798 lines
22 KiB
ArmAsm
798 lines
22 KiB
ArmAsm
/* $NetBSD: n_argred.S,v 1.8 2003/08/07 16:44:44 agc Exp $ */
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/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* @(#)argred.s 8.1 (Berkeley) 6/4/93
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*/
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#include <machine/asm.h>
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/*
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* libm$argred implements Bob Corbett's argument reduction and
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* libm$sincos implements Peter Tang's double precision sin/cos.
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*
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* Note: The two entry points libm$argred and libm$sincos are meant
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* to be used only by _sin, _cos and _tan.
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*
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* method: true range reduction to [-pi/4,pi/4], P. Tang & B. Corbett
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* S. McDonald, April 4, 1985
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*/
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ENTRY(__libm_argred, 0)
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/*
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* Compare the argument with the largest possible that can
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* be reduced by table lookup. %r3 := |x| will be used in table_lookup .
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*/
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movd %r0,%r3
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bgeq abs1
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mnegd %r3,%r3
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abs1:
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cmpd %r3,$0d+4.55530934770520019583e+01
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blss small_arg
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jsb trigred
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rsb
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small_arg:
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jsb table_lookup
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rsb
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/*
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* At this point,
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* %r0 contains the quadrant number, 0, 1, 2, or 3;
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* %r2/%r1 contains the reduced argument as a D-format number;
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* %r3 contains a F-format extension to the reduced argument;
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* %r4 contains a 0 or 1 corresponding to a sin or cos entry.
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*/
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ENTRY(__libm_sincos, 0)
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/*
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* Compensate for a cosine entry by adding one to the quadrant number.
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*/
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addl2 %r4,%r0
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/*
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* Polyd clobbers %r5-%r0 ; save X in %r7/%r6 .
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* This can be avoided by rewriting trigred .
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*/
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movd %r1,%r6
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/*
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* Likewise, save alpha in %r8 .
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* This can be avoided by rewriting trigred .
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*/
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movf %r3,%r8
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/*
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* Odd or even quadrant? cosine if odd, sine otherwise.
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* Save floor(quadrant/2) in %r9 ; it determines the final sign.
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*/
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rotl $-1,%r0,%r9
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blss cosine
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sine:
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muld2 %r1,%r1 # Xsq = X * X
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cmpw $0x2480,%r1 # [zl] Xsq > 2^-56?
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blss 1f # [zl] yes, go ahead and do polyd
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clrq %r1 # [zl] work around 11/780 FPA polyd bug
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1:
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polyd %r1,$7,sin_coef # Q = P(Xsq) , of deg 7
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mulf3 $0f3.0,%r8,%r4 # beta = 3 * alpha
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mulf2 %r0,%r4 # beta = Q * beta
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addf2 %r8,%r4 # beta = alpha + beta
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muld2 %r6,%r0 # S(X) = X * Q
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/* cvtfd %r4,%r4 ... %r5 = 0 after a polyd. */
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addd2 %r4,%r0 # S(X) = beta + S(X)
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addd2 %r6,%r0 # S(X) = X + S(X)
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jbr done
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cosine:
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muld2 %r6,%r6 # Xsq = X * X
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beql zero_arg
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mulf2 %r1,%r8 # beta = X * alpha
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polyd %r6,$7,cos_coef /* Q = P'(Xsq) , of deg 7 */
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subd3 %r0,%r8,%r0 # beta = beta - Q
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subw2 $0x80,%r6 # Xsq = Xsq / 2
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addd2 %r0,%r6 # Xsq = Xsq + beta
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zero_arg:
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subd3 %r6,$0d1.0,%r0 # C(X) = 1 - Xsq
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done:
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blbc %r9,even
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mnegd %r0,%r0
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even:
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rsb
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#ifdef __ELF__
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.section .rodata
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#else
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.text
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#endif
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_ALIGN_TEXT
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sin_coef:
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.double 0d-7.53080332264191085773e-13 # s7 = 2^-29 -1.a7f2504ffc49f8..
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.double 0d+1.60573519267703489121e-10 # s6 = 2^-21 1.611adaede473c8..
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.double 0d-2.50520965150706067211e-08 # s5 = 2^-1a -1.ae644921ed8382..
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.double 0d+2.75573191800593885716e-06 # s4 = 2^-13 1.71de3a4b884278..
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.double 0d-1.98412698411850507950e-04 # s3 = 2^-0d -1.a01a01a0125e7d..
