/* $NetBSD: n_argred.S,v 1.9 2007/04/19 00:37:20 matt Exp $ */
/*
* Copyright (c) 1985, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* @(#)argred.s 8.1 (Berkeley) 6/4/93
*/
#include <machine/asm.h>
/*
* libm$argred implements Bob Corbett's argument reduction and
* libm$sincos implements Peter Tang's double precision sin/cos.
*
* Note: The two entry points libm$argred and libm$sincos are meant
* to be used only by _sin, _cos and _tan.
*
* method: true range reduction to [-pi/4,pi/4], P. Tang & B. Corbett
* S. McDonald, April 4, 1985
*/
.hidden __libm_argred
ENTRY(__libm_argred, 0)
/*
* Compare the argument with the largest possible that can
* be reduced by table lookup. %r3 := |x| will be used in table_lookup .
*/
movd %r0,%r3
bgeq abs1
mnegd %r3,%r3
abs1:
cmpd %r3,$0d+4.55530934770520019583e+01
blss small_arg
jsb trigred
rsb
small_arg:
jsb table_lookup
rsb
/*
* At this point,
* %r0 contains the quadrant number, 0, 1, 2, or 3;
* %r2/%r1 contains the reduced argument as a D-format number;
* %r3 contains a F-format extension to the reduced argument;
* %r4 contains a 0 or 1 corresponding to a sin or cos entry.
*/
.hidden __libm_sincos
ENTRY(__libm_sincos, 0)
/*
* Compensate for a cosine entry by adding one to the quadrant number.
*/
addl2 %r4,%r0
/*
* Polyd clobbers %r5-%r0 ; save X in %r7/%r6 .
* This can be avoided by rewriting trigred .
*/
movd %r1,%r6
/*
* Likewise, save alpha in %r8 .
* This can be avoided by rewriting trigred .
*/
movf %r3,%r8
/*
* Odd or even quadrant? cosine if odd, sine otherwise.
* Save floor(quadrant/2) in %r9 ; it determines the final sign.
*/
rotl $-1,%r0,%r9
blss cosine
sine:
muld2 %r1,%r1 # Xsq = X * X
cmpw $0x2480,%r1 # [zl] Xsq > 2^-56?
blss 1f # [zl] yes, go ahead and do polyd
clrq %r1 # [zl] work around 11/780 FPA polyd bug
1:
polyd %r1,$7,sin_coef # Q = P(Xsq) , of deg 7
mulf3 $0f3.0,%r8,%r4 # beta = 3 * alpha
mulf2 %r0,%r4 # beta = Q * beta
addf2 %r8,%r4 # beta = alpha + beta
muld2 %r6,%r0 # S(X) = X * Q
/* cvtfd %r4,%r4 ... %r5 = 0 after a polyd. */
addd2 %r4,%r0 # S(X) = beta + S(X)
addd2 %r6,%r0 # S(X) = X + S(X)
jbr done
cosine:
muld2 %r6,%r6 # Xsq = X * X
beql zero_arg
mulf2 %r1,%r8 # beta = X * alpha
polyd %r6,$7,cos_coef /* Q = P'(Xsq) , of deg 7 */
subd3 %r0,%r8,%r0 # beta = beta - Q
subw2 $0x80,%r6 # Xsq = Xsq / 2
addd2 %r0,%r6 # Xsq = Xsq + beta
zero_arg:
subd3 %r6,$0d1.0,%r0 # C(X) = 1 - Xsq
done:
blbc %r9,even
mnegd %r0,%r0
even:
rsb
#ifdef __ELF__
.section .rodata
#else
.text
#endif
_ALIGN_TEXT
sin_coef:
.double 0d-7.53080332264191085773e-13 # s7 = 2^-29 -1.a7f2504ffc49f8..
.double 0d+1.60573519267703489121e-10 # s6 = 2^-21 1.611adaede473c8..
