scosh.s

RTEMS (Real-Time Executive for Multiprocessor Systems) is a free open source real-time operating sys

//
//      $Id: scosh.S,v 1.1 1998/12/14 23:15:26 joel Exp $
//
//	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//	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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