1/*	$NetBSD: n_argred.S,v 1.8 2003/08/07 16:44:44 agc Exp $	*/
2/*
3 * Copyright (c) 1985, 1993
4 *	The Regents of the University of California.  All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 *    may be used to endorse or promote products derived from this software
16 *    without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 *
30 *	@(#)argred.s	8.1 (Berkeley) 6/4/93
31 */
32
33#include <machine/asm.h>
34
35/*
36 *  libm$argred implements Bob Corbett's argument reduction and
37 *  libm$sincos implements Peter Tang's double precision sin/cos.
38 *
39 *  Note: The two entry points libm$argred and libm$sincos are meant
40 *        to be used only by _sin, _cos and _tan.
41 *
42 * method: true range reduction to [-pi/4,pi/4], P. Tang  &  B. Corbett
43 * S. McDonald, April 4,  1985
44 */
45
46	.hidden	__libm_argred
47ENTRY(__libm_argred, 0)
48/*
49 *  Compare the argument with the largest possible that can
50 *  be reduced by table lookup.  %r3 := |x|  will be used in  table_lookup .
51 */
52	movd	%r0,%r3
53	bgeq	abs1
54	mnegd	%r3,%r3
55abs1:
56	cmpd	%r3,$0d+4.55530934770520019583e+01
57	blss	small_arg
58	jsb	trigred
59	rsb
60small_arg:
61	jsb	table_lookup
62	rsb
63/*
64 *  At this point,
65 *	   %r0  contains the quadrant number, 0, 1, 2, or 3;
66 *	%r2/%r1  contains the reduced argument as a D-format number;
67 *  	   %r3  contains a F-format extension to the reduced argument;
68 *          %r4  contains a  0 or 1  corresponding to a  sin or cos  entry.
69 */
70
71	.hidden	__libm_sincos
72ENTRY(__libm_sincos, 0)
73/*
74 *  Compensate for a cosine entry by adding one to the quadrant number.
75 */
76	addl2	%r4,%r0
77/*
78 *  Polyd clobbers  %r5-%r0 ;  save  X  in  %r7/%r6 .
79 *  This can be avoided by rewriting  trigred .
80 */
81	movd	%r1,%r6
82/*
83 *  Likewise, save  alpha  in  %r8 .
84 *  This can be avoided by rewriting  trigred .
85 */
86	movf	%r3,%r8
87/*
88 *  Odd or even quadrant?  cosine if odd, sine otherwise.
89 *  Save  floor(quadrant/2) in  %r9  ; it determines the final sign.
90 */
91	rotl	$-1,%r0,%r9
92	blss	cosine
93sine:
94	muld2	%r1,%r1		# Xsq = X * X
95	cmpw	$0x2480,%r1	# [zl] Xsq > 2^-56?
96	blss	1f		# [zl] yes, go ahead and do polyd
97	clrq	%r1		# [zl] work around 11/780 FPA polyd bug
981:
99	polyd	%r1,$7,sin_coef	# Q = P(Xsq) , of deg 7
100	mulf3	$0f3.0,%r8,%r4	# beta = 3 * alpha
101	mulf2	%r0,%r4		# beta = Q * beta
102	addf2	%r8,%r4		# beta = alpha + beta
103	muld2	%r6,%r0		# S(X) = X * Q
104/*	cvtfd	%r4,%r4		... %r5 = 0 after a polyd. */
105	addd2	%r4,%r0		# S(X) = beta + S(X)
106	addd2	%r6,%r0		# S(X) = X + S(X)
107	jbr	done
108cosine:
109	muld2	%r6,%r6		# Xsq = X * X
110	beql	zero_arg
111	mulf2	%r1,%r8		# beta = X * alpha
112	polyd	%r6,$7,cos_coef	/* Q = P'(Xsq) , of deg 7 */
113	subd3	%r0,%r8,%r0	# beta = beta - Q
114	subw2	$0x80,%r6	# Xsq = Xsq / 2
115	addd2	%r0,%r6		# Xsq = Xsq + beta
116zero_arg:
117	subd3	%r6,$0d1.0,%r0	# C(X) = 1 - Xsq
118done:
119	blbc	%r9,even
120	mnegd	%r0,%r0
121even:
122	rsb
123
124#ifdef __ELF__
125	.section .rodata
126#else
127	.text
128#endif
129	_ALIGN_TEXT
130
131sin_coef:
132	.double	0d-7.53080332264191085773e-13	# s7 = 2^-29 -1.a7f2504ffc49f8..
