^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 1) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 2) | sacos.sa 3.3 12/19/90
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 3) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 4) | Description: The entry point sAcos computes the inverse cosine of
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 5) | an input argument; sAcosd does the same except for denormalized
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 6) | input.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 7) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 8) | Input: Double-extended number X in location pointed to
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 9) | by address register a0.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 10) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 11) | Output: The value arccos(X) returned in floating-point register Fp0.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 12) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 13) | Accuracy and Monotonicity: The returned result is within 3 ulps in
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 14) | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 15) | result is subsequently rounded to double precision. The
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 16) | result is provably monotonic in double precision.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 17) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 18) | Speed: The program sCOS takes approximately 310 cycles.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 19) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 20) | Algorithm:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 21) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 22) | ACOS
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 23) | 1. If |X| >= 1, go to 3.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 24) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 25) | 2. (|X| < 1) Calculate acos(X) by
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 26) | z := (1-X) / (1+X)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 27) | acos(X) = 2 * atan( sqrt(z) ).
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 28) | Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 29) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 30) | 3. If |X| > 1, go to 5.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 31) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 32) | 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 33) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 34) | 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 35) | Exit.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 36) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 37)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 38) | Copyright (C) Motorola, Inc. 1990
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 39) | All Rights Reserved
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 40) |
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 41) | For details on the license for this file, please see the
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 42) | file, README, in this same directory.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 43)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 44) |SACOS idnt 2,1 | Motorola 040 Floating Point Software Package
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 45)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 46) |section 8
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 47)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 48) PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 49) PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 50)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 51) |xref t_operr
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 52) |xref t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 53) |xref satan
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 54)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 55) .global sacosd
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 56) sacosd:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 57) |--ACOS(X) = PI/2 FOR DENORMALIZED X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 58) fmovel %d1,%fpcr | ...load user's rounding mode/precision
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 59) fmovex PIBY2,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 60) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 61)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 62) .global sacos
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 63) sacos:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 64) fmovex (%a0),%fp0 | ...LOAD INPUT
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 65)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 66) movel (%a0),%d0 | ...pack exponent with upper 16 fraction
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 67) movew 4(%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 68) andil #0x7FFFFFFF,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 69) cmpil #0x3FFF8000,%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 70) bges ACOSBIG
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 71)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 72) |--THIS IS THE USUAL CASE, |X| < 1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 73) |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 74)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 75) fmoves #0x3F800000,%fp1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 76) faddx %fp0,%fp1 | ...1+X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 77) fnegx %fp0 | ... -X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 78) fadds #0x3F800000,%fp0 | ...1-X
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 79) fdivx %fp1,%fp0 | ...(1-X)/(1+X)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 80) fsqrtx %fp0 | ...SQRT((1-X)/(1+X))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 81) fmovemx %fp0-%fp0,(%a0) | ...overwrite input
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 82) movel %d1,-(%sp) |save original users fpcr
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 83) clrl %d1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 84) bsr satan | ...ATAN(SQRT([1-X]/[1+X]))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 85) fmovel (%sp)+,%fpcr |restore users exceptions
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 86) faddx %fp0,%fp0 | ...2 * ATAN( STUFF )
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 87) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 88)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 89) ACOSBIG:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 90) fabsx %fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 91) fcmps #0x3F800000,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 92) fbgt t_operr |cause an operr exception
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 93)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 94) |--|X| = 1, ACOS(X) = 0 OR PI
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 95) movel (%a0),%d0 | ...pack exponent with upper 16 fraction
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 96) movew 4(%a0),%d0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 97) cmpl #0,%d0 |D0 has original exponent+fraction
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 98) bgts ACOSP1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 99)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 100) |--X = -1
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 101) |Returns PI and inexact exception
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 102) fmovex PI,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 103) fmovel %d1,%FPCR
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 104) fadds #0x00800000,%fp0 |cause an inexact exception to be put
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 105) | ;into the 040 - will not trap until next
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 106) | ;fp inst.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 107) bra t_frcinx
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 108)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 109) ACOSP1:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 110) fmovel %d1,%FPCR
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 111) fmoves #0x00000000,%fp0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 112) rts |Facos ; of +1 is exact
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 113)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 114) |end
Orange Pi5 kernel
Deprecated Linux kernel 5.10.110 for OrangePi 5/5B/5+ boards
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