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

1.1     ! nbrk        1: *      $OpenBSD: satanh.sa,v 1.2 1996/05/29 21:05:35 niklas Exp $
        !             2: *      $NetBSD: satanh.sa,v 1.2 1994/10/26 07:49:33 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: *      satanh.sa 3.3 12/19/90
        !            36: *
        !            37: *      The entry point satanh computes the inverse
        !            38: *      hyperbolic tangent of
        !            39: *      an input argument; satanhd does the same except for denormalized
        !            40: *      input.
        !            41: *
        !            42: *      Input: Double-extended number X in location pointed to
        !            43: *              by address register a0.
        !            44: *
        !            45: *      Output: The value arctanh(X) returned in floating-point register Fp0.
        !            46: *
        !            47: *      Accuracy and Monotonicity: The returned result is within 3 ulps in
        !            48: *              64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
        !            49: *              result is subsequently rounded to double precision. The
        !            50: *              result is provably monotonic in double precision.
        !            51: *
        !            52: *      Speed: The program satanh takes approximately 270 cycles.
        !            53: *
        !            54: *      Algorithm:
        !            55: *
        !            56: *      ATANH
        !            57: *      1. If |X| >= 1, go to 3.
        !            58: *
        !            59: *      2. (|X| < 1) Calculate atanh(X) by
        !            60: *              sgn := sign(X)
        !            61: *              y := |X|
        !            62: *              z := 2y/(1-y)
        !            63: *              atanh(X) := sgn * (1/2) * logp1(z)
        !            64: *              Exit.
        !            65: *
        !            66: *      3. If |X| > 1, go to 5.
        !            67: *
        !            68: *      4. (|X| = 1) Generate infinity with an appropriate sign and
        !            69: *              divide-by-zero by
        !            70: *              sgn := sign(X)
        !            71: *              atan(X) := sgn / (+0).
        !            72: *              Exit.
        !            73: *
        !            74: *      5. (|X| > 1) Generate an invalid operation by 0 * infinity.
        !            75: *              Exit.
        !            76: *
        !            77:
        !            78: satanh IDNT    2,1 Motorola 040 Floating Point Software Package
        !            79:
        !            80:        section 8
        !            81:
        !            82:        xref    t_dz
        !            83:        xref    t_operr
        !            84:        xref    t_frcinx
        !            85:        xref    t_extdnrm
        !            86:        xref    slognp1
        !            87:
        !            88:        xdef    satanhd
        !            89: satanhd:
        !            90: *--ATANH(X) = X FOR DENORMALIZED X
        !            91:
        !            92:        bra             t_extdnrm
        !            93:
        !            94:        xdef    satanh
        !            95: satanh:
        !            96:        move.l          (a0),d0
        !            97:        move.w          4(a0),d0
        !            98:        ANDI.L          #$7FFFFFFF,D0
        !            99:        CMPI.L          #$3FFF8000,D0
        !           100:        BGE.B           ATANHBIG
        !           101:
        !           102: *--THIS IS THE USUAL CASE, |X| < 1
        !           103: *--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
        !           104:
        !           105:        FABS.X          (a0),FP0        ...Y = |X|
        !           106:        FMOVE.X         FP0,FP1
        !           107:        FNEG.X          FP1             ...-Y
        !           108:        FADD.X          FP0,FP0         ...2Y
        !           109:        FADD.S          #:3F800000,FP1  ...1-Y
        !           110:        FDIV.X          FP1,FP0         ...2Y/(1-Y)
        !           111:        move.l          (a0),d0
        !           112:        ANDI.L          #$80000000,D0
        !           113:        ORI.L           #$3F000000,D0   ...SIGN(X)*HALF
        !           114:        move.l          d0,-(sp)
        !           115:
        !           116:        fmovem.x        fp0,(a0)        ...overwrite input
        !           117:        move.l          d1,-(sp)
        !           118:        clr.l           d1
        !           119:        bsr             slognp1         ...LOG1P(Z)
        !           120:        fmove.l         (sp)+,fpcr
        !           121:        FMUL.S          (sp)+,FP0
        !           122:        bra             t_frcinx
        !           123:
        !           124: ATANHBIG:
        !           125:        FABS.X          (a0),FP0        ...|X|
        !           126:        FCMP.S          #:3F800000,FP0
        !           127:        fbgt            t_operr
        !           128:        bra             t_dz
        !           129:
        !           130:        end