xref: /original-bsd/lib/libm/vax/argred.s (revision 6ff19daa) 
1# Copyright (c) 1985 Regents of the University of California.
2# All rights reserved.
3#
4# %sccs.include.redist.sh%
5#
6#	@(#)argred.s	5.4 (Berkeley) 10/09/90
7#
8	.data
9	.align	2
10_sccsid:
11.asciz	"@(#)argred.s	1.1 (Berkeley) 8/21/85; 5.4 (ucb.elefunt) 10/09/90"
12
13#  libm$argred implements Bob Corbett's argument reduction and
14#  libm$sincos implements Peter Tang's double precision sin/cos.
15#
16#  Note: The two entry points libm$argred and libm$sincos are meant
17#        to be used only by _sin, _cos and _tan.
18#
19# method: true range reduction to [-pi/4,pi/4], P. Tang  &  B. Corbett
20# S. McDonald, April 4,  1985
21#
22	.globl	libm$argred
23	.globl	libm$sincos
24	.text
25	.align	1
26
27libm$argred:
28#
29#  Compare the argument with the largest possible that can
30#  be reduced by table lookup.  r3 := |x|  will be used in  table_lookup .
31#
32	movd	r0,r3
33	bgeq	abs1
34	mnegd	r3,r3
35abs1:
36	cmpd	r3,$0d+4.55530934770520019583e+01
37	blss	small_arg
38	jsb	trigred
39	rsb
40small_arg:
41	jsb	table_lookup
42	rsb
43#
44#  At this point,
45#	   r0  contains the quadrant number, 0, 1, 2, or 3;
46#	r2/r1  contains the reduced argument as a D-format number;
47#  	   r3  contains a F-format extension to the reduced argument;
48#          r4  contains a  0 or 1  corresponding to a  sin or cos  entry.
49#
50libm$sincos:
51#
52#  Compensate for a cosine entry by adding one to the quadrant number.
53#
54	addl2	r4,r0
55#
56#  Polyd clobbers  r5-r0 ;  save  X  in  r7/r6 .
57#  This can be avoided by rewriting  trigred .
58#
59	movd	r1,r6
60#
61#  Likewise, save  alpha  in  r8 .
62#  This can be avoided by rewriting  trigred .
63#
64	movf	r3,r8
65#
66#  Odd or even quadrant?  cosine if odd, sine otherwise.
67#  Save  floor(quadrant/2) in  r9  ; it determines the final sign.
68#
69	rotl	$-1,r0,r9
70	blss	cosine
71sine:
72	muld2	r1,r1		# Xsq = X * X
73	cmpw	$0x2480,r1	# [zl] Xsq > 2^-56?
74	blss	1f		# [zl] yes, go ahead and do polyd
75	clrq	r1		# [zl] work around 11/780 FPA polyd bug
761:
77	polyd	r1,$7,sin_coef	# Q = P(Xsq) , of deg 7
78	mulf3	$0f3.0,r8,r4	# beta = 3 * alpha
79	mulf2	r0,r4		# beta = Q * beta
80	addf2	r8,r4		# beta = alpha + beta
81	muld2	r6,r0		# S(X) = X * Q
82#	cvtfd	r4,r4		... r5 = 0 after a polyd.
83	addd2	r4,r0		# S(X) = beta + S(X)
84	addd2	r6,r0		# S(X) = X + S(X)
85	brb	done
86cosine:
87	muld2	r6,r6		# Xsq = X * X
88	beql	zero_arg
89	mulf2	r1,r8		# beta = X * alpha
90	polyd	r6,$7,cos_coef	# Q = P'(Xsq) , of deg 7
91	subd3	r0,r8,r0	# beta = beta - Q
92	subw2	$0x80,r6	# Xsq = Xsq / 2
93	addd2	r0,r6		# Xsq = Xsq + beta
94zero_arg:
95	subd3	r6,$0d1.0,r0	# C(X) = 1 - Xsq
96done:
97	blbc	r9,even
98	mnegd	r0,r0
99even:
100	rsb
101
102.data
103.align	2
104
105sin_coef:
106	.double	0d-7.53080332264191085773e-13	# s7 = 2^-29 -1.a7f2504ffc49f8..
