LXR linux/arch/m68k/fpsp040/satanh.S

   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
  62satanhd:
  63|--ATANH(X) = X FOR DENORMALIZED X
  64
  65        bra             t_extdnrm
  66
  67        .global satanh
  68satanh:
  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
  97ATANHBIG:
  98        fabsx           (%a0),%fp0      | ...|X|
  99        fcmps           #0x3F800000,%fp0
 100        fbgt            t_operr
 101        bra             t_dz
 102
 103        |end
 104