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   1 |
   2 |       sacos.sa 3.3 12/19/90
   3 |
   4 |       Description: The entry point sAcos computes the inverse cosine of
   5 |               an input argument; sAcosd does the same except for denormalized
   6 |               input.
   7 |
   8 |       Input: Double-extended number X in location pointed to
   9 |               by address register a0.
  10 |
  11 |       Output: The value arccos(X) returned in floating-point register Fp0.
  12 |
  13 |       Accuracy and Monotonicity: The returned result is within 3 ulps in
  14 |               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
  15 |               result is subsequently rounded to double precision. The
  16 |               result is provably monotonic in double precision.
  17 |
  18 |       Speed: The program sCOS takes approximately 310 cycles.
  19 |
  20 |       Algorithm:
  21 |
  22 |       ACOS
  23 |       1. If |X| >= 1, go to 3.
  24 |
  25 |       2. (|X| < 1) Calculate acos(X) by
  26 |               z := (1-X) / (1+X)
  27 |               acos(X) = 2 * atan( sqrt(z) ).
  28 |               Exit.
  29 |
  30 |       3. If |X| > 1, go to 5.
  31 |
  32 |       4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
  33 |
  34 |       5. (|X| > 1) Generate an invalid operation by 0 * infinity.
  35 |               Exit.
  36 |
  37
  38 |               Copyright (C) Motorola, Inc. 1990
  39 |                       All Rights Reserved
  40 |
  41 |       For details on the license for this file, please see the
  42 |       file, README, in this same directory.
  43
  44 |SACOS  idnt    2,1 | Motorola 040 Floating Point Software Package
  45
  46         |section        8
  47
  48 PI:     .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
  49 PIBY2:  .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
  50
  51         |xref   t_operr
  52         |xref   t_frcinx
  53         |xref   satan
  54
  55         .global sacosd
  56 sacosd:
  57 |--ACOS(X) = PI/2 FOR DENORMALIZED X
  58         fmovel          %d1,%fpcr               | ...load user's rounding mode/precision
  59         fmovex          PIBY2,%fp0
  60         bra             t_frcinx
  61
  62         .global sacos
  63 sacos:
  64         fmovex          (%a0),%fp0      | ...LOAD INPUT
  65
  66         movel           (%a0),%d0               | ...pack exponent with upper 16 fraction
  67         movew           4(%a0),%d0
  68         andil           #0x7FFFFFFF,%d0
  69         cmpil           #0x3FFF8000,%d0
  70         bges            ACOSBIG
  71
  72 |--THIS IS THE USUAL CASE, |X| < 1
  73 |--ACOS(X) = 2 * ATAN(  SQRT( (1-X)/(1+X) )     )
  74
  75         fmoves          #0x3F800000,%fp1
  76         faddx           %fp0,%fp1               | ...1+X
  77         fnegx           %fp0            | ... -X
  78         fadds           #0x3F800000,%fp0        | ...1-X
  79         fdivx           %fp1,%fp0               | ...(1-X)/(1+X)
  80         fsqrtx          %fp0            | ...SQRT((1-X)/(1+X))
  81         fmovemx %fp0-%fp0,(%a0) | ...overwrite input
  82         movel           %d1,-(%sp)      |save original users fpcr
  83         clrl            %d1
  84         bsr             satan           | ...ATAN(SQRT([1-X]/[1+X]))
  85         fmovel          (%sp)+,%fpcr    |restore users exceptions
  86         faddx           %fp0,%fp0               | ...2 * ATAN( STUFF )
  87         bra             t_frcinx
  88
  89 ACOSBIG:
  90         fabsx           %fp0
  91         fcmps           #0x3F800000,%fp0
  92         fbgt            t_operr         |cause an operr exception
  93
  94 |--|X| = 1, ACOS(X) = 0 OR PI
  95         movel           (%a0),%d0               | ...pack exponent with upper 16 fraction
  96         movew           4(%a0),%d0
  97         cmpl            #0,%d0          |D0 has original exponent+fraction
  98         bgts            ACOSP1
  99
 100 |--X = -1
 101 |Returns PI and inexact exception
 102         fmovex          PI,%fp0
 103         fmovel          %d1,%FPCR
 104         fadds           #0x00800000,%fp0        |cause an inexact exception to be put
 105 |                                       ;into the 040 - will not trap until next
 106 |                                       ;fp inst.
 107         bra             t_frcinx
 108
 109 ACOSP1:
 110         fmovel          %d1,%FPCR
 111         fmoves          #0x00000000,%fp0
 112         rts                             |Facos ; of +1 is exact
 113
 114         |end