.double 0d-2.50520965150706067211e-08 # s5 = 2^-1a -1.ae644921ed8382..
.double 0d+2.75573191800593885716e-06 # s4 = 2^-13 1.71de3a4b884278..
.double 0d-1.98412698411850507950e-04 # s3 = 2^-0d -1.a01a01a0125e7d..
.double 0d+8.33333333333325688985e-03 # s2 = 2^-07 1.11111111110e50
.double 0d-1.66666666666666664354e-01 # s1 = 2^-03 -1.55555555555554
.double 0d+0.00000000000000000000e+00 # s0 = 0
cos_coef:
.double 0d-1.13006966202629430300e-11 # s7 = 2^-25 -1.8D9BA04D1374BE..
.double 0d+2.08746646574796004700e-09 # s6 = 2^-1D 1.1EE632650350BA..
.double 0d-2.75573073031284417300e-07 # s5 = 2^-16 -1.27E4F31411719E..
.double 0d+2.48015872682668025200e-05 # s4 = 2^-10 1.A01A0196B902E8..
.double 0d-1.38888888888464709200e-03 # s3 = 2^-0A -1.6C16C16C11FACE..
.double 0d+4.16666666666664761400e-02 # s2 = 2^-05 1.5555555555539E
.double 0d+0.00000000000000000000e+00 # s1 = 0
.double 0d+0.00000000000000000000e+00 # s0 = 0
/*
* Multiples of pi/2 expressed as the sum of three doubles,
*
* trailing: n * pi/2 , n = 0, 1, 2, ..., 29
* trailing[n] ,
*
* middle: n * pi/2 , n = 0, 1, 2, ..., 29
* middle[n] ,
*
* leading: n * pi/2 , n = 0, 1, 2, ..., 29
* leading[n] ,
*
* where
* leading[n] := (n * pi/2) rounded,
* middle[n] := (n * pi/2 - leading[n]) rounded,
* trailing[n] := (( n * pi/2 - leading[n]) - middle[n]) rounded .
*/
trailing:
.double 0d+0.00000000000000000000e+00 # 0 * pi/2 trailing
.double 0d+4.33590506506189049611e-35 # 1 * pi/2 trailing
.double 0d+8.67181013012378099223e-35 # 2 * pi/2 trailing
.double 0d+1.30077151951856714215e-34 # 3 * pi/2 trailing
.double 0d+1.73436202602475619845e-34 # 4 * pi/2 trailing
.double 0d-1.68390735624352669192e-34 # 5 * pi/2 trailing
.double 0d+2.60154303903713428430e-34 # 6 * pi/2 trailing
.double 0d-8.16726343231148352150e-35 # 7 * pi/2 trailing
.double 0d+3.46872405204951239689e-34 # 8 * pi/2 trailing
.double 0d+3.90231455855570147991e-34 # 9 * pi/2 trailing
.double 0d-3.36781471248705338384e-34 # 10 * pi/2 trailing
.double 0d-1.06379439835298071785e-33 # 11 * pi/2 trailing
.double 0d+5.20308607807426856861e-34 # 12 * pi/2 trailing
.double 0d+5.63667658458045770509e-34 # 13 * pi/2 trailing
.double 0d-1.63345268646229670430e-34 # 14 * pi/2 trailing
.double 0d-1.19986217995610764801e-34 # 15 * pi/2 trailing
.double 0d+6.93744810409902479378e-34 # 16 * pi/2 trailing
.double 0d-8.03640094449267300110e-34 # 17 * pi/2 trailing
.double 0d+7.80462911711140295982e-34 # 18 * pi/2 trailing
.double 0d-7.16921993148029483506e-34 # 19 * pi/2 trailing
.double 0d-6.73562942497410676769e-34 # 20 * pi/2 trailing
.double 0d-6.30203891846791677593e-34 # 21 * pi/2 trailing
.double 0d-2.12758879670596143570e-33 # 22 * pi/2 trailing
