4 | handle rounding and normalization tasks
8 | Copyright (C) Motorola, Inc. 1990
11 | For details on the license for this file, please see the
12 | file, README, in this same directory.
14 |ROUND idnt 2,1 | Motorola 040 Floating Point Software Package
21 | round --- round result according to precision/mode
23 | a0 points to the input operand in the internal extended format
24 | d1(high word) contains rounding precision:
28 | d1(low word) contains rounding mode:
33 | d0{31:29} contains the g,r,s bits (extended)
35 | On return the value pointed to by a0 is correctly rounded,
36 | a0 is preserved and the g-r-s bits in d0 are cleared.
37 | The result is not typed - the tag field is invalid. The
38 | result is still in the internal extended format.
40 | The INEX bit of USER_FPSR will be set if the rounded result was
41 | inexact (i.e. if any of the g-r-s bits were set).
46 | If g=r=s=0 then result is exact and round is done, else set
47 | the inex flag in status reg and continue.
49 bsrs ext_grs |this subroutine looks at the
50 | :rounding precision and sets
51 | ;the appropriate g-r-s bits.
52 tstl %d0 |if grs are zero, go force
53 bne rnd_cont |lower bits to zero for size
55 swap %d1 |set up d1.w for round prec.
60 | Use rounding mode as an index into a jump table for these modes.
62 orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
64 movel (%a1,%d1.w*4),%a1
67 | Jump table indexed by rounding mode in d1.w. All following assumes
78 | If sign of fp number = 0 (positive), then add 1 to l.
81 swap %d1 |set up d1 for round prec.
82 tstb LOCAL_SGN(%a0) |check for sign
83 bmi truncate |if positive then truncate
84 movel #0xffffffff,%d0 |force g,r,s to be all f's
86 movel (%a1,%d1.w*4),%a1
89 | ROUND MINUS INFINITY
91 | If sign of fp number = 1 (negative), then add 1 to l.
94 swap %d1 |set up d1 for round prec.
95 tstb LOCAL_SGN(%a0) |check for sign
96 bpl truncate |if negative then truncate
97 movel #0xffffffff,%d0 |force g,r,s to be all f's
99 movel (%a1,%d1.w*4),%a1
106 swap %d1 |set up d1 for round prec.
112 | If (g=1), then add 1 to l and if (r=s=0), then clear l
113 | Note that this will round to even in case of a tie.
116 swap %d1 |set up d1 for round prec.
117 asll #1,%d0 |shift g-bit to c-bit
118 bcc truncate |if (g=1) then
120 movel (%a1,%d1.w*4),%a1
124 | ext_grs --- extract guard, round and sticky bits
126 | Input: d1 = PREC:ROUND
127 | Output: d0{31:29}= guard, round, sticky
129 | The ext_grs extract the guard/round/sticky bits according to the
130 | selected rounding precision. It is called by the round subroutine
131 | only. All registers except d0 are kept intact. d0 becomes an
132 | updated guard,round,sticky in d0{31:29}
134 | Notes: the ext_grs uses the round PREC, and therefore has to swap d1
135 | prior to usage, and needs to restore d1 to original.
138 swap %d1 |have d1.w point to round precision
144 moveml %d2/%d3,-(%a7) |make some temp registers
148 bfextu LOCAL_HI(%a0){#24:#2},%d3 |sgl prec. g-r are 2 bits right
149 movel #30,%d2 |of the sgl prec. limits
150 lsll %d2,%d3 |shift g-r bits to MSB of d3
151 movel LOCAL_HI(%a0),%d2 |get word 2 for s-bit test
152 andil #0x0000003f,%d2 |s bit is the or of all other
153 bnes st_stky |bits to the right of g-r
154 tstl LOCAL_LO(%a0) |test lower mantissa
155 bnes st_stky |if any are set, set sticky
156 tstl %d0 |test original g,r,s
157 bnes st_stky |if any are set, set sticky
158 bras end_sd |if words 3 and 4 are clr, exit
160 bfextu LOCAL_LO(%a0){#21:#2},%d3 |dbl-prec. g-r are 2 bits right
161 movel #30,%d2 |of the dbl prec. limits
162 lsll %d2,%d3 |shift g-r bits to the MSB of d3
163 movel LOCAL_LO(%a0),%d2 |get lower mantissa for s-bit test
164 andil #0x000001ff,%d2 |s bit is the or-ing of all
165 bnes st_stky |other bits to the right of g-r
166 tstl %d0 |test word original g,r,s