107	.double	0d+1.60573519267703489121e-10	# s6 = 2^-21  1.611adaede473c8..
108	.double	0d-2.50520965150706067211e-08	# s5 = 2^-1a -1.ae644921ed8382..
109	.double	0d+2.75573191800593885716e-06	# s4 = 2^-13  1.71de3a4b884278..
110	.double	0d-1.98412698411850507950e-04	# s3 = 2^-0d -1.a01a01a0125e7d..
111	.double	0d+8.33333333333325688985e-03	# s2 = 2^-07  1.11111111110e50
112	.double	0d-1.66666666666666664354e-01	# s1 = 2^-03 -1.55555555555554
113	.double	0d+0.00000000000000000000e+00	# s0 = 0
114
115cos_coef:
116	.double	0d-1.13006966202629430300e-11	# s7 = 2^-25 -1.8D9BA04D1374BE..
117	.double	0d+2.08746646574796004700e-09	# s6 = 2^-1D  1.1EE632650350BA..
118	.double	0d-2.75573073031284417300e-07	# s5 = 2^-16 -1.27E4F31411719E..
119	.double	0d+2.48015872682668025200e-05	# s4 = 2^-10  1.A01A0196B902E8..
120	.double	0d-1.38888888888464709200e-03	# s3 = 2^-0A -1.6C16C16C11FACE..
121	.double	0d+4.16666666666664761400e-02	# s2 = 2^-05  1.5555555555539E
122	.double	0d+0.00000000000000000000e+00	# s1 = 0
123	.double	0d+0.00000000000000000000e+00	# s0 = 0
124
125#
126#  Multiples of  pi/2  expressed as the sum of three doubles,
127#
128#  trailing:	n * pi/2 ,  n = 0, 1, 2, ..., 29
129#			trailing[n] ,
130#
131#  middle:	n * pi/2 ,  n = 0, 1, 2, ..., 29
132#			middle[n]   ,
133#
134#  leading:	n * pi/2 ,  n = 0, 1, 2, ..., 29
135#			leading[n]  ,
136#
137#	where
138#		leading[n]  := (n * pi/2)  rounded,
139#		middle[n]   := (n * pi/2  -  leading[n])  rounded,
140#		trailing[n] := (( n * pi/2 - leading[n]) - middle[n])  rounded .
141
142trailing:
143	.double	0d+0.00000000000000000000e+00	#  0 * pi/2  trailing
144	.double	0d+4.33590506506189049611e-35	#  1 * pi/2  trailing
145	.double	0d+8.67181013012378099223e-35	#  2 * pi/2  trailing
146	.double	0d+1.30077151951856714215e-34	#  3 * pi/2  trailing
147	.double	0d+1.73436202602475619845e-34	#  4 * pi/2  trailing
148	.double	0d-1.68390735624352669192e-34	#  5 * pi/2  trailing
149	.double	0d+2.60154303903713428430e-34	#  6 * pi/2  trailing
150	.double	0d-8.16726343231148352150e-35	#  7 * pi/2  trailing
151	.double	0d+3.46872405204951239689e-34	#  8 * pi/2  trailing
152	.double	0d+3.90231455855570147991e-34	#  9 * pi/2  trailing
153	.double	0d-3.36781471248705338384e-34	# 10 * pi/2  trailing
154	.double	0d-1.06379439835298071785e-33	# 11 * pi/2  trailing
155	.double	0d+5.20308607807426856861e-34	# 12 * pi/2  trailing
156	.double	0d+5.63667658458045770509e-34	# 13 * pi/2  trailing
157	.double	0d-1.63345268646229670430e-34	# 14 * pi/2  trailing
158	.double	0d-1.19986217995610764801e-34	# 15 * pi/2  trailing
159	.double	0d+6.93744810409902479378e-34	# 16 * pi/2  trailing
160	.double	0d-8.03640094449267300110e-34	# 17 * pi/2  trailing
161	.double	0d+7.80462911711140295982e-34	# 18 * pi/2  trailing
162	.double	0d-7.16921993148029483506e-34	# 19 * pi/2  trailing
163	.double	0d-6.73562942497410676769e-34	# 20 * pi/2  trailing
164	.double	0d-6.30203891846791677593e-34	# 21 * pi/2  trailing
165	.double	0d-2.12758879670596143570e-33	# 22 * pi/2  trailing
166	.double	0d+2.53800212047402350390e-33	# 23 * pi/2  trailing
167	.double	0d+1.04061721561485371372e-33	# 24 * pi/2  trailing
168	.double	0d+6.11729905311472319056e-32	# 25 * pi/2  trailing
