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   1 |
   2 |       ssinh.sa 3.1 12/10/90
   3 |
   4 |       The entry point sSinh computes the hyperbolic sine of
   5 |       an input argument; sSinhd 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 sinh(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 sSINH takes approximately 280 cycles.
  19 |
  20 |       Algorithm:
  21 |
  22 |       SINH
  23 |       1. If |X| > 16380 log2, go to 3.
  24 |
  25 |       2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
  26 |               y = |X|, sgn = sign(X), and z = expm1(Y),
  27 |               sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
  28 |          Exit.
  29 |
  30 |       3. If |X| > 16480 log2, go to 5.
  31 |
  32 |       4. (16380 log2 < |X| <= 16480 log2)
  33 |               sinh(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 |             sgn     := sign(X)
  38 |             sgnFact := sgn * 2**(16380)
  39 |             Y'      := Y - 16381 log2
  40 |             sinh(X) := sgnFact * exp(Y').
  41 |          Exit.
  42 |
  43 |       5. (|X| > 16480 log2) sinh(X) must overflow. Return
  44 |          sign(X)*Huge*Huge to generate overflow and an infinity with
  45 |          the appropriate sign. Huge is the largest finite number in
  46 |          extended format. 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 |SSINH  idnt    2,1 | Motorola 040 Floating Point Software Package
  56
  57         |section        8
  58
  59 T1:     .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
  60 T2:     .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
  61
  62         |xref   t_frcinx
  63         |xref   t_ovfl
  64         |xref   t_extdnrm
  65         |xref   setox
  66         |xref   setoxm1
  67
  68         .global ssinhd
  69 ssinhd:
  70 |--SINH(X) = X FOR DENORMALIZED X
  71
  72         bra     t_extdnrm
  73
  74         .global ssinh
  75 ssinh:
  76         fmovex  (%a0),%fp0      | ...LOAD INPUT
  77
  78         movel   (%a0),%d0
  79         movew   4(%a0),%d0
  80         movel   %d0,%a1         | save a copy of original (compacted) operand
  81         andl    #0x7FFFFFFF,%d0
  82         cmpl    #0x400CB167,%d0
  83         bgts    SINHBIG
  84
  85 |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
  86 |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
  87
  88         fabsx   %fp0            | ...Y = |X|
  89
  90         moveml  %a1/%d1,-(%sp)
  91         fmovemx %fp0-%fp0,(%a0)
  92         clrl    %d1
  93         bsr     setoxm1         | ...FP0 IS Z = EXPM1(Y)
  94         fmovel  #0,%fpcr
  95         moveml  (%sp)+,%a1/%d1
  96
  97         fmovex  %fp0,%fp1
  98         fadds   #0x3F800000,%fp1        | ...1+Z
  99         fmovex  %fp0,-(%sp)
 100         fdivx   %fp1,%fp0               | ...Z/(1+Z)
 101         movel   %a1,%d0
 102         andl    #0x80000000,%d0
 103         orl     #0x3F000000,%d0
 104         faddx   (%sp)+,%fp0
 105         movel   %d0,-(%sp)
 106
 107         fmovel  %d1,%fpcr
 108         fmuls   (%sp)+,%fp0     |last fp inst - possible exceptions set
 109
 110         bra     t_frcinx
 111
 112 SINHBIG:
 113         cmpl    #0x400CB2B3,%d0
 114         bgt     t_ovfl
 115         fabsx   %fp0
 116         fsubd   T1(%pc),%fp0    | ...(|X|-16381LOG2_LEAD)
 117         movel   #0,-(%sp)
 118         movel   #0x80000000,-(%sp)
 119         movel   %a1,%d0
 120         andl    #0x80000000,%d0
 121         orl     #0x7FFB0000,%d0
 122         movel   %d0,-(%sp)      | ...EXTENDED FMT
 123         fsubd   T2(%pc),%fp0    | ...|X| - 16381 LOG2, ACCURATE
 124
 125         movel   %d1,-(%sp)
 126         clrl    %d1
 127         fmovemx %fp0-%fp0,(%a0)
 128         bsr     setox
 129         fmovel  (%sp)+,%fpcr
 130
 131         fmulx   (%sp)+,%fp0     |possible exception
 132         bra     t_frcinx
 133
 134         |end