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Annotation of sys/arch/m68k/fpsp/sasin.sa, Revision 1.1

1.1     ! nbrk        1: *      $OpenBSD: sasin.sa,v 1.2 1996/05/29 21:05:34 niklas Exp $
        !             2: *      $NetBSD: sasin.sa,v 1.2 1994/10/26 07:49:29 cgd Exp $
        !             3:
        !             4: *      MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
        !             5: *      M68000 Hi-Performance Microprocessor Division
        !             6: *      M68040 Software Package
        !             7: *
        !             8: *      M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
        !             9: *      All rights reserved.
        !            10: *
        !            11: *      THE SOFTWARE is provided on an "AS IS" basis and without warranty.
        !            12: *      To the maximum extent permitted by applicable law,
        !            13: *      MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
        !            14: *      INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
        !            15: *      PARTICULAR PURPOSE and any warranty against infringement with
        !            16: *      regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
        !            17: *      and any accompanying written materials.
        !            18: *
        !            19: *      To the maximum extent permitted by applicable law,
        !            20: *      IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
        !            21: *      (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
        !            22: *      PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
        !            23: *      OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
        !            24: *      SOFTWARE.  Motorola assumes no responsibility for the maintenance
        !            25: *      and support of the SOFTWARE.
        !            26: *
        !            27: *      You are hereby granted a copyright license to use, modify, and
        !            28: *      distribute the SOFTWARE so long as this entire notice is retained
        !            29: *      without alteration in any modified and/or redistributed versions,
        !            30: *      and that such modified versions are clearly identified as such.
        !            31: *      No licenses are granted by implication, estoppel or otherwise
        !            32: *      under any patents or trademarks of Motorola, Inc.
        !            33:
        !            34: *
        !            35: *      sasin.sa 3.3 12/19/90
        !            36: *
        !            37: *      Description: The entry point sAsin computes the inverse sine of
        !            38: *              an input argument; sAsind does the same except for denormalized
        !            39: *              input.
        !            40: *
        !            41: *      Input: Double-extended number X in location pointed to
        !            42: *              by address register a0.
        !            43: *
        !            44: *      Output: The value arcsin(X) returned in floating-point register Fp0.
        !            45: *
        !            46: *      Accuracy and Monotonicity: The returned result is within 3 ulps in
        !            47: *              64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
        !            48: *              result is subsequently rounded to double precision. The
        !            49: *              result is provably monotonic in double precision.
        !            50: *
        !            51: *      Speed: The program sASIN takes approximately 310 cycles.
        !            52: *
        !            53: *      Algorithm:
        !            54: *
        !            55: *      ASIN
        !            56: *      1. If |X| >= 1, go to 3.
        !            57: *
        !            58: *      2. (|X| < 1) Calculate asin(X) by
        !            59: *              z := sqrt( [1-X][1+X] )
        !            60: *              asin(X) = atan( x / z ).
        !            61: *              Exit.
        !            62: *
        !            63: *      3. If |X| > 1, go to 5.
        !            64: *
        !            65: *      4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
        !            66: *
        !            67: *      5. (|X| > 1) Generate an invalid operation by 0 * infinity.
        !            68: *              Exit.
        !            69: *
        !            70:
        !            71: SASIN  IDNT    2,1 Motorola 040 Floating Point Software Package
        !            72:
        !            73:        section 8
        !            74:
        !            75: PIBY2  DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
        !            76:
        !            77:        xref    t_operr
        !            78:        xref    t_frcinx
        !            79:        xref    t_extdnrm
        !            80:        xref    satan
        !            81:
        !            82:        xdef    sasind
        !            83: sasind:
        !            84: *--ASIN(X) = X FOR DENORMALIZED X
        !            85:
        !            86:        bra             t_extdnrm
        !            87:
        !            88:        xdef    sasin
        !            89: sasin:
        !            90:        FMOVE.X         (a0),FP0        ...LOAD INPUT
        !            91:
        !            92:        move.l          (a0),d0
        !            93:        move.w          4(a0),d0
        !            94:        ANDI.L          #$7FFFFFFF,D0
        !            95:        CMPI.L          #$3FFF8000,D0
        !            96:        BGE.B           asinbig
        !            97:
        !            98: *--THIS IS THE USUAL CASE, |X| < 1
        !            99: *--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
        !           100:
        !           101:        FMOVE.S         #:3F800000,FP1
        !           102:        FSUB.X          FP0,FP1         ...1-X
        !           103:        fmovem.x        fp2,-(a7)
        !           104:        FMOVE.S         #:3F800000,FP2
        !           105:        FADD.X          FP0,FP2         ...1+X
        !           106:        FMUL.X          FP2,FP1         ...(1+X)(1-X)
        !           107:        fmovem.x        (a7)+,fp2
        !           108:        FSQRT.X         FP1             ...SQRT([1-X][1+X])
        !           109:        FDIV.X          FP1,FP0         ...X/SQRT([1-X][1+X])
        !           110:        fmovem.x        fp0,(a0)
        !           111:        bsr             satan
        !           112:        bra             t_frcinx
        !           113:
        !           114: asinbig:
        !           115:        FABS.X          FP0      ...|X|
        !           116:        FCMP.S          #:3F800000,FP0
        !           117:        fbgt            t_operr         ;cause an operr exception
        !           118:
        !           119: *--|X| = 1, ASIN(X) = +- PI/2.
        !           120:
        !           121:        FMOVE.X         PIBY2,FP0
        !           122:        move.l          (a0),d0
        !           123:        ANDI.L          #$80000000,D0   ...SIGN BIT OF X
        !           124:        ORI.L           #$3F800000,D0   ...+-1 IN SGL FORMAT
        !           125:        MOVE.L          D0,-(sp)        ...push SIGN(X) IN SGL-FMT
        !           126:        FMOVE.L         d1,FPCR
        !           127:        FMUL.S          (sp)+,FP0
        !           128:        bra             t_frcinx
        !           129:
        !           130:        end