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authorTheo de Raadt <deraadt@cvs.openbsd.org>1995-10-18 08:53:40 +0000
committerTheo de Raadt <deraadt@cvs.openbsd.org>1995-10-18 08:53:40 +0000
commitd6583bb2a13f329cf0332ef2570eb8bb8fc0e39c (patch)
treeece253b876159b39c620e62b6c9b1174642e070e /sys/arch/m68k/fpsp/stan.sa
initial import of NetBSD tree
Diffstat (limited to 'sys/arch/m68k/fpsp/stan.sa')
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diff --git a/sys/arch/m68k/fpsp/stan.sa b/sys/arch/m68k/fpsp/stan.sa
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+++ b/sys/arch/m68k/fpsp/stan.sa
@@ -0,0 +1,480 @@
+* $NetBSD: stan.sa,v 1.3 1994/10/26 07:50:10 cgd Exp $
+
+* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
+* M68000 Hi-Performance Microprocessor Division
+* M68040 Software Package
+*
+* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
+* All rights reserved.
+*
+* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
+* To the maximum extent permitted by applicable law,
+* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
+* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
+* PARTICULAR PURPOSE and any warranty against infringement with
+* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
+* and any accompanying written materials.
+*
+* To the maximum extent permitted by applicable law,
+* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
+* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
+* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
+* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
+* SOFTWARE. Motorola assumes no responsibility for the maintenance
+* and support of the SOFTWARE.
+*
+* You are hereby granted a copyright license to use, modify, and
+* distribute the SOFTWARE so long as this entire notice is retained
+* without alteration in any modified and/or redistributed versions,
+* and that such modified versions are clearly identified as such.
+* No licenses are granted by implication, estoppel or otherwise
+* under any patents or trademarks of Motorola, Inc.
+
+*
+* stan.sa 3.3 7/29/91
+*
+* The entry point stan computes the tangent of
+* an input argument;
+* stand does the same except for denormalized input.
+*
+* Input: Double-extended number X in location pointed to
+* by address register a0.
+*
+* Output: The value tan(X) returned in floating-point register Fp0.
+*
+* Accuracy and Monotonicity: The returned result is within 3 ulp in
+* 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
+* result is subsequently rounded to double precision. The
+* result is provably monotonic in double precision.
+*
+* Speed: The program sTAN takes approximately 170 cycles for
+* input argument X such that |X| < 15Pi, which is the the usual
+* situation.
+*
+* Algorithm:
+*
+* 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
+*
+* 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
+* k = N mod 2, so in particular, k = 0 or 1.
+*
+* 3. If k is odd, go to 5.
+*
+* 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a
+* rational function U/V where
+* U = r + r*s*(P1 + s*(P2 + s*P3)), and
+* V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r.
+* Exit.
+*
+* 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by a
+* rational function U/V where
+* U = r + r*s*(P1 + s*(P2 + s*P3)), and
+* V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r,
+* -Cot(r) = -V/U. Exit.
+*
+* 6. If |X| > 1, go to 8.
+*
+* 7. (|X|<2**(-40)) Tan(X) = X. Exit.
+*
+* 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
+*
+
+STAN IDNT 2,1 Motorola 040 Floating Point Software Package
+
+ section 8
+
+ include fpsp.h
+
+BOUNDS1 DC.L $3FD78000,$4004BC7E
+TWOBYPI DC.L $3FE45F30,$6DC9C883
+
+TANQ4 DC.L $3EA0B759,$F50F8688
+TANP3 DC.L $BEF2BAA5,$A8924F04
+
+TANQ3 DC.L $BF346F59,$B39BA65F,$00000000,$00000000
+
+TANP2 DC.L $3FF60000,$E073D3FC,$199C4A00,$00000000
+
+TANQ2 DC.L $3FF90000,$D23CD684,$15D95FA1,$00000000
+
+TANP1 DC.L $BFFC0000,$8895A6C5,$FB423BCA,$00000000
+
+TANQ1 DC.L $BFFD0000,$EEF57E0D,$A84BC8CE,$00000000
+
+INVTWOPI DC.L $3FFC0000,$A2F9836E,$4E44152A,$00000000
+
+TWOPI1 DC.L $40010000,$C90FDAA2,$00000000,$00000000
+TWOPI2 DC.L $3FDF0000,$85A308D4,$00000000,$00000000
+
+*--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING
+*--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
+*--MOST 69 BITS LONG.