133	.double	0d+1.60573519267703489121e-10	# s6 = 2^-21  1.611adaede473c8..
134	.double	0d-2.50520965150706067211e-08	# s5 = 2^-1a -1.ae644921ed8382..
135	.double	0d+2.75573191800593885716e-06	# s4 = 2^-13  1.71de3a4b884278..
136	.double	0d-1.98412698411850507950e-04	# s3 = 2^-0d -1.a01a01a0125e7d..
137	.double	0d+8.33333333333325688985e-03	# s2 = 2^-07  1.11111111110e50
138	.double	0d-1.66666666666666664354e-01	# s1 = 2^-03 -1.55555555555554
139	.double	0d+0.00000000000000000000e+00	# s0 = 0
140
141cos_coef:
142	.double	0d-1.13006966202629430300e-11	# s7 = 2^-25 -1.8D9BA04D1374BE..
143	.double	0d+2.08746646574796004700e-09	# s6 = 2^-1D  1.1EE632650350BA..
144	.double	0d-2.75573073031284417300e-07	# s5 = 2^-16 -1.27E4F31411719E..
145	.double	0d+2.48015872682668025200e-05	# s4 = 2^-10  1.A01A0196B902E8..
146	.double	0d-1.38888888888464709200e-03	# s3 = 2^-0A -1.6C16C16C11FACE..
147	.double	0d+4.16666666666664761400e-02	# s2 = 2^-05  1.5555555555539E
148	.double	0d+0.00000000000000000000e+00	# s1 = 0
149	.double	0d+0.00000000000000000000e+00	# s0 = 0
150
151/*
152 *  Multiples of  pi/2  expressed as the sum of three doubles,
153 *
154 *  trailing:	n * pi/2 ,  n = 0, 1, 2, ..., 29
155 *			trailing[n] ,
156 *
157 *  middle:	n * pi/2 ,  n = 0, 1, 2, ..., 29
158 *			middle[n]   ,
159 *
160 *  leading:	n * pi/2 ,  n = 0, 1, 2, ..., 29
161 *			leading[n]  ,
162 *
163 *	where
164 *		leading[n]  := (n * pi/2)  rounded,
165 *		middle[n]   := (n * pi/2  -  leading[n])  rounded,
166 *		trailing[n] := (( n * pi/2 - leading[n]) - middle[n])  rounded .
