1| 2| bindec.sa 3.4 1/3/91 3| 4| bindec 5| 6| Description: 7| Converts an input in extended precision format 8| to bcd format. 9| 10| Input: 11| a0 points to the input extended precision value 12| value in memory; d0 contains the k-factor sign-extended 13| to 32-bits. The input may be either normalized, 14| unnormalized, or denormalized. 15| 16| Output: result in the FP_SCR1 space on the stack. 17| 18| Saves and Modifies: D2-D7,A2,FP2 19| 20| Algorithm: 21| 22| A1. Set RM and size ext; Set SIGMA = sign of input. 23| The k-factor is saved for use in d7. Clear the 24| BINDEC_FLG for separating normalized/denormalized 25| input. If input is unnormalized or denormalized, 26| normalize it. 27| 28| A2. Set X = abs(input). 29| 30| A3. Compute ILOG. 31| ILOG is the log base 10 of the input value. It is 32| approximated by adding e + 0.f when the original 33| value is viewed as 2^^e * 1.f in extended precision. 34| This value is stored in d6. 35| 36| A4. Clr INEX bit. 37| The operation in A3 above may have set INEX2. 38| 39| A5. Set ICTR = 0; 40| ICTR is a flag used in A13. It must be set before the 41| loop entry A6. 42| 43| A6. Calculate LEN. 44| LEN is the number of digits to be displayed. The 45| k-factor can dictate either the total number of digits, 46| if it is a positive number, or the number of digits 47| after the decimal point which are to be included as 48| significant. See the 68882 manual for examples. 49| If LEN is computed to be greater than 17, set OPERR in 50| USER_FPSR. LEN is stored in d4. 51| 52| A7. Calculate SCALE. 53| SCALE is equal to 10^ISCALE, where ISCALE is the number 54| of decimal places needed to insure LEN integer digits 55| in the output before conversion to bcd. LAMBDA is the 56| sign of ISCALE, used in A9. Fp1 contains 57| 10^^(abs(ISCALE)) using a rounding mode which is a 58| function of the original rounding mode and the signs 59| of ISCALE and X. A table is given in the code. 60| 61| A8. Clr INEX; Force RZ. 62| The operation in A3 above may have set INEX2. 63| RZ mode is forced for the scaling operation to insure 64| only one rounding error. The grs bits are collected in 65| the INEX flag for use in A10. 66| 67| A9. Scale X -> Y. 68| The mantissa is scaled to the desired number of 69| significant digits. The excess digits are collected 70| in INEX2. 71| 72| A10. Or in INEX. 73| If INEX is set, round error occurred. This is 74| compensated for by 'or-ing' in the INEX2 flag to 75| the lsb of Y. 76| 77| A11. Restore original FPCR; set size ext. 78| Perform FINT operation in the user's rounding mode. 79| Keep the size to extended. 80| 81| A12. Calculate YINT = FINT(Y) according to user's rounding 82| mode. The FPSP routine sintd0 is used. The output 83| is in fp0. 84| 85| A13. Check for LEN digits. 86| If the int operation results in more than LEN digits, 87| or less than LEN -1 digits, adjust ILOG and repeat from 88| A6. This test occurs only on the first pass. If the 89| result is exactly 10^LEN, decrement ILOG and divide 90| the mantissa by 10. 91| 92| A14. Convert the mantissa to bcd. 93| The binstr routine is used to convert the LEN digit 94| mantissa to bcd in memory. The input to binstr is 95| to be a fraction; i.e. (mantissa)/10^LEN and adjusted 96| such that the decimal point is to the left of bit 63. 97| The bcd digits are stored in the correct position in 98| the final string area in memory. 99| 100| A15. Convert the exponent to bcd. 101| As in A14 above, the exp is converted to bcd and the 102| digits are stored in the final string. 103| Test the length of the final exponent string. If the 104| length is 4, set operr. 105| 106| A16. Write sign bits to final string. 