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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
generated by cgit v1.2.2 (git 2.25.0) at 2024-11-17 21:08:05 -0500