1994-07-05 21:50:24 +04:00
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* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
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* M68000 Hi-Performance Microprocessor Division
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* M68040 Software Package
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*
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* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
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* All rights reserved.
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*
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* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
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* To the maximum extent permitted by applicable law,
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* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
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* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
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* PARTICULAR PURPOSE and any warranty against infringement with
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* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
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* and any accompanying written materials.
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*
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* To the maximum extent permitted by applicable law,
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* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
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* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
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* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
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* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
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* SOFTWARE. Motorola assumes no responsibility for the maintenance
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* and support of the SOFTWARE.
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*
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* You are hereby granted a copyright license to use, modify, and
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* distribute the SOFTWARE so long as this entire notice is retained
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* without alteration in any modified and/or redistributed versions,
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* and that such modified versions are clearly identified as such.
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* No licenses are granted by implication, estoppel or otherwise
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* under any patents or trademarks of Motorola, Inc.
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*
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* sacos.sa 3.3 12/19/90
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*
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* Description: The entry point sAcos computes the inverse cosine of
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* an input argument; sAcosd does the same except for denormalized
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* input.
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*
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* Input: Double-extended number X in location pointed to
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* by address register a0.
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*
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* Output: The value arccos(X) returned in floating-point register Fp0.
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*
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* Accuracy and Monotonicity: The returned result is within 3 ulps in
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* 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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* result is subsequently rounded to double precision. The
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* result is provably monotonic in double precision.
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*
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* Speed: The program sCOS takes approximately 310 cycles.
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*
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* Algorithm:
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*
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* ACOS
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* 1. If |X| >= 1, go to 3.
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*
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* 2. (|X| < 1) Calculate acos(X) by
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* z := (1-X) / (1+X)
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* acos(X) = 2 * atan( sqrt(z) ).
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* Exit.
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*
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* 3. If |X| > 1, go to 5.
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*
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* 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
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*
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* 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
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* Exit.
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*
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SACOS IDNT 2,1 Motorola 040 Floating Point Software Package
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section 8
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PI DC.L $40000000,$C90FDAA2,$2168C235,$00000000
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PIBY2 DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
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xref t_operr
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xref t_frcinx
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xref satan
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xdef sacosd
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sacosd:
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*--ACOS(X) = PI/2 FOR DENORMALIZED X
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fmove.l d1,fpcr ...load user's rounding mode/precision
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FMOVE.X PIBY2,FP0
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bra t_frcinx
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xdef sacos
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sacos:
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FMOVE.X (a0),FP0 ...LOAD INPUT
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move.l (a0),d0 ...pack exponent with upper 16 fraction
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move.w 4(a0),d0
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ANDI.L #$7FFFFFFF,D0
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CMPI.L #$3FFF8000,D0
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BGE.B ACOSBIG
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*--THIS IS THE USUAL CASE, |X| < 1
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*--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
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FMOVE.S #:3F800000,FP1
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FADD.X FP0,FP1 ...1+X
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FNEG.X FP0 ... -X
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FADD.S #:3F800000,FP0 ...1-X
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FDIV.X FP1,FP0 ...(1-X)/(1+X)
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FSQRT.X FP0 ...SQRT((1-X)/(1+X))
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fmovem.x fp0,(a0) ...overwrite input
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move.l d1,-(sp) ;save original users fpcr
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clr.l d1
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bsr satan ...ATAN(SQRT([1-X]/[1+X]))
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fMOVE.L (sp)+,fpcr ;restore users exceptions
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FADD.X FP0,FP0 ...2 * ATAN( STUFF )
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bra t_frcinx
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ACOSBIG:
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FABS.X FP0
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FCMP.S #:3F800000,FP0
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fbgt t_operr ;cause an operr exception
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*--|X| = 1, ACOS(X) = 0 OR PI
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move.l (a0),d0 ...pack exponent with upper 16 fraction
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move.w 4(a0),d0
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1994-07-05 21:56:52 +04:00
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TST.L D0 ;D0 has original exponent+fraction
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1994-07-05 21:50:24 +04:00
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BGT.B ACOSP1
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*--X = -1
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*Returns PI and inexact exception
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FMOVE.X PI,FP0
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FMOVE.L d1,FPCR
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FADD.S #:00800000,FP0 ;cause an inexact exception to be put
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* ;into the 040 - will not trap until next
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* ;fp inst.
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bra t_frcinx
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ACOSP1:
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FMOVE.L d1,FPCR
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FMOVE.S #:00000000,FP0
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rts ;Facos of +1 is exact
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end
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