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   1 |
   2 |       satanh.sa 3.3 12/19/90
   3 |
   4 |       The entry point satanh computes the inverse
   5 |       hyperbolic tangent of
   6 |       an input argument; satanhd does the same except for denormalized
   7 |       input.
   8 |
   9 |       Input: Double-extended number X in location pointed to
  10 |               by address register a0.
  11 |
  12 |       Output: The value arctanh(X) returned in floating-point register Fp0.
  13 |
  14 |       Accuracy and Monotonicity: The returned result is within 3 ulps in
  15 |               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
  16 |               result is subsequently rounded to double precision. The
  17 |               result is provably monotonic in double precision.
  18 |
  19 |       Speed: The program satanh takes approximately 270 cycles.
  20 |
  21 |       Algorithm:
  22 |
  23 |       ATANH
  24 |       1. If |X| >= 1, go to 3.
  25 |
  26 |       2. (|X| < 1) Calculate atanh(X) by
  27 |               sgn := sign(X)
  28 |               y := |X|
  29 |               z := 2y/(1-y)
  30 |               atanh(X) := sgn * (1/2) * logp1(z)
  31 |               Exit.
  32 |
  33 |       3. If |X| > 1, go to 5.
  34 |
  35 |       4. (|X| = 1) Generate infinity with an appropriate sign and
  36 |               divide-by-zero by
  37 |               sgn := sign(X)
  38 |               atan(X) := sgn / (+0).
  39 |               Exit.
  40 |
  41 |       5. (|X| > 1) Generate an invalid operation by 0 * infinity.
  42 |               Exit.
  43 |
  44
  45 |               Copyright (C) Motorola, Inc. 1990
  46 |                       All Rights Reserved
  47 |
  48 |       For details on the license for this file, please see the
  49 |       file, README, in this same directory.
  50
  51 |satanh idnt    2,1 | Motorola 040 Floating Point Software Package
  52
  53         |section        8
  54
  55         |xref   t_dz
  56         |xref   t_operr
  57         |xref   t_frcinx
  58         |xref   t_extdnrm
  59         |xref   slognp1
  60
  61         .global satanhd
  62 satanhd:
  63 |--ATANH(X) = X FOR DENORMALIZED X
  64
  65         bra             t_extdnrm
  66
  67         .global satanh
  68 satanh:
  69         movel           (%a0),%d0
  70         movew           4(%a0),%d0
  71         andil           #0x7FFFFFFF,%d0
  72         cmpil           #0x3FFF8000,%d0
  73         bges            ATANHBIG
  74
  75 |--THIS IS THE USUAL CASE, |X| < 1
  76 |--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
  77
  78         fabsx           (%a0),%fp0      | ...Y = |X|
  79         fmovex          %fp0,%fp1
  80         fnegx           %fp1            | ...-Y
  81         faddx           %fp0,%fp0               | ...2Y
  82         fadds           #0x3F800000,%fp1        | ...1-Y
  83         fdivx           %fp1,%fp0               | ...2Y/(1-Y)
  84         movel           (%a0),%d0
  85         andil           #0x80000000,%d0
  86         oril            #0x3F000000,%d0 | ...SIGN(X)*HALF
  87         movel           %d0,-(%sp)
  88
  89         fmovemx %fp0-%fp0,(%a0) | ...overwrite input
  90         movel           %d1,-(%sp)
  91         clrl            %d1
  92         bsr             slognp1         | ...LOG1P(Z)
  93         fmovel          (%sp)+,%fpcr
  94         fmuls           (%sp)+,%fp0
  95         bra             t_frcinx
  96
  97 ATANHBIG:
  98         fabsx           (%a0),%fp0      | ...|X|
  99         fcmps           #0x3F800000,%fp0
 100         fbgt            t_operr
 101         bra             t_dz
 102
 103         |end