53 /* greater than half, increment needed */ /* Exactly half, increment only if 53rd bit is 1 (round to even) */ testl $0x00000800,%ebx jz LTruncate_53 LGreater_Half_53: /* Rounding: increment at the 53rd bit */ LDo_53_round_up: movb LOST_UP,FPU_bits_lost andl $0xfffff800,%ebx /* Truncate to 53 bits */ addl $0x00000800,%ebx adcl $0,%eax jmp LCheck_Round_Overflow LCheck_truncate_53: movl %ebx,%ecx andl $0x000007ff,%ecx orl %edx,%ecx jz L_Re_normalise LTruncate_53: movb LOST_DOWN,FPU_bits_lost andl $0xfffff800,%ebx /* Truncate to 53 bits */ jmp L_Re_normalise /* Round etc to 64 bit precision */ LRound_To_64: movl %esi,%ecx andl CW_RC,%ecx cmpl RC_RND,%ecx je LRound_nearest_64 cmpl RC_CHOP,%ecx je LCheck_truncate_64 cmpl RC_UP,%ecx /* Towards +infinity */ je LUp_64 cmpl RC_DOWN,%ecx /* Towards -infinity */ je LDown_64 #ifdef PARANOID jmp L_bugged_round64 #endif PARANOID LUp_64: cmpb SIGN_POS,PARAM5 jne LCheck_truncate_64 /* If negative then up==truncate */ orl %edx,%edx jnz LDo_64_round_up jmp L_Re_normalise LDown_64: cmpb SIGN_POS,PARAM5 je LCheck_truncate_64 /* If positive then down==truncate */ orl %edx,%edx jnz LDo_64_round_up jmp L_Re_normalise LRound_nearest_64: cmpl $0x80000000,%edx jc LCheck_truncate_64 jne LDo_64_round_up /* Now test for round-to-even */ testb $1,%bl jz LCheck_truncate_64 LDo_64_round_up: movb LOST_UP,FPU_bits_lost addl $1,%ebx adcl $0,%eax LCheck_Round_Overflow: jnc L_Re_normalise /* Overflow, adjust the result (significand to 1.0) */ rcrl $1,%eax rcrl $1,%ebx incw EXP(%edi) jmp L_Re_normalise LCheck_truncate_64: orl %edx,%edx jz L_Re_normalise LTruncate_64: movb LOST_DOWN,FPU_bits_lost L_Re_normalise: testb $0xff,FPU_denormal jnz Normalise_result L_Normalised: movl TAG_Valid,%edx L_deNormalised: cmpb LOST_UP,FPU_bits_lost je L_precision_lost_up cmpb LOST_DOWN,FPU_bits_lost je L_precision_lost_down L_no_precision_loss: /* store the result */ L_Store_significand: movl %eax,SIGH(%edi) movl %ebx,SIGL(%edi) cmpw EXP_OVER,EXP(%edi) jge L_overflow movl %edx,%eax /* Convert the exponent to 80x87 form. */ addw EXTENDED_Ebias,EXP(%edi) andw $0x7fff,EXP(%edi) fpu_reg_round_signed_special_exit: cmpb SIGN_POS,PARAM5 je fpu_reg_round_special_exit orw $0x8000,EXP(%edi) /* Negative sign for the result. */ fpu_reg_round_special_exit: #ifndef NON_REENTRANT_FPU popl %ebx /* adjust the stack pointer */ #endif NON_REENTRANT_FPU fpu_Arith_exit: popl %ebx popl %edi popl %esi leave ret /* * Set the FPU status flags to represent precision loss due to * round-up. */ L_precision_lost_up: push %edx push %eax call SYMBOL_NAME(set_precision_flag_up) popl %eax popl %edx jmp L_no_precision_loss /* * Set the FPU status flags to represent precision loss due to * truncation. */ L_precision_lost_down: push %edx push %eax call SYMBOL_NAME(set_precision_flag_down) popl %eax popl %edx jmp L_no_precision_loss /* * The number is a denormal (which might get rounded up to a normal) * Shift the number right the required number of bits, which will * have to be undone later... */ L_Make_denorm: /* The action to be taken depends upon whether the underflow exception is masked */ testb CW_Underflow,%cl /* Underflow mask. */ jz Unmasked_underflow /* Do not make a denormal. */ movb DENORMAL,FPU_denormal pushl %ecx /* Save */ movw EXP_UNDER+1,%cx subw EXP(%edi),%cx cmpw $64,%cx /* shrd only works for 0..31 bits */ jnc Denorm_shift_more_than_63 cmpw $32,%cx /* shrd only works for 0..31 bits */ jnc Denorm_shift_more_than_32 /* * We got here without jumps by assuming that the most common requirement * is for a small de-normalising shift. * Shift by [1..31] bits */ addw %cx,EXP(%edi) orl %edx,%edx /* extension */ setne %ch /* Save whether %edx is non-zero */ xorl %edx,%edx shrd %cl,%ebx,%edx shrd %cl,%eax,%ebx