107| 108| Implementation Notes: 109| 110| The registers are used as follows: 111| 112| d0: scratch; LEN input to binstr 113| d1: scratch 114| d2: upper 32-bits of mantissa for binstr 115| d3: scratch;lower 32-bits of mantissa for binstr 116| d4: LEN 117| d5: LAMBDA/ICTR 118| d6: ILOG 119| d7: k-factor 120| a0: ptr for original operand/final result 121| a1: scratch pointer 122| a2: pointer to FP_X; abs(original value) in ext 123| fp0: scratch 124| fp1: scratch 125| fp2: scratch 126| F_SCR1: 127| F_SCR2: 128| L_SCR1: 129| L_SCR2: 130 131| Copyright (C) Motorola, Inc. 1990 132| All Rights Reserved 133| 134| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 135| The copyright notice above does not evidence any 136| actual or intended publication of such source code. 137 138|BINDEC idnt 2,1 | Motorola 040 Floating Point Software Package 139 140 .include "fpsp.h" 141 142 |section 8 143 144| Constants in extended precision 145LOG2: .long 0x3FFD0000,0x9A209A84,0xFBCFF798,0x00000000 146LOG2UP1: .long 0x3FFD0000,0x9A209A84,0xFBCFF799,0x00000000 147 148| Constants in single precision 149FONE: .long 0x3F800000,0x00000000,0x00000000,0x00000000 150FTWO: .long 0x40000000,0x00000000,0x00000000,0x00000000 151FTEN: .long 0x41200000,0x00000000,0x00000000,0x00000000 152F4933: .long 0x459A2800,0x00000000,0x00000000,0x00000000 153 154RBDTBL: .byte 0,0,0,0 155 .byte 3,3,2,2 156 .byte 3,2,2,3 157 .byte 2,3,3,2 158 159 |xref binstr 160 |xref sintdo 161 |xref ptenrn,ptenrm,ptenrp 162 163 .global bindec 164 .global sc_mul 165bindec: 166 moveml %d2-%d7/%a2,-(%a7) 167 fmovemx %fp0-%fp2,-(%a7) 168 169| A1. Set RM and size ext. Set SIGMA = sign input; 170| The k-factor is saved for use in d7. Clear BINDEC_FLG for 171| separating normalized/denormalized input. If the input 172| is a denormalized number, set the BINDEC_FLG memory word 173| to signal denorm. If the input is unnormalized, normalize 174| the input and test for denormalized result. 175| 176 fmovel #rm_mode,%FPCR |set RM and ext 177 movel (%a0),L_SCR2(%a6) |save exponent for sign check 178 movel %d0,%d7 |move k-factor to d7 179 clrb BINDEC_FLG(%a6) |clr norm/denorm flag 180 movew STAG(%a6),%d0 |get stag 181 andiw #0xe000,%d0 |isolate stag bits 182 beq A2_str |if zero, input is norm 183| 184| Normalize the denorm 185| 186un_de_norm: 187 movew (%a0),%d0 188 andiw #0x7fff,%d0 |strip sign of normalized exp 189 movel 4(%a0),%d1 190 movel 8(%a0),%d2 191norm_loop: 192 subw #1,%d0 193 lsll #1,%d2 194 roxll #1,%d1 195 tstl %d1 196 bges norm_loop 197| 198| Test if the normalized input is denormalized 199| 200 tstw %d0 201 bgts pos_exp |if greater than zero, it is a norm 202 st BINDEC_FLG(%a6) |set flag for denorm 203pos_exp: 204 andiw #0x7fff,%d0 |strip sign of normalized exp 205 movew %d0,(%a0) 206 movel %d1,4(%a0) 207 movel %d2,8(%a0) 208 209| A2. Set X = abs(input). 210| 211A2_str: 212 movel (%a0),FP_SCR2(%a6) | move input to work space 213 movel 4(%a0),FP_SCR2+4(%a6) | move input to work space 214 movel 8(%a0),FP_SCR2+8(%a6) | move input to work space 215 andil #0x7fffffff,FP_SCR2(%a6) |create abs(X) 216 217| A3. Compute ILOG. 218| ILOG is the log base 10 of the input value. It is approx- 219| imated by adding e + 0.f when the original value is viewed 220| as 2^^e * 1.f in extended precision. This value is stored 221| in d6. 