4 | handle rounding and normalization tasks
8 | Copyright (C) Motorola, Inc. 1990
11 | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
12 | The copyright notice above does not evidence any
13 | actual or intended publication of such source code.
15 |ROUND idnt 2,1 | Motorola 040 Floating Point Software Package
22 | round --- round result according to precision/mode
24 | a0 points to the input operand in the internal extended format
25 | d1(high word) contains rounding precision:
29 | d1(low word) contains rounding mode:
34 | d0{31:29} contains the g,r,s bits (extended)
36 | On return the value pointed to by a0 is correctly rounded,
37 | a0 is preserved and the g-r-s bits in d0 are cleared.
38 | The result is not typed - the tag field is invalid. The
39 | result is still in the internal extended format.
41 | The INEX bit of USER_FPSR will be set if the rounded result was
42 | inexact (i.e. if any of the g-r-s bits were set).
47 | If g=r=s=0 then result is exact and round is done, else set
48 | the inex flag in status reg and continue.
50 bsrs ext_grs |this subroutine looks at the
51 | :rounding precision and sets
52 | ;the appropriate g-r-s bits.
53 tstl %d0 |if grs are zero, go force
54 bne rnd_cont |lower bits to zero for size
56 swap %d1 |set up d1.w for round prec.
61 | Use rounding mode as an index into a jump table for these modes.
63 orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
65 movel (%a1,%d1.w*4),%a1
68 | Jump table indexed by rounding mode in d1.w. All following assumes
79 | If sign of fp number = 0 (positive), then add 1 to l.
82 swap %d1 |set up d1 for round prec.
83 tstb LOCAL_SGN(%a0) |check for sign
84 bmi truncate |if positive then truncate
85 movel #0xffffffff,%d0 |force g,r,s to be all f's
87 movel (%a1,%d1.w*4),%a1
90 | ROUND MINUS INFINITY
92 | If sign of fp number = 1 (negative), then add 1 to l.
95 swap %d1 |set up d1 for round prec.
96 tstb LOCAL_SGN(%a0) |check for sign
97 bpl truncate |if negative then truncate
98 movel #0xffffffff,%d0 |force g,r,s to be all f's
100 movel (%a1,%d1.w*4),%a1
107 swap %d1 |set up d1 for round prec.
113 | If (g=1), then add 1 to l and if (r=s=0), then clear l
114 | Note that this will round to even in case of a tie.
117 swap %d1 |set up d1 for round prec.
118 asll #1,%d0 |shift g-bit to c-bit
119 bcc truncate |if (g=1) then
121 movel (%a1,%d1.w*4),%a1
125 | ext_grs --- extract guard, round and sticky bits
127 | Input: d1 = PREC:ROUND
128 | Output: d0{31:29}= guard, round, sticky
130 | The ext_grs extract the guard/round/sticky bits according to the
131 | selected rounding precision. It is called by the round subroutine
132 | only. All registers except d0 are kept intact. d0 becomes an
133 | updated guard,round,sticky in d0{31:29}
135 | Notes: the ext_grs uses the round PREC, and therefore has to swap d1
136 | prior to usage, and needs to restore d1 to original.
139 swap %d1 |have d1.w point to round precision
145 moveml %d2/%d3,-(%a7) |make some temp registers
149 bfextu LOCAL_HI(%a0){#24:#2},%d3 |sgl prec. g-r are 2 bits right
150 movel #30,%d2 |of the sgl prec. limits
151 lsll %d2,%d3 |shift g-r bits to MSB of d3
152 movel LOCAL_HI(%a0),%d2 |get word 2 for s-bit test
153 andil #0x0000003f,%d2 |s bit is the or of all other
154 bnes st_stky |bits to the right of g-r
155 tstl LOCAL_LO(%a0) |test lower mantissa
156 bnes st_stky |if any are set, set sticky
157 tstl %d0 |test original g,r,s
158 bnes st_stky |if any are set, set sticky
159 bras end_sd |if words 3 and 4 are clr, exit
161 bfextu LOCAL_LO(%a0){#21:#2},%d3 |dbl-prec. g-r are 2 bits right
162 movel #30,%d2 |of the dbl prec. limits
163 lsll %d2,%d3 |shift g-r bits to the MSB of d3
164 movel LOCAL_LO(%a0),%d2 |get lower mantissa for s-bit test
165 andil #0x000001ff,%d2 |s bit is the or-ing of all
166 bnes st_stky |other bits to the right of g-r
