1 | 2 | decbin.sa 3.3 12/19/90 3 | 4 | Description: Converts normalized packed bcd value pointed to by 5 | register A6 to extended-precision value in FP0. 6 | 7 | Input: Normalized packed bcd value in ETEMP(a6). 8 | 9 | Output: Exact floating-point representation of the packed bcd value. 10 | 11 | Saves and Modifies: D2-D5 12 | 13 | Speed: The program decbin takes ??? cycles to execute. 14 | 15 | Object Size: 16 | 17 | External Reference(s): None. 18 | 19 | Algorithm: 20 | Expected is a normal bcd (i.e. non-exceptional; all inf, zero, 21 | and NaN operands are dispatched without entering this routine) 22 | value in 68881/882 format at location ETEMP(A6). 23 | 24 | A1. Convert the bcd exponent to binary by successive adds and muls. 25 | Set the sign according to SE. Subtract 16 to compensate 26 | for the mantissa which is to be interpreted as 17 integer 27 | digits, rather than 1 integer and 16 fraction digits. 28 | Note: this operation can never overflow. 29 | 30 | A2. Convert the bcd mantissa to binary by successive 31 | adds and muls in FP0. Set the sign according to SM. 32 | The mantissa digits will be converted with the decimal point 33 | assumed following the least-significant digit. 34 | Note: this operation can never overflow. 35 | 36 | A3. Count the number of leading/trailing zeros in the 37 | bcd string. If SE is positive, count the leading zeros; 38 | if negative, count the trailing zeros. Set the adjusted 39 | exponent equal to the exponent from A1 and the zero count 40 | added if SM = 1 and subtracted if SM = 0. Scale the 41 | mantissa the equivalent of forcing in the bcd value: 42 | 43 | SM = 0 a non-zero digit in the integer position 44 | SM = 1 a non-zero digit in Mant0, lsd of the fraction 45 | 46 | this will insure that any value, regardless of its 47 | representation (ex. 0.1E2, 1E1, 10E0, 100E-1), is converted 48 | consistently. 49 | 50 | A4. Calculate the factor 10^exp in FP1 using a table of 51 | 10^(2^n) values. To reduce the error in forming factors 52 | greater than 10^27, a directed rounding scheme is used with 53 | tables rounded to RN, RM, and RP, according to the table 54 | in the comments of the pwrten section. 55 | 56 | A5. Form the final binary number by scaling the mantissa by 57 | the exponent factor. This is done by multiplying the 58 | mantissa in FP0 by the factor in FP1 if the adjusted 59 | exponent sign is positive, and dividing FP0 by FP1 if 60 | it is negative. 61 | 62 | Clean up and return. Check if the final mul or div resulted 63 | in an inex2 exception. If so, set inex1 in the fpsr and 64 | check if the inex1 exception is enabled. If so, set d7 upper 65 | word to $0100. This will signal unimp.sa that an enabled inex1 66 | exception occurred. Unimp will fix the stack. 67 | 68 69 | Copyright (C) Motorola, Inc. 1990 70 | All Rights Reserved 71 | 72 | For details on the license for this file, please see the 73 | file, README, in this same directory. 74 75 |DECBIN idnt 2,1 | Motorola 040 Floating Point Software Package 76 77 |section 8 78 79 #include "fpsp.h" 80 81 | 82 | PTENRN, PTENRM, and PTENRP are arrays of powers of 10 rounded 83 | to nearest, minus, and plus, respectively. The tables include 84 | 10**{1,2,4,8,16,32,64,128,256,512,1024,2048,4096}. No rounding 85 | is required until the power is greater than 27, however, all 86 | tables include the first 5 for ease of indexing. 