222| 223| Register usage: 224| Input/Output 225| d0: k-factor/exponent 226| d2: x/x 227| d3: x/x 228| d4: x/x 229| d5: x/x 230| d6: x/ILOG 231| d7: k-factor/Unchanged 232| a0: ptr for original operand/final result 233| a1: x/x 234| a2: x/x 235| fp0: x/float(ILOG) 236| fp1: x/x 237| fp2: x/x 238| F_SCR1:x/x 239| F_SCR2:Abs(X)/Abs(X) with $3fff exponent 240| L_SCR1:x/x 241| L_SCR2:first word of X packed/Unchanged 242 243 tstb BINDEC_FLG(%a6) |check for denorm 244 beqs A3_cont |if clr, continue with norm 245 movel #-4933,%d6 |force ILOG = -4933 246 bras A4_str 247A3_cont: 248 movew FP_SCR2(%a6),%d0 |move exp to d0 249 movew #0x3fff,FP_SCR2(%a6) |replace exponent with 0x3fff 250 fmovex FP_SCR2(%a6),%fp0 |now fp0 has 1.f 251 subw #0x3fff,%d0 |strip off bias 252 faddw %d0,%fp0 |add in exp 253 fsubs FONE,%fp0 |subtract off 1.0 254 fbge pos_res |if pos, branch 255 fmulx LOG2UP1,%fp0 |if neg, mul by LOG2UP1 256 fmovel %fp0,%d6 |put ILOG in d6 as a lword 257 bras A4_str |go move out ILOG 258pos_res: 259 fmulx LOG2,%fp0 |if pos, mul by LOG2 260 fmovel %fp0,%d6 |put ILOG in d6 as a lword 261 262 263| A4. Clr INEX bit. 264| The operation in A3 above may have set INEX2. 265 266A4_str: 267 fmovel #0,%FPSR |zero all of fpsr - nothing needed 268 269 270| A5. Set ICTR = 0; 271| ICTR is a flag used in A13. It must be set before the 272| loop entry A6. The lower word of d5 is used for ICTR. 273 274 clrw %d5 |clear ICTR 275 276 277| A6. Calculate LEN. 278| LEN is the number of digits to be displayed. The k-factor 279| can dictate either the total number of digits, if it is 280| a positive number, or the number of digits after the 281| original decimal point which are to be included as 282| significant. See the 68882 manual for examples. 283| If LEN is computed to be greater than 17, set OPERR in 284| USER_FPSR. LEN is stored in d4. 285| 286| Register usage: 287| Input/Output 288| d0: exponent/Unchanged 289| d2: x/x/scratch 290| d3: x/x 291| d4: exc picture/LEN 292| d5: ICTR/Unchanged 293| d6: ILOG/Unchanged 294| d7: k-factor/Unchanged 295| a0: ptr for original operand/final result 296| a1: x/x 297| a2: x/x 298| fp0: float(ILOG)/Unchanged 299| fp1: x/x 300| fp2: x/x 301| F_SCR1:x/x 302| F_SCR2:Abs(X) with $3fff exponent/Unchanged 303| L_SCR1:x/x 304| L_SCR2:first word of X packed/Unchanged 305 306A6_str: 307 tstl %d7 |branch on sign of k 308 bles k_neg |if k <= 0, LEN = ILOG + 1 - k 309 movel %d7,%d4 |if k > 0, LEN = k 310 bras len_ck |skip to LEN check 311k_neg: 312 movel %d6,%d4 |first load ILOG to d4 313 subl %d7,%d4 |subtract off k 314 addql #1,%d4 |add in the 1 315len_ck: 316 tstl %d4 |LEN check: branch on sign of LEN 317 bles LEN_ng |if neg, set LEN = 1 318 cmpl #17,%d4 |test if LEN > 17 319 bles A7_str |if not, forget it 320 movel #17,%d4 |set max LEN = 17 321 tstl %d7 |if negative, never set OPERR 322 bles A7_str |if positive, continue 323 orl #opaop_mask,USER_FPSR(%a6) |set OPERR & AIOP in USER_FPSR 324 bras A7_str |finished here 325LEN_ng: 326 moveql #1,%d4 |min LEN is 1 327 328 329| A7. Calculate SCALE. 330| SCALE is equal to 10^ISCALE, where ISCALE is the number 331| of decimal places needed to insure LEN integer digits 332| in the output before conversion to bcd. LAMBDA is the sign 333| of ISCALE, used in A9. Fp1 contains 10^^(abs(ISCALE)) using 334| the rounding mode as given in the following table (see 335| Coonen, p. 7.23 as ref.; however, the SCALE variable is 336| of opposite sign in bindec.sa from Coonen). 337| 338| Initial USE 339| FPCR[6:5] LAMBDA SIGN(X) FPCR[6:5] 340| ---------------------------------------------- 341| RN 00 0 0 00/0 RN 342| RN 00 0 1 00/0 RN 343| RN 00 1 0 00/0 RN 344| RN 00 1 1 00/0 RN 345| RZ 01 0 0 11/3 RP 346| RZ 01 0 1 11/3 RP 347| RZ 01 1 0 10/2 RM 348| RZ 01 1 1 10/2 RM 349| RM 10 0 0 11/3 RP 350| RM 10 0 1 10/2 RM 351| RM 10 1 0 10/2 RM 352| RM 10 1 1 11/3 RP 353| RP 11 0 0 10/2 RM 354| RP 11 0 1 11/3 RP 355| RP 11 1 0 11/3 RP 356| RP 11 1 1 10/2 RM 357| 358| Register usage: 359| Input/Output 360| d0: exponent/scratch - final is 0 361| d2: x/0 or 24 for A9 362| d3: x/scratch - offset ptr into PTENRM array 363| d4: LEN/Unchanged 364| d5: 0/ICTR:LAMBDA 365| d6: ILOG/ILOG or k if ((k<=0)&(ILOG<k)) 366| d7: k-factor/Unchanged 367| a0: ptr for original operand/final result 368| a1: x/ptr to