167 tstl %d0 |test word original g,r,s
168 bnes st_stky |if any are set, set sticky
169 bras end_sd |if clear, exit
171 bset #rnd_stky_bit,%d3
173 movel %d3,%d0 |return grs to d0
174 moveml (%a7)+,%d2/%d3 |restore scratch registers
176 swap %d1 |restore d1 to original
179 |******************* Local Equates
180 .set ad_1_sgl,0x00000100 | constant to add 1 to l-bit in sgl prec
181 .set ad_1_dbl,0x00000800 | constant to add 1 to l-bit in dbl prec
184 |Jump table for adding 1 to the l-bit indexed by rnd prec
195 addl #ad_1_sgl,LOCAL_HI(%a0)
196 bccs scc_clr |no mantissa overflow
197 roxrw LOCAL_HI(%a0) |shift v-bit back in
198 roxrw LOCAL_HI+2(%a0) |shift v-bit back in
199 addw #0x1,LOCAL_EX(%a0) |and incr exponent
201 tstl %d0 |test for rs = 0
203 andiw #0xfe00,LOCAL_HI+2(%a0) |clear the l-bit
205 andil #0xffffff00,LOCAL_HI(%a0) |truncate bits beyond sgl limit
206 clrl LOCAL_LO(%a0) |clear d2
213 addql #1,LOCAL_LO(%a0) |add 1 to l-bit
214 bccs xcc_clr |test for carry out
215 addql #1,LOCAL_HI(%a0) |propagate carry
217 roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
218 roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
220 roxrw LOCAL_LO+2(%a0)
221 addw #0x1,LOCAL_EX(%a0) |and inc exp
223 tstl %d0 |test rs = 0
225 andib #0xfe,LOCAL_LO+3(%a0) |clear the l bit
232 addl #ad_1_dbl,LOCAL_LO(%a0)
234 addql #1,LOCAL_HI(%a0) |propagate carry
236 roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
237 roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
239 roxrw LOCAL_LO+2(%a0)
240 addw #0x1,LOCAL_EX(%a0) |incr exponent
242 tstl %d0 |test for rs = 0
244 andiw #0xf000,LOCAL_LO+2(%a0) |clear the l-bit
247 andil #0xfffff800,LOCAL_LO(%a0) |truncate bits beyond dbl limit
253 | Truncate all other bits
263 movel (%a1,%d1.w*4),%a1
272 | These routines (nrm_zero & nrm_set) normalize the unnorm. This
273 | is done by shifting the mantissa left while decrementing the
276 | NRM_SET shifts and decrements until there is a 1 set in the integer
277 | bit of the mantissa (msb in d1).
279 | NRM_ZERO shifts and decrements until there is a 1 set in the integer
280 | bit of the mantissa (msb in d1) unless this would mean the exponent
281 | would go less than 0. In that case the number becomes a denorm - the
282 | exponent (d0) is set to 0 and the mantissa (d1 & d2) is not
285 | Note that both routines have been optimized (for the worst case) and
286 | therefore do not have the easy to follow decrement/shift loop.
290 | Distance to first 1 bit in mantissa = X
291 | Distance to 0 from exponent = Y
296 | shift mantissa by Y
300 | FP_SCR1 = exponent, ms mantissa part, ls mantissa part
302 | L_SCR1{4} = fpte15 or ete15 bit
306 movew LOCAL_EX(%a0),%d0
307 cmpw #64,%d0 |see if exp > 64
309 bsr nrm_set |exp > 64 so exp won't exceed 0
312 moveml %d2/%d3/%d5/%d6,-(%a7)
313 movel LOCAL_HI(%a0),%d1
314 movel LOCAL_LO(%a0),%d2
316 bfffo %d1{#0:#32},%d3 |get the distance to the first 1
318 beqs ms_clr |branch if no bits were set
320 bmis greater |then exp will go past 0 (neg) if
321 | ;it is just shifted
322 bsr nrm_set |else exp won't go past 0
323 moveml (%a7)+,%d2/%d3/%d5/%d6
326 movel %d2,%d6 |save ls mant in d6
327 lsll %d0,%d2 |shift ls mant by count
328 lsll %d0,%d1 |shift ms mant by count
330 subl %d0,%d5 |make op a denorm by shifting bits
331 lsrl %d5,%d6 |by the number in the exp, then
333 orl %d6,%d1 |shift the ls mant bits into the ms mant
334 movel #0,%d0 |same as if decremented exp to 0
336 movew %d0,LOCAL_EX(%a0)
337 movel %d1,LOCAL_HI(%a0)
338 movel %d2,LOCAL_LO(%a0)
339 moveml (%a7)+,%d2/%d3/%d5/%d6
342 bfffo %d2{#0:#32},%d3 |check if any bits set in ls mant
343 beqs all_clr |branch if none set
346 bmis greater |then branch
347 bsr nrm_set |else exp won't go past 0
348 moveml (%a7)+,%d2/%d3/%d5/%d6
351 movew #0,LOCAL_EX(%a0) |no mantissa bits set. Set exp = 0.
