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   1 |
   2 |       stanh.sa 3.1 12/10/90
   3 |
   4 |       The entry point sTanh computes the hyperbolic tangent of
   5 |       an input argument; sTanhd 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 tanh(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 stanh takes approximately 270 cycles.
  19 |
  20 |       Algorithm:
  21 |
  22 |       TANH
  23 |       1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
  24 |
  25 |       2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
  26 |               sgn := sign(X), y := 2|X|, z := expm1(Y), and
  27 |               tanh(X) = sgn*( z/(2+z) ).
  28 |               Exit.
  29 |
  30 |       3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
  31 |               go to 7.
  32 |
  33 |       4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
  34 |
  35 |       5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
  36 |               sgn := sign(X), y := 2|X|, z := exp(Y),
  37 |               tanh(X) = sgn - [ sgn*2/(1+z) ].
  38 |               Exit.
  39 |
  40 |       6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
  41 |               calculate Tanh(X) by
  42 |               sgn := sign(X), Tiny := 2**(-126),
  43 |               tanh(X) := sgn - sgn*Tiny.
  44 |               Exit.
  45 |
  46 |       7. (|X| < 2**(-40)). Tanh(X) = X.       Exit.
  47 |
  48
  49 |               Copyright (C) Motorola, Inc. 1990
  50 |                       All Rights Reserved
  51 |
  52 |       For details on the license for this file, please see the
  53 |       file, README, in this same directory.
  54
  55 |STANH  idnt    2,1 | Motorola 040 Floating Point Software Package
  56
  57         |section        8
  58
  59 #include "fpsp.h"
  60
  61         .set    X,FP_SCR5
  62         .set    XDCARE,X+2
  63         .set    XFRAC,X+4
  64
  65         .set    SGN,L_SCR3
  66
  67         .set    V,FP_SCR6
  68
  69 BOUNDS1:        .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2
  70
  71         |xref   t_frcinx
  72         |xref   t_extdnrm
  73         |xref   setox
  74         |xref   setoxm1
  75
  76         .global stanhd
  77 stanhd:
  78 |--TANH(X) = X FOR DENORMALIZED X
  79
  80         bra             t_extdnrm
  81
  82         .global stanh
  83 stanh:
  84         fmovex          (%a0),%fp0      | ...LOAD INPUT
  85
  86         fmovex          %fp0,X(%a6)
  87         movel           (%a0),%d0
  88         movew           4(%a0),%d0
  89         movel           %d0,X(%a6)
  90         andl            #0x7FFFFFFF,%d0
  91         cmp2l           BOUNDS1(%pc),%d0        | ...2**(-40) < |X| < (5/2)LOG2 ?
  92         bcss            TANHBORS
  93
  94 |--THIS IS THE USUAL CASE
  95 |--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
  96
  97         movel           X(%a6),%d0
  98         movel           %d0,SGN(%a6)
  99         andl            #0x7FFF0000,%d0
 100         addl            #0x00010000,%d0 | ...EXPONENT OF 2|X|
 101         movel           %d0,X(%a6)
 102         andl            #0x80000000,SGN(%a6)
 103         fmovex          X(%a6),%fp0             | ...FP0 IS Y = 2|X|
 104
 105         movel           %d1,-(%a7)
 106         clrl            %d1
 107         fmovemx %fp0-%fp0,(%a0)
 108         bsr             setoxm1         | ...FP0 IS Z = EXPM1(Y)
 109         movel           (%a7)+,%d1
 110
 111         fmovex          %fp0,%fp1
 112         fadds           #0x40000000,%fp1        | ...Z+2
 113         movel           SGN(%a6),%d0
 114         fmovex          %fp1,V(%a6)
 115         eorl            %d0,V(%a6)
 116
 117         fmovel          %d1,%FPCR               |restore users exceptions
 118         fdivx           V(%a6),%fp0
 119         bra             t_frcinx
 120
 121 TANHBORS:
 122         cmpl            #0x3FFF8000,%d0
 123         blt             TANHSM
 124
 125         cmpl            #0x40048AA1,%d0
 126         bgt             TANHHUGE
 127
 128 |-- (5/2) LOG2 < |X| < 50 LOG2,
 129 |--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
 130 |--TANH(X) = SGN -      SGN*2/[EXP(Y)+1].
 131
 132         movel           X(%a6),%d0
 133         movel           %d0,SGN(%a6)
 134         andl            #0x7FFF0000,%d0
 135         addl            #0x00010000,%d0 | ...EXPO OF 2|X|
 136         movel           %d0,X(%a6)              | ...Y = 2|X|
 137         andl            #0x80000000,SGN(%a6)
 138         movel           SGN(%a6),%d0
 139         fmovex          X(%a6),%fp0             | ...Y = 2|X|
 140
 141         movel           %d1,-(%a7)
 142         clrl            %d1
 143         fmovemx %fp0-%fp0,(%a0)
 144         bsr             setox           | ...FP0 IS EXP(Y)
 145         movel           (%a7)+,%d1
 146         movel           SGN(%a6),%d0
 147         fadds           #0x3F800000,%fp0        | ...EXP(Y)+1
 148
 149         eorl            #0xC0000000,%d0 | ...-SIGN(X)*2
 150         fmoves          %d0,%fp1                | ...-SIGN(X)*2 IN SGL FMT
 151         fdivx           %fp0,%fp1               | ...-SIGN(X)2 / [EXP(Y)+1 ]
 152
 153         movel           SGN(%a6),%d0
 154         orl             #0x3F800000,%d0 | ...SGN
 155         fmoves          %d0,%fp0                | ...SGN IN SGL FMT
 156
 157         fmovel          %d1,%FPCR               |restore users exceptions
 158         faddx           %fp1,%fp0
 159
 160         bra             t_frcinx
 161
 162 TANHSM:
 163         movew           #0x0000,XDCARE(%a6)
 164
 165         fmovel          %d1,%FPCR               |restore users exceptions
 166         fmovex          X(%a6),%fp0             |last inst - possible exception set
 167
 168         bra             t_frcinx
 169
 170 TANHHUGE:
 171 |---RETURN SGN(X) - SGN(X)EPS
 172         movel           X(%a6),%d0
 173         andl            #0x80000000,%d0
 174         orl             #0x3F800000,%d0
 175         fmoves          %d0,%fp0
 176         andl            #0x80000000,%d0
 177         eorl            #0x80800000,%d0 | ...-SIGN(X)*EPS
 178
 179         fmovel          %d1,%FPCR               |restore users exceptions
 180         fadds           %d0,%fp0
 181
 182         bra             t_frcinx
 183
 184         |end