169	.double	0d+1.12733531691609154102e-33	# 26 * pi/2  trailing
170	.double	0d-3.70049587943078297272e-34	# 27 * pi/2  trailing
171	.double	0d-3.26690537292459340860e-34	# 28 * pi/2  trailing
172	.double	0d-1.14812616507957271361e-34	# 29 * pi/2  trailing
173
174middle:
175	.double	0d+0.00000000000000000000e+00	#  0 * pi/2  middle
176	.double	0d+5.72118872610983179676e-18	#  1 * pi/2  middle
177	.double	0d+1.14423774522196635935e-17	#  2 * pi/2  middle
178	.double	0d-3.83475850529283316309e-17	#  3 * pi/2  middle
179	.double	0d+2.28847549044393271871e-17	#  4 * pi/2  middle
180	.double	0d-2.69052076007086676522e-17	#  5 * pi/2  middle
181	.double	0d-7.66951701058566632618e-17	#  6 * pi/2  middle
182	.double	0d-1.54628301484890040587e-17	#  7 * pi/2  middle
183	.double	0d+4.57695098088786543741e-17	#  8 * pi/2  middle
184	.double	0d+1.07001849766246313192e-16	#  9 * pi/2  middle
185	.double	0d-5.38104152014173353044e-17	# 10 * pi/2  middle
186	.double	0d-2.14622680169080983801e-16	# 11 * pi/2  middle
187	.double	0d-1.53390340211713326524e-16	# 12 * pi/2  middle
188	.double	0d-9.21580002543456677056e-17	# 13 * pi/2  middle
189	.double	0d-3.09256602969780081173e-17	# 14 * pi/2  middle
190	.double	0d+3.03066796603896507006e-17	# 15 * pi/2  middle
191	.double	0d+9.15390196177573087482e-17	# 16 * pi/2  middle
192	.double	0d+1.52771359575124969107e-16	# 17 * pi/2  middle
193	.double	0d+2.14003699532492626384e-16	# 18 * pi/2  middle
194	.double	0d-1.68853170360202329427e-16	# 19 * pi/2  middle
195	.double	0d-1.07620830402834670609e-16	# 20 * pi/2  middle
196	.double	0d+3.97700719404595604379e-16	# 21 * pi/2  middle
197	.double	0d-4.29245360338161967602e-16	# 22 * pi/2  middle
198	.double	0d-3.68013020380794313406e-16	# 23 * pi/2  middle
199	.double	0d-3.06780680423426653047e-16	# 24 * pi/2  middle
200	.double	0d-2.45548340466059054318e-16	# 25 * pi/2  middle
201	.double	0d-1.84316000508691335411e-16	# 26 * pi/2  middle
202	.double	0d-1.23083660551323675053e-16	# 27 * pi/2  middle
203	.double	0d-6.18513205939560162346e-17	# 28 * pi/2  middle
204	.double	0d-6.18980636588357585202e-19	# 29 * pi/2  middle
205
206leading:
207	.double	0d+0.00000000000000000000e+00	#  0 * pi/2  leading
208	.double	0d+1.57079632679489661351e+00	#  1 * pi/2  leading
209	.double	0d+3.14159265358979322702e+00	#  2 * pi/2  leading
210	.double	0d+4.71238898038468989604e+00	#  3 * pi/2  leading
211	.double	0d+6.28318530717958645404e+00	#  4 * pi/2  leading
212	.double	0d+7.85398163397448312306e+00	#  5 * pi/2  leading
213	.double	0d+9.42477796076937979208e+00	#  6 * pi/2  leading
214	.double	0d+1.09955742875642763501e+01	#  7 * pi/2  leading
215	.double	0d+1.25663706143591729081e+01	#  8 * pi/2  leading
216	.double	0d+1.41371669411540694661e+01	#  9 * pi/2  leading
217	.double	0d+1.57079632679489662461e+01	# 10 * pi/2  leading
218	.double	0d+1.72787595947438630262e+01	# 11 * pi/2  leading
219	.double	0d+1.88495559215387595842e+01	# 12 * pi/2  leading
220	.double	0d+2.04203522483336561422e+01	# 13 * pi/2  leading
221	.double	0d+2.19911485751285527002e+01	# 14 * pi/2  leading
222	.double	0d+2.35619449019234492582e+01	# 15 * pi/2  leading
223	.double	0d+2.51327412287183458162e+01	# 16 * pi/2  leading