PTENRM array 369| a2: x/x 370| fp0: float(ILOG)/Unchanged 371| fp1: x/10^ISCALE 372| fp2: x/x 373| F_SCR1:x/x 374| F_SCR2:Abs(X) with $3fff exponent/Unchanged 375| L_SCR1:x/x 376| L_SCR2:first word of X packed/Unchanged 377 378A7_str: 379 tstl %d7 |test sign of k 380 bgts k_pos |if pos and > 0, skip this 381 cmpl %d6,%d7 |test k - ILOG 382 blts k_pos |if ILOG >= k, skip this 383 movel %d7,%d6 |if ((k<0) & (ILOG < k)) ILOG = k 384k_pos: 385 movel %d6,%d0 |calc ILOG + 1 - LEN in d0 386 addql #1,%d0 |add the 1 387 subl %d4,%d0 |sub off LEN 388 swap %d5 |use upper word of d5 for LAMBDA 389 clrw %d5 |set it zero initially 390 clrw %d2 |set up d2 for very small case 391 tstl %d0 |test sign of ISCALE 392 bges iscale |if pos, skip next inst 393 addqw #1,%d5 |if neg, set LAMBDA true 394 cmpl #0xffffecd4,%d0 |test iscale <= -4908 395 bgts no_inf |if false, skip rest 396 addil #24,%d0 |add in 24 to iscale 397 movel #24,%d2 |put 24 in d2 for A9 398no_inf: 399 negl %d0 |and take abs of ISCALE 400iscale: 401 fmoves FONE,%fp1 |init fp1 to 1 402 bfextu USER_FPCR(%a6){#26:#2},%d1 |get initial rmode bits 403 lslw #1,%d1 |put them in bits 2:1 404 addw %d5,%d1 |add in LAMBDA 405 lslw #1,%d1 |put them in bits 3:1 406 tstl L_SCR2(%a6) |test sign of original x 407 bges x_pos |if pos, don't set bit 0 408 addql #1,%d1 |if neg, set bit 0 409x_pos: 410 leal RBDTBL,%a2 |load rbdtbl base 411 moveb (%a2,%d1),%d3 |load d3 with new rmode 412 lsll #4,%d3 |put bits in proper position 413 fmovel %d3,%fpcr |load bits into fpu 414 lsrl #4,%d3 |put bits in proper position 415 tstb %d3 |decode new rmode for pten table 416 bnes not_rn |if zero, it is RN 417 leal PTENRN,%a1 |load a1 with RN table base 418 bras rmode |exit decode 419not_rn: 420 lsrb #1,%d3 |get lsb in carry 421 bccs not_rp |if carry clear, it is RM 422 leal PTENRP,%a1 |load a1 with RP table base 423 bras rmode |exit decode 424not_rp: 425 leal PTENRM,%a1 |load a1 with RM table base 426rmode: 427 clrl %d3 |clr table index 428e_loop: 429 lsrl #1,%d0 |shift next bit into carry 430 bccs e_next |if zero, skip the mul 431 fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no) 432e_next: 433 addl #12,%d3 |inc d3 to next pwrten table entry 434 tstl %d0 |test if ISCALE is zero 435 bnes e_loop |if not, loop 436 437 438| A8. Clr INEX; Force RZ. 439| The operation in A3 above may have set INEX2. 440| RZ mode is forced for the scaling operation to insure 441| only one rounding error. The grs bits are collected in 442| the INEX flag for use in A10. 443| 444| Register usage: 445| Input/Output 446 447 fmovel #0,%FPSR |clr INEX 448 fmovel #rz_mode,%FPCR |set RZ rounding mode 449 450 451| A9. Scale X -> Y. 452| The mantissa is scaled to the desired number of significant 453| digits. The excess digits are collected in INEX2. If mul, 454| Check d2 for excess 10 exponential value. If not zero, 455| the iscale value would have caused the pwrten calculation 456| to overflow. Only a negative iscale can cause this, so 457| multiply by 10^(d2), which is now only allowed to be 24, 458| with a multiply by 10^8 and 10^16, which is exact since 459| 10^24 is exact. If the input was denormalized, we must 460| create a busy stack frame with the mul command and the 461| two operands, and allow the fpu to complete the multiply. 