+ xdef PITBL
+PITBL:
+ DC.L $C0040000,$C90FDAA2,$2168C235,$21800000
+ DC.L $C0040000,$C2C75BCD,$105D7C23,$A0D00000
+ DC.L $C0040000,$BC7EDCF7,$FF523611,$A1E80000
+ DC.L $C0040000,$B6365E22,$EE46F000,$21480000
+ DC.L $C0040000,$AFEDDF4D,$DD3BA9EE,$A1200000
+ DC.L $C0040000,$A9A56078,$CC3063DD,$21FC0000
+ DC.L $C0040000,$A35CE1A3,$BB251DCB,$21100000
+ DC.L $C0040000,$9D1462CE,$AA19D7B9,$A1580000
+ DC.L $C0040000,$96CBE3F9,$990E91A8,$21E00000
+ DC.L $C0040000,$90836524,$88034B96,$20B00000
+ DC.L $C0040000,$8A3AE64F,$76F80584,$A1880000
+ DC.L $C0040000,$83F2677A,$65ECBF73,$21C40000
+ DC.L $C0030000,$FB53D14A,$A9C2F2C2,$20000000
+ DC.L $C0030000,$EEC2D3A0,$87AC669F,$21380000
+ DC.L $C0030000,$E231D5F6,$6595DA7B,$A1300000
+ DC.L $C0030000,$D5A0D84C,$437F4E58,$9FC00000
+ DC.L $C0030000,$C90FDAA2,$2168C235,$21000000
+ DC.L $C0030000,$BC7EDCF7,$FF523611,$A1680000
+ DC.L $C0030000,$AFEDDF4D,$DD3BA9EE,$A0A00000
+ DC.L $C0030000,$A35CE1A3,$BB251DCB,$20900000
+ DC.L $C0030000,$96CBE3F9,$990E91A8,$21600000
+ DC.L $C0030000,$8A3AE64F,$76F80584,$A1080000
+ DC.L $C0020000,$FB53D14A,$A9C2F2C2,$1F800000
+ DC.L $C0020000,$E231D5F6,$6595DA7B,$A0B00000
+ DC.L $C0020000,$C90FDAA2,$2168C235,$20800000
+ DC.L $C0020000,$AFEDDF4D,$DD3BA9EE,$A0200000
+ DC.L $C0020000,$96CBE3F9,$990E91A8,$20E00000
+ DC.L $C0010000,$FB53D14A,$A9C2F2C2,$1F000000
+ DC.L $C0010000,$C90FDAA2,$2168C235,$20000000
+ DC.L $C0010000,$96CBE3F9,$990E91A8,$20600000
+ DC.L $C0000000,$C90FDAA2,$2168C235,$1F800000
+ DC.L $BFFF0000,$C90FDAA2,$2168C235,$1F000000
+ DC.L $00000000,$00000000,$00000000,$00000000
+ DC.L $3FFF0000,$C90FDAA2,$2168C235,$9F000000
+ DC.L $40000000,$C90FDAA2,$2168C235,$9F800000
+ DC.L $40010000,$96CBE3F9,$990E91A8,$A0600000
+ DC.L $40010000,$C90FDAA2,$2168C235,$A0000000
+ DC.L $40010000,$FB53D14A,$A9C2F2C2,$9F000000
+ DC.L $40020000,$96CBE3F9,$990E91A8,$A0E00000
+ DC.L $40020000,$AFEDDF4D,$DD3BA9EE,$20200000
+ DC.L $40020000,$C90FDAA2,$2168C235,$A0800000
+ DC.L $40020000,$E231D5F6,$6595DA7B,$20B00000
+ DC.L $40020000,$FB53D14A,$A9C2F2C2,$9F800000
+ DC.L $40030000,$8A3AE64F,$76F80584,$21080000
+ DC.L $40030000,$96CBE3F9,$990E91A8,$A1600000
+ DC.L $40030000,$A35CE1A3,$BB251DCB,$A0900000
+ DC.L $40030000,$AFEDDF4D,$DD3BA9EE,$20A00000
+ DC.L $40030000,$BC7EDCF7,$FF523611,$21680000
+ DC.L $40030000,$C90FDAA2,$2168C235,$A1000000
+ DC.L $40030000,$D5A0D84C,$437F4E58,$1FC00000