87 | 88 |xref PTENRN 89 |xref PTENRM 90 |xref PTENRP 91 92 RTABLE: .byte 0,0,0,0 93 .byte 2,3,2,3 94 .byte 2,3,3,2 95 .byte 3,2,2,3 96 97 .global decbin 98 .global calc_e 99 .global pwrten 100 .global calc_m 101 .global norm 102 .global ap_st_z 103 .global ap_st_n 104 | 105 .set FNIBS,7 106 .set FSTRT,0 107 | 108 .set ESTRT,4 109 .set EDIGITS,2 | 110 | 111 | Constants in single precision 112 FZERO: .long 0x00000000 113 FONE: .long 0x3F800000 114 FTEN: .long 0x41200000 115 116 .set TEN,10 117 118 | 119 decbin: 120 | fmovel #0,FPCR ;clr real fpcr 121 moveml %d2-%d5,-(%a7) 122 | 123 | Calculate exponent: 124 | 1. Copy bcd value in memory for use as a working copy. 125 | 2. Calculate absolute value of exponent in d1 by mul and add. 126 | 3. Correct for exponent sign. 127 | 4. Subtract 16 to compensate for interpreting the mant as all integer digits. 128 | (i.e., all digits assumed left of the decimal point.) 129 | 130 | Register usage: 131 | 132 | calc_e: 133 | (*) d0: temp digit storage 134 | (*) d1: accumulator for binary exponent 135 | (*) d2: digit count 136 | (*) d3: offset pointer 137 | ( ) d4: first word of bcd 138 | ( ) a0: pointer to working bcd value 139 | ( ) a6: pointer to original bcd value 140 | (*) FP_SCR1: working copy of original bcd value 141 | (*) L_SCR1: copy of original exponent word 142 | 143 calc_e: 144 movel #EDIGITS,%d2 |# of nibbles (digits) in fraction part 145 moveql #ESTRT,%d3 |counter to pick up digits 146 leal FP_SCR1(%a6),%a0 |load tmp bcd storage address 147 movel ETEMP(%a6),(%a0) |save input bcd value 148 movel ETEMP_HI(%a6),4(%a0) |save words 2 and 3 149 movel ETEMP_LO(%a6),8(%a0) |and work with these 150 movel (%a0),%d4 |get first word of bcd 151 clrl %d1 |zero d1 for accumulator 152 e_gd: 153 mulul #TEN,%d1 |mul partial product by one digit place 154 bfextu %d4{%d3:#4},%d0 |get the digit and zero extend into d0 155 addl %d0,%d1 |d1 = d1 + d0 156 addqb #4,%d3 |advance d3 to the next digit 157 dbf %d2,e_gd |if we have used all 3 digits, exit loop 158 btst #30,%d4 |get SE 159 beqs e_pos |don't negate if pos 160 negl %d1 |negate before subtracting 161 e_pos: 162 subl #16,%d1 |sub to compensate for shift of mant 163 bges e_save |if still pos, do not neg 164 negl %d1 |now negative, make pos and set SE 165 orl #0x40000000,%d4 |set SE in d4, 166 orl #0x40000000,(%a0) |and in working bcd 167 e_save: 168 movel %d1,L_SCR1(%a6) |save exp in memory 169 | 170 | 171 | Calculate mantissa: 172 | 1. Calculate absolute value of mantissa in fp0 by mul and add. 173 | 2. Correct for mantissa sign. 174 | (i.e., all digits assumed left of the decimal point.) 175 | 176 | Register usage: 177 | 178 | calc_m: 179 | (*) d0: temp digit storage 180 | (*) d1: lword counter 181 | (*) d2: digit count 182 | (*) d3: offset pointer 183 | ( ) d4: words 2 and 3 of bcd 184 | ( ) a0: pointer to working bcd value 185 | ( ) a6: pointer to original bcd value 186 | (*) fp0: mantissa accumulator 187 | ( ) FP_SCR1: working copy of original bcd value 188 | ( ) L_SCR1: copy of original exponent word 189 | 190 calc_m: 191 moveql #1,%d1 |word counter, init to 1 192 fmoves FZERO,%fp0 |accumulator 193 | 194 | 195 | Since the packed number has a long word between the first & second parts, 196 | get the integer digit then skip down & get the rest of the 197 | mantissa. We will unroll the loop once. 198 | 199 bfextu (%a0){#28:#4},%d0 |integer part is ls digit in long word 200 faddb %d0,%fp0 |add digit to sum in fp0 201 | 202 | 203 | Get the rest of the mantissa. 