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.double 0d+8.33333333333325688985e-03 # s2 = 2^-07 1.11111111110e50
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.double 0d-1.66666666666666664354e-01 # s1 = 2^-03 -1.55555555555554
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.double 0d+0.00000000000000000000e+00 # s0 = 0
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cos_coef:
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.double 0d-1.13006966202629430300e-11 # s7 = 2^-25 -1.8D9BA04D1374BE..
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.double 0d+2.08746646574796004700e-09 # s6 = 2^-1D 1.1EE632650350BA..
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.double 0d-2.75573073031284417300e-07 # s5 = 2^-16 -1.27E4F31411719E..
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.double 0d+2.48015872682668025200e-05 # s4 = 2^-10 1.A01A0196B902E8..
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.double 0d-1.38888888888464709200e-03 # s3 = 2^-0A -1.6C16C16C11FACE..
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.double 0d+4.16666666666664761400e-02 # s2 = 2^-05 1.5555555555539E
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.double 0d+0.00000000000000000000e+00 # s1 = 0
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.double 0d+0.00000000000000000000e+00 # s0 = 0
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/*
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* Multiples of pi/2 expressed as the sum of three doubles,
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*
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* trailing: n * pi/2 , n = 0, 1, 2, ..., 29
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* trailing[n] ,
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*
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* middle: n * pi/2 , n = 0, 1, 2, ..., 29
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* middle[n] ,
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*
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* leading: n * pi/2 , n = 0, 1, 2, ..., 29
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* leading[n] ,
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*
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* where
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* leading[n] := (n * pi/2) rounded,
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* middle[n] := (n * pi/2 - leading[n]) rounded,
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* trailing[n] := (( n * pi/2 - leading[n]) - middle[n]) rounded .
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*/
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trailing:
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.double 0d+0.00000000000000000000e+00 # 0 * pi/2 trailing
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.double 0d+4.33590506506189049611e-35 # 1 * pi/2 trailing
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.double 0d+8.67181013012378099223e-35 # 2 * pi/2 trailing
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.double 0d+1.30077151951856714215e-34 # 3 * pi/2 trailing
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.double 0d+1.73436202602475619845e-34 # 4 * pi/2 trailing
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.double 0d-1.68390735624352669192e-34 # 5 * pi/2 trailing
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.double 0d+2.60154303903713428430e-34 # 6 * pi/2 trailing
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.double 0d-8.16726343231148352150e-35 # 7 * pi/2 trailing
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.double 0d+3.46872405204951239689e-34 # 8 * pi/2 trailing
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.double 0d+3.90231455855570147991e-34 # 9 * pi/2 trailing
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.double 0d-3.36781471248705338384e-34 # 10 * pi/2 trailing
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.double 0d-1.06379439835298071785e-33 # 11 * pi/2 trailing
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.double 0d+5.20308607807426856861e-34 # 12 * pi/2 trailing
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.double 0d+5.63667658458045770509e-34 # 13 * pi/2 trailing
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.double 0d-1.63345268646229670430e-34 # 14 * pi/2 trailing
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.double 0d-1.19986217995610764801e-34 # 15 * pi/2 trailing
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.double 0d+6.93744810409902479378e-34 # 16 * pi/2 trailing
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.double 0d-8.03640094449267300110e-34 # 17 * pi/2 trailing
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.double 0d+7.80462911711140295982e-34 # 18 * pi/2 trailing
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.double 0d-7.16921993148029483506e-34 # 19 * pi/2 trailing
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.double 0d-6.73562942497410676769e-34 # 20 * pi/2 trailing
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.double 0d-6.30203891846791677593e-34 # 21 * pi/2 trailing
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.double 0d-2.12758879670596143570e-33 # 22 * pi/2 trailing
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.double 0d+2.53800212047402350390e-33 # 23 * pi/2 trailing
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.double 0d+1.04061721561485371372e-33 # 24 * pi/2 trailing
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.double 0d+6.11729905311472319056e-32 # 25 * pi/2 trailing
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.double 0d+1.12733531691609154102e-33 # 26 * pi/2 trailing
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.double 0d-3.70049587943078297272e-34 # 27 * pi/2 trailing
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.double 0d-3.26690537292459340860e-34 # 28 * pi/2 trailing
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.double 0d-1.14812616507957271361e-34 # 29 * pi/2 trailing
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middle:
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.double 0d+0.00000000000000000000e+00 # 0 * pi/2 middle
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.double 0d+5.72118872610983179676e-18 # 1 * pi/2 middle
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.double 0d+1.14423774522196635935e-17 # 2 * pi/2 middle
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.double 0d-3.83475850529283316309e-17 # 3 * pi/2 middle
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.double 0d+2.28847549044393271871e-17 # 4 * pi/2 middle
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.double 0d-2.69052076007086676522e-17 # 5 * pi/2 middle
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.double 0d-7.66951701058566632618e-17 # 6 * pi/2 middle
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.double 0d-1.54628301484890040587e-17 # 7 * pi/2 middle
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.double 0d+4.57695098088786543741e-17 # 8 * pi/2 middle
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.double 0d+1.07001849766246313192e-16 # 9 * pi/2 middle