.double 0d+2.53800212047402350390e-33 # 23 * pi/2 trailing
.double 0d+1.04061721561485371372e-33 # 24 * pi/2 trailing
.double 0d+6.11729905311472319056e-32 # 25 * pi/2 trailing
.double 0d+1.12733531691609154102e-33 # 26 * pi/2 trailing
.double 0d-3.70049587943078297272e-34 # 27 * pi/2 trailing
.double 0d-3.26690537292459340860e-34 # 28 * pi/2 trailing
.double 0d-1.14812616507957271361e-34 # 29 * pi/2 trailing
middle:
.double 0d+0.00000000000000000000e+00 # 0 * pi/2 middle
.double 0d+5.72118872610983179676e-18 # 1 * pi/2 middle
.double 0d+1.14423774522196635935e-17 # 2 * pi/2 middle
.double 0d-3.83475850529283316309e-17 # 3 * pi/2 middle
.double 0d+2.28847549044393271871e-17 # 4 * pi/2 middle
.double 0d-2.69052076007086676522e-17 # 5 * pi/2 middle
.double 0d-7.66951701058566632618e-17 # 6 * pi/2 middle
.double 0d-1.54628301484890040587e-17 # 7 * pi/2 middle
.double 0d+4.57695098088786543741e-17 # 8 * pi/2 middle
.double 0d+1.07001849766246313192e-16 # 9 * pi/2 middle
.double 0d-5.38104152014173353044e-17 # 10 * pi/2 middle
.double 0d-2.14622680169080983801e-16 # 11 * pi/2 middle
.double 0d-1.53390340211713326524e-16 # 12 * pi/2 middle
.double 0d-9.21580002543456677056e-17 # 13 * pi/2 middle
.double 0d-3.09256602969780081173e-17 # 14 * pi/2 middle
.double 0d+3.03066796603896507006e-17 # 15 * pi/2 middle
.double 0d+9.15390196177573087482e-17 # 16 * pi/2 middle
.double 0d+1.52771359575124969107e-16 # 17 * pi/2 middle
.double 0d+2.14003699532492626384e-16 # 18 * pi/2 middle
.double 0d-1.68853170360202329427e-16 # 19 * pi/2 middle
.double 0d-1.07620830402834670609e-16 # 20 * pi/2 middle
.double 0d+3.97700719404595604379e-16 # 21 * pi/2 middle
.double 0d-4.29245360338161967602e-16 # 22 * pi/2 middle
.double 0d-3.68013020380794313406e-16 # 23 * pi/2 middle
.double 0d-3.06780680423426653047e-16 # 24 * pi/2 middle
.double 0d-2.45548340466059054318e-16 # 25 * pi/2 middle
.double 0d-1.84316000508691335411e-16 # 26 * pi/2 middle
.double 0d-1.23083660551323675053e-16 # 27 * pi/2 middle
.double 0d-6.18513205939560162346e-17 # 28 * pi/2 middle
.double 0d-6.18980636588357585202e-19 # 29 * pi/2 middle
leading:
.double 0d+0.00000000000000000000e+00 # 0 * pi/2 leading
.double 0d+1.57079632679489661351e+00 # 1 * pi/2 leading
.double 0d+3.14159265358979322702e+00 # 2 * pi/2 leading
.double 0d+4.71238898038468989604e+00 # 3 * pi/2 leading
.double 0d+6.28318530717958645404e+00 # 4 * pi/2 leading
.double 0d+7.85398163397448312306e+00 # 5 * pi/2 leading
.double 0d+9.42477796076937979208e+00 # 6 * pi/2 leading
.double 0d+1.09955742875642763501e+01 # 7 * pi/2 leading
.double 0d+1.25663706143591729081e+01 # 8 * pi/2 leading
.double 0d+1.41371669411540694661e+01 # 9 * pi/2 leading