224	.double	0d+2.67035375555132423742e+01	# 17 * pi/2  leading
225	.double	0d+2.82743338823081389322e+01	# 18 * pi/2  leading
226	.double	0d+2.98451302091030359342e+01	# 19 * pi/2  leading
227	.double	0d+3.14159265358979324922e+01	# 20 * pi/2  leading
228	.double	0d+3.29867228626928286062e+01	# 21 * pi/2  leading
229	.double	0d+3.45575191894877260523e+01	# 22 * pi/2  leading
230	.double	0d+3.61283155162826226103e+01	# 23 * pi/2  leading
231	.double	0d+3.76991118430775191683e+01	# 24 * pi/2  leading
232	.double	0d+3.92699081698724157263e+01	# 25 * pi/2  leading
233	.double	0d+4.08407044966673122843e+01	# 26 * pi/2  leading
234	.double	0d+4.24115008234622088423e+01	# 27 * pi/2  leading
235	.double	0d+4.39822971502571054003e+01	# 28 * pi/2  leading
236	.double	0d+4.55530934770520019583e+01	# 29 * pi/2  leading
237
238twoOverPi:
239	.double	0d+6.36619772367581343076e-01
240	.text
241	.align	1
242
243table_lookup:
244	muld3	r3,twoOverPi,r0
245	cvtrdl	r0,r0			# n = nearest int to ((2/pi)*|x|) rnded
246	mull3	$8,r0,r5
247	subd2	leading(r5),r3		# p = (|x| - leading n*pi/2) exactly
248	subd3	middle(r5),r3,r1	# q = (p - middle  n*pi/2) rounded
249	subd2	r1,r3			# r = (p - q)
250	subd2	middle(r5),r3		# r =  r - middle  n*pi/2
251	subd2	trailing(r5),r3		# r =  r - trailing n*pi/2  rounded
252#
253#  If the original argument was negative,
254#  negate the reduce argument and
255#  adjust the octant/quadrant number.
256#
257	tstw	4(ap)
258	bgeq	abs2
259	mnegf	r1,r1
260	mnegf	r3,r3
261#	subb3	r0,$8,r0	...used for  pi/4  reduction -S.McD
262	subb3	r0,$4,r0
263abs2:
264#
265#  Clear all unneeded octant/quadrant bits.
266#
267#	bicb2	$0xf8,r0	...used for  pi/4  reduction -S.McD
268	bicb2	$0xfc,r0
269	rsb
270#
271#						p.0
272	.text
273	.align	2
274#
275# Only 256 (actually 225) bits of 2/pi are needed for VAX double
276# precision; this was determined by enumerating all the nearest
277# machine integer multiples of pi/2 using continued fractions.
278# (8a8d3673775b7ff7 required the most bits.)		-S.McD
279#
280	.long	0
281	.long	0
282	.long	0xaef1586d
283	.long	0x9458eaf7
284	.long	0x10e4107f
285	.long	0xd8a5664f
286	.long	0x4d377036
287	.long	0x09d5f47d
288	.long	0x91054a7f
289	.long	0xbe60db93
290bits2opi:
291	.long	0x00000028
292	.long	0
293#
294#  Note: wherever you see the word `octant', read `quadrant'.
295#  Currently this code is set up for  pi/2  argument reduction.
296#  By uncommenting/commenting the appropriate lines, it will
297#  also serve as a  pi/4  argument reduction code.
298#
299
300#						p.1
301#  Trigred  preforms argument reduction
302#  for the trigonometric functions.  It
303#  takes one input argument, a D-format
304#  number in  r1/r0 .  The magnitude of
305#  the input argument must be greater
306#  than or equal to  1/2 .  Trigred produces
307#  three results:  the number of the octant
308#  occupied by the argument, the reduced
309#  argument, and an extension of the
310#  reduced argument.  The octant number is
311#  returned in  r0 .  The reduced argument
312#  is returned as a D-format number in
313#  r2/r1 .  An 8 bit extension of the
314#  reduced argument is returned as an
315#  F-format number in r3.