167 */
168trailing:
169	.double	0d+0.00000000000000000000e+00	#  0 * pi/2  trailing
170	.double	0d+4.33590506506189049611e-35	#  1 * pi/2  trailing
171	.double	0d+8.67181013012378099223e-35	#  2 * pi/2  trailing
172	.double	0d+1.30077151951856714215e-34	#  3 * pi/2  trailing
173	.double	0d+1.73436202602475619845e-34	#  4 * pi/2  trailing
174	.double	0d-1.68390735624352669192e-34	#  5 * pi/2  trailing
175	.double	0d+2.60154303903713428430e-34	#  6 * pi/2  trailing
176	.double	0d-8.16726343231148352150e-35	#  7 * pi/2  trailing
177	.double	0d+3.46872405204951239689e-34	#  8 * pi/2  trailing
178	.double	0d+3.90231455855570147991e-34	#  9 * pi/2  trailing
179	.double	0d-3.36781471248705338384e-34	# 10 * pi/2  trailing
180	.double	0d-1.06379439835298071785e-33	# 11 * pi/2  trailing
181	.double	0d+5.20308607807426856861e-34	# 12 * pi/2  trailing
182	.double	0d+5.63667658458045770509e-34	# 13 * pi/2  trailing
183	.double	0d-1.63345268646229670430e-34	# 14 * pi/2  trailing
184	.double	0d-1.19986217995610764801e-34	# 15 * pi/2  trailing
185	.double	0d+6.93744810409902479378e-34	# 16 * pi/2  trailing
186	.double	0d-8.03640094449267300110e-34	# 17 * pi/2  trailing
187	.double	0d+7.80462911711140295982e-34	# 18 * pi/2  trailing
188	.double	0d-7.16921993148029483506e-34	# 19 * pi/2  trailing
189	.double	0d-6.73562942497410676769e-34	# 20 * pi/2  trailing
190	.double	0d-6.30203891846791677593e-34	# 21 * pi/2  trailing
191	.double	0d-2.12758879670596143570e-33	# 22 * pi/2  trailing
192	.double	0d+2.53800212047402350390e-33	# 23 * pi/2  trailing
193	.double	0d+1.04061721561485371372e-33	# 24 * pi/2  trailing
194	.double	0d+6.11729905311472319056e-32	# 25 * pi/2  trailing
195	.double	0d+1.12733531691609154102e-33	# 26 * pi/2  trailing
196	.double	0d-3.70049587943078297272e-34	# 27 * pi/2  trailing
197	.double	0d-3.26690537292459340860e-34	# 28 * pi/2  trailing
198	.double	0d-1.14812616507957271361e-34	# 29 * pi/2  trailing
199
200middle:
201	.double	0d+0.00000000000000000000e+00	#  0 * pi/2  middle
202	.double	0d+5.72118872610983179676e-18	#  1 * pi/2  middle
203	.double	0d+1.14423774522196635935e-17	#  2 * pi/2  middle
204	.double	0d-3.83475850529283316309e-17	#  3 * pi/2  middle
205	.double	0d+2.28847549044393271871e-17	#  4 * pi/2  middle
206	.double	0d-2.69052076007086676522e-17	#  5 * pi/2  middle
207	.double	0d-7.66951701058566632618e-17	#  6 * pi/2  middle
208	.double	0d-1.54628301484890040587e-17	#  7 * pi/2  middle
209	.double	0d+4.57695098088786543741e-17	#  8 * pi/2  middle
210	.double	0d+1.07001849766246313192e-16	#  9 * pi/2  middle
211	.double	0d-5.38104152014173353044e-17	# 10 * pi/2  middle
212	.double	0d-2.14622680169080983801e-16	# 11 * pi/2  middle
213	.double	0d-1.53390340211713326524e-16	# 12 * pi/2  middle
214	.double	0d-9.21580002543456677056e-17	# 13 * pi/2  middle
215	.double	0d-3.09256602969780081173e-17	# 14 * pi/2  middle
216	.double	0d+3.03066796603896507006e-17	# 15 * pi/2  middle
217	.double	0d+9.15390196177573087482e-17	# 16 * pi/2  middle
218	.double	0d+1.52771359575124969107e-16	# 17 * pi/2  middle
219	.double	0d+2.14003699532492626384e-16	# 18 * pi/2  middle
220	.double	0d-1.68853170360202329427e-16	# 19 * pi/2  middle
221	.double	0d-1.07620830402834670609e-16	# 20 * pi/2  middle