+ DC.L $40030000,$E231D5F6,$6595DA7B,$21300000
+ DC.L $40030000,$EEC2D3A0,$87AC669F,$A1380000
+ DC.L $40030000,$FB53D14A,$A9C2F2C2,$A0000000
+ DC.L $40040000,$83F2677A,$65ECBF73,$A1C40000
+ DC.L $40040000,$8A3AE64F,$76F80584,$21880000
+ DC.L $40040000,$90836524,$88034B96,$A0B00000
+ DC.L $40040000,$96CBE3F9,$990E91A8,$A1E00000
+ DC.L $40040000,$9D1462CE,$AA19D7B9,$21580000
+ DC.L $40040000,$A35CE1A3,$BB251DCB,$A1100000
+ DC.L $40040000,$A9A56078,$CC3063DD,$A1FC0000
+ DC.L $40040000,$AFEDDF4D,$DD3BA9EE,$21200000
+ DC.L $40040000,$B6365E22,$EE46F000,$A1480000
+ DC.L $40040000,$BC7EDCF7,$FF523611,$21E80000
+ DC.L $40040000,$C2C75BCD,$105D7C23,$20D00000
+ DC.L $40040000,$C90FDAA2,$2168C235,$A1800000
+
+INARG equ FP_SCR4
+
+TWOTO63 equ L_SCR1
+ENDFLAG equ L_SCR2
+N equ L_SCR3
+
+ xref t_frcinx
+ xref t_extdnrm
+
+ xdef stand
+stand:
+*--TAN(X) = X FOR DENORMALIZED X
+
+ bra t_extdnrm
+
+ xdef stan
+stan:
+ FMOVE.X (a0),FP0 ...LOAD INPUT
+
+ MOVE.L (A0),D0
+ MOVE.W 4(A0),D0
+ ANDI.L #$7FFFFFFF,D0
+
+ CMPI.L #$3FD78000,D0 ...|X| >= 2**(-40)?
+ BGE.B TANOK1
+ BRA.W TANSM
+TANOK1:
+ CMPI.L #$4004BC7E,D0 ...|X| < 15 PI?
+ BLT.B TANMAIN
+ BRA.W REDUCEX
+
+
+TANMAIN:
+*--THIS IS THE USUAL CASE, |X| <= 15 PI.
+*--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
+ FMOVE.X FP0,FP1
+ FMUL.D TWOBYPI,FP1 ...X*2/PI
+
+*--HIDE THE NEXT TWO INSTRUCTIONS
+ lea.l PITBL+$200,a1 ...TABLE OF N*PI/2, N = -32,...,32
+
+*--FP1 IS NOW READY
+ FMOVE.L FP1,D0 ...CONVERT TO INTEGER
+
+ ASL.L #4,D0
+ ADDA.L D0,a1 ...ADDRESS N*PIBY2 IN Y1, Y2
+
+ FSUB.X (a1)+,FP0 ...X-Y1
+*--HIDE THE NEXT ONE
+
+ FSUB.S (a1),FP0 ...FP0 IS R = (X-Y1)-Y2
+
+ ROR.L #5,D0
+ ANDI.L #$80000000,D0 ...D0 WAS ODD IFF D0 < 0
+
+TANCONT:
+
+ TST.L D0
+ BLT.W NODD
+
+ FMOVE.X FP0,FP1
+ FMUL.X FP1,FP1 ...S = R*R
+
+ FMOVE.D TANQ4,FP3
+ FMOVE.D TANP3,FP2
+
+ FMUL.X FP1,FP3 ...SQ4
+ FMUL.X FP1,FP2 ...SP3
+
+ FADD.D TANQ3,FP3 ...Q3+SQ4
+ FADD.X TANP2,FP2 ...P2+SP3
+
+ FMUL.X FP1,FP3 ...S(Q3+SQ4)
+ FMUL.X FP1,FP2 ...S(P2+SP3)
+
+ FADD.X TANQ2,FP3 ...Q2+S(Q3+SQ4)
+ FADD.X TANP1,FP2 ...P1+S(P2+SP3)
+
+ FMUL.X FP1,FP3 ...S(Q2+S(Q3+SQ4))
+ FMUL.X FP1,FP2 ...S(P1+S(P2+SP3))
+
+ FADD.X TANQ1,FP3 ...Q1+S(Q2+S(Q3+SQ4))
+ FMUL.X FP0,FP2 ...RS(P1+S(P2+SP3))
+
+ FMUL.X FP3,FP1 ...S(Q1+S(Q2+S(Q3+SQ4)))
+
+
+ FADD.X FP2,FP0 ...R+RS(P1+S(P2+SP3))
+
+
+ FADD.S #:3F800000,FP1 ...1+S(Q1+...)
