sacos.S 2.8 KB

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  1. |
  2. | sacos.sa 3.3 12/19/90
  3. |
  4. | Description: The entry point sAcos computes the inverse cosine of
  5. | an input argument; sAcosd 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 arccos(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 sCOS takes approximately 310 cycles.
  19. |
  20. | Algorithm:
  21. |
  22. | ACOS
  23. | 1. If |X| >= 1, go to 3.
  24. |
  25. | 2. (|X| < 1) Calculate acos(X) by
  26. | z := (1-X) / (1+X)
  27. | acos(X) = 2 * atan( sqrt(z) ).
  28. | Exit.
  29. |
  30. | 3. If |X| > 1, go to 5.
  31. |
  32. | 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
  33. |
  34. | 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
  35. | Exit.
  36. |
  37. | Copyright (C) Motorola, Inc. 1990
  38. | All Rights Reserved
  39. |
  40. | For details on the license for this file, please see the
  41. | file, README, in this same directory.
  42. |SACOS idnt 2,1 | Motorola 040 Floating Point Software Package
  43. |section 8
  44. PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
  45. PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
  46. |xref t_operr
  47. |xref t_frcinx
  48. |xref satan
  49. .global sacosd
  50. sacosd:
  51. |--ACOS(X) = PI/2 FOR DENORMALIZED X
  52. fmovel %d1,%fpcr | ...load user's rounding mode/precision
  53. fmovex PIBY2,%fp0
  54. bra t_frcinx
  55. .global sacos
  56. sacos:
  57. fmovex (%a0),%fp0 | ...LOAD INPUT
  58. movel (%a0),%d0 | ...pack exponent with upper 16 fraction
  59. movew 4(%a0),%d0
  60. andil #0x7FFFFFFF,%d0
  61. cmpil #0x3FFF8000,%d0
  62. bges ACOSBIG
  63. |--THIS IS THE USUAL CASE, |X| < 1
  64. |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
  65. fmoves #0x3F800000,%fp1
  66. faddx %fp0,%fp1 | ...1+X
  67. fnegx %fp0 | ... -X
  68. fadds #0x3F800000,%fp0 | ...1-X
  69. fdivx %fp1,%fp0 | ...(1-X)/(1+X)
  70. fsqrtx %fp0 | ...SQRT((1-X)/(1+X))
  71. fmovemx %fp0-%fp0,(%a0) | ...overwrite input
  72. movel %d1,-(%sp) |save original users fpcr
  73. clrl %d1
  74. bsr satan | ...ATAN(SQRT([1-X]/[1+X]))
  75. fmovel (%sp)+,%fpcr |restore users exceptions
  76. faddx %fp0,%fp0 | ...2 * ATAN( STUFF )
  77. bra t_frcinx
  78. ACOSBIG:
  79. fabsx %fp0
  80. fcmps #0x3F800000,%fp0
  81. fbgt t_operr |cause an operr exception
  82. |--|X| = 1, ACOS(X) = 0 OR PI
  83. movel (%a0),%d0 | ...pack exponent with upper 16 fraction
  84. movew 4(%a0),%d0
  85. cmpl #0,%d0 |D0 has original exponent+fraction
  86. bgts ACOSP1
  87. |--X = -1
  88. |Returns PI and inexact exception
  89. fmovex PI,%fp0
  90. fmovel %d1,%FPCR
  91. fadds #0x00800000,%fp0 |cause an inexact exception to be put
  92. | ;into the 040 - will not trap until next
  93. | ;fp inst.
  94. bra t_frcinx
  95. ACOSP1:
  96. fmovel %d1,%FPCR
  97. fmoves #0x00000000,%fp0
  98. rts |Facos ; of +1 is exact
  99. |end