167 bnes st_stky |if any are set, set sticky
168 bras end_sd |if clear, exit
170 bset #rnd_stky_bit,%d3
172 movel %d3,%d0 |return grs to d0
173 moveml (%a7)+,%d2/%d3 |restore scratch registers
175 swap %d1 |restore d1 to original
178 |******************* Local Equates
179 .set ad_1_sgl,0x00000100 | constant to add 1 to l-bit in sgl prec
180 .set ad_1_dbl,0x00000800 | constant to add 1 to l-bit in dbl prec
183 |Jump table for adding 1 to the l-bit indexed by rnd prec
194 addl #ad_1_sgl,LOCAL_HI(%a0)
195 bccs scc_clr |no mantissa overflow
196 roxrw LOCAL_HI(%a0) |shift v-bit back in
197 roxrw LOCAL_HI+2(%a0) |shift v-bit back in
198 addw #0x1,LOCAL_EX(%a0) |and incr exponent
200 tstl %d0 |test for rs = 0
202 andiw #0xfe00,LOCAL_HI+2(%a0) |clear the l-bit
204 andil #0xffffff00,LOCAL_HI(%a0) |truncate bits beyond sgl limit
205 clrl LOCAL_LO(%a0) |clear d2
212 addql #1,LOCAL_LO(%a0) |add 1 to l-bit
213 bccs xcc_clr |test for carry out
214 addql #1,LOCAL_HI(%a0) |propagate carry
216 roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
217 roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
219 roxrw LOCAL_LO+2(%a0)
220 addw #0x1,LOCAL_EX(%a0) |and inc exp
222 tstl %d0 |test rs = 0
224 andib #0xfe,LOCAL_LO+3(%a0) |clear the l bit
231 addl #ad_1_dbl,LOCAL_LO(%a0)
233 addql #1,LOCAL_HI(%a0) |propagate carry
235 roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
236 roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
238 roxrw LOCAL_LO+2(%a0)
239 addw #0x1,LOCAL_EX(%a0) |incr exponent
241 tstl %d0 |test for rs = 0
243 andiw #0xf000,LOCAL_LO+2(%a0) |clear the l-bit
246 andil #0xfffff800,LOCAL_LO(%a0) |truncate bits beyond dbl limit
252 | Truncate all other bits
262 movel (%a1,%d1.w*4),%a1
271 | These routines (nrm_zero & nrm_set) normalize the unnorm. This
272 | is done by shifting the mantissa left while decrementing the
275 | NRM_SET shifts and decrements until there is a 1 set in the integer
276 | bit of the mantissa (msb in d1).
278 | NRM_ZERO shifts and decrements until there is a 1 set in the integer
279 | bit of the mantissa (msb in d1) unless this would mean the exponent
280 | would go less than 0. In that case the number becomes a denorm - the
281 | exponent (d0) is set to 0 and the mantissa (d1 & d2) is not
284 | Note that both routines have been optimized (for the worst case) and
285 | therefore do not have the easy to follow decrement/shift loop.
289 | Distance to first 1 bit in mantissa = X
290 | Distance to 0 from exponent = Y
295 | shift mantissa by Y
299 | FP_SCR1 = exponent, ms mantissa part, ls mantissa part
301 | L_SCR1{4} = fpte15 or ete15 bit
305 movew LOCAL_EX(%a0),%d0
306 cmpw #64,%d0 |see if exp > 64
308 bsr nrm_set |exp > 64 so exp won't exceed 0
311 moveml %d2/%d3/%d5/%d6,-(%a7)
312 movel LOCAL_HI(%a0),%d1
313 movel LOCAL_LO(%a0),%d2
315 bfffo %d1{#0:#32},%d3 |get the distance to the first 1
317 beqs ms_clr |branch if no bits were set
319 bmis greater |then exp will go past 0 (neg) if
320 | ;it is just shifted
321 bsr nrm_set |else exp won't go past 0
322 moveml (%a7)+,%d2/%d3/%d5/%d6
325 movel %d2,%d6 |save ls mant in d6
326 lsll %d0,%d2 |shift ls mant by count
327 lsll %d0,%d1 |shift ms mant by count
329 subl %d0,%d5 |make op a denorm by shifting bits
330 lsrl %d5,%d6 |by the number in the exp, then
332 orl %d6,%d1 |shift the ls mant bits into the ms mant
333 movel #0,%d0 |same as if decremented exp to 0
335 movew %d0,LOCAL_EX(%a0)
336 movel %d1,LOCAL_HI(%a0)
337 movel %d2,LOCAL_LO(%a0)
338 moveml (%a7)+,%d2/%d3/%d5/%d6
341 bfffo %d2{#0:#32},%d3 |check if any bits set in ls mant
342 beqs all_clr |branch if none set
345 bmis greater |then branch
346 bsr nrm_set |else exp won't go past 0
347 moveml (%a7)+,%d2/%d3/%d5/%d6
350 movew #0,LOCAL_EX(%a0) |no mantissa bits set. Set exp = 0.