.double 0d+1.57079632679489662461e+01 # 10 * pi/2 leading
.double 0d+1.72787595947438630262e+01 # 11 * pi/2 leading
.double 0d+1.88495559215387595842e+01 # 12 * pi/2 leading
.double 0d+2.04203522483336561422e+01 # 13 * pi/2 leading
.double 0d+2.19911485751285527002e+01 # 14 * pi/2 leading
.double 0d+2.35619449019234492582e+01 # 15 * pi/2 leading
.double 0d+2.51327412287183458162e+01 # 16 * pi/2 leading
.double 0d+2.67035375555132423742e+01 # 17 * pi/2 leading
.double 0d+2.82743338823081389322e+01 # 18 * pi/2 leading
.double 0d+2.98451302091030359342e+01 # 19 * pi/2 leading
.double 0d+3.14159265358979324922e+01 # 20 * pi/2 leading
.double 0d+3.29867228626928286062e+01 # 21 * pi/2 leading
.double 0d+3.45575191894877260523e+01 # 22 * pi/2 leading
.double 0d+3.61283155162826226103e+01 # 23 * pi/2 leading
.double 0d+3.76991118430775191683e+01 # 24 * pi/2 leading
.double 0d+3.92699081698724157263e+01 # 25 * pi/2 leading
.double 0d+4.08407044966673122843e+01 # 26 * pi/2 leading
.double 0d+4.24115008234622088423e+01 # 27 * pi/2 leading
.double 0d+4.39822971502571054003e+01 # 28 * pi/2 leading
.double 0d+4.55530934770520019583e+01 # 29 * pi/2 leading
twoOverPi:
.double 0d+6.36619772367581343076e-01
.text
_ALIGN_TEXT
table_lookup:
muld3 %r3,twoOverPi,%r0
cvtrdl %r0,%r0 # n = nearest int to ((2/pi)*|x|) rnded
subd2 leading[%r0],%r3 # p = (|x| - leading n*pi/2) exactly
subd3 middle[%r0],%r3,%r1 # q = (p - middle n*pi/2) rounded
subd2 %r1,%r3 # r = (p - q)
subd2 middle[%r0],%r3 # r = r - middle n*pi/2
subd2 trailing[%r0],%r3 # r = r - trailing n*pi/2 rounded
/*
* If the original argument was negative,
* negate the reduce argument and
* adjust the octant/quadrant number.
*/
tstw 4(%ap)
bgeq abs2
mnegf %r1,%r1
mnegf %r3,%r3
/* subb3 %r0,$8,%r0 ...used for pi/4 reduction -S.McD */
subb3 %r0,$4,%r0
abs2:
/*
* Clear all unneeded octant/quadrant bits.
*/
/* bicb2 $0xf8,%r0 ...used for pi/4 reduction -S.McD */
bicb2 $0xfc,%r0
rsb
/*
* p.0
*/
#ifdef __ELF__
.section .rodata
#else
.text
#endif
_ALIGN_TEXT
/*
* Only 256 (actually 225) bits of 2/pi are needed for VAX double
* precision; this was determined by enumerating all the nearest
* machine integer multiples of pi/2 using continued fractions.
* (8a8d3673775b7ff7 required the most bits.) -S.McD
*/
.long 0
.long 0
.long 0xaef1586d
.long 0x9458eaf7
.long 0x10e4107f
.long 0xd8a5664f
.long 0x4d377036
.long 0x09d5f47d
.long 0x91054a7f
.long 0xbe60db93
bits2opi:
.long 0x00000028
.long 0
/*
* Note: wherever you see the word `octant', read `quadrant'.
* Currently this code is set up for pi/2 argument reduction.
* By uncommenting/commenting the appropriate lines, it will
* also serve as a pi/4 argument reduction code.