462| 463| Register usage: 464| Input/Output 465| d0: FPCR with RZ mode/Unchanged 466| d2: 0 or 24/unchanged 467| d3: x/x 468| d4: LEN/Unchanged 469| d5: ICTR:LAMBDA 470| d6: ILOG/Unchanged 471| d7: k-factor/Unchanged 472| a0: ptr for original operand/final result 473| a1: ptr to PTENRM array/Unchanged 474| a2: x/x 475| fp0: float(ILOG)/X adjusted for SCALE (Y) 476| fp1: 10^ISCALE/Unchanged 477| fp2: x/x 478| F_SCR1:x/x 479| F_SCR2:Abs(X) with $3fff exponent/Unchanged 480| L_SCR1:x/x 481| L_SCR2:first word of X packed/Unchanged 482 483A9_str: 484 fmovex (%a0),%fp0 |load X from memory 485 fabsx %fp0 |use abs(X) 486 tstw %d5 |LAMBDA is in lower word of d5 487 bne sc_mul |if neg (LAMBDA = 1), scale by mul 488 fdivx %fp1,%fp0 |calculate X / SCALE -> Y to fp0 489 bras A10_st |branch to A10 490 491sc_mul: 492 tstb BINDEC_FLG(%a6) |check for denorm 493 beqs A9_norm |if norm, continue with mul 494 fmovemx %fp1-%fp1,-(%a7) |load ETEMP with 10^ISCALE 495 movel 8(%a0),-(%a7) |load FPTEMP with input arg 496 movel 4(%a0),-(%a7) 497 movel (%a0),-(%a7) 498 movel #18,%d3 |load count for busy stack 499A9_loop: 500 clrl -(%a7) |clear lword on stack 501 dbf %d3,A9_loop 502 moveb VER_TMP(%a6),(%a7) |write current version number 503 moveb #BUSY_SIZE-4,1(%a7) |write current busy size 504 moveb #0x10,0x44(%a7) |set fcefpte[15] bit 505 movew #0x0023,0x40(%a7) |load cmdreg1b with mul command 506 moveb #0xfe,0x8(%a7) |load all 1s to cu savepc 507 frestore (%a7)+ |restore frame to fpu for completion 508 fmulx 36(%a1),%fp0 |multiply fp0 by 10^8 509 fmulx 48(%a1),%fp0 |multiply fp0 by 10^16 510 bras A10_st 511A9_norm: 512 tstw %d2 |test for small exp case 513 beqs A9_con |if zero, continue as normal 514 fmulx 36(%a1),%fp0 |multiply fp0 by 10^8 515 fmulx 48(%a1),%fp0 |multiply fp0 by 10^16 516A9_con: 517 fmulx %fp1,%fp0 |calculate X * SCALE -> Y to fp0 518 519 520| A10. Or in INEX. 521| If INEX is set, round error occurred. This is compensated 522| for by 'or-ing' in the INEX2 flag to the lsb of Y. 523| 524| Register usage: 525| Input/Output 526| d0: FPCR with RZ mode/FPSR with INEX2 isolated 527| d2: x/x 528| d3: x/x 529| d4: LEN/Unchanged 530| d5: ICTR:LAMBDA 531| d6: ILOG/Unchanged 532| d7: k-factor/Unchanged 533| a0: ptr for original operand/final result 534| a1: ptr to PTENxx array/Unchanged 535| a2: x/ptr to FP_SCR2(a6) 536| fp0: Y/Y with lsb adjusted 537| fp1: 10^ISCALE/Unchanged 538| fp2: x/x 539 540A10_st: 541 fmovel %FPSR,%d0 |get FPSR 542 fmovex %fp0,FP_SCR2(%a6) |move Y to memory 543 leal FP_SCR2(%a6),%a2 |load a2 with ptr to FP_SCR2 544 btstl #9,%d0 |check if INEX2 set 545 beqs A11_st |if clear, skip rest 546 oril #1,8(%a2) |or in 1 to lsb of mantissa 547 fmovex FP_SCR2(%a6),%fp0 |write adjusted Y back to fpu 548 549 550| A11. Restore original FPCR; set size ext. 551| Perform FINT operation in the user's rounding mode. Keep 552| the size to extended. The sintdo entry point in the sint 553| routine expects the FPCR value to be in USER_FPCR for 554| mode and precision. The original FPCR is saved in L_SCR1. 555 556A11_st: 557 movel USER_FPCR(%a6),L_SCR1(%a6) |save it for later 558 andil #0x00000030,USER_FPCR(%a6) |set size to ext, 559| ;block exceptions 560 561 562| A12. Calculate YINT = FINT(Y) according to user's rounding mode. 563| The FPSP routine sintd0 is used. The output is in fp0. 564| 565| Register usage: 566| Input/Output 567| d0: FPSR with AINEX cleared/FPCR with size set to ext 568| d2: x/x/scratch 569| d3: x/x 570| d4: LEN/Unchanged 571| d5: ICTR:LAMBDA/Unchanged 572| d6: ILOG/Unchanged 573| d7: k-factor/Unchanged 574| a0: ptr for original operand/src ptr for sintdo 575| a1: ptr to PTENxx array/Unchanged 576| a2: ptr to FP_SCR2(a6)/Unchanged 577| a6: temp pointer to FP_SCR2(a6) - orig value saved and restored 578| fp0: Y/YINT 579| fp1: 10^ISCALE/Unchanged 580| fp2: x/x 581| F_SCR1:x/x 582| F_SCR2:Y adjusted for inex/Y with original exponent 583| L_SCR1:x/original USER_FPCR 584| L_SCR2:first word of X packed/Unchanged 585 586A12_st: 587 moveml %d0-%d1/%a0-%a1,-(%a7) |save regs used by sintd0 588 movel L_SCR1(%a6),-(%a7) 589 movel L_SCR2(%a6),-(%a7) 590 leal FP_SCR2(%a6),%a0 |a0 is ptr to F_SCR2(a6) 591 fmovex %fp0,(%a0) |move Y to memory at FP_SCR2(a6) 592 tstl L_SCR2(%a6) |test sign of original operand 593 bges do_fint |if pos, use Y 594 orl #0x80000000,(%a0) |if neg, use -Y 595do_fint: 596 movel USER_FPSR(%a6),-(%a7) 597 bsr sintdo |sint routine returns int in fp0 598 moveb (%a7),USER_FPSR(%a6) 599 addl #4,%a7 600 movel (%a7)+,L_SCR2(%a6) 601 movel (%a7)+,L_SCR1(%a6) 602 moveml (%a7)+,%d0-%d1/%a0-%a1 |restore regs used by sint 603 movel L_SCR2(%a6),FP_SCR2(%a6) |restore original exponent 604 movel L_SCR1(%a6),USER_FPCR(%a6) |restore user's FPCR 605 606 607| A13. Check for LEN digits. 