222	.double	0d+3.97700719404595604379e-16	# 21 * pi/2  middle
223	.double	0d-4.29245360338161967602e-16	# 22 * pi/2  middle
224	.double	0d-3.68013020380794313406e-16	# 23 * pi/2  middle
225	.double	0d-3.06780680423426653047e-16	# 24 * pi/2  middle
226	.double	0d-2.45548340466059054318e-16	# 25 * pi/2  middle
227	.double	0d-1.84316000508691335411e-16	# 26 * pi/2  middle
228	.double	0d-1.23083660551323675053e-16	# 27 * pi/2  middle
229	.double	0d-6.18513205939560162346e-17	# 28 * pi/2  middle
230	.double	0d-6.18980636588357585202e-19	# 29 * pi/2  middle
231
232leading:
233	.double	0d+0.00000000000000000000e+00	#  0 * pi/2  leading
234	.double	0d+1.57079632679489661351e+00	#  1 * pi/2  leading
235	.double	0d+3.14159265358979322702e+00	#  2 * pi/2  leading
236	.double	0d+4.71238898038468989604e+00	#  3 * pi/2  leading
237	.double	0d+6.28318530717958645404e+00	#  4 * pi/2  leading
238	.double	0d+7.85398163397448312306e+00	#  5 * pi/2  leading
239	.double	0d+9.42477796076937979208e+00	#  6 * pi/2  leading
240	.double	0d+1.09955742875642763501e+01	#  7 * pi/2  leading
241	.double	0d+1.25663706143591729081e+01	#  8 * pi/2  leading
242	.double	0d+1.41371669411540694661e+01	#  9 * pi/2  leading
243	.double	0d+1.57079632679489662461e+01	# 10 * pi/2  leading
244	.double	0d+1.72787595947438630262e+01	# 11 * pi/2  leading
245	.double	0d+1.88495559215387595842e+01	# 12 * pi/2  leading
246	.double	0d+2.04203522483336561422e+01	# 13 * pi/2  leading
247	.double	0d+2.19911485751285527002e+01	# 14 * pi/2  leading
248	.double	0d+2.35619449019234492582e+01	# 15 * pi/2  leading
249	.double	0d+2.51327412287183458162e+01	# 16 * pi/2  leading
250	.double	0d+2.67035375555132423742e+01	# 17 * pi/2  leading
251	.double	0d+2.82743338823081389322e+01	# 18 * pi/2  leading
252	.double	0d+2.98451302091030359342e+01	# 19 * pi/2  leading
253	.double	0d+3.14159265358979324922e+01	# 20 * pi/2  leading
254	.double	0d+3.29867228626928286062e+01	# 21 * pi/2  leading
255	.double	0d+3.45575191894877260523e+01	# 22 * pi/2  leading
256	.double	0d+3.61283155162826226103e+01	# 23 * pi/2  leading
257	.double	0d+3.76991118430775191683e+01	# 24 * pi/2  leading
258	.double	0d+3.92699081698724157263e+01	# 25 * pi/2  leading
259	.double	0d+4.08407044966673122843e+01	# 26 * pi/2  leading
260	.double	0d+4.24115008234622088423e+01	# 27 * pi/2  leading
261	.double	0d+4.39822971502571054003e+01	# 28 * pi/2  leading
262	.double	0d+4.55530934770520019583e+01	# 29 * pi/2  leading
263
264twoOverPi:
265	.double	0d+6.36619772367581343076e-01
266
267	.text
268	_ALIGN_TEXT
269
270table_lookup:
271	muld3	%r3,twoOverPi,%r0
272	cvtrdl	%r0,%r0			# n = nearest int to ((2/pi)*|x|) rnded
273	subd2	leading[%r0],%r3		# p = (|x| - leading n*pi/2) exactly
274	subd3	middle[%r0],%r3,%r1	# q = (p - middle  n*pi/2) rounded
275	subd2	%r1,%r3			# r = (p - q)
276	subd2	middle[%r0],%r3		# r =  r - middle  n*pi/2
277	subd2	trailing[%r0],%r3		# r =  r - trailing n*pi/2  rounded
278/*
279 *  If the original argument was negative,
280 *  negate the reduce argument and
281 *  adjust the octant/quadrant number.
282 */
283	tstw	4(%ap)
284	bgeq	abs2
285	mnegf	%r1,%r1
286	mnegf	%r3,%r3
287/*	subb3	%r0,$8,%r0	...used for  pi/4  reduction -S.McD */
288	subb3	%r0,$4,%r0
289abs2:
290/*
291 *  Clear all unneeded octant/quadrant bits.
