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|
//
// $Id$
//
// scosh.sa 3.1 12/10/90
//
// The entry point sCosh computes the hyperbolic cosine of
// an input argument; sCoshd does the same except for denormalized
// input.
//
// Input: Double-extended number X in location pointed to
// by address register a0.
//
// Output: The value cosh(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 sCOSH takes approximately 250 cycles.
//
// Algorithm:
//
// COSH
// 1. If |X| > 16380 log2, go to 3.
//
// 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae
// y = |X|, z = exp(Y), and
// cosh(X) = (1/2)*( z + 1/z ).
// Exit.
//
// 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.
//
// 4. (16380 log2 < |X| <= 16480 log2)
// cosh(X) = sign(X) * exp(|X|)/2.
// However, invoking exp(|X|) may cause premature overflow.
// Thus, we calculate sinh(X) as follows:
// Y := |X|
// Fact := 2**(16380)
// Y' := Y - 16381 log2
// cosh(X) := Fact * exp(Y').
// Exit.
//
// 5. (|X| > 16480 log2) sinh(X) must overflow. Return
// Huge*Huge to generate overflow and an infinity with
// the appropriate sign. Huge is the largest finite number in
// extended format. 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// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
//SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
|xref t_ovfl
|xref t_frcinx
|xref setox
T1: .long 0x40C62D38,0xD3D64634 // ... 16381 LOG2 LEAD
T2: .long 0x3D6F90AE,0xB1E75CC7 // ... 16381 LOG2 TRAIL
TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000
.global scoshd
scoshd:
//--COSH(X) = 1 FOR DENORMALIZED X
fmoves #0x3F800000,%fp0
fmovel %d1,%FPCR
fadds #0x00800000,%fp0
bra t_frcinx
.global scosh
scosh:
fmovex (%a0),%fp0 // ...LOAD INPUT
movel (%a0),%d0
movew 4(%a0),%d0
andil #0x7FFFFFFF,%d0
cmpil #0x400CB167,%d0
bgts COSHBIG
//--THIS IS THE USUAL CASE, |X| < 16380 LOG2
//--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
fabsx %fp0 // ...|X|
movel %d1,-(%sp)
clrl %d1
fmovemx %fp0-%fp0,(%a0) //pass parameter to setox
bsr setox // ...FP0 IS EXP(|X|)
fmuls #0x3F000000,%fp0 // ...(1/2)EXP(|X|)
movel (%sp)+,%d1
fmoves #0x3E800000,%fp1 // ...(1/4)
fdivx %fp0,%fp1 // ...1/(2 EXP(|X|))
fmovel %d1,%FPCR
faddx %fp1,%fp0
bra t_frcinx
COSHBIG:
cmpil #0x400CB2B3,%d0
bgts COSHHUGE
fabsx %fp0
fsubd T1(%pc),%fp0 // ...(|X|-16381LOG2_LEAD)
fsubd T2(%pc),%fp0 // ...|X| - 16381 LOG2, ACCURATE
movel %d1,-(%sp)
clrl %d1
fmovemx %fp0-%fp0,(%a0)
bsr setox
fmovel (%sp)+,%fpcr
fmulx TWO16380(%pc),%fp0
bra t_frcinx
COSHHUGE:
fmovel #0,%fpsr //clr N bit if set by source
bclrb #7,(%a0) //always return positive value
fmovemx (%a0),%fp0-%fp0
bra t_ovfl
|end
|
