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

   1|
   2|       sasin.sa 3.3 12/19/90
   3|
   4|       Description: The entry point sAsin computes the inverse sine of
   5|               an input argument; sAsind 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 arcsin(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 sASIN takes approximately 310 cycles.
  19|
  20|       Algorithm:
  21|
  22|       ASIN
  23|       1. If |X| >= 1, go to 3.
  24|
  25|       2. (|X| < 1) Calculate asin(X) by
  26|               z := sqrt( [1-X][1+X] )
  27|               asin(X) = atan( x / z ).
  28|               Exit.
  29|
  30|       3. If |X| > 1, go to 5.
  31|
  32|       4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
  33|
  34|       5. (|X| > 1) Generate an invalid operation by 0 * infinity.
  35|               Exit.
  36|
  37
  38|               Copyright (C) Motorola, Inc. 1990
  39|                       All Rights Reserved
  40|
  41|       For details on the license for this file, please see the
  42|       file, README, in this same directory.
  43
  44|SASIN  idnt    2,1 | Motorola 040 Floating Point Software Package
  45
  46        |section        8
  47
  48PIBY2:  .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
  49
  50        |xref   t_operr
  51        |xref   t_frcinx
  52        |xref   t_extdnrm
  53        |xref   satan
  54
  55        .global sasind
  56sasind:
  57|--ASIN(X) = X FOR DENORMALIZED X
  58
  59        bra             t_extdnrm
  60
  61        .global sasin
  62sasin:
  63        fmovex          (%a0),%fp0      | ...LOAD INPUT
  64
  65        movel           (%a0),%d0
  66        movew           4(%a0),%d0
  67        andil           #0x7FFFFFFF,%d0
  68        cmpil           #0x3FFF8000,%d0
  69        bges            asinbig
  70
  71|--THIS IS THE USUAL CASE, |X| < 1
  72|--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
  73
  74        fmoves          #0x3F800000,%fp1
  75        fsubx           %fp0,%fp1               | ...1-X
  76        fmovemx %fp2-%fp2,-(%a7)
  77        fmoves          #0x3F800000,%fp2
  78        faddx           %fp0,%fp2               | ...1+X
  79        fmulx           %fp2,%fp1               | ...(1+X)(1-X)
  80        fmovemx (%a7)+,%fp2-%fp2
  81        fsqrtx          %fp1            | ...SQRT([1-X][1+X])
  82        fdivx           %fp1,%fp0               | ...X/SQRT([1-X][1+X])
  83        fmovemx %fp0-%fp0,(%a0)
  84        bsr             satan
  85        bra             t_frcinx
  86
  87asinbig:
  88        fabsx           %fp0     | ...|X|
  89        fcmps           #0x3F800000,%fp0
  90        fbgt            t_operr         |cause an operr exception
  91
  92|--|X| = 1, ASIN(X) = +- PI/2.
  93
  94        fmovex          PIBY2,%fp0
  95        movel           (%a0),%d0
  96        andil           #0x80000000,%d0 | ...SIGN BIT OF X
  97        oril            #0x3F800000,%d0 | ...+-1 IN SGL FORMAT
  98        movel           %d0,-(%sp)      | ...push SIGN(X) IN SGL-FMT
  99        fmovel          %d1,%FPCR
 100        fmuls           (%sp)+,%fp0
 101        bra             t_frcinx
 102
 103        |end
 104