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|
|
| sacos.sa 3.3 12/19/90
|
| Description: The entry point sAcos computes the inverse cosine of
| an input argument; sAcosd does the same except for denormalized
| input.
|
| Input: Double-extended number X in location pointed to
| by address register a0.
|
| Output: The value arccos(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 sCOS takes approximately 310 cycles.
|
| Algorithm:
|
| ACOS
| 1. If |X| >= 1, go to 3.
|
| 2. (|X| < 1) Calculate acos(X) by
| z := (1-X) / (1+X)
| acos(X) = 2 * atan( sqrt(z) ).
| Exit.
|
| 3. If |X| > 1, go to 5.
|
| 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. 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| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
|SACOS idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
|xref t_operr
|xref t_frcinx
|xref satan
.global sacosd
sacosd:
|--ACOS(X) = PI/2 FOR DENORMALIZED X
fmovel %d1,%fpcr | ...load user's rounding mode/precision
fmovex PIBY2,%fp0
bra t_frcinx
.global sacos
sacos:
fmovex (%a0),%fp0 | ...LOAD INPUT
movel (%a0),%d0 | ...pack exponent with upper 16 fraction
movew 4(%a0),%d0
andil #0x7FFFFFFF,%d0
cmpil #0x3FFF8000,%d0
bges ACOSBIG
|--THIS IS THE USUAL CASE, |X| < 1
|--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
fmoves #0x3F800000,%fp1
faddx %fp0,%fp1 | ...1+X
fnegx %fp0 | ... -X
fadds #0x3F800000,%fp0 | ...1-X
fdivx %fp1,%fp0 | ...(1-X)/(1+X)
fsqrtx %fp0 | ...SQRT((1-X)/(1+X))
fmovemx %fp0-%fp0,(%a0) | ...overwrite input
movel %d1,-(%sp) |save original users fpcr
clrl %d1
bsr satan | ...ATAN(SQRT([1-X]/[1+X]))
fmovel (%sp)+,%fpcr |restore users exceptions
faddx %fp0,%fp0 | ...2 * ATAN( STUFF )
bra t_frcinx
ACOSBIG:
fabsx %fp0
fcmps #0x3F800000,%fp0
fbgt t_operr |cause an operr exception
|--|X| = 1, ACOS(X) = 0 OR PI
movel (%a0),%d0 | ...pack exponent with upper 16 fraction
movew 4(%a0),%d0
cmpl #0,%d0 |D0 has original exponent+fraction
bgts ACOSP1
|--X = -1
|Returns PI and inexact exception
fmovex PI,%fp0
fmovel %d1,%FPCR
fadds #0x00800000,%fp0 |cause an inexact exception to be put
| ;into the 040 - will not trap until next
| ;fp inst.
bra t_frcinx
ACOSP1:
fmovel %d1,%FPCR
fmoves #0x00000000,%fp0
rts |Facos ; of +1 is exact
|end
|