+
+ FMOVE.L d1,fpcr ;restore users exceptions
+ FDIV.X FP1,FP0 ;last inst - possible exception set
+
+ bra t_frcinx
+
+NODD:
+ FMOVE.X FP0,FP1
+ FMUL.X FP0,FP0 ...S = R*R
+
+ FMOVE.D TANQ4,FP3
+ FMOVE.D TANP3,FP2
+
+ FMUL.X FP0,FP3 ...SQ4
+ FMUL.X FP0,FP2 ...SP3
+
+ FADD.D TANQ3,FP3 ...Q3+SQ4
+ FADD.X TANP2,FP2 ...P2+SP3
+
+ FMUL.X FP0,FP3 ...S(Q3+SQ4)
+ FMUL.X FP0,FP2 ...S(P2+SP3)
+
+ FADD.X TANQ2,FP3 ...Q2+S(Q3+SQ4)
+ FADD.X TANP1,FP2 ...P1+S(P2+SP3)
+
+ FMUL.X FP0,FP3 ...S(Q2+S(Q3+SQ4))
+ FMUL.X FP0,FP2 ...S(P1+S(P2+SP3))
+
+ FADD.X TANQ1,FP3 ...Q1+S(Q2+S(Q3+SQ4))
+ FMUL.X FP1,FP2 ...RS(P1+S(P2+SP3))
+
+ FMUL.X FP3,FP0 ...S(Q1+S(Q2+S(Q3+SQ4)))
+
+
+ FADD.X FP2,FP1 ...R+RS(P1+S(P2+SP3))
+ FADD.S #:3F800000,FP0 ...1+S(Q1+...)
+
+
+ FMOVE.X FP1,-(sp)
+ EORI.L #$80000000,(sp)
+
+ FMOVE.L d1,fpcr ;restore users exceptions
+ FDIV.X (sp)+,FP0 ;last inst - possible exception set
+
+ bra t_frcinx
+
+TANBORS:
+*--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
+*--IF |X| < 2**(-40), RETURN X OR 1.
+ CMPI.L #$3FFF8000,D0
+ BGT.B REDUCEX
+
+TANSM:
+
+ FMOVE.X FP0,-(sp)
+ FMOVE.L d1,fpcr ;restore users exceptions
+ FMOVE.X (sp)+,FP0 ;last inst - posibble exception set
+
+ bra t_frcinx
+
+
+REDUCEX:
+*--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
+*--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
+*--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
+
+ FMOVEM.X FP2-FP5,-(A7) ...save FP2 through FP5
+ MOVE.L D2,-(A7)
+ FMOVE.S #:00000000,FP1
+
+*--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
+*--there is a danger of unwanted overflow in first LOOP iteration. In this
+*--case, reduce argument by one remainder step to make subsequent reduction
+*--safe.
+ cmpi.l #$7ffeffff,d0 ;is argument dangerously large?
+ bne.b LOOP
+ move.l #$7ffe0000,FP_SCR2(a6) ;yes
+* ;create 2**16383*PI/2
+ move.l #$c90fdaa2,FP_SCR2+4(a6)
+ clr.l FP_SCR2+8(a6)
+ ftst.x fp0 ;test sign of argument
+ move.l #$7fdc0000,FP_SCR3(a6) ;create low half of 2**16383*
+* ;PI/2 at FP_SCR3
+ move.l #$85a308d3,FP_SCR3+4(a6)
+ clr.l FP_SCR3+8(a6)
+ fblt.w red_neg
+ or.w #$8000,FP_SCR2(a6) ;positive arg
+ or.w #$8000,FP_SCR3(a6)
+red_neg:
+ fadd.x FP_SCR2(a6),fp0 ;high part of reduction is exact
+ fmove.x fp0,fp1 ;save high result in fp1
+ fadd.x FP_SCR3(a6),fp0 ;low part of reduction
+ fsub.x fp0,fp1 ;determine low component of result
+ fadd.x FP_SCR3(a6),fp1 ;fp0/fp1 are reduced argument.