351 moveml (%a7)+,%d2/%d3/%d5/%d6
359 bfffo LOCAL_HI(%a0){#0:#32},%d7 |find first 1 in ms mant to d7)
360 beqs lower |branch if ms mant is all 0's
364 subw %d7,LOCAL_EX(%a0) |sub exponent by count
365 movel LOCAL_HI(%a0),%d0 |d0 has ms mant
366 movel LOCAL_LO(%a0),%d1 |d1 has ls mant
368 lsll %d7,%d0 |shift first 1 to j bit position
369 movel %d1,%d6 |copy ls mant into d6
370 lsll %d7,%d6 |shift ls mant by count
371 movel %d6,LOCAL_LO(%a0) |store ls mant into memory
373 subl %d7,%d6 |continue shift
374 lsrl %d6,%d1 |shift off all bits but those that will
375 | ;be shifted into ms mant
376 orl %d1,%d0 |shift the ls mant bits into the ms mant
377 movel %d0,LOCAL_HI(%a0) |store ms mant into memory
378 moveml (%a7)+,%d7/%d6 |restore registers
382 | We get here if ms mant was = 0, and we assume ls mant has bits
383 | set (otherwise this would have been tagged a zero not a denorm).
386 movew LOCAL_EX(%a0),%d0 |d0 has exponent
387 movel LOCAL_LO(%a0),%d1 |d1 has ls mant
388 subw #32,%d0 |account for ms mant being all zeros
389 bfffo %d1{#0:#32},%d7 |find first 1 in ls mant to d7)
390 subw %d7,%d0 |subtract shift count from exp
391 lsll %d7,%d1 |shift first 1 to integer bit in ms mant
392 movew %d0,LOCAL_EX(%a0) |store ms mant
393 movel %d1,LOCAL_HI(%a0) |store exp
394 clrl LOCAL_LO(%a0) |clear ls mant
398 | denorm --- denormalize an intermediate result
403 | a0 points to the operand to be denormalized
404 | (in the internal extended format)
406 | d0: rounding precision
408 | a0 points to the denormalized result
409 | (in the internal extended format)
411 | d0 is guard,round,sticky
413 | d0 comes into this routine with the rounding precision. It
414 | is then loaded with the denormalized exponent threshold for the
415 | rounding precision.
420 btstb #6,LOCAL_EX(%a0) |check for exponents between $7fff-$4000
422 bsetb #7,LOCAL_EX(%a0) |sign extend if it is so
425 cmpib #0,%d0 |if 0 then extended precision
426 bnes not_ext |else branch
428 clrl %d1 |load d1 with ext threshold
429 clrl %d0 |clear the sticky flag
430 bsr dnrm_lp |denormalize the number
431 tstb %d1 |check for inex
432 beq no_inex |if clr, no inex
433 bras dnrm_inex |if set, set inex
436 cmpil #1,%d0 |if 1 then single precision
437 beqs load_sgl |else must be 2, double prec
440 movew #dbl_thresh,%d1 |put copy of threshold in d1
441 movel %d1,%d0 |copy d1 into d0
442 subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
443 cmpw #67,%d0 |if diff > 67 (mant + grs bits)
444 bpls chk_stky |then branch (all bits would be
445 | ; shifted off in denorm routine)
446 clrl %d0 |else clear the sticky flag
447 bsr dnrm_lp |denormalize the number
449 beqs no_inex |if clr, no inex
450 bras dnrm_inex |if set, set inex
453 movew #sgl_thresh,%d1 |put copy of threshold in d1
454 movel %d1,%d0 |copy d1 into d0
455 subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
456 cmpw #67,%d0 |if diff > 67 (mant + grs bits)
457 bpls chk_stky |then branch (all bits would be
458 | ; shifted off in denorm routine)
459 clrl %d0 |else clear the sticky flag
460 bsr dnrm_lp |denormalize the number
462 beqs no_inex |if clr, no inex
463 bras dnrm_inex |if set, set inex
466 tstl LOCAL_HI(%a0) |check for any bits set
468 tstl LOCAL_LO(%a0) |check for any bits set
472 orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
473 movel #0x20000000,%d0 |set sticky bit in return value
475 movew %d1,LOCAL_EX(%a0) |load exp with threshold
476 movel #0,LOCAL_HI(%a0) |set d1 = 0 (ms mantissa)
477 movel #0,LOCAL_LO(%a0) |set d2 = 0 (ms mantissa)
480 orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
485 | dnrm_lp --- normalize exponent/mantissa to specified threshold
488 | a0 points to the operand to be denormalized
489 | d0{31:29} initial guard,round,sticky
490 | d1{15:0} denormalization threshold
492 | a0 points to the denormalized operand
493 | d0{31:29} final guard,round,sticky
494 | d1.b inexact flag: all ones means inexact result
496 | The LOCAL_LO and LOCAL_GRS parts of the value are copied to FP_SCR2
497 | so that bfext can be used to extract the new low part of the mantissa.
