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   1 |
   2 |       scosh.sa 3.1 12/10/90
   3 |
   4 |       The entry point sCosh computes the hyperbolic cosine of
   5 |       an input argument; sCoshd 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 cosh(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 sCOSH takes approximately 250 cycles.
  19 |
  20 |       Algorithm:
  21 |
  22 |       COSH
  23 |       1. If |X| > 16380 log2, go to 3.
  24 |
  25 |       2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
  26 |               y = |X|, z = exp(Y), and
  27 |               cosh(X) = (1/2)*( z + 1/z ).
  28 |               Exit.
  29 |
  30 |       3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
  31 |
  32 |       4. (16380 log2 < |X| <= 16480 log2)
  33 |               cosh(X) = sign(X) * exp(|X|)/2.
  34 |               However, invoking exp(|X|) may cause premature overflow.
  35 |               Thus, we calculate sinh(X) as follows:
  36 |               Y       := |X|
  37 |               Fact    :=      2**(16380)
  38 |               Y'      := Y - 16381 log2
  39 |               cosh(X) := Fact * exp(Y').
  40 |               Exit.
  41 |
  42 |       5. (|X| > 16480 log2) sinh(X) must overflow. Return
  43 |               Huge*Huge to generate overflow and an infinity with
  44 |               the appropriate sign. Huge is the largest finite number in
  45 |               extended format. Exit.
  46 |
  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 |SCOSH  idnt    2,1 | Motorola 040 Floating Point Software Package
  56
  57         |section        8
  58
  59         |xref   t_ovfl
  60         |xref   t_frcinx
  61         |xref   setox
  62
  63 T1:     .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
  64 T2:     .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
  65
  66 TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
  67
  68         .global scoshd
  69 scoshd:
  70 |--COSH(X) = 1 FOR DENORMALIZED X
  71
  72         fmoves          #0x3F800000,%fp0
  73
  74         fmovel          %d1,%FPCR
  75         fadds           #0x00800000,%fp0
  76         bra             t_frcinx
  77
  78         .global scosh
  79 scosh:
  80         fmovex          (%a0),%fp0      | ...LOAD INPUT
  81
  82         movel           (%a0),%d0
  83         movew           4(%a0),%d0
  84         andil           #0x7FFFFFFF,%d0
  85         cmpil           #0x400CB167,%d0
  86         bgts            COSHBIG
  87
  88 |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
  89 |--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
  90
  91         fabsx           %fp0            | ...|X|
  92
  93         movel           %d1,-(%sp)
  94         clrl            %d1
  95         fmovemx %fp0-%fp0,(%a0) |pass parameter to setox
  96         bsr             setox           | ...FP0 IS EXP(|X|)
  97         fmuls           #0x3F000000,%fp0        | ...(1/2)EXP(|X|)
  98         movel           (%sp)+,%d1
  99
 100         fmoves          #0x3E800000,%fp1        | ...(1/4)
 101         fdivx           %fp0,%fp1               | ...1/(2 EXP(|X|))
 102
 103         fmovel          %d1,%FPCR
 104         faddx           %fp1,%fp0
 105
 106         bra             t_frcinx
 107
 108 COSHBIG:
 109         cmpil           #0x400CB2B3,%d0
 110         bgts            COSHHUGE
 111
 112         fabsx           %fp0
 113         fsubd           T1(%pc),%fp0            | ...(|X|-16381LOG2_LEAD)
 114         fsubd           T2(%pc),%fp0            | ...|X| - 16381 LOG2, ACCURATE
 115
 116         movel           %d1,-(%sp)
 117         clrl            %d1
 118         fmovemx %fp0-%fp0,(%a0)
 119         bsr             setox
 120         fmovel          (%sp)+,%fpcr
 121
 122         fmulx           TWO16380(%pc),%fp0
 123         bra             t_frcinx
 124
 125 COSHHUGE:
 126         fmovel          #0,%fpsr                |clr N bit if set by source
 127         bclrb           #7,(%a0)                |always return positive value
 128         fmovemx (%a0),%fp0-%fp0
 129         bra             t_ovfl
 130
 131         |end