+
+*--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
+*--integer quotient will be stored in N
+*--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1)
+
+LOOP:
+ FMOVE.X FP0,INARG(a6) ...+-2**K * F, 1 <= F < 2
+ MOVE.W INARG(a6),D0
+ MOVE.L D0,A1 ...save a copy of D0
+ ANDI.L #$00007FFF,D0
+ SUBI.L #$00003FFF,D0 ...D0 IS K
+ CMPI.L #28,D0
+ BLE.B LASTLOOP
+CONTLOOP:
+ SUBI.L #27,D0 ...D0 IS L := K-27
+ CLR.L ENDFLAG(a6)
+ BRA.B WORK
+LASTLOOP:
+ CLR.L D0 ...D0 IS L := 0
+ MOVE.L #1,ENDFLAG(a6)
+
+WORK:
+*--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
+*--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
+
+*--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
+*--2**L * (PIby2_1), 2**L * (PIby2_2)
+
+ MOVE.L #$00003FFE,D2 ...BIASED EXPO OF 2/PI
+ SUB.L D0,D2 ...BIASED EXPO OF 2**(-L)*(2/PI)
+
+ MOVE.L #$A2F9836E,FP_SCR1+4(a6)
+ MOVE.L #$4E44152A,FP_SCR1+8(a6)
+ MOVE.W D2,FP_SCR1(a6) ...FP_SCR1 is 2**(-L)*(2/PI)
+
+ FMOVE.X FP0,FP2
+ FMUL.X FP_SCR1(a6),FP2
+*--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
+*--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
+*--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
+*--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
+*--US THE DESIRED VALUE IN FLOATING POINT.
+
+*--HIDE SIX CYCLES OF INSTRUCTION
+ MOVE.L A1,D2
+ SWAP D2
+ ANDI.L #$80000000,D2
+ ORI.L #$5F000000,D2 ...D2 IS SIGN(INARG)*2**63 IN SGL
+ MOVE.L D2,TWOTO63(a6)
+
+ MOVE.L D0,D2
+ ADDI.L #$00003FFF,D2 ...BIASED EXPO OF 2**L * (PI/2)
+
+*--FP2 IS READY
+ FADD.S TWOTO63(a6),FP2 ...THE FRACTIONAL PART OF FP1 IS ROUNDED
+
+*--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2
+ MOVE.W D2,FP_SCR2(a6)
+ CLR.W FP_SCR2+2(a6)
+ MOVE.L #$C90FDAA2,FP_SCR2+4(a6)
+ CLR.L FP_SCR2+8(a6) ...FP_SCR2 is 2**(L) * Piby2_1
+
+*--FP2 IS READY
+ FSUB.S TWOTO63(a6),FP2 ...FP2 is N
+
+ ADDI.L #$00003FDD,D0
+ MOVE.W D0,FP_SCR3(a6)
+ CLR.W FP_SCR3+2(a6)
+ MOVE.L #$85A308D3,FP_SCR3+4(a6)
+ CLR.L FP_SCR3+8(a6) ...FP_SCR3 is 2**(L) * Piby2_2
+
+ MOVE.L ENDFLAG(a6),D0
+
+*--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
+*--P2 = 2**(L) * Piby2_2
+ FMOVE.X FP2,FP4
+ FMul.X FP_SCR2(a6),FP4 ...W = N*P1
+ FMove.X FP2,FP5
+ FMul.X FP_SCR3(a6),FP5 ...w = N*P2
+ FMove.X FP4,FP3
+*--we want P+p = W+w but |p| <= half ulp of P
+*--Then, we need to compute A := R-P and a := r-p
+ FAdd.X FP5,FP3 ...FP3 is P
+ FSub.X FP3,FP4 ...W-P
+
+ FSub.X FP3,FP0 ...FP0 is A := R - P
+ FAdd.X FP5,FP4 ...FP4 is p = (W-P)+w
+
+ FMove.X FP0,FP3 ...FP3 A
+ FSub.X FP4,FP1 ...FP1 is a := r - p
+
+*--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
+*--|r| <= half ulp of R.
+ FAdd.X FP1,FP0 ...FP0 is R := A+a
+*--No need to calculate r if this is the last loop
+ TST.L D0
+ BGT.W RESTORE
+
+*--Need to calculate r
+ FSub.X FP0,FP3 ...A-R
+ FAdd.X FP3,FP1 ...FP1 is r := (A-R)+a
+ BRA.W LOOP
+
+RESTORE:
+ FMOVE.L FP2,N(a6)
+ MOVE.L (A7)+,D2
+ FMOVEM.X (A7)+,FP2-FP5
+
+
+ MOVE.L N(a6),D0
+ ROR.L #1,D0
+
+
+ BRA.W TANCONT
+
+ end