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