shr %cl,%eax orb %ch,%dl popl %ecx jmp Denorm_done /* Shift by [32..63] bits */ Denorm_shift_more_than_32: addw %cx,EXP(%edi) subb $32,%cl orl %edx,%edx setne %ch orb %ch,%bl xorl %edx,%edx shrd %cl,%ebx,%edx shrd %cl,%eax,%ebx shr %cl,%eax orl %edx,%edx /* test these 32 bits */ setne %cl orb %ch,%bl orb %cl,%bl movl %ebx,%edx movl %eax,%ebx xorl %eax,%eax popl %ecx jmp Denorm_done /* Shift by [64..) bits */ Denorm_shift_more_than_63: cmpw $64,%cx jne Denorm_shift_more_than_64 /* Exactly 64 bit shift */ addw %cx,EXP(%edi) xorl %ecx,%ecx orl %edx,%edx setne %cl orl %ebx,%ebx setne %ch orb %ch,%cl orb %cl,%al movl %eax,%edx xorl %eax,%eax xorl %ebx,%ebx popl %ecx jmp Denorm_done Denorm_shift_more_than_64: movw EXP_UNDER+1,EXP(%edi) /* This is easy, %eax must be non-zero, so.. */ movl $1,%edx xorl %eax,%eax xorl %ebx,%ebx popl %ecx jmp Denorm_done Unmasked_underflow: movb UNMASKED_UNDERFLOW,FPU_denormal jmp Denorm_done /* Undo the de-normalisation. */ Normalise_result: cmpb UNMASKED_UNDERFLOW,FPU_denormal je Signal_underflow /* The number must be a denormal if we got here. */ #ifdef PARANOID /* But check it... just in case. */ cmpw EXP_UNDER+1,EXP(%edi) jne L_norm_bugged #endif PARANOID #ifdef PECULIAR_486 /* * This implements a special feature of 80486 behaviour. * Underflow will be signalled even if the number is * not a denormal after rounding. * This difference occurs only for masked underflow, and not * in the unmasked case. * Actual 80486 behaviour differs from this in some circumstances. */ orl %eax,%eax /* ms bits */ js LPseudoDenormal /* Will be masked underflow */ #else orl %eax,%eax /* ms bits */ js L_Normalised /* No longer a denormal */ #endif PECULIAR_486 jnz LDenormal_adj_exponent orl %ebx,%ebx jz L_underflow_to_zero /* The contents are zero */ LDenormal_adj_exponent: decw EXP(%edi) LPseudoDenormal: testb $0xff,FPU_bits_lost /* bits lost == underflow */ movl TAG_Special,%edx jz L_deNormalised /* There must be a masked underflow */ push %eax pushl EX_Underflow call EXCEPTION popl %eax popl %eax movl TAG_Special,%edx jmp L_deNormalised /* * The operations resulted in a number too small to represent. * Masked response. */ L_underflow_to_zero: push %eax call SYMBOL_NAME(set_precision_flag_down) popl %eax push %eax pushl EX_Underflow call EXCEPTION popl %eax popl %eax /* Reduce the exponent to EXP_UNDER */ movw EXP_UNDER,EXP(%edi) movl TAG_Zero,%edx jmp L_Store_significand /* The operations resulted in a number too large to represent. */ L_overflow: addw EXTENDED_Ebias,EXP(%edi) /* Set for unmasked response. */ push %edi call SYMBOL_NAME(arith_overflow) pop %edi jmp fpu_reg_round_signed_special_exit Signal_underflow: /* The number may have been changed to a non-denormal */ /* by the rounding operations. */ cmpw EXP_UNDER,EXP(%edi) jle Do_unmasked_underflow jmp L_Normalised Do_unmasked_underflow: /* Increase the exponent by the magic number */ addw $(3*(1<<13)),EXP(%edi) push %eax pushl EX_Underflow call EXCEPTION popl %eax popl %eax jmp L_Normalised #ifdef PARANOID #ifdef PECULIAR_486 L_bugged_denorm_486: pushl EX_INTERNAL|0x236 call EXCEPTION popl %ebx jmp L_exception_exit #else L_bugged_denorm: pushl EX_INTERNAL|0x230 call EXCEPTION popl %ebx jmp L_exception_exit #endif PECULIAR_486 L_bugged_round24: pushl EX_INTERNAL|0x231 call EXCEPTION popl %ebx jmp L_exception_exit L_bugged_round53: pushl EX_INTERNAL|0x232 call EXCEPTION popl %ebx jmp L_exception_exit L_bugged_round64: pushl EX_INTERNAL|0x233 call EXCEPTION popl %ebx jmp L_exception_exit L_norm_bugged: pushl EX_INTERNAL|0x234 call EXCEPTION popl %ebx jmp L_exception_exit L_entry_bugged: pushl EX_INTERNAL|0x235 call EXCEPTION popl %ebx L_exception_exit: mov $-1,%eax jmp fpu_reg_round_special_exit #endif PARANOID |