352 moveml (%a7)+,%d2/%d3/%d5/%d6
360 bfffo LOCAL_HI(%a0){#0:#32},%d7 |find first 1 in ms mant to d7)
361 beqs lower |branch if ms mant is all 0's
365 subw %d7,LOCAL_EX(%a0) |sub exponent by count
366 movel LOCAL_HI(%a0),%d0 |d0 has ms mant
367 movel LOCAL_LO(%a0),%d1 |d1 has ls mant
369 lsll %d7,%d0 |shift first 1 to j bit position
370 movel %d1,%d6 |copy ls mant into d6
371 lsll %d7,%d6 |shift ls mant by count
372 movel %d6,LOCAL_LO(%a0) |store ls mant into memory
374 subl %d7,%d6 |continue shift
375 lsrl %d6,%d1 |shift off all bits but those that will
376 | ;be shifted into ms mant
377 orl %d1,%d0 |shift the ls mant bits into the ms mant
378 movel %d0,LOCAL_HI(%a0) |store ms mant into memory
379 moveml (%a7)+,%d7/%d6 |restore registers
383 | We get here if ms mant was = 0, and we assume ls mant has bits
384 | set (otherwise this would have been tagged a zero not a denorm).
387 movew LOCAL_EX(%a0),%d0 |d0 has exponent
388 movel LOCAL_LO(%a0),%d1 |d1 has ls mant
389 subw #32,%d0 |account for ms mant being all zeros
390 bfffo %d1{#0:#32},%d7 |find first 1 in ls mant to d7)
391 subw %d7,%d0 |subtract shift count from exp
392 lsll %d7,%d1 |shift first 1 to integer bit in ms mant
393 movew %d0,LOCAL_EX(%a0) |store ms mant
394 movel %d1,LOCAL_HI(%a0) |store exp
395 clrl LOCAL_LO(%a0) |clear ls mant
399 | denorm --- denormalize an intermediate result
404 | a0 points to the operand to be denormalized
405 | (in the internal extended format)
407 | d0: rounding precision
409 | a0 points to the denormalized result
410 | (in the internal extended format)
412 | d0 is guard,round,sticky
414 | d0 comes into this routine with the rounding precision. It
415 | is then loaded with the denormalized exponent threshold for the
416 | rounding precision.
421 btstb #6,LOCAL_EX(%a0) |check for exponents between $7fff-$4000
423 bsetb #7,LOCAL_EX(%a0) |sign extend if it is so
426 cmpib #0,%d0 |if 0 then extended precision
427 bnes not_ext |else branch
429 clrl %d1 |load d1 with ext threshold
430 clrl %d0 |clear the sticky flag
431 bsr dnrm_lp |denormalize the number
432 tstb %d1 |check for inex
433 beq no_inex |if clr, no inex
434 bras dnrm_inex |if set, set inex
437 cmpil #1,%d0 |if 1 then single precision
438 beqs load_sgl |else must be 2, double prec
441 movew #dbl_thresh,%d1 |put copy of threshold in d1
442 movel %d1,%d0 |copy d1 into d0
443 subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
444 cmpw #67,%d0 |if diff > 67 (mant + grs bits)
445 bpls chk_stky |then branch (all bits would be
446 | ; shifted off in denorm routine)
447 clrl %d0 |else clear the sticky flag
448 bsr dnrm_lp |denormalize the number
450 beqs no_inex |if clr, no inex
451 bras dnrm_inex |if set, set inex
454 movew #sgl_thresh,%d1 |put copy of threshold in d1
455 movel %d1,%d0 |copy d1 into d0
456 subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
457 cmpw #67,%d0 |if diff > 67 (mant + grs bits)
458 bpls chk_stky |then branch (all bits would be
459 | ; shifted off in denorm routine)
460 clrl %d0 |else clear the sticky flag
461 bsr dnrm_lp |denormalize the number
463 beqs no_inex |if clr, no inex
464 bras dnrm_inex |if set, set inex
467 tstl LOCAL_HI(%a0) |check for any bits set
469 tstl LOCAL_LO(%a0) |check for any bits set
473 orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
474 movel #0x20000000,%d0 |set sticky bit in return value
476 movew %d1,LOCAL_EX(%a0) |load exp with threshold
477 movel #0,LOCAL_HI(%a0) |set d1 = 0 (ms mantissa)
478 movel #0,LOCAL_LO(%a0) |set d2 = 0 (ms mantissa)
481 orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
486 | dnrm_lp --- normalize exponent/mantissa to specified threshold
489 | a0 points to the operand to be denormalized
490 | d0{31:29} initial guard,round,sticky
491 | d1{15:0} denormalization threshold
493 | a0 points to the denormalized operand
494 | d0{31:29} final guard,round,sticky
495 | d1.b inexact flag: all ones means inexact result
497 | The LOCAL_LO and LOCAL_GRS parts of the value are copied to FP_SCR2
498 | so that bfext can be used to extract the new low part of the mantissa.