*/
.text
/* p.1
* Trigred preforms argument reduction
* for the trigonometric functions. It
* takes one input argument, a D-format
* number in %r1/%r0 . The magnitude of
* the input argument must be greater
* than or equal to 1/2 . Trigred produces
* three results: the number of the octant
* occupied by the argument, the reduced
* argument, and an extension of the
* reduced argument. The octant number is
* returned in %r0 . The reduced argument
* is returned as a D-format number in
* %r2/%r1 . An 8 bit extension of the
* reduced argument is returned as an
* F-format number in %r3.
* p.2
*/
trigred:
/*
* Save the sign of the input argument.
*/
movw %r0,-(%sp)
/*
* Extract the exponent field.
*/
extzv $7,$7,%r0,%r2
/*
* Convert the fraction part of the input
* argument into a quadword integer.
*/
bicw2 $0xff80,%r0
bisb2 $0x80,%r0 # -S.McD
rotl $16,%r0,%r0
rotl $16,%r1,%r1
/*
* If %r1 is negative, add 1 to %r0 . This
* adjustment is made so that the two's
* complement multiplications done later
* will produce unsigned results.
*/
bgeq posmid
incl %r0
posmid:
/* p.3
*
* Set %r3 to the address of the first quadword
* used to obtain the needed portion of 2/pi .
* The address is longword aligned to ensure
* efficient access.
*/
ashl $-3,%r2,%r3
bicb2 $3,%r3
mnegl %r3,%r3
movab bits2opi[%r3],%r3
/*
* Set %r2 to the size of the shift needed to
* obtain the correct portion of 2/pi .
*/
bicb2 $0xe0,%r2
/* p.4
*
* Move the needed 128 bits of 2/pi into
* %r11 - %r8 . Adjust the numbers to allow
* for unsigned multiplication.
*/
ashq %r2,(%r3),%r10
subl2 $4,%r3
ashq %r2,(%r3),%r9
bgeq signoff1
incl %r11
signoff1:
subl2 $4,%r3
ashq %r2,(%r3),%r8
bgeq signoff2
incl %r10
signoff2:
subl2 $4,%r3
ashq %r2,(%r3),%r7
bgeq signoff3
incl %r9
signoff3:
/* p.5
*
* Multiply the contents of %r0/%r1 by the
* slice of 2/pi in %r11 - %r8 .
*/
emul %r0,%r8,$0,%r4
emul %r0,%r9,%r5,%r5
emul %r0,%r10,%r6,%r6
emul %r1,%r8,$0,%r7
emul %r1,%r9,%r8,%r8
emul %r1,%r10,%r9,%r9
emul %r1,%r11,%r10,%r10
addl2 %r4,%r8
adwc %r5,%r9
adwc %r6,%r10
/* p.6
*
* If there are more than five leading zeros
* after the first two quotient bits or if there
* are more than five leading ones after the first
* two quotient bits, generate more fraction bits.
* Otherwise, branch to code to produce the result.
*/
bicl3 $0xc1ffffff,%r10,%r4
beql more1
cmpl $0x3e000000,%r4
bneq result
more1:
/* p.7
*
* generate another 32 result bits.
*/
subl2 $4,%r3
ashq %r2,(%r3),%r5
bgeq signoff4
emul %r1,%r6,$0,%r4
addl2 %r1,%r5
emul %r0,%r6,%r5,%r5
addl2 %r0,%r6
jbr addbits1
signoff4:
emul %r1,%r6,$0,%r4
emul %r0,%r6,%r5,%r5
addbits1:
addl2 %r5,%r7
adwc %r6,%r8
adwc $0,%r9
adwc $0,%r10
/* p.8
*
* Check for massive cancellation.
*/
bicl3 $0xc0000000,%r10,%r6
/* bneq more2 -S.McD Test was backwards */
beql more2
cmpl $0x3fffffff,%r6
bneq result
more2:
/* p.9
*
* If massive cancellation has occurred,
* generate another 24 result bits.
* Testing has shown there will always be
* enough bits after this point.
