220 lines
6.6 KiB
ArmAsm
220 lines
6.6 KiB
ArmAsm
# Copyright (c) 1985 Regents of the University of California.
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# 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. All advertising materials mentioning features or use of this software
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# must display the following acknowledgement:
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# This product includes software developed by the University of
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# California, Berkeley and its contributors.
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# 4. 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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.data
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.align 2
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;_sccsid:
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;.asciz "from: @(#)atan2.s 1.2 (Berkeley) 8/21/85; 5.4 (ucb.elefunt) 10/9/90"
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_rcsid:
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.asciz "$Id: atan2.S,v 1.1 1993/08/14 13:44:07 mycroft Exp $"
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# ATAN2(Y,X)
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# RETURN ARG (X+iY)
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# VAX D FORMAT (56 BITS PRECISION)
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# CODED IN VAX ASSEMBLY LANGUAGE BY K.C. NG, 4/16/85;
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#
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#
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# Method :
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# 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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# 2. Reduce x to positive by (if x and y are unexceptional):
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# ARG (x+iy) = arctan(y/x) ... if x > 0,
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# ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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# 3. According to the integer k=4t+0.25 truncated , t=y/x, the argument
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# is further reduced to one of the following intervals and the
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# arctangent of y/x is evaluated by the corresponding formula:
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#
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# [0,7/16] atan(y/x) = t - t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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# [7/16,11/16] atan(y/x) = atan(1/2) + atan( (y-x/2)/(x+y/2) )
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# [11/16.19/16] atan(y/x) = atan( 1 ) + atan( (y-x)/(x+y) )
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# [19/16,39/16] atan(y/x) = atan(3/2) + atan( (y-1.5x)/(x+1.5y) )
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# [39/16,INF] atan(y/x) = atan(INF) + atan( -x/y )
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#
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# Special cases:
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# Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y).
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#
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# ARG( NAN , (anything) ) is NaN;
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# ARG( (anything), NaN ) is NaN;
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# ARG(+(anything but NaN), +-0) is +-0 ;
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# ARG(-(anything but NaN), +-0) is +-PI ;
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# ARG( 0, +-(anything but 0 and NaN) ) is +-PI/2;
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# ARG( +INF,+-(anything but INF and NaN) ) is +-0 ;
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# ARG( -INF,+-(anything but INF and NaN) ) is +-PI;
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# ARG( +INF,+-INF ) is +-PI/4 ;
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# ARG( -INF,+-INF ) is +-3PI/4;
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# ARG( (anything but,0,NaN, and INF),+-INF ) is +-PI/2;
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#
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# Accuracy:
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# atan2(y,x) returns the exact ARG(x+iy) nearly rounded.
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#
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.text
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.align 1
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.globl _atan2
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_atan2 :
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.word 0x0ff4
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movq 4(ap),r2 # r2 = y
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movq 12(ap),r4 # r4 = x
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bicw3 $0x7f,r2,r0
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bicw3 $0x7f,r4,r1
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cmpw r0,$0x8000 # y is the reserved operand
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jeql resop
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cmpw r1,$0x8000 # x is the reserved operand
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jeql resop
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subl2 $8,sp
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bicw3 $0x7fff,r2,-4(fp) # copy y sign bit to -4(fp)
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bicw3 $0x7fff,r4,-8(fp) # copy x sign bit to -8(fp)
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cmpd r4,$0x4080 # x = 1.0 ?
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bneq xnot1
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movq r2,r0
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bicw2 $0x8000,r0 # t = |y|
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movq r0,r2 # y = |y|
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brb begin
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xnot1:
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bicw3 $0x807f,r2,r11 # yexp
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jeql yeq0 # if y=0 goto yeq0
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bicw3 $0x807f,r4,r10 # xexp
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jeql pio2 # if x=0 goto pio2
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subw2 r10,r11 # k = yexp - xexp
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cmpw r11,$0x2000 # k >= 64 (exp) ?
