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//
// $Id$
//
// 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// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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
|