*/
subl2 $4,%r3
ashq %r2,(%r3),%r5
bgeq signoff5
emul %r0,%r6,%r4,%r5
addl2 %r0,%r6
jbr addbits2
signoff5:
emul %r0,%r6,%r4,%r5
addbits2:
addl2 %r6,%r7
adwc $0,%r8
adwc $0,%r9
adwc $0,%r10
/* p.10
*
* The following code produces the reduced
* argument from the product bits contained
* in %r10 - %r7 .
*/
result:
/*
* Extract the octant number from %r10 .
*/
/* extzv $29,$3,%r10,%r0 ...used for pi/4 reduction -S.McD */
extzv $30,$2,%r10,%r0
/*
* Clear the octant bits in %r10 .
*/
/* bicl2 $0xe0000000,%r10 ...used for pi/4 reduction -S.McD */
bicl2 $0xc0000000,%r10
/*
* Zero the sign flag.
*/
clrl %r5
/* p.11
*
* Check to see if the fraction is greater than
* or equal to one-half. If it is, add one
* to the octant number, set the sign flag
* on, and replace the fraction with 1 minus
* the fraction.
*/
/* bitl $0x10000000,%r10 ...used for pi/4 reduction -S.McD */
bitl $0x20000000,%r10
beql small
incl %r0
incl %r5
/* subl3 %r10,$0x1fffffff,%r10 ...used for pi/4 reduction -S.McD */
subl3 %r10,$0x3fffffff,%r10
mcoml %r9,%r9
mcoml %r8,%r8
mcoml %r7,%r7
small:
/* p.12
*
* Test whether the first 29 bits of the ...used for pi/4 reduction -S.McD
* Test whether the first 30 bits of the
* fraction are zero.
*/
tstl %r10
beql tiny
/*
* Find the position of the first one bit in %r10 .
*/
cvtld %r10,%r1
extzv $7,$7,%r1,%r1
/*
* Compute the size of the shift needed.
*/
subl3 %r1,$32,%r6
/*
* Shift up the high order 64 bits of the
* product.
*/
ashq %r6,%r9,%r10
ashq %r6,%r8,%r9
jbr mult
/* p.13
*
* Test to see if the sign bit of %r9 is on.
*/
tiny:
tstl %r9
bgeq tinier
/*
* If it is, shift the product bits up 32 bits.
*/
movl $32,%r6
movq %r8,%r10
tstl %r10
jbr mult
/* p.14
*
* Test whether %r9 is zero. It is probably
* impossible for both %r10 and %r9 to be
* zero, but until proven to be so, the test
* must be made.
*/
tinier:
beql zero
/*
* Find the position of the first one bit in %r9 .
*/
cvtld %r9,%r1
extzv $7,$7,%r1,%r1
/*
* Compute the size of the shift needed.
*/
subl3 %r1,$32,%r1
addl3 $32,%r1,%r6
/*
* Shift up the high order 64 bits of the
* product.
*/
ashq %r1,%r8,%r10
ashq %r1,%r7,%r9
jbr mult
/* p.15
*
* The following code sets the reduced
* argument to zero.
*/
zero:
clrl %r1
clrl %r2
clrl %r3
jbr return
/* p.16
*
* At this point, %r0 contains the octant number,
* %r6 indicates the number of bits the fraction
* has been shifted, %r5 indicates the sign of
* the fraction, %r11/%r10 contain the high order
* 64 bits of the fraction, and the condition
* codes indicate where the sign bit of %r10
* is on. The following code multiplies the
* fraction by pi/2 .
*/
mult:
/*
* Save %r11/%r10 in %r4/%r1 . -S.McD
*/
movl %r11,%r4
movl %r10,%r1
/*
* If the sign bit of %r10 is on, add 1 to %r11 .
*/
bgeq signoff6
incl %r11
signoff6:
/* p.17
*
* Move pi/2 into %r3/%r2 .
