|
  |	ssinh.sa 3.1 12/10/90
  |
  |       The entry point sSinh computes the hyperbolic sine of
  |       an input argument; sSinhd does the same except for denormalized
  |       input.
  |
  |       Input: Double-extended number X in location pointed to
  |		by address register a0.
  |
  |       Output: The value sinh(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 sSINH takes approximately 280 cycles.
  |
  |       Algorithm:
  |
  |       SINH
  |       1. If |X| > 16380 log2, go to 3.
  |
  |       2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
  |               y = |X|, sgn = sign(X), and z = expm1(Y),
  |               sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
  |          Exit.
  |
  |       3. If |X| > 16480 log2, go to 5.
  |
  |       4. (16380 log2 < |X| <= 16480 log2)
  |               sinh(X) = sign(X) * exp(|X|)/2.
  |          However, invoking exp(|X|) may cause premature overflow.
  |          Thus, we calculate sinh(X) as follows:
  |             Y       := |X|
  |             sgn     := sign(X)
  |             sgnFact := sgn * 2**(16380)
  |             Y'      := Y - 16381 log2
  |             sinh(X) := sgnFact * exp(Y').
  |          Exit.
  |
  |       5. (|X| > 16480 log2) sinh(X) must overflow. Return
  |          sign(X)*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
  |

  |       For details on the license for this file, please see the
  |       file, README, in this same directory.

  
  |SSINH	idnt	2,1 | Motorola 040 Floating Point Software Package
  
  	|section	8
  
  T1:	.long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD
  T2:	.long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL
  
  	|xref	t_frcinx
  	|xref	t_ovfl
  	|xref	t_extdnrm
  	|xref	setox
  	|xref	setoxm1
  
  	.global	ssinhd
  ssinhd:
  |--SINH(X) = X FOR DENORMALIZED X
  
  	bra	t_extdnrm
  
  	.global	ssinh
  ssinh:
  	fmovex	(%a0),%fp0	| ...LOAD INPUT
  
  	movel	(%a0),%d0
  	movew	4(%a0),%d0
  	movel	%d0,%a1		| save a copy of original (compacted) operand
  	andl	#0x7FFFFFFF,%d0
  	cmpl	#0x400CB167,%d0
  	bgts	SINHBIG
  
  |--THIS IS THE USUAL CASE, |X| < 16380 LOG2
  |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
  
  	fabsx	%fp0		| ...Y = |X|
  
  	moveml	%a1/%d1,-(%sp)
  	fmovemx %fp0-%fp0,(%a0)
  	clrl	%d1
  	bsr	setoxm1		| ...FP0 IS Z = EXPM1(Y)
  	fmovel	#0,%fpcr
  	moveml	(%sp)+,%a1/%d1
  
  	fmovex	%fp0,%fp1
  	fadds	#0x3F800000,%fp1	| ...1+Z
  	fmovex	%fp0,-(%sp)
  	fdivx	%fp1,%fp0		| ...Z/(1+Z)
  	movel	%a1,%d0
  	andl	#0x80000000,%d0
  	orl	#0x3F000000,%d0
  	faddx	(%sp)+,%fp0
  	movel	%d0,-(%sp)
  
  	fmovel	%d1,%fpcr
  	fmuls	(%sp)+,%fp0	|last fp inst - possible exceptions set
  
  	bra	t_frcinx
  
  SINHBIG:
  	cmpl	#0x400CB2B3,%d0
  	bgt	t_ovfl
  	fabsx	%fp0
  	fsubd	T1(%pc),%fp0	| ...(|X|-16381LOG2_LEAD)
  	movel	#0,-(%sp)
  	movel	#0x80000000,-(%sp)
  	movel	%a1,%d0
  	andl	#0x80000000,%d0
  	orl	#0x7FFB0000,%d0
  	movel	%d0,-(%sp)	| ...EXTENDED FMT
  	fsubd	T2(%pc),%fp0	| ...|X| - 16381 LOG2, ACCURATE
  
  	movel	%d1,-(%sp)
  	clrl	%d1
  	fmovemx %fp0-%fp0,(%a0)
  	bsr	setox
  	fmovel	(%sp)+,%fpcr
  
  	fmulx	(%sp)+,%fp0	|possible exception
  	bra	t_frcinx
  
  	|end