292 */
293/*	bicb2	$0xf8,%r0	...used for  pi/4  reduction -S.McD */
294	bicb2	$0xfc,%r0
295	rsb
296/*
297 *						p.0
298 */
299#ifdef __ELF__
300	.section .rodata
301#else
302	.text
303#endif
304	_ALIGN_TEXT
305/*
306 * Only 256 (actually 225) bits of 2/pi are needed for VAX double
307 * precision; this was determined by enumerating all the nearest
308 * machine integer multiples of pi/2 using continued fractions.
309 * (8a8d3673775b7ff7 required the most bits.)		-S.McD
310 */
311	.long	0
312	.long	0
313	.long	0xaef1586d
314	.long	0x9458eaf7
315	.long	0x10e4107f
316	.long	0xd8a5664f
317	.long	0x4d377036
318	.long	0x09d5f47d
319	.long	0x91054a7f
320	.long	0xbe60db93
321bits2opi:
322	.long	0x00000028
323	.long	0
324/*
325 *  Note: wherever you see the word `octant', read `quadrant'.
326 *  Currently this code is set up for  pi/2  argument reduction.
327 *  By uncommenting/commenting the appropriate lines, it will
328 *  also serve as a  pi/4  argument reduction code.
329 */
330	.text
331
332/*						p.1
333 *  Trigred  preforms argument reduction
334 *  for the trigonometric functions.  It
335 *  takes one input argument, a D-format
336 *  number in  %r1/%r0 .  The magnitude of
337 *  the input argument must be greater
338 *  than or equal to  1/2 .  Trigred produces
339 *  three results:  the number of the octant
340 *  occupied by the argument, the reduced
341 *  argument, and an extension of the
342 *  reduced argument.  The octant number is
343 *  returned in  %r0 .  The reduced argument
344 *  is returned as a D-format number in
345 *  %r2/%r1 .  An 8 bit extension of the
346 *  reduced argument is returned as an
347 *  F-format number in %r3.
348 *						p.2
349 */
350trigred:
351/*
352 *  Save the sign of the input argument.
353 */
354	movw	%r0,-(%sp)
355/*
356 *  Extract the exponent field.
357 */
358	extzv	$7,$7,%r0,%r2
359/*
360 *  Convert the fraction part of the input
361 *  argument into a quadword integer.
362 */
363	bicw2	$0xff80,%r0
364	bisb2	$0x80,%r0	# -S.McD
365	rotl	$16,%r0,%r0
366	rotl	$16,%r1,%r1
367/*
368 *  If  %r1  is negative, add  1  to  %r0 .  This
369 *  adjustment is made so that the two's
370 *  complement multiplications done later
371 *  will produce unsigned results.
372 */
373	bgeq	posmid
374	incl	%r0
375posmid:
376/*						p.3
377 *
378 *  Set  %r3  to the address of the first quadword
379 *  used to obtain the needed portion of  2/pi .
380 *  The address is longword aligned to ensure
381 *  efficient access.
382 */
383	ashl	$-3,%r2,%r3
384	bicb2	$3,%r3
385	mnegl	%r3,%r3
386	movab	bits2opi[%r3],%r3
387/*
388 *  Set  %r2  to the size of the shift needed to
389 *  obtain the correct portion of  2/pi .
390 */
391	bicb2	$0xe0,%r2
392/*						p.4
393 *
394 *  Move the needed  128  bits of  2/pi  into
395 *  %r11 - %r8 .  Adjust the numbers to allow
396 *  for unsigned multiplication.
397 */
398	ashq	%r2,(%r3),%r10
399
400	subl2	$4,%r3
401	ashq	%r2,(%r3),%r9
402	bgeq	signoff1
403	incl	%r11
404signoff1:
405	subl2	$4,%r3
406	ashq	%r2,(%r3),%r8
407	bgeq	signoff2
408	incl	%r10
409signoff2:
410	subl2	$4,%r3
411	ashq	%r2,(%r3),%r7
412	bgeq	signoff3
413	incl	%r9
414signoff3:
415/*						p.5
416 *
417 *  Multiply the contents of  %r0/%r1  by the
418 *  slice of  2/pi  in  %r11 - %r8 .
