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 occured. 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
145 LOG2: .long 0x3FFD0000,0x9A209A84,0xFBCFF798,0x00000000
146 LOG2UP1: .long 0x3FFD0000,0x9A209A84,0xFBCFF799,0x00000000
147
148 | Constants in single precision
149 FONE: .long 0x3F800000,0x00000000,0x00000000,0x00000000
150 FTWO: .long 0x40000000,0x00000000,0x00000000,0x00000000
151 FTEN: .long 0x41200000,0x00000000,0x00000000,0x00000000
152 F4933: .long 0x459A2800,0x00000000,0x00000000,0x00000000
153
154 RBDTBL: .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
165 bindec:
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 |
186 un_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
191 norm_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
203 pos_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 |
211 A2_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
247 A3_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
258 pos_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
266 A4_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
306 A6_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
311 k_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
315 len_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
325 LEN_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
378 A7_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
384 k_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
398 no_inf:
399 negl %d0 |and take abs of ISCALE
400 iscale:
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
409 x_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
419 not_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
424 not_rp:
425 leal PTENRM,%a1 |load a1 with RM table base
426 rmode:
427 clrl %d3 |clr table index
428 e_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)
432 e_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
483 A9_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 bnes 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
491 sc_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
499 A9_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
511 A9_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
516 A9_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 occured. 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
540 A10_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
556 A11_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
586 A12_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
595 do_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
638 A13_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
649 l_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)
653 l_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 |
668 A13_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
677 test_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
685 fix_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 |
696 not_zr:
697 fmoves FONE,%fp2 |init fp2 to 1.0
698 movel %d4,%d0 |put LEN in d0
699 clrl %d3 |clr table index
700 z_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)
704 z_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
748 A14_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
764 m_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
768 no_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
773 no_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
778 zer_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
820 A15_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
828 den_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
833 use_ilog:
834 fmovel %d6,%fp0 |float ILOG
835 fabsx %fp0 |get abs of ILOG
836 bras convrt
837 not_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
842 not_zero:
843 fmovel %d6,%fp0 |float ILOG
844 fabsx %fp0 |get abs of ILOG
845 convrt:
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
854 x_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
858 x_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
900 A16_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
906 mant_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
910 wr_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
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