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.double 0d-5.38104152014173353044e-17 # 10 * pi/2 middle
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.double 0d-2.14622680169080983801e-16 # 11 * pi/2 middle
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.double 0d-1.53390340211713326524e-16 # 12 * pi/2 middle
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.double 0d-9.21580002543456677056e-17 # 13 * pi/2 middle
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.double 0d-3.09256602969780081173e-17 # 14 * pi/2 middle
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.double 0d+3.03066796603896507006e-17 # 15 * pi/2 middle
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.double 0d+9.15390196177573087482e-17 # 16 * pi/2 middle
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.double 0d+1.52771359575124969107e-16 # 17 * pi/2 middle
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.double 0d+2.14003699532492626384e-16 # 18 * pi/2 middle
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.double 0d-1.68853170360202329427e-16 # 19 * pi/2 middle
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.double 0d-1.07620830402834670609e-16 # 20 * pi/2 middle
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.double 0d+3.97700719404595604379e-16 # 21 * pi/2 middle
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.double 0d-4.29245360338161967602e-16 # 22 * pi/2 middle
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.double 0d-3.68013020380794313406e-16 # 23 * pi/2 middle
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.double 0d-3.06780680423426653047e-16 # 24 * pi/2 middle
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.double 0d-2.45548340466059054318e-16 # 25 * pi/2 middle
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.double 0d-1.84316000508691335411e-16 # 26 * pi/2 middle
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.double 0d-1.23083660551323675053e-16 # 27 * pi/2 middle
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.double 0d-6.18513205939560162346e-17 # 28 * pi/2 middle
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.double 0d-6.18980636588357585202e-19 # 29 * pi/2 middle
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leading:
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.double 0d+0.00000000000000000000e+00 # 0 * pi/2 leading
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.double 0d+1.57079632679489661351e+00 # 1 * pi/2 leading
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.double 0d+3.14159265358979322702e+00 # 2 * pi/2 leading
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.double 0d+4.71238898038468989604e+00 # 3 * pi/2 leading
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.double 0d+6.28318530717958645404e+00 # 4 * pi/2 leading
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.double 0d+7.85398163397448312306e+00 # 5 * pi/2 leading
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.double 0d+9.42477796076937979208e+00 # 6 * pi/2 leading
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.double 0d+1.09955742875642763501e+01 # 7 * pi/2 leading
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.double 0d+1.25663706143591729081e+01 # 8 * pi/2 leading
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.double 0d+1.41371669411540694661e+01 # 9 * pi/2 leading
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.double 0d+1.57079632679489662461e+01 # 10 * pi/2 leading
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.double 0d+1.72787595947438630262e+01 # 11 * pi/2 leading
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.double 0d+1.88495559215387595842e+01 # 12 * pi/2 leading
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.double 0d+2.04203522483336561422e+01 # 13 * pi/2 leading
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.double 0d+2.19911485751285527002e+01 # 14 * pi/2 leading
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.double 0d+2.35619449019234492582e+01 # 15 * pi/2 leading
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.double 0d+2.51327412287183458162e+01 # 16 * pi/2 leading
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.double 0d+2.67035375555132423742e+01 # 17 * pi/2 leading
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.double 0d+2.82743338823081389322e+01 # 18 * pi/2 leading
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.double 0d+2.98451302091030359342e+01 # 19 * pi/2 leading
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.double 0d+3.14159265358979324922e+01 # 20 * pi/2 leading
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.double 0d+3.29867228626928286062e+01 # 21 * pi/2 leading
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.double 0d+3.45575191894877260523e+01 # 22 * pi/2 leading
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.double 0d+3.61283155162826226103e+01 # 23 * pi/2 leading
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.double 0d+3.76991118430775191683e+01 # 24 * pi/2 leading
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.double 0d+3.92699081698724157263e+01 # 25 * pi/2 leading
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.double 0d+4.08407044966673122843e+01 # 26 * pi/2 leading
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.double 0d+4.24115008234622088423e+01 # 27 * pi/2 leading
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.double 0d+4.39822971502571054003e+01 # 28 * pi/2 leading
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.double 0d+4.55530934770520019583e+01 # 29 * pi/2 leading
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twoOverPi:
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.double 0d+6.36619772367581343076e-01
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.text
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_ALIGN_TEXT
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table_lookup:
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muld3 %r3,twoOverPi,%r0
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cvtrdl %r0,%r0 # n = nearest int to ((2/pi)*|x|) rnded
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subd2 leading[%r0],%r3 # p = (|x| - leading n*pi/2) exactly
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subd3 middle[%r0],%r3,%r1 # q = (p - middle n*pi/2) rounded
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subd2 %r1,%r3 # r = (p - q)
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subd2 middle[%r0],%r3 # r = r - middle n*pi/2
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subd2 trailing[%r0],%r3 # r = r - trailing n*pi/2 rounded
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/*
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* If the original argument was negative,
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* negate the reduce argument and
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* adjust the octant/quadrant number.
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*/
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tstw 4(%ap)
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bgeq abs2
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mnegf %r1,%r1
