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

   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
  59T1:     .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
  60T2:     .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
  69ssinhd:
  70|--SINH(X) = X FOR DENORMALIZED X
  71
  72        bra     t_extdnrm
  73
  74        .global ssinh
  75ssinh:
  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
 112SINHBIG:
 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
 135