316#						p.2
317trigred:
318#
319#  Save the sign of the input argument.
320#
321	movw	r0,-(sp)
322#
323#  Extract the exponent field.
324#
325	extzv	$7,$7,r0,r2
326#
327#  Convert the fraction part of the input
328#  argument into a quadword integer.
329#
330	bicw2	$0xff80,r0
331	bisb2	$0x80,r0	# -S.McD
332	rotl	$16,r0,r0
333	rotl	$16,r1,r1
334#
335#  If  r1  is negative, add  1  to  r0 .  This
336#  adjustment is made so that the two's
337#  complement multiplications done later
338#  will produce unsigned results.
339#
340	bgeq	posmid
341	incl	r0
342posmid:
343#						p.3
344#
345#  Set  r3  to the address of the first quadword
346#  used to obtain the needed portion of  2/pi .
347#  The address is longword aligned to ensure
348#  efficient access.
349#
350	ashl	$-3,r2,r3
351	bicb2	$3,r3
352	subl3	r3,$bits2opi,r3
353#
354#  Set  r2  to the size of the shift needed to
355#  obtain the correct portion of  2/pi .
356#
357	bicb2	$0xe0,r2
358#						p.4
359#
360#  Move the needed  128  bits of  2/pi  into
361#  r11 - r8 .  Adjust the numbers to allow
362#  for unsigned multiplication.
363#
364	ashq	r2,(r3),r10
365
366	subl2	$4,r3
367	ashq	r2,(r3),r9
368	bgeq	signoff1
369	incl	r11
370signoff1:
371	subl2	$4,r3
372	ashq	r2,(r3),r8
373	bgeq	signoff2
374	incl	r10
375signoff2:
376	subl2	$4,r3
377	ashq	r2,(r3),r7
378	bgeq	signoff3
379	incl	r9
380signoff3:
381#						p.5
382#
383#  Multiply the contents of  r0/r1  by the
384#  slice of  2/pi  in  r11 - r8 .
385#
386	emul	r0,r8,$0,r4
387	emul	r0,r9,r5,r5
388	emul	r0,r10,r6,r6
389
390	emul	r1,r8,$0,r7
391	emul	r1,r9,r8,r8
392	emul	r1,r10,r9,r9
393	emul	r1,r11,r10,r10
394
395	addl2	r4,r8
396	adwc	r5,r9
397	adwc	r6,r10
398#						p.6
399#
400#  If there are more than five leading zeros
401#  after the first two quotient bits or if there
402#  are more than five leading ones after the first
403#  two quotient bits, generate more fraction bits.
404#  Otherwise, branch to code to produce the result.
405#
406	bicl3	$0xc1ffffff,r10,r4
407	beql	more1
408	cmpl	$0x3e000000,r4
409	bneq	result
410more1:
411#						p.7
412#
413#  generate another  32  result bits.
414#
415	subl2	$4,r3
416	ashq	r2,(r3),r5
417	bgeq	signoff4
418
419	emul	r1,r6,$0,r4
420	addl2	r1,r5
421	emul	r0,r6,r5,r5
422	addl2	r0,r6
423	brb	addbits1
424
425signoff4:
426	emul	r1,r6,$0,r4
427	emul	r0,r6,r5,r5
428
429addbits1:
430	addl2	r5,r7
431	adwc	r6,r8
432	adwc	$0,r9
433	adwc	$0,r10
434#						p.8
435#
436#  Check for massive cancellation.
437#
438	bicl3	$0xc0000000,r10,r6
439#	bneq	more2			-S.McD  Test was backwards
440	beql	more2
441	cmpl	$0x3fffffff,r6
442	bneq	result
443more2:
444#						p.9
445#
446#  If massive cancellation has occurred,
447#  generate another  24  result bits.
448#  Testing has shown there will always be
449#  enough bits after this point.
