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//
// $Id$
//
// satanh.sa 3.3 12/19/90
//
// The entry point satanh computes the inverse
// hyperbolic tangent of
// an input argument; satanhd does the same except for denormalized
// input.
//
// Input: Double-extended number X in location pointed to
// by address register a0.
//
// Output: The value arctanh(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 satanh takes approximately 270 cycles.
//
// Algorithm:
//
// ATANH
// 1. If |X| >= 1, go to 3.
//
// 2. (|X| < 1) Calculate atanh(X) by
// sgn := sign(X)
// y := |X|
// z := 2y/(1-y)
// atanh(X) := sgn * (1/2) * logp1(z)
// Exit.
//
// 3. If |X| > 1, go to 5.
//
// 4. (|X| = 1) Generate infinity with an appropriate sign and
// divide-by-zero by
// sgn := sign(X)
// atan(X) := sgn / (+0).
// 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// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
//satanh idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
|xref t_dz
|xref t_operr
|xref t_frcinx
|xref t_extdnrm
|xref slognp1
.global satanhd
satanhd:
//--ATANH(X) = X FOR DENORMALIZED X
bra t_extdnrm
.global satanh
satanh:
movel (%a0),%d0
movew 4(%a0),%d0
andil #0x7FFFFFFF,%d0
cmpil #0x3FFF8000,%d0
bges ATANHBIG
//--THIS IS THE USUAL CASE, |X| < 1
//--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
fabsx (%a0),%fp0 // ...Y = |X|
fmovex %fp0,%fp1
fnegx %fp1 // ...-Y
faddx %fp0,%fp0 // ...2Y
fadds #0x3F800000,%fp1 // ...1-Y
fdivx %fp1,%fp0 // ...2Y/(1-Y)
movel (%a0),%d0
andil #0x80000000,%d0
oril #0x3F000000,%d0 // ...SIGN(X)*HALF
movel %d0,-(%sp)
fmovemx %fp0-%fp0,(%a0) // ...overwrite input
movel %d1,-(%sp)
clrl %d1
bsr slognp1 // ...LOG1P(Z)
fmovel (%sp)+,%fpcr
fmuls (%sp)+,%fp0
bra t_frcinx
ATANHBIG:
fabsx (%a0),%fp0 // ...|X|
fcmps #0x3F800000,%fp0
fbgt t_operr
bra t_dz
|end
|
