|
| 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
|
| For details on the license for this file, please see the
| file, README, in this same directory.
|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