419 */
420	emul	%r0,%r8,$0,%r4
421	emul	%r0,%r9,%r5,%r5
422	emul	%r0,%r10,%r6,%r6
423
424	emul	%r1,%r8,$0,%r7
425	emul	%r1,%r9,%r8,%r8
426	emul	%r1,%r10,%r9,%r9
427	emul	%r1,%r11,%r10,%r10
428
429	addl2	%r4,%r8
430	adwc	%r5,%r9
431	adwc	%r6,%r10
432/*						p.6
433 *
434 *  If there are more than five leading zeros
435 *  after the first two quotient bits or if there
436 *  are more than five leading ones after the first
437 *  two quotient bits, generate more fraction bits.
438 *  Otherwise, branch to code to produce the result.
439 */
440	bicl3	$0xc1ffffff,%r10,%r4
441	beql	more1
442	cmpl	$0x3e000000,%r4
443	bneq	result
444more1:
445/*						p.7
446 *
447 *  generate another  32  result bits.
448 */
449	subl2	$4,%r3
450	ashq	%r2,(%r3),%r5
451	bgeq	signoff4
452
453	emul	%r1,%r6,$0,%r4
454	addl2	%r1,%r5
455	emul	%r0,%r6,%r5,%r5
456	addl2	%r0,%r6
457	jbr	addbits1
458
459signoff4:
460	emul	%r1,%r6,$0,%r4
461	emul	%r0,%r6,%r5,%r5
462
463addbits1:
464	addl2	%r5,%r7
465	adwc	%r6,%r8
466	adwc	$0,%r9
467	adwc	$0,%r10
468/*						p.8
469 *
470 *  Check for massive cancellation.
471 */
472	bicl3	$0xc0000000,%r10,%r6
473/*	bneq	more2			-S.McD  Test was backwards */
474	beql	more2
475	cmpl	$0x3fffffff,%r6
476	bneq	result
477more2:
478/*						p.9
479 *
480 *  If massive cancellation has occurred,
481 *  generate another  24  result bits.
482 *  Testing has shown there will always be
483 *  enough bits after this point.
484 */
485	subl2	$4,%r3
486	ashq	%r2,(%r3),%r5
487	bgeq	signoff5
488
489	emul	%r0,%r6,%r4,%r5
490	addl2	%r0,%r6
491	jbr	addbits2
492
493signoff5:
494	emul	%r0,%r6,%r4,%r5
495
496addbits2:
497	addl2	%r6,%r7
498	adwc	$0,%r8
499	adwc	$0,%r9
500	adwc	$0,%r10
501/*						p.10
502 *
503 *  The following code produces the reduced
504 *  argument from the product bits contained
505 *  in  %r10 - %r7 .
506 */
507result:
508/*
509 *  Extract the octant number from  %r10 .
510 */
511/*	extzv	$29,$3,%r10,%r0	...used for  pi/4  reduction -S.McD */
512	extzv	$30,$2,%r10,%r0
513/*
514 *  Clear the octant bits in  %r10 .
515 */
516/*	bicl2	$0xe0000000,%r10	...used for  pi/4  reduction -S.McD */
517	bicl2	$0xc0000000,%r10
518/*
519 *  Zero the sign flag.
520 */
521	clrl	%r5
522/*						p.11
523 *
524 *  Check to see if the fraction is greater than
525 *  or equal to one-half.  If it is, add one
526 *  to the octant number, set the sign flag
527 *  on, and replace the fraction with  1 minus
528 *  the fraction.