608| If the int operation results in more than LEN digits, 609| or less than LEN -1 digits, adjust ILOG and repeat from 610| A6. This test occurs only on the first pass. If the 611| result is exactly 10^LEN, decrement ILOG and divide 612| the mantissa by 10. The calculation of 10^LEN cannot 613| be inexact, since all powers of ten upto 10^27 are exact 614| in extended precision, so the use of a previous power-of-ten 615| table will introduce no error. 616| 617| 618| Register usage: 619| Input/Output 620| d0: FPCR with size set to ext/scratch final = 0 621| d2: x/x 622| d3: x/scratch final = x 623| d4: LEN/LEN adjusted 624| d5: ICTR:LAMBDA/LAMBDA:ICTR 625| d6: ILOG/ILOG adjusted 626| d7: k-factor/Unchanged 627| a0: pointer into memory for packed bcd string formation 628| a1: ptr to PTENxx array/Unchanged 629| a2: ptr to FP_SCR2(a6)/Unchanged 630| fp0: int portion of Y/abs(YINT) adjusted 631| fp1: 10^ISCALE/Unchanged 632| fp2: x/10^LEN 633| F_SCR1:x/x 634| F_SCR2:Y with original exponent/Unchanged 635| L_SCR1:original USER_FPCR/Unchanged 636| L_SCR2:first word of X packed/Unchanged 637 638A13_st: 639 swap %d5 |put ICTR in lower word of d5 640 tstw %d5 |check if ICTR = 0 641 bne not_zr |if non-zero, go to second test 642| 643| Compute 10^(LEN-1) 644| 645 fmoves FONE,%fp2 |init fp2 to 1.0 646 movel %d4,%d0 |put LEN in d0 647 subql #1,%d0 |d0 = LEN -1 648 clrl %d3 |clr table index 649l_loop: 650 lsrl #1,%d0 |shift next bit into carry 651 bccs l_next |if zero, skip the mul 652 fmulx (%a1,%d3),%fp2 |mul by 10**(d3_bit_no) 653l_next: 654 addl #12,%d3 |inc d3 to next pwrten table entry 655 tstl %d0 |test if LEN is zero 656 bnes l_loop |if not, loop 657| 658| 10^LEN-1 is computed for this test and A14. If the input was 659| denormalized, check only the case in which YINT > 10^LEN. 660| 661 tstb BINDEC_FLG(%a6) |check if input was norm 662 beqs A13_con |if norm, continue with checking 663 fabsx %fp0 |take abs of YINT 664 bra test_2 665| 666| Compare abs(YINT) to 10^(LEN-1) and 10^LEN 667| 668A13_con: 669 fabsx %fp0 |take abs of YINT 670 fcmpx %fp2,%fp0 |compare abs(YINT) with 10^(LEN-1) 671 fbge test_2 |if greater, do next test 672 subql #1,%d6 |subtract 1 from ILOG 673 movew #1,%d5 |set ICTR 674 fmovel #rm_mode,%FPCR |set rmode to RM 675 fmuls FTEN,%fp2 |compute 10^LEN 676 bra A6_str |return to A6 and recompute YINT 677test_2: 678 fmuls FTEN,%fp2 |compute 10^LEN 679 fcmpx %fp2,%fp0 |compare abs(YINT) with 10^LEN 680 fblt A14_st |if less, all is ok, go to A14 681 fbgt fix_ex |if greater, fix and redo 682 fdivs FTEN,%fp0 |if equal, divide by 10 683 addql #1,%d6 | and inc ILOG 684 bras A14_st | and continue elsewhere 685fix_ex: 686 addql #1,%d6 |increment ILOG by 1 687 movew #1,%d5 |set ICTR 688 fmovel #rm_mode,%FPCR |set rmode to RM 689 bra A6_str |return to A6 and recompute YINT 690| 691| Since ICTR <> 0, we have already been through one adjustment, 692| and shouldn't have another; this is to check if abs(YINT) = 10^LEN 693| 10^LEN is again computed using whatever table is in a1 since the 694| value calculated cannot be inexact. 