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Annotation of sys/arch/m68k/fpsp/sasin.sa, Revision 1.1.1.1

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