498 | Dnrm_lp can be called with a0 pointing to ETEMP or WBTEMP and there
499 | is no LOCAL_GRS scratch word following it on the fsave frame.
503 movel %d2,-(%sp) |save d2 for temp use
504 btstb #E3,E_BYTE(%a6) |test for type E3 exception
505 beqs not_E3 |not type E3 exception
506 bfextu WBTEMP_GRS(%a6){#6:#3},%d2 |extract guard,round, sticky bit
508 lsll %d0,%d2 |shift g,r,s to their positions
511 movel (%sp)+,%d2 |restore d2
512 movel LOCAL_LO(%a0),FP_SCR2+LOCAL_LO(%a6)
513 movel %d0,FP_SCR2+LOCAL_GRS(%a6)
514 movel %d1,%d0 |copy the denorm threshold
515 subw LOCAL_EX(%a0),%d1 |d1 = threshold - uns exponent
518 blts case_1 |0 = d1 < 32
520 blts case_2 |32 <= d1 < 64
523 | No normalization necessary
526 clrb %d1 |set no inex2 reported
527 movel FP_SCR2+LOCAL_GRS(%a6),%d0 |restore original g,r,s
534 movew %d0,LOCAL_EX(%a0) |exponent = denorm threshold
536 subw %d1,%d0 |d0 = 32 - d1
537 bfextu LOCAL_EX(%a0){%d0:#32},%d2
538 bfextu %d2{%d1:%d0},%d2 |d2 = new LOCAL_HI
539 bfextu LOCAL_HI(%a0){%d0:#32},%d1 |d1 = new LOCAL_LO
540 bfextu FP_SCR2+LOCAL_LO(%a6){%d0:#32},%d0 |d0 = new G,R,S
541 movel %d2,LOCAL_HI(%a0) |store new LOCAL_HI
542 movel %d1,LOCAL_LO(%a0) |store new LOCAL_LO
546 bsetl #rnd_stky_bit,%d0
549 movel FP_SCR2+LOCAL_GRS(%a6),%d2 |restore original g,r,s
550 andil #0xe0000000,%d2 |clear all but G,R,S
551 tstl %d2 |test if original G,R,S are clear
553 orl #0x20000000,%d0 |set sticky bit in d0
555 andil #0xe0000000,%d0 |clear all but G,R,S
563 movew %d0,LOCAL_EX(%a0) |unsigned exponent = threshold
564 subw #32,%d1 |d1 now between 0 and 32
566 subw %d1,%d0 |d0 = 32 - d1
567 bfextu LOCAL_EX(%a0){%d0:#32},%d2
568 bfextu %d2{%d1:%d0},%d2 |d2 = new LOCAL_LO
569 bfextu LOCAL_HI(%a0){%d0:#32},%d1 |d1 = new G,R,S
571 bnes c2_sstky |bra if sticky bit to be set
572 bftst FP_SCR2+LOCAL_LO(%a6){%d0:#32}
573 bnes c2_sstky |bra if sticky bit to be set
579 bsetl #rnd_stky_bit,%d0
582 clrl LOCAL_HI(%a0) |store LOCAL_HI = 0
583 movel %d2,LOCAL_LO(%a0) |store LOCAL_LO
584 movel FP_SCR2+LOCAL_GRS(%a6),%d2 |restore original g,r,s
585 andil #0xe0000000,%d2 |clear all but G,R,S
586 tstl %d2 |test if original G,R,S are clear
588 orl #0x20000000,%d0 |set sticky bit in d0
590 andil #0xe0000000,%d0 |get rid of all but G,R,S
594 | d1 >= 64 Force the exponent to be the denorm threshold with the
598 movew %d0,LOCAL_EX(%a0)
602 orl #0x80000000,LOCAL_EX(%a0)
609 | Shift value is out of range. Set d1 for inex2 flag and
610 | return a zero with the given threshold.
614 movel #0x20000000,%d0
619 movel LOCAL_HI(%a0),%d0
620 bfextu %d0{#2:#30},%d1
621 andil #0xc0000000,%d0
625 movel LOCAL_HI(%a0),%d0
626 bfextu %d0{#1:#31},%d1
627 andil #0x80000000,%d0
628 lsrl #1,%d0 |shift high bit into R bit
635 tstb FP_SCR2+LOCAL_GRS(%a6)
641 bsetl #rnd_stky_bit,%d0