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awilliam
GitHub Repository: awilliam/linux-vfio
 Path: blob/master/arch/m68k/fpsp040/scosh.S
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|	scosh.sa 3.1 12/10/90

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|

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|	The entry point sCosh computes the hyperbolic cosine of

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|	an input argument; sCoshd does the same except for denormalized

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|	input.

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|

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|	Input: Double-extended number X in location pointed to

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|		by address register a0.

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|

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|	Output: The value cosh(X) returned in floating-point register Fp0.

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|

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|	Accuracy and Monotonicity: The returned result is within 3 ulps in

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|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the

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|		result is subsequently rounded to double precision. The

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|		result is provably monotonic in double precision.

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|

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|	Speed: The program sCOSH takes approximately 250 cycles.

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|

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|	Algorithm:

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|

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|	COSH

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|	1. If |X| > 16380 log2, go to 3.

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|

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|	2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae

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|		y = |X|, z = exp(Y), and

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|		cosh(X) = (1/2)*( z + 1/z ).

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|		Exit.

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|

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|	3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.

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|

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|	4. (16380 log2 < |X| <= 16480 log2)

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|		cosh(X) = sign(X) * exp(|X|)/2.

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|		However, invoking exp(|X|) may cause premature overflow.

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|		Thus, we calculate sinh(X) as follows:

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|		Y	:= |X|

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|		Fact	:=	2**(16380)

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|		Y'	:= Y - 16381 log2

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|		cosh(X) := Fact * exp(Y').

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|		Exit.

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|

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|	5. (|X| > 16480 log2) sinh(X) must overflow. Return

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|		Huge*Huge to generate overflow and an infinity with

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|		the appropriate sign. Huge is the largest finite number in

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|		extended format. Exit.

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|

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|

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|		Copyright (C) Motorola, Inc. 1990

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|			All Rights Reserved

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|

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|       For details on the license for this file, please see the

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|       file, README, in this same directory.

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|SCOSH	idnt	2,1 | Motorola 040 Floating Point Software Package

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	|section	8

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	|xref	t_ovfl

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	|xref	t_frcinx

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	|xref	setox

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T1:	.long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD

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T2:	.long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL

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TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000

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	.global	scoshd

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scoshd:

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|--COSH(X) = 1 FOR DENORMALIZED X

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	fmoves		#0x3F800000,%fp0

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	fmovel		%d1,%FPCR

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	fadds		#0x00800000,%fp0

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	bra		t_frcinx

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	.global	scosh

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scosh:

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	fmovex		(%a0),%fp0	| ...LOAD INPUT

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	movel		(%a0),%d0

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	movew		4(%a0),%d0

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	andil		#0x7FFFFFFF,%d0

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	cmpil		#0x400CB167,%d0

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	bgts		COSHBIG

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|--THIS IS THE USUAL CASE, |X| < 16380 LOG2

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|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )

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	fabsx		%fp0		| ...|X|

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	movel		%d1,-(%sp)

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	clrl		%d1

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	fmovemx	%fp0-%fp0,(%a0)	|pass parameter to setox

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	bsr		setox		| ...FP0 IS EXP(|X|)

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	fmuls		#0x3F000000,%fp0	| ...(1/2)EXP(|X|)

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	movel		(%sp)+,%d1

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	fmoves		#0x3E800000,%fp1	| ...(1/4)

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	fdivx		%fp0,%fp1		| ...1/(2 EXP(|X|))

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	fmovel		%d1,%FPCR

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	faddx		%fp1,%fp0

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	bra		t_frcinx

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COSHBIG:

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	cmpil		#0x400CB2B3,%d0

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	bgts		COSHHUGE

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	fabsx		%fp0

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	fsubd		T1(%pc),%fp0		| ...(|X|-16381LOG2_LEAD)

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	fsubd		T2(%pc),%fp0		| ...|X| - 16381 LOG2, ACCURATE

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	movel		%d1,-(%sp)

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	clrl		%d1

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	fmovemx	%fp0-%fp0,(%a0)

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	bsr		setox

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	fmovel		(%sp)+,%fpcr

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	fmulx		TWO16380(%pc),%fp0

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	bra		t_frcinx

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COSHHUGE:

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	fmovel		#0,%fpsr		|clr N bit if set by source

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	bclrb		#7,(%a0)		|always return positive value

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	fmovemx	(%a0),%fp0-%fp0

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	bra		t_ovfl

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	|end

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