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jgeq pio2 # atan2 = +-pi/2
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divd3 r4,r2,r0 # t = y/x never overflow
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bicw2 $0x8000,r0 # t > 0
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bicw2 $0xff80,r2 # clear the exponent of y
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bicw2 $0xff80,r4 # clear the exponent of x
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bisw2 $0x4080,r2 # normalize y to [1,2)
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bisw2 $0x4080,r4 # normalize x to [1,2)
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subw2 r11,r4 # scale x so that yexp-xexp=k
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begin:
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cmpw r0,$0x411c # t : 39/16
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jgeq L50
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addl3 $0x180,r0,r10 # 8*t
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cvtrfl r10,r10 # [8*t] rounded to int
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ashl $-1,r10,r10 # [8*t]/2
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casel r10,$0,$4
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L1:
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.word L20-L1
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.word L20-L1
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.word L30-L1
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.word L40-L1
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.word L40-L1
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L10:
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movq $0xb4d9940f985e407b,r6 # Hi=.98279372324732906796d0
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movq $0x21b1879a3bc2a2fc,r8 # Lo=-.17092002525602665777d-17
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subd3 r4,r2,r0 # y-x
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addw2 $0x80,r0 # 2(y-x)
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subd2 r4,r0 # 2(y-x)-x
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addw2 $0x80,r4 # 2x
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movq r2,r10
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addw2 $0x80,r10 # 2y
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addd2 r10,r2 # 3y
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addd2 r4,r2 # 3y+2x
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divd2 r2,r0 # (2y-3x)/(2x+3y)
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brw L60
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L20:
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cmpw r0,$0x3280 # t : 2**(-28)
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jlss L80
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clrq r6 # Hi=r6=0, Lo=r8=0
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clrq r8
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brw L60
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L30:
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movq $0xda7b2b0d63383fed,r6 # Hi=.46364760900080611433d0
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movq $0xf0ea17b2bf912295,r8 # Lo=.10147340032515978826d-17
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movq r2,r0
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addw2 $0x80,r0 # 2y
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subd2 r4,r0 # 2y-x
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addw2 $0x80,r4 # 2x
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addd2 r2,r4 # 2x+y
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divd2 r4,r0 # (2y-x)/(2x+y)
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brb L60
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L50:
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movq $0x68c2a2210fda40c9,r6 # Hi=1.5707963267948966135d1
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movq $0x06e0145c26332326,r8 # Lo=.22517417741562176079d-17
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cmpw r0,$0x5100 # y : 2**57
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bgeq L90
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divd3 r2,r4,r0
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bisw2 $0x8000,r0 # -x/y
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brb L60
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L40:
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movq $0x68c2a2210fda4049,r6 # Hi=.78539816339744830676d0
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movq $0x06e0145c263322a6,r8 # Lo=.11258708870781088040d-17
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subd3 r4,r2,r0 # y-x
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addd2 r4,r2 # y+x
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divd2 r2,r0 # (y-x)/(y+x)
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L60:
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movq r0,r10
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muld2 r0,r0
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polyd r0,$12,ptable
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muld2 r10,r0
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subd2 r0,r8
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addd3 r8,r10,r0
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addd2 r6,r0
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L80:
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movw -8(fp),r2
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bneq pim
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bisw2 -4(fp),r0 # return sign(y)*r0
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ret
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L90: # x >= 2**25
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movq r6,r0
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brb L80
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pim:
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subd3 r0,$0x68c2a2210fda4149,r0 # pi-t
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bisw2 -4(fp),r0
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ret
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yeq0:
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movw -8(fp),r2
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beql zero # if sign(x)=1 return pi
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movq $0x68c2a2210fda4149,r0 # pi=3.1415926535897932270d1
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ret
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zero:
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clrq r0 # return 0
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ret
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pio2:
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movq $0x68c2a2210fda40c9,r0 # pi/2=1.5707963267948966135d1
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bisw2 -4(fp),r0 # return sign(y)*pi/2
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ret
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resop:
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movq $0x8000,r0 # propagate the reserved operand
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ret
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.align 2
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ptable:
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.quad 0xb50f5ce96e7abd60
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.quad 0x51e44a42c1073e02
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.quad 0x3487e3289643be35
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.quad 0xdb62066dffba3e54
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.quad 0xcf8e2d5199abbe70
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.quad 0x26f39cb884883e88
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.quad 0x135117d18998be9d
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.quad 0x602ce9742e883eba
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.quad 0xa35ad0be8e38bee3
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.quad 0xffac922249243f12
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.quad 0x7f14ccccccccbf4c
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.quad 0xaa8faaaaaaaa3faa
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.quad 0x0000000000000000
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