450#
451	subl2	$4,r3
452	ashq	r2,(r3),r5
453	bgeq	signoff5
454
455	emul	r0,r6,r4,r5
456	addl2	r0,r6
457	brb	addbits2
458
459signoff5:
460	emul	r0,r6,r4,r5
461
462addbits2:
463	addl2	r6,r7
464	adwc	$0,r8
465	adwc	$0,r9
466	adwc	$0,r10
467#						p.10
468#
469#  The following code produces the reduced
470#  argument from the product bits contained
471#  in  r10 - r7 .
472#
473result:
474#
475#  Extract the octant number from  r10 .
476#
477#	extzv	$29,$3,r10,r0	...used for  pi/4  reduction -S.McD
478	extzv	$30,$2,r10,r0
479#
480#  Clear the octant bits in  r10 .
481#
482#	bicl2	$0xe0000000,r10	...used for  pi/4  reduction -S.McD
483	bicl2	$0xc0000000,r10
484#
485#  Zero the sign flag.
486#
487	clrl	r5
488#						p.11
489#
490#  Check to see if the fraction is greater than
491#  or equal to one-half.  If it is, add one
492#  to the octant number, set the sign flag
493#  on, and replace the fraction with  1 minus
494#  the fraction.
495#
496#	bitl	$0x10000000,r10		...used for  pi/4  reduction -S.McD
497	bitl	$0x20000000,r10
498	beql	small
499	incl	r0
500	incl	r5
501#	subl3	r10,$0x1fffffff,r10	...used for  pi/4  reduction -S.McD
502	subl3	r10,$0x3fffffff,r10
503	mcoml	r9,r9
504	mcoml	r8,r8
505	mcoml	r7,r7
506small:
507#						p.12
508#
509##  Test whether the first  29  bits of the ...used for  pi/4  reduction -S.McD
510#  Test whether the first  30  bits of the
511#  fraction are zero.
512#
513	tstl	r10
514	beql	tiny
515#
516#  Find the position of the first one bit in  r10 .
517#
518	cvtld	r10,r1
519	extzv	$7,$7,r1,r1
520#
521#  Compute the size of the shift needed.
522#
523	subl3	r1,$32,r6
524#
525#  Shift up the high order  64  bits of the
526#  product.
527#
528	ashq	r6,r9,r10
529	ashq	r6,r8,r9
530	brb	mult
531#						p.13
532#
533#  Test to see if the sign bit of  r9  is on.
534#
535tiny:
536	tstl	r9
537	bgeq	tinier
538#
539#  If it is, shift the product bits up  32  bits.
540#
541	movl	$32,r6
542	movq	r8,r10
543	tstl	r10
544	brb	mult
545#						p.14
546#
547#  Test whether  r9  is zero.  It is probably
548#  impossible for both  r10  and  r9  to be
549#  zero, but until proven to be so, the test
550#  must be made.
551#
552tinier:
553	beql	zero
554#
555#  Find the position of the first one bit in  r9 .
556#
557	cvtld	r9,r1
558	extzv	$7,$7,r1,r1
559#
560#  Compute the size of the shift needed.
561#
562	subl3	r1,$32,r1
563	addl3	$32,r1,r6
564#
565#  Shift up the high order  64  bits of the
566#  product.
567#
568	ashq	r1,r8,r10
569	ashq	r1,r7,r9
570	brb	mult
571#						p.15
572#
573#  The following code sets the reduced
574#  argument to zero.
575#
576zero:
577	clrl	r1
578	clrl	r2
579	clrl	r3
580	brw	return
581#						p.16
582#
583#  At this point,  r0  contains the octant number,
584#  r6  indicates the number of bits the fraction
585#  has been shifted,  r5  indicates the sign of
586#  the fraction,  r11/r10  contain the high order
587#  64  bits of the fraction, and the condition
588#  codes indicate where the sign bit of  r10
589#  is on.  The following code multiplies the
590#  fraction by  pi/2 .
591#
592mult:
593#
594#  Save  r11/r10  in  r4/r1 .		-S.McD
595	movl	r11,r4
596	movl	r10,r1
597#
598#  If the sign bit of  r10  is on, add  1  to  r11 .
599#
600	bgeq	signoff6
601	incl	r11
602signoff6:
603#						p.17
604#
605#  Move  pi/2  into  r3/r2 .
606#
607	movq	$0xc90fdaa22168c235,r2
608#
609#  Multiply the fraction by the portion of  pi/2
610#  in  r2 .