529 */
530/*	bitl	$0x10000000,%r10		...used for  pi/4  reduction -S.McD */
531	bitl	$0x20000000,%r10
532	beql	small
533	incl	%r0
534	incl	%r5
535/*	subl3	%r10,$0x1fffffff,%r10	...used for  pi/4  reduction -S.McD */
536	subl3	%r10,$0x3fffffff,%r10
537	mcoml	%r9,%r9
538	mcoml	%r8,%r8
539	mcoml	%r7,%r7
540small:
541/*						p.12
542 *
543 *  Test whether the first  29  bits of the ...used for  pi/4  reduction -S.McD
544 *  Test whether the first  30  bits of the
545 *  fraction are zero.
546 */
547	tstl	%r10
548	beql	tiny
549/*
550 *  Find the position of the first one bit in  %r10 .
551 */
552	cvtld	%r10,%r1
553	extzv	$7,$7,%r1,%r1
554/*
555 *  Compute the size of the shift needed.
556 */
557	subl3	%r1,$32,%r6
558/*
559 *  Shift up the high order  64  bits of the
560 *  product.
561 */
562	ashq	%r6,%r9,%r10
563	ashq	%r6,%r8,%r9
564	jbr	mult
565/*						p.13
566 *
567 *  Test to see if the sign bit of  %r9  is on.
568 */
569tiny:
570	tstl	%r9
571	bgeq	tinier
572/*
573 *  If it is, shift the product bits up  32  bits.
574 */
575	movl	$32,%r6
576	movq	%r8,%r10
577	tstl	%r10
578	jbr	mult
579/*						p.14
580 *
581 *  Test whether  %r9  is zero.  It is probably
582 *  impossible for both  %r10  and  %r9  to be
583 *  zero, but until proven to be so, the test
584 *  must be made.
585 */
586tinier:
587	beql	zero
588/*
589 *  Find the position of the first one bit in  %r9 .
590 */
591	cvtld	%r9,%r1
592	extzv	$7,$7,%r1,%r1
593/*
594 *  Compute the size of the shift needed.
595 */
596	subl3	%r1,$32,%r1
597	addl3	$32,%r1,%r6
598/*
599 *  Shift up the high order  64  bits of the
600 *  product.
601 */
602	ashq	%r1,%r8,%r10
603	ashq	%r1,%r7,%r9
604	jbr	mult
605/*						p.15
606 *
607 *  The following code sets the reduced
608 *  argument to zero.
609 */
610zero:
611	clrl	%r1
612	clrl	%r2
613	clrl	%r3
614	jbr	return
615/*						p.16
616 *
617 *  At this point,  %r0  contains the octant number,
618 *  %r6  indicates the number of bits the fraction
619 *  has been shifted,  %r5  indicates the sign of
620 *  the fraction,  %r11/%r10  contain the high order
621 *  64  bits of the fraction, and the condition
622 *  codes indicate where the sign bit of  %r10
623 *  is on.  The following code multiplies the
624 *  fraction by  pi/2 .
625 */
626mult:
627/*
628 *  Save  %r11/%r10  in  %r4/%r1 .		-S.McD
629 */
630	movl	%r11,%r4
631	movl	%r10,%r1
632/*
633 *  If the sign bit of  %r10  is on, add  1  to  %r11 .
634 */
635	bgeq	signoff6
636	incl	%r11
637signoff6:
638/*						p.17
639 *
640 *  Move  pi/2  into  %r3/%r2 .
641 */
642	movq	$0xc90fdaa22168c235,%r2
643/*
644 *  Multiply the fraction by the portion of  pi/2
645 *  in  %r2 .
646 */
647	emul	%r2,%r10,$0,%r7
648	emul	%r2,%r11,%r8,%r7
649/*
650 *  Multiply the fraction by the portion of  pi/2
651 *  in  %r3 .
652 */
653	emul	%r3,%r10,$0,%r9
654	emul	%r3,%r11,%r10,%r10
655/*
656 *  Add the product bits together.