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mnegf %r3,%r3
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/* subb3 %r0,$8,%r0 ...used for pi/4 reduction -S.McD */
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subb3 %r0,$4,%r0
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abs2:
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/*
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* Clear all unneeded octant/quadrant bits.
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*/
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/* bicb2 $0xf8,%r0 ...used for pi/4 reduction -S.McD */
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bicb2 $0xfc,%r0
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rsb
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/*
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* p.0
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*/
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#ifdef __ELF__
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.section .rodata
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#else
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.text
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#endif
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_ALIGN_TEXT
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/*
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* Only 256 (actually 225) bits of 2/pi are needed for VAX double
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* precision; this was determined by enumerating all the nearest
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* machine integer multiples of pi/2 using continued fractions.
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* (8a8d3673775b7ff7 required the most bits.) -S.McD
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*/
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.long 0
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.long 0
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.long 0xaef1586d
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.long 0x9458eaf7
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.long 0x10e4107f
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.long 0xd8a5664f
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.long 0x4d377036
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.long 0x09d5f47d
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.long 0x91054a7f
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.long 0xbe60db93
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bits2opi:
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.long 0x00000028
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.long 0
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/*
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* Note: wherever you see the word `octant', read `quadrant'.
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* Currently this code is set up for pi/2 argument reduction.
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* By uncommenting/commenting the appropriate lines, it will
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* also serve as a pi/4 argument reduction code.
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*/
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.text
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/* p.1
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* Trigred preforms argument reduction
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* for the trigonometric functions. It
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* takes one input argument, a D-format
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* number in %r1/%r0 . The magnitude of
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* the input argument must be greater
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* than or equal to 1/2 . Trigred produces
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* three results: the number of the octant
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* occupied by the argument, the reduced
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* argument, and an extension of the
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* reduced argument. The octant number is
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* returned in %r0 . The reduced argument
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* is returned as a D-format number in
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* %r2/%r1 . An 8 bit extension of the
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* reduced argument is returned as an
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* F-format number in %r3.
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* p.2
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*/
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trigred:
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/*
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* Save the sign of the input argument.
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*/
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movw %r0,-(%sp)
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/*
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* Extract the exponent field.
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*/
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extzv $7,$7,%r0,%r2
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/*
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* Convert the fraction part of the input
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* argument into a quadword integer.
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*/
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bicw2 $0xff80,%r0
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bisb2 $0x80,%r0 # -S.McD
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rotl $16,%r0,%r0
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rotl $16,%r1,%r1
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/*
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* If %r1 is negative, add 1 to %r0 . This
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* adjustment is made so that the two's
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* complement multiplications done later
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* will produce unsigned results.
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*/
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bgeq posmid
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incl %r0
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posmid:
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/* p.3
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*
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* Set %r3 to the address of the first quadword
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* used to obtain the needed portion of 2/pi .
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* 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
|