204 | 205 loadlw: 206 movel (%a0,%d1.L*4),%d4 |load mantissa longword into d4 207 moveql #FSTRT,%d3 |counter to pick up digits 208 moveql #FNIBS,%d2 |reset number of digits per a0 ptr 209 md2b: 210 fmuls FTEN,%fp0 |fp0 = fp0 * 10 211 bfextu %d4{%d3:#4},%d0 |get the digit and zero extend 212 faddb %d0,%fp0 |fp0 = fp0 + digit 213 | 214 | 215 | If all the digits (8) in that long word have been converted (d2=0), 216 | then inc d1 (=2) to point to the next long word and reset d3 to 0 217 | to initialize the digit offset, and set d2 to 7 for the digit count; 218 | else continue with this long word. 219 | 220 addqb #4,%d3 |advance d3 to the next digit 221 dbf %d2,md2b |check for last digit in this lw 222 nextlw: 223 addql #1,%d1 |inc lw pointer in mantissa 224 cmpl #2,%d1 |test for last lw 225 ble loadlw |if not, get last one 226 227 | 228 | Check the sign of the mant and make the value in fp0 the same sign. 229 | 230 m_sign: 231 btst #31,(%a0) |test sign of the mantissa 232 beq ap_st_z |if clear, go to append/strip zeros 233 fnegx %fp0 |if set, negate fp0 234 235 | 236 | Append/strip zeros: 237 | 238 | For adjusted exponents which have an absolute value greater than 27*, 239 | this routine calculates the amount needed to normalize the mantissa 240 | for the adjusted exponent. That number is subtracted from the exp 241 | if the exp was positive, and added if it was negative. The purpose 242 | of this is to reduce the value of the exponent and the possibility 243 | of error in calculation of pwrten. 244 | 245 | 1. Branch on the sign of the adjusted exponent. 246 | 2p.(positive exp) 247 | 2. Check M16 and the digits in lwords 2 and 3 in descending order. 248 | 3. Add one for each zero encountered until a non-zero digit. 249 | 4. Subtract the count from the exp. 250 | 5. Check if the exp has crossed zero in #3 above; make the exp abs 251 | and set SE. 252 | 6. Multiply the mantissa by 10**count. 253 | 2n.(negative exp) 254 | 2. Check the digits in lwords 3 and 2 in descending order. 255 | 3. Add one for each zero encountered until a non-zero digit. 256 | 4. Add the count to the exp. 257 | 5. Check if the exp has crossed zero in #3 above; clear SE. 258 | 6. Divide the mantissa by 10**count. 259 | 260 | *Why 27? If the adjusted exponent is within -28 < expA < 28, than 261 | any adjustment due to append/strip zeros will drive the resultant 262 | exponent towards zero. Since all pwrten constants with a power 263 | of 27 or less are exact, there is no need to use this routine to 264 | attempt to lessen the resultant exponent. 265 | 266 | Register usage: 267 | 268 | ap_st_z: 269 | (*) d0: temp digit storage 270 | (*) d1: zero count 271 | (*) d2: digit count 272 | (*) d3: offset pointer 273 | ( ) d4: first word of bcd 274 | (*) d5: lword counter 275 | ( ) a0: pointer to working bcd value 276 | ( ) FP_SCR1: working copy of original bcd value 277 | ( ) L_SCR1: copy of original exponent word 278 | 279 | 280 | First check the absolute value of the exponent to see if this 281 | routine is necessary. If so, then check the sign of the exponent 282 | and do append (+) or strip (-) zeros accordingly. 283 | This section handles a positive adjusted exponent. 