611#
612	emul	r2,r10,$0,r7
613	emul	r2,r11,r8,r7
614#
615#  Multiply the fraction by the portion of  pi/2
616#  in  r3 .
617	emul	r3,r10,$0,r9
618	emul	r3,r11,r10,r10
619#
620#  Add the product bits together.
621#
622	addl2	r7,r9
623	adwc	r8,r10
624	adwc	$0,r11
625#
626#  Compensate for not sign extending  r8  above.-S.McD
627#
628	tstl	r8
629	bgeq	signoff6a
630	decl	r11
631signoff6a:
632#
633#  Compensate for  r11/r10  being unsigned.	-S.McD
634#
635	addl2	r2,r10
636	adwc	r3,r11
637#
638#  Compensate for  r3/r2  being unsigned.	-S.McD
639#
640	addl2	r1,r10
641	adwc	r4,r11
642#						p.18
643#
644#  If the sign bit of  r11  is zero, shift the
645#  product bits up one bit and increment  r6 .
646#
647	blss	signon
648	incl	r6
649	ashq	$1,r10,r10
650	tstl	r9
651	bgeq	signoff7
652	incl	r10
653signoff7:
654signon:
655#						p.19
656#
657#  Shift the  56  most significant product
658#  bits into  r9/r8 .  The sign extension
659#  will be handled later.
660#
661	ashq	$-8,r10,r8
662#
663#  Convert the low order  8  bits of  r10
664#  into an F-format number.
665#
666	cvtbf	r10,r3
667#
668#  If the result of the conversion was
669#  negative, add  1  to  r9/r8 .
670#
671	bgeq	chop
672	incl	r8
673	adwc	$0,r9
674#
675#  If  r9  is now zero, branch to special
676#  code to handle that possibility.
677#
678	beql	carryout
679chop:
680#						p.20
681#
682#  Convert the number in  r9/r8  into
683#  D-format number in  r2/r1 .
684#
685	rotl	$16,r8,r2
686	rotl	$16,r9,r1
687#
688#  Set the exponent field to the appropriate
689#  value.  Note that the extra bits created by
690#  sign extension are now eliminated.
691#
692	subw3	r6,$131,r6
693	insv	r6,$7,$9,r1
694#
695#  Set the exponent field of the F-format
696#  number in  r3  to the appropriate value.
697#
698	tstf	r3
699	beql	return
700#	extzv	$7,$8,r3,r4	-S.McD
701	extzv	$7,$7,r3,r4
702	addw2	r4,r6
703#	subw2	$217,r6		-S.McD
704	subw2	$64,r6
705	insv	r6,$7,$8,r3
706	brb	return
707#						p.21
708#
709#  The following code generates the appropriate
710#  result for the unlikely possibility that
711#  rounding the number in  r9/r8  resulted in
712#  a carry out.
713#
714carryout:
715	clrl	r1
716	clrl	r2
717	subw3	r6,$132,r6
718	insv	r6,$7,$9,r1
719	tstf	r3
720	beql	return
721	extzv	$7,$8,r3,r4
722	addw2	r4,r6
723	subw2	$218,r6
724	insv	r6,$7,$8,r3
725#						p.22
726#
727#  The following code makes an needed
728#  adjustments to the signs of the
729#  results or to the octant number, and
730#  then returns.
731#
732return:
733#
734#  Test if the fraction was greater than or
735#  equal to  1/2 .  If so, negate the reduced
736#  argument.
737#
738	blbc	r5,signoff8
739	mnegf	r1,r1
740	mnegf	r3,r3
741signoff8:
742#						p.23
743#
744#  If the original argument was negative,
745#  negate the reduce argument and
746#  adjust the octant number.
747#
748	tstw	(sp)+
749	bgeq	signoff9
750	mnegf	r1,r1
751	mnegf	r3,r3
752#	subb3	r0,$8,r0	...used for  pi/4  reduction -S.McD
753	subb3	r0,$4,r0
754signoff9:
755#
756#  Clear all unneeded octant bits.
757#
758#	bicb2	$0xf8,r0	...used for  pi/4  reduction -S.McD
759	bicb2	$0xfc,r0
760#
761#  Return.
762#
763	rsb
764