657 */
658	addl2	%r7,%r9
659	adwc	%r8,%r10
660	adwc	$0,%r11
661/*
662 *  Compensate for not sign extending  %r8  above.-S.McD
663 */
664	tstl	%r8
665	bgeq	signoff6a
666	decl	%r11
667signoff6a:
668/*
669 *  Compensate for  %r11/%r10  being unsigned.	-S.McD
670 */
671	addl2	%r2,%r10
672	adwc	%r3,%r11
673/*
674 *  Compensate for  %r3/%r2  being unsigned.	-S.McD
675 */
676	addl2	%r1,%r10
677	adwc	%r4,%r11
678/*						p.18
679 *
680 *  If the sign bit of  %r11  is zero, shift the
681 *  product bits up one bit and increment  %r6 .
682 */
683	blss	signon
684	incl	%r6
685	ashq	$1,%r10,%r10
686	tstl	%r9
687	bgeq	signoff7
688	incl	%r10
689signoff7:
690signon:
691/*						p.19
692 *
693 *  Shift the  56  most significant product
694 *  bits into  %r9/%r8 .  The sign extension
695 *  will be handled later.
696 */
697	ashq	$-8,%r10,%r8
698/*
699 *  Convert the low order  8  bits of  %r10
700 *  into an F-format number.
701 */
702	cvtbf	%r10,%r3
703/*
704 *  If the result of the conversion was
705 *  negative, add  1  to  %r9/%r8 .
706 */
707	bgeq	chop
708	incl	%r8
709	adwc	$0,%r9
710/*
711 *  If  %r9  is now zero, branch to special
712 *  code to handle that possibility.
713 */
714	beql	carryout
715chop:
716/*						p.20
717 *
718 *  Convert the number in  %r9/%r8  into
719 *  D-format number in  %r2/%r1 .
720 */
721	rotl	$16,%r8,%r2
722	rotl	$16,%r9,%r1
723/*
724 *  Set the exponent field to the appropriate
725 *  value.  Note that the extra bits created by
726 *  sign extension are now eliminated.
727 */
728	subw3	%r6,$131,%r6
729	insv	%r6,$7,$9,%r1
730/*
731 *  Set the exponent field of the F-format
732 *  number in  %r3  to the appropriate value.
733 */
734	tstf	%r3
735	beql	return
736/*	extzv	$7,$8,%r3,%r4	-S.McD */
737	extzv	$7,$7,%r3,%r4
738	addw2	%r4,%r6
739/*	subw2	$217,%r6		-S.McD */
740	subw2	$64,%r6
741	insv	%r6,$7,$8,%r3
742	jbr	return
743/*						p.21
744 *
745 *  The following code generates the appropriate
746 *  result for the unlikely possibility that
747 *  rounding the number in  %r9/%r8  resulted in
748 *  a carry out.
749 */
750carryout:
751	clrl	%r1
752	clrl	%r2
753	subw3	%r6,$132,%r6
754	insv	%r6,$7,$9,%r1
755	tstf	%r3
756	beql	return
757	extzv	$7,$8,%r3,%r4
758	addw2	%r4,%r6
759	subw2	$218,%r6
760	insv	%r6,$7,$8,%r3
761/*						p.22
762 *
763 *  The following code makes an needed
764 *  adjustments to the signs of the
765 *  results or to the octant number, and
766 *  then returns.
767 */
768return:
769/*
770 *  Test if the fraction was greater than or
771 *  equal to  1/2 .  If so, negate the reduced
772 *  argument.
773 */
774	blbc	%r5,signoff8
775	mnegf	%r1,%r1
776	mnegf	%r3,%r3
777signoff8:
778/*						p.23
779 *
780 *  If the original argument was negative,
781 *  negate the reduce argument and
782 *  adjust the octant number.
783 */
784	tstw	(%sp)+
785	bgeq	signoff9
786	mnegf	%r1,%r1
787	mnegf	%r3,%r3
788/*	subb3	%r0,$8,%r0	...used for  pi/4  reduction -S.McD */
789	subb3	%r0,$4,%r0
790signoff9:
791/*
792 *  Clear all unneeded octant bits.
793 *
794 *	bicb2	$0xf8,%r0	...used for  pi/4  reduction -S.McD */
795	bicb2	$0xfc,%r0
796/*
797 *  Return.
798 */
799	rsb
800