695| 696not_zr: 697 fmoves FONE,%fp2 |init fp2 to 1.0 698 movel %d4,%d0 |put LEN in d0 699 clrl %d3 |clr table index 700z_loop: 701 lsrl #1,%d0 |shift next bit into carry 702 bccs z_next |if zero, skip the mul 703 fmulx (%a1,%d3),%fp2 |mul by 10**(d3_bit_no) 704z_next: 705 addl #12,%d3 |inc d3 to next pwrten table entry 706 tstl %d0 |test if LEN is zero 707 bnes z_loop |if not, loop 708 fabsx %fp0 |get abs(YINT) 709 fcmpx %fp2,%fp0 |check if abs(YINT) = 10^LEN 710 fbne A14_st |if not, skip this 711 fdivs FTEN,%fp0 |divide abs(YINT) by 10 712 addql #1,%d6 |and inc ILOG by 1 713 addql #1,%d4 | and inc LEN 714 fmuls FTEN,%fp2 | if LEN++, the get 10^^LEN 715 716 717| A14. Convert the mantissa to bcd. 718| The binstr routine is used to convert the LEN digit 719| mantissa to bcd in memory. The input to binstr is 720| to be a fraction; i.e. (mantissa)/10^LEN and adjusted 721| such that the decimal point is to the left of bit 63. 722| The bcd digits are stored in the correct position in 723| the final string area in memory. 724| 725| 726| Register usage: 727| Input/Output 728| d0: x/LEN call to binstr - final is 0 729| d1: x/0 730| d2: x/ms 32-bits of mant of abs(YINT) 731| d3: x/ls 32-bits of mant of abs(YINT) 732| d4: LEN/Unchanged 733| d5: ICTR:LAMBDA/LAMBDA:ICTR 734| d6: ILOG 735| d7: k-factor/Unchanged 736| a0: pointer into memory for packed bcd string formation 737| /ptr to first mantissa byte in result string 738| a1: ptr to PTENxx array/Unchanged 739| a2: ptr to FP_SCR2(a6)/Unchanged 740| fp0: int portion of Y/abs(YINT) adjusted 741| fp1: 10^ISCALE/Unchanged 742| fp2: 10^LEN/Unchanged 743| F_SCR1:x/Work area for final result 744| F_SCR2:Y with original exponent/Unchanged 745| L_SCR1:original USER_FPCR/Unchanged 746| L_SCR2:first word of X packed/Unchanged 747 748A14_st: 749 fmovel #rz_mode,%FPCR |force rz for conversion 750 fdivx %fp2,%fp0 |divide abs(YINT) by 10^LEN 751 leal FP_SCR1(%a6),%a0 752 fmovex %fp0,(%a0) |move abs(YINT)/10^LEN to memory 753 movel 4(%a0),%d2 |move 2nd word of FP_RES to d2 754 movel 8(%a0),%d3 |move 3rd word of FP_RES to d3 755 clrl 4(%a0) |zero word 2 of FP_RES 756 clrl 8(%a0) |zero word 3 of FP_RES 757 movel (%a0),%d0 |move exponent to d0 758 swap %d0 |put exponent in lower word 759 beqs no_sft |if zero, don't shift 760 subil #0x3ffd,%d0 |sub bias less 2 to make fract 761 tstl %d0 |check if > 1 762 bgts no_sft |if so, don't shift 763 negl %d0 |make exp positive 764m_loop: 765 lsrl #1,%d2 |shift d2:d3 right, add 0s 766 roxrl #1,%d3 |the number of places 767 dbf %d0,m_loop |given in d0 768no_sft: 769 tstl %d2 |check for mantissa of zero 770 bnes no_zr |if not, go on 771 tstl %d3 |continue zero check 772 beqs zer_m |if zero, go directly to binstr 773no_zr: 774 clrl %d1 |put zero in d1 for addx 775 addil #0x00000080,%d3 |inc at bit 7 776 addxl %d1,%d2 |continue inc 777 andil #0xffffff80,%d3 |strip off lsb not used by 882 778zer_m: 779 movel %d4,%d0 |put LEN in d0 for binstr call 780 addql #3,%a0 |a0 points to M16 byte in result 781 bsr binstr |call binstr to convert mant 782 783 784| A15. Convert the exponent to bcd. 785| As in A14 above, the exp is converted to bcd and the 786| digits are stored in the final string. 787| 788| Digits are stored in L_SCR1(a6) on return from BINDEC as: 789| 790| 32 16 15 0 791| ----------------------------------------- 792| | 0 | e3 | e2 | e1 | e4 | X | X | X | 793| ----------------------------------------- 794| 795| And are moved into their proper places in FP_SCR1. If digit e4 796| is non-zero, OPERR is signaled. In all cases, all 4 digits are 797| written as specified in the 881/882 manual for packed decimal. 