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* $OpenBSD: ssinh.sa,v 1.2 1996/05/29 21:05:42 niklas Exp $
* $NetBSD: ssinh.sa,v 1.3 1994/10/26 07:50:05 cgd Exp $
* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
* M68000 Hi-Performance Microprocessor Division
* M68040 Software Package
*
* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
* All rights reserved.
*
* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
* To the maximum extent permitted by applicable law,
* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
* PARTICULAR PURPOSE and any warranty against infringement with
* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
* and any accompanying written materials.
*
* To the maximum extent permitted by applicable law,
* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
* SOFTWARE. Motorola assumes no responsibility for the maintenance
* and support of the SOFTWARE.
*
* You are hereby granted a copyright license to use, modify, and
* distribute the SOFTWARE so long as this entire notice is retained
* without alteration in