499 | Dnrm_lp can be called with a0 pointing to ETEMP or WBTEMP and there
500 | is no LOCAL_GRS scratch word following it on the fsave frame.
504 movel %d2,-(%sp) |save d2 for temp use
505 btstb #E3,E_BYTE(%a6) |test for type E3 exception
506 beqs not_E3 |not type E3 exception
507 bfextu WBTEMP_GRS(%a6){#6:#3},%d2 |extract guard,round, sticky bit
509 lsll %d0,%d2 |shift g,r,s to their positions
512 movel (%sp)+,%d2 |restore d2
513 movel LOCAL_LO(%a0),FP_SCR2+LOCAL_LO(%a6)
514 movel %d0,FP_SCR2+LOCAL_GRS(%a6)
515 movel %d1,%d0 |copy the denorm threshold
516 subw LOCAL_EX(%a0),%d1 |d1 = threshold - uns exponent
519 blts case_1 |0 = d1 < 32
521 blts case_2 |32 <= d1 < 64
524 | No normalization necessary
527 clrb %d1 |set no inex2 reported
528 movel FP_SCR2+LOCAL_GRS(%a6),%d0 |restore original g,r,s
535 movew %d0,LOCAL_EX(%a0) |exponent = denorm threshold
537 subw %d1,%d0 |d0 = 32 - d1
538 bfextu LOCAL_EX(%a0){%d0:#32},%d2
539 bfextu %d2{%d1:%d0},%d2 |d2 = new LOCAL_HI
540 bfextu LOCAL_HI(%a0){%d0:#32},%d1 |d1 = new LOCAL_LO
541 bfextu FP_SCR2+LOCAL_LO(%a6){%d0:#32},%d0 |d0 = new G,R,S
542 movel %d2,LOCAL_HI(%a0) |store new LOCAL_HI
543 movel %d1,LOCAL_LO(%a0) |store new LOCAL_LO
547 bsetl #rnd_stky_bit,%d0
550 movel FP_SCR2+LOCAL_GRS(%a6),%d2 |restore original g,r,s
551 andil #0xe0000000,%d2 |clear all but G,R,S
552 tstl %d2 |test if original G,R,S are clear
554 orl #0x20000000,%d0 |set sticky bit in d0
556 andil #0xe0000000,%d0 |clear all but G,R,S
564 movew %d0,LOCAL_EX(%a0) |unsigned exponent = threshold
565 subw #32,%d1 |d1 now between 0 and 32
567 subw %d1,%d0 |d0 = 32 - d1
568 bfextu LOCAL_EX(%a0){%d0:#32},%d2
569 bfextu %d2{%d1:%d0},%d2 |d2 = new LOCAL_LO
570 bfextu LOCAL_HI(%a0){%d0:#32},%d1 |d1 = new G,R,S
572 bnes c2_sstky |bra if sticky bit to be set
573 bftst FP_SCR2+LOCAL_LO(%a6){%d0:#32}
574 bnes c2_sstky |bra if sticky bit to be set
580 bsetl #rnd_stky_bit,%d0
583 clrl LOCAL_HI(%a0) |store LOCAL_HI = 0
584 movel %d2,LOCAL_LO(%a0) |store LOCAL_LO
585 movel FP_SCR2+LOCAL_GRS(%a6),%d2 |restore original g,r,s
586 andil #0xe0000000,%d2 |clear all but G,R,S
587 tstl %d2 |test if original G,R,S are clear
589 orl #0x20000000,%d0 |set sticky bit in d0
591 andil #0xe0000000,%d0 |get rid of all but G,R,S
595 | d1 >= 64 Force the exponent to be the denorm threshold with the
599 movew %d0,LOCAL_EX(%a0)
603 orl #0x80000000,LOCAL_EX(%a0)
610 | Shift value is out of range. Set d1 for inex2 flag and
611 | return a zero with the given threshold.
615 movel #0x20000000,%d0
620 movel LOCAL_HI(%a0),%d0
621 bfextu %d0{#2:#30},%d1
622 andil #0xc0000000,%d0
626 movel LOCAL_HI(%a0),%d0
627 bfextu %d0{#1:#31},%d1
628 andil #0x80000000,%d0
629 lsrl #1,%d0 |shift high bit into R bit
636 tstb FP_SCR2+LOCAL_GRS(%a6)
642 bsetl #rnd_stky_bit,%d0