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

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|

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|       The entry point sSinh computes the hyperbolic sine of

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|       an input argument; sSinhd 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 sinh(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 sSINH takes approximately 280 cycles.

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|

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|       Algorithm:

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|

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|       SINH

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

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|

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

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|               y = |X|, sgn = sign(X), and z = expm1(Y),

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

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|          Exit.

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|

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|       3. 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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|               sinh(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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|             sgn     := sign(X)

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|             sgnFact := sgn * 2**(16380)

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|             Y'      := Y - 16381 log2

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|             sinh(X) := sgnFact * 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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|          sign(X)*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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|		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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|SSINH	idnt	2,1 | Motorola 040 Floating Point Software Package

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	|section	8

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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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	|xref	t_frcinx

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	|xref	t_ovfl

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	|xref	t_extdnrm

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	|xref	setox

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	|xref	setoxm1

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	.global	ssinhd

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ssinhd:

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|--SINH(X) = X FOR DENORMALIZED X

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	bra	t_extdnrm

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	.global	ssinh

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ssinh:

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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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	movel	%d0,%a1		| save a copy of original (compacted) operand

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	andl	#0x7FFFFFFF,%d0

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	cmpl	#0x400CB167,%d0

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	bgts	SINHBIG

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

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|--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )

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	fabsx	%fp0		| ...Y = |X|

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	moveml	%a1/%d1,-(%sp)

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	fmovemx %fp0-%fp0,(%a0)

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	clrl	%d1

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	bsr	setoxm1		| ...FP0 IS Z = EXPM1(Y)

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	fmovel	#0,%fpcr

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	moveml	(%sp)+,%a1/%d1

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	fmovex	%fp0,%fp1

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	fadds	#0x3F800000,%fp1	| ...1+Z

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	fmovex	%fp0,-(%sp)

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	fdivx	%fp1,%fp0		| ...Z/(1+Z)

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	movel	%a1,%d0

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	andl	#0x80000000,%d0

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	orl	#0x3F000000,%d0

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	faddx	(%sp)+,%fp0

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	movel	%d0,-(%sp)

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	fmovel	%d1,%fpcr

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	fmuls	(%sp)+,%fp0	|last fp inst - possible exceptions set

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	bra	t_frcinx

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SINHBIG:

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	cmpl	#0x400CB2B3,%d0

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	bgt	t_ovfl

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	fabsx	%fp0

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

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	movel	#0,-(%sp)

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	movel	#0x80000000,-(%sp)

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	movel	%a1,%d0

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	andl	#0x80000000,%d0

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	orl	#0x7FFB0000,%d0

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	movel	%d0,-(%sp)	| ...EXTENDED FMT

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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	(%sp)+,%fp0	|possible exception

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	bra	t_frcinx

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	|end

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