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
CVSweb