ssinh.S
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Linux/Unix编程

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Unix_Linux

  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. | Copyright (C) Motorola, Inc. 1990
  49. | All Rights Reserved
  50. |
  51. | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 
  52. | The copyright notice above does not evidence any  
  53. | actual or intended publication of such source code.
  54. |SSINH idnt 2,1 | Motorola 040 Floating Point Software Package
  55. |section 8
  56. T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
  57. T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
  58. |xref t_frcinx
  59. |xref t_ovfl
  60. |xref t_extdnrm
  61. |xref setox
  62. |xref setoxm1
  63. .global ssinhd
  64. ssinhd:
  65. |--SINH(X) = X FOR DENORMALIZED X
  66. bra t_extdnrm
  67. .global ssinh
  68. ssinh:
  69. fmovex (%a0),%fp0 | ...LOAD INPUT
  70. movel (%a0),%d0
  71. movew 4(%a0),%d0
  72. movel %d0,%a1 | save a copy of original (compacted) operand
  73. andl #0x7FFFFFFF,%d0
  74. cmpl #0x400CB167,%d0
  75. bgts SINHBIG
  76. |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
  77. |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
  78. fabsx %fp0 | ...Y = |X|
  79. moveml %a1/%d1,-(%sp)
  80. fmovemx %fp0-%fp0,(%a0)
  81. clrl %d1
  82. bsr setoxm1   | ...FP0 IS Z = EXPM1(Y)
  83. fmovel #0,%fpcr
  84. moveml (%sp)+,%a1/%d1
  85. fmovex %fp0,%fp1
  86. fadds #0x3F800000,%fp1 | ...1+Z
  87. fmovex %fp0,-(%sp)
  88. fdivx %fp1,%fp0 | ...Z/(1+Z)
  89. movel %a1,%d0
  90. andl #0x80000000,%d0
  91. orl #0x3F000000,%d0
  92. faddx (%sp)+,%fp0
  93. movel %d0,-(%sp)
  94. fmovel %d1,%fpcr
  95. fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set
  96. bra t_frcinx
  97. SINHBIG:
  98. cmpl #0x400CB2B3,%d0
  99. bgt t_ovfl
  100. fabsx %fp0
  101. fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD)
  102. movel #0,-(%sp)
  103. movel #0x80000000,-(%sp)
  104. movel %a1,%d0
  105. andl #0x80000000,%d0
  106. orl #0x7FFB0000,%d0
  107. movel %d0,-(%sp) | ...EXTENDED FMT
  108. fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE
  109. movel %d1,-(%sp)
  110. clrl %d1
  111. fmovemx %fp0-%fp0,(%a0)
  112. bsr setox
  113. fmovel (%sp)+,%fpcr
  114. fmulx (%sp)+,%fp0 |possible exception
  115. bra t_frcinx
  116. |end