284 | 285 ap_st_z: 286 movel L_SCR1(%a6),%d1 |load expA for range test 287 cmpl #27,%d1 |test is with 27 288 ble pwrten |if abs(expA) <28, skip ap/st zeros 289 btst #30,(%a0) |check sign of exp 290 bne ap_st_n |if neg, go to neg side 291 clrl %d1 |zero count reg 292 movel (%a0),%d4 |load lword 1 to d4 293 bfextu %d4{#28:#4},%d0 |get M16 in d0 294 bnes ap_p_fx |if M16 is non-zero, go fix exp 295 addql #1,%d1 |inc zero count 296 moveql #1,%d5 |init lword counter 297 movel (%a0,%d5.L*4),%d4 |get lword 2 to d4 298 bnes ap_p_cl |if lw 2 is zero, skip it 299 addql #8,%d1 |and inc count by 8 300 addql #1,%d5 |inc lword counter 301 movel (%a0,%d5.L*4),%d4 |get lword 3 to d4 302 ap_p_cl: 303 clrl %d3 |init offset reg 304 moveql #7,%d2 |init digit counter 305 ap_p_gd: 306 bfextu %d4{%d3:#4},%d0 |get digit 307 bnes ap_p_fx |if non-zero, go to fix exp 308 addql #4,%d3 |point to next digit 309 addql #1,%d1 |inc digit counter 310 dbf %d2,ap_p_gd |get next digit 311 ap_p_fx: 312 movel %d1,%d0 |copy counter to d2 313 movel L_SCR1(%a6),%d1 |get adjusted exp from memory 314 subl %d0,%d1 |subtract count from exp 315 bges ap_p_fm |if still pos, go to pwrten 316 negl %d1 |now its neg; get abs 317 movel (%a0),%d4 |load lword 1 to d4 318 orl #0x40000000,%d4 | and set SE in d4 319 orl #0x40000000,(%a0) | and in memory 320 | 321 | Calculate the mantissa multiplier to compensate for the striping of 322 | zeros from the mantissa. 323 | 324 ap_p_fm: 325 movel #PTENRN,%a1 |get address of power-of-ten table 326 clrl %d3 |init table index 327 fmoves FONE,%fp1 |init fp1 to 1 328 moveql #3,%d2 |init d2 to count bits in counter 329 ap_p_el: 330 asrl #1,%d0 |shift lsb into carry 331 bccs ap_p_en |if 1, mul fp1 by pwrten factor 332 fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no) 333 ap_p_en: 334 addl #12,%d3 |inc d3 to next rtable entry 335 tstl %d0 |check if d0 is zero 336 bnes ap_p_el |if not, get next bit 337 fmulx %fp1,%fp0 |mul mantissa by 10**(no_bits_shifted) 338 bra pwrten |go calc pwrten 339 | 340 | This section handles a negative adjusted exponent. 341 | 342 ap_st_n: 343 clrl %d1 |clr counter 344 moveql #2,%d5 |set up d5 to point to lword 3 345 movel (%a0,%d5.L*4),%d4 |get lword 3 346 bnes ap_n_cl |if not zero, check digits 347 subl #1,%d5 |dec d5 to point to lword 2 348 addql #8,%d1 |inc counter by 8 349 movel (%a0,%d5.L*4),%d4 |get lword 2 350 ap_n_cl: 351 movel #28,%d3 |point to last digit 352 moveql #7,%d2 |init digit counter 353 ap_n_gd: 354 bfextu %d4{%d3:#4},%d0 |get digit 355 bnes ap_n_fx |if non-zero, go to exp fix 356 subql #4,%d3 |point to previous digit 357 addql #1,%d1 |inc digit counter 358 dbf %d2,ap_n_gd |get next digit 359 ap_n_fx: 360 movel %d1,%d0 |copy counter to d0 361 movel L_SCR1(%a6),%d1 |get adjusted exp from memory 362 subl %d0,%d1 |subtract count from exp 363 bgts ap_n_fm |if still pos, go fix mantissa 364 negl %d1 |take abs of exp and clr SE 365 movel (%a0),%d4 |load lword 1 to d4 366 andl #0xbfffffff,%d4 | and clr SE in d4 367 andl #0xbfffffff,(%a0) | and in memory 368 | 369 | Calculate the mantissa multiplier to compensate for the appending of 370 | zeros to the mantissa. 371 | 372 ap_n_fm: 373 movel #PTENRN,%a1 |get address of power-of-ten table 374 clrl %d3 |init table index 375 fmoves FONE,%fp1 |init fp1 to 1 376 moveql #3,%d2 |init d2 to count bits in counter 377 ap_n_el: 378 asrl #1,%d0 |shift lsb into carry 379 bccs ap_n_en |if 1, mul fp1 by pwrten factor 380 fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no) 381 ap_n_en: 382 addl #12,%d3 |inc d3 to next rtable entry 383 tstl %d0 |check if d0 is zero 384 bnes ap_n_el |if not, get next bit 385 fdivx %fp1,%fp0 |div mantissa by 10**(no_bits_shifted) 386 | 387 | 388 | Calculate power-of-ten factor from adjusted and shifted exponent. 