sasin.S
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- |
- | sasin.sa 3.3 12/19/90
- |
- | Description: The entry point sAsin computes the inverse sine of
- | an input argument; sAsind does the same except for denormalized
- | input.
- |
- | Input: Double-extended number X in location pointed to
- | by address register a0.
- |
- | Output: The value arcsin(X) returned in floating-point register Fp0.
- |
- | Accuracy and Monotonicity: The returned result is within 3 ulps in
- | 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
- | result is subsequently rounded to double precision. The
- | result is provably monotonic in double precision.
- |
- | Speed: The program sASIN takes approximately 310 cycles.
- |
- | Algorithm:
- |
- | ASIN
- | 1. If |X| >= 1, go to 3.
- |
- | 2. (|X| < 1) Calculate asin(X) by
- | z := sqrt( [1-X][1+X] )
- | asin(X) = atan( x / z ).
- | Exit.
- |
- | 3. If |X| > 1, go to 5.
- |
- | 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
- |
- | 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
- | Exit.
- |
- | Copyright (C) Motorola, Inc. 1990
- | All Rights Reserved
- |
- | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
- | The copyright notice above does not evidence any
- | actual or intended publication of such source code.
- |SASIN idnt 2,1 | Motorola 040 Floating Point Software Package
- |section 8
- PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
- |xref t_operr
- |xref t_frcinx
- |xref t_extdnrm
- |xref satan
- .global sasind
- sasind:
- |--ASIN(X) = X FOR DENORMALIZED X
- bra t_extdnrm
- .global sasin
- sasin:
- fmovex (%a0),%fp0 | ...LOAD INPUT
- movel (%a0),%d0
- movew 4(%a0),%d0
- andil #0x7FFFFFFF,%d0
- cmpil #0x3FFF8000,%d0
- bges asinbig
- |--THIS IS THE USUAL CASE, |X| < 1
- |--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
- fmoves #0x3F800000,%fp1
- fsubx %fp0,%fp1 | ...1-X
- fmovemx %fp2-%fp2,-(%a7)
- fmoves #0x3F800000,%fp2
- faddx %fp0,%fp2 | ...1+X
- fmulx %fp2,%fp1 | ...(1+X)(1-X)
- fmovemx (%a7)+,%fp2-%fp2
- fsqrtx %fp1 | ...SQRT([1-X][1+X])
- fdivx %fp1,%fp0 | ...X/SQRT([1-X][1+X])
- fmovemx %fp0-%fp0,(%a0)
- bsr satan
- bra t_frcinx
- asinbig:
- fabsx %fp0 | ...|X|
- fcmps #0x3F800000,%fp0
- fbgt t_operr |cause an operr exception
- |--|X| = 1, ASIN(X) = +- PI/2.
- fmovex PIBY2,%fp0
- movel (%a0),%d0
- andil #0x80000000,%d0 | ...SIGN BIT OF X
- oril #0x3F800000,%d0 | ...+-1 IN SGL FORMAT
- movel %d0,-(%sp) | ...push SIGN(X) IN SGL-FMT
- fmovel %d1,%FPCR
- fmuls (%sp)+,%fp0
- bra t_frcinx
- |end