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| sasin.sa 3.3 12/19/90
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| Description: The entry point sAsin computes the inverse sine of
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| an input argument; sAsind does the same except for denormalized
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| input.
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| Input: Double-extended number X in location pointed to
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| by address register a0.
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| Output: The value arcsin(X) returned in floating-point register Fp0.
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| Accuracy and Monotonicity: The returned result is within 3 ulps in
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| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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| result is subsequently rounded to double precision. The
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| result is provably monotonic in double precision.
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| Speed: The program sASIN takes approximately 310 cycles.
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| Algorithm:
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| ASIN
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| 1. If |X| >= 1, go to 3.
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| 2. (|X| < 1) Calculate asin(X) by
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| z := sqrt( [1-X][1+X] )
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| asin(X) = atan( x / z ).
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| Exit.
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| 3. If |X| > 1, go to 5.
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| 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
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| 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
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| Exit.
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| Copyright (C) Motorola, Inc. 1990
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| All Rights Reserved
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| For details on the license for this file, please see the
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| file, README, in this same directory.
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|SASIN idnt 2,1 | Motorola 040 Floating Point Software Package
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|section 8
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PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
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|xref t_operr
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|xref t_frcinx
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|xref t_extdnrm
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|xref satan
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.global sasind
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sasind:
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|--ASIN(X) = X FOR DENORMALIZED X
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bra t_extdnrm
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.global sasin
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sasin:
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fmovex (%a0),%fp0 | ...LOAD INPUT
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movel (%a0),%d0
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movew 4(%a0),%d0
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andil #0x7FFFFFFF,%d0
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cmpil #0x3FFF8000,%d0
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bges asinbig
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|--THIS IS THE USUAL CASE, |X| < 1
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|--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
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fmoves #0x3F800000,%fp1
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fsubx %fp0,%fp1 | ...1-X
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fmovemx %fp2-%fp2,-(%a7)
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fmoves #0x3F800000,%fp2
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faddx %fp0,%fp2 | ...1+X
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fmulx %fp2,%fp1 | ...(1+X)(1-X)
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fmovemx (%a7)+,%fp2-%fp2
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fsqrtx %fp1 | ...SQRT([1-X][1+X])
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fdivx %fp1,%fp0 | ...X/SQRT([1-X][1+X])
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fmovemx %fp0-%fp0,(%a0)
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bsr satan
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bra t_frcinx
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asinbig:
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fabsx %fp0 | ...|X|
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fcmps #0x3F800000,%fp0
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fbgt t_operr |cause an operr exception
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|--|X| = 1, ASIN(X) = +- PI/2.
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fmovex PIBY2,%fp0
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movel (%a0),%d0
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andil #0x80000000,%d0 | ...SIGN BIT OF X
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oril #0x3F800000,%d0 | ...+-1 IN SGL FORMAT
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movel %d0,-(%sp) | ...push SIGN(X) IN SGL-FMT
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fmovel %d1,%FPCR
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fmuls (%sp)+,%fp0
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bra t_frcinx
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|end
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