*/
movq $0xc90fdaa22168c235,%r2
/*
* Multiply the fraction by the portion of pi/2
* in %r2 .
*/
emul %r2,%r10,$0,%r7
emul %r2,%r11,%r8,%r7
/*
* Multiply the fraction by the portion of pi/2
* in %r3 .
*/
emul %r3,%r10,$0,%r9
emul %r3,%r11,%r10,%r10
/*
* Add the product bits together.
*/
addl2 %r7,%r9
adwc %r8,%r10
adwc $0,%r11
/*
* Compensate for not sign extending %r8 above.-S.McD
*/
tstl %r8
bgeq signoff6a
decl %r11
signoff6a:
/*
* Compensate for %r11/%r10 being unsigned. -S.McD
*/
addl2 %r2,%r10
adwc %r3,%r11
/*
* Compensate for %r3/%r2 being unsigned. -S.McD
*/
addl2 %r1,%r10
adwc %r4,%r11
/* p.18
*
* If the sign bit of %r11 is zero, shift the
* product bits up one bit and increment %r6 .
*/
blss signon
incl %r6
ashq $1,%r10,%r10
tstl %r9
bgeq signoff7
incl %r10
signoff7:
signon:
/* p.19
*
* Shift the 56 most significant product
* bits into %r9/%r8 . The sign extension
* will be handled later.
*/
ashq $-8,%r10,%r8
/*
* Convert the low order 8 bits of %r10
* into an F-format number.
*/
cvtbf %r10,%r3
/*
* If the result of the conversion was
* negative, add 1 to %r9/%r8 .
*/
bgeq chop
incl %r8
adwc $0,%r9
/*
* If %r9 is now zero, branch to special
* code to handle that possibility.
*/
beql carryout
chop:
/* p.20
*
* Convert the number in %r9/%r8 into
* D-format number in %r2/%r1 .
*/
rotl $16,%r8,%r2
rotl $16,%r9,%r1
/*
* Set the exponent field to the appropriate
* value. Note that the extra bits created by
* sign extension are now eliminated.
*/
subw3 %r6,$131,%r6
insv %r6,$7,$9,%r1
/*
* Set the exponent field of the F-format
* number in %r3 to the appropriate value.
*/
tstf %r3
beql return
/* extzv $7,$8,%r3,%r4 -S.McD */
extzv $7,$7,%r3,%r4
addw2 %r4,%r6
/* subw2 $217,%r6 -S.McD */
subw2 $64,%r6
insv %r6,$7,$8,%r3
jbr return
/* p.21
*
* The following code generates the appropriate
* result for the unlikely possibility that
* rounding the number in %r9/%r8 resulted in
* a carry out.
*/
carryout:
clrl %r1
clrl %r2
subw3 %r6,$132,%r6
insv %r6,$7,$9,%r1
tstf %r3
beql return
extzv $7,$8,%r3,%r4
addw2 %r4,%r6
subw2 $218,%r6
insv %r6,$7,$8,%r3
/* p.22
*
* The following code makes an needed
* adjustments to the signs of the
* results or to the octant number, and
* then returns.
*/
return:
/*
* Test if the fraction was greater than or
* equal to 1/2 . If so, negate the reduced
* argument.
*/
blbc %r5,signoff8
mnegf %r1,%r1
mnegf %r3,%r3
signoff8:
/* p.23
*
* If the original argument was negative,
* negate the reduce argument and
* adjust the octant number.
*/
tstw (%sp)+
bgeq signoff9
mnegf %r1,%r1
mnegf %r3,%r3
/* subb3 %r0,$8,%r0 ...used for pi/4 reduction -S.McD */
subb3 %r0,$4,%r0
signoff9:
/*
* Clear all unneeded octant bits.
*
* bicb2 $0xf8,%r0 ...used for pi/4 reduction -S.McD */
bicb2 $0xfc,%r0
/*
* Return.
*/
rsb