389 | 390 | Register usage: 391 | 392 | pwrten: 393 | (*) d0: temp 394 | ( ) d1: exponent 395 | (*) d2: {FPCR[6:5],SM,SE} as index in RTABLE; temp 396 | (*) d3: FPCR work copy 397 | ( ) d4: first word of bcd 398 | (*) a1: RTABLE pointer 399 | calc_p: 400 | (*) d0: temp 401 | ( ) d1: exponent 402 | (*) d3: PWRTxx table index 403 | ( ) a0: pointer to working copy of bcd 404 | (*) a1: PWRTxx pointer 405 | (*) fp1: power-of-ten accumulator 406 | 407 | Pwrten calculates the exponent factor in the selected rounding mode 408 | according to the following table: 409 | 410 | Sign of Mant Sign of Exp Rounding Mode PWRTEN Rounding Mode 411 | 412 | ANY ANY RN RN 413 | 414 | + + RP RP 415 | - + RP RM 416 | + - RP RM 417 | - - RP RP 418 | 419 | + + RM RM 420 | - + RM RP 421 | + - RM RP 422 | - - RM RM 423 | 424 | + + RZ RM 425 | - + RZ RM 426 | + - RZ RP 427 | - - RZ RP 428 | 429 | 430 pwrten: 431 movel USER_FPCR(%a6),%d3 |get user's FPCR 432 bfextu %d3{#26:#2},%d2 |isolate rounding mode bits 433 movel (%a0),%d4 |reload 1st bcd word to d4 434 asll #2,%d2 |format d2 to be 435 bfextu %d4{#0:#2},%d0 | {FPCR[6],FPCR[5],SM,SE} 436 addl %d0,%d2 |in d2 as index into RTABLE 437 leal RTABLE,%a1 |load rtable base 438 moveb (%a1,%d2),%d0 |load new rounding bits from table 439 clrl %d3 |clear d3 to force no exc and extended 440 bfins %d0,%d3{#26:#2} |stuff new rounding bits in FPCR 441 fmovel %d3,%FPCR |write new FPCR 442 asrl #1,%d0 |write correct PTENxx table 443 bccs not_rp |to a1 444 leal PTENRP,%a1 |it is RP 445 bras calc_p |go to init section 446 not_rp: 447 asrl #1,%d0 |keep checking 448 bccs not_rm 449 leal PTENRM,%a1 |it is RM 450 bras calc_p |go to init section 451 not_rm: 452 leal PTENRN,%a1 |it is RN 453 calc_p: 454 movel %d1,%d0 |copy exp to d0;use d0 455 bpls no_neg |if exp is negative, 456 negl %d0 |invert it 457 orl #0x40000000,(%a0) |and set SE bit 458 no_neg: 459 clrl %d3 |table index 460 fmoves FONE,%fp1 |init fp1 to 1 461 e_loop: 462 asrl #1,%d0 |shift next bit into carry 463 bccs e_next |if zero, skip the mul 464 fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no) 465 e_next: 466 addl #12,%d3 |inc d3 to next rtable entry 467 tstl %d0 |check if d0 is zero 468 bnes e_loop |not zero, continue shifting 469 | 470 | 471 | Check the sign of the adjusted exp and make the value in fp0 the 472 | same sign. If the exp was pos then multiply fp1*fp0; 473 | else divide fp0/fp1. 474 | 475 | Register Usage: 476 | norm: 477 | ( ) a0: pointer to working bcd value 478 | (*) fp0: mantissa accumulator 479 | ( ) fp1: scaling factor - 10**(abs(exp)) 480 | 481 norm: 482 btst #30,(%a0) |test the sign of the exponent 483 beqs mul |if clear, go to multiply 484 div: 485 fdivx %fp1,%fp0 |exp is negative, so divide mant by exp 486 bras end_dec 487 mul: 488 fmulx %fp1,%fp0 |exp is positive, so multiply by exp 489 | 490 | 491 | Clean up and return with result in fp0. 492 | 493 | If the final mul/div in decbin incurred an inex exception, 494 | it will be inex2, but will be reported as inex1 by get_op. 495 | 496 end_dec: 497 fmovel %FPSR,%d0 |get status register 498 bclrl #inex2_bit+8,%d0 |test for inex2 and clear it 499 fmovel %d0,%FPSR |return status reg w/o inex2 500 beqs no_exc |skip this if no exc 501 orl #inx1a_mask,USER_FPSR(%a6) |set inex1/ainex 502 no_exc: 503 moveml (%a7)+,%d2-%d5 504 rts 505 |end 506