798| 799| Register usage: 800| Input/Output 801| d0: x/LEN call to binstr - final is 0 802| d1: x/scratch (0);shift count for final exponent packing 803| d2: x/ms 32-bits of exp fraction/scratch 804| d3: x/ls 32-bits of exp fraction 805| d4: LEN/Unchanged 806| d5: ICTR:LAMBDA/LAMBDA:ICTR 807| d6: ILOG 808| d7: k-factor/Unchanged 809| a0: ptr to result string/ptr to L_SCR1(a6) 810| a1: ptr to PTENxx array/Unchanged 811| a2: ptr to FP_SCR2(a6)/Unchanged 812| fp0: abs(YINT) adjusted/float(ILOG) 813| fp1: 10^ISCALE/Unchanged 814| fp2: 10^LEN/Unchanged 815| F_SCR1:Work area for final result/BCD result 816| F_SCR2:Y with original exponent/ILOG/10^4 817| L_SCR1:original USER_FPCR/Exponent digits on return from binstr 818| L_SCR2:first word of X packed/Unchanged 819 820A15_st: 821 tstb BINDEC_FLG(%a6) |check for denorm 822 beqs not_denorm 823 ftstx %fp0 |test for zero 824 fbeq den_zero |if zero, use k-factor or 4933 825 fmovel %d6,%fp0 |float ILOG 826 fabsx %fp0 |get abs of ILOG 827 bras convrt 828den_zero: 829 tstl %d7 |check sign of the k-factor 830 blts use_ilog |if negative, use ILOG 831 fmoves F4933,%fp0 |force exponent to 4933 832 bras convrt |do it 833use_ilog: 834 fmovel %d6,%fp0 |float ILOG 835 fabsx %fp0 |get abs of ILOG 836 bras convrt 837not_denorm: 838 ftstx %fp0 |test for zero 839 fbne not_zero |if zero, force exponent 840 fmoves FONE,%fp0 |force exponent to 1 841 bras convrt |do it 842not_zero: 843 fmovel %d6,%fp0 |float ILOG 844 fabsx %fp0 |get abs of ILOG 845convrt: 846 fdivx 24(%a1),%fp0 |compute ILOG/10^4 847 fmovex %fp0,FP_SCR2(%a6) |store fp0 in memory 848 movel 4(%a2),%d2 |move word 2 to d2 849 movel 8(%a2),%d3 |move word 3 to d3 850 movew (%a2),%d0 |move exp to d0 851 beqs x_loop_fin |if zero, skip the shift 852 subiw #0x3ffd,%d0 |subtract off bias 853 negw %d0 |make exp positive 854x_loop: 855 lsrl #1,%d2 |shift d2:d3 right 856 roxrl #1,%d3 |the number of places 857 dbf %d0,x_loop |given in d0 858x_loop_fin: 859 clrl %d1 |put zero in d1 for addx 860 addil #0x00000080,%d3 |inc at bit 6 861 addxl %d1,%d2 |continue inc 862 andil #0xffffff80,%d3 |strip off lsb not used by 882 863 movel #4,%d0 |put 4 in d0 for binstr call 864 leal L_SCR1(%a6),%a0 |a0 is ptr to L_SCR1 for exp digits 865 bsr binstr |call binstr to convert exp 866 movel L_SCR1(%a6),%d0 |load L_SCR1 lword to d0 867 movel #12,%d1 |use d1 for shift count 868 lsrl %d1,%d0 |shift d0 right by 12 869 bfins %d0,FP_SCR1(%a6){#4:#12} |put e3:e2:e1 in FP_SCR1 870 lsrl %d1,%d0 |shift d0 right by 12 871 bfins %d0,FP_SCR1(%a6){#16:#4} |put e4 in FP_SCR1 872 tstb %d0 |check if e4 is zero 873 beqs A16_st |if zero, skip rest 874 orl #opaop_mask,USER_FPSR(%a6) |set OPERR & AIOP in USER_FPSR 875 876 877| A16. Write sign bits to final string. 878| Sigma is bit 31 of initial value; RHO is bit 31 of d6 (ILOG). 879| 880| Register usage: 881| Input/Output 882| d0: x/scratch - final is x 883| d2: x/x 884| d3: x/x 885| d4: LEN/Unchanged 886| d5: ICTR:LAMBDA/LAMBDA:ICTR 887| d6: ILOG/ILOG adjusted 888| d7: k-factor/Unchanged 889| a0: ptr to L_SCR1(a6)/Unchanged 890| a1: ptr to PTENxx array/Unchanged 891| a2: ptr to FP_SCR2(a6)/Unchanged 892| fp0: float(ILOG)/Unchanged 893| fp1: 10^ISCALE/Unchanged 894| fp2: 10^LEN/Unchanged 895| F_SCR1:BCD result with correct signs 896| F_SCR2:ILOG/10^4 897| L_SCR1:Exponent digits on return from binstr 898| L_SCR2:first word of X packed/Unchanged 899 900A16_st: 901 clrl %d0 |clr d0 for collection of signs 902 andib #0x0f,FP_SCR1(%a6) |clear first nibble of FP_SCR1 903 tstl L_SCR2(%a6) |check sign of original mantissa 904 bges mant_p |if pos, don't set SM 905 moveql #2,%d0 |move 2 in to d0 for SM 906mant_p: 907 tstl %d6 |check sign of ILOG 908 bges wr_sgn |if pos, don't set SE 909 addql #1,%d0 |set bit 0 in d0 for SE 910wr_sgn: 911 bfins %d0,FP_SCR1(%a6){#0:#2} |insert SM and SE into FP_SCR1 912 913| Clean up and restore all registers used. 914 915 fmovel #0,%FPSR |clear possible inex2/ainex bits 916 fmovemx (%a7)+,%fp0-%fp2 917 moveml (%a7)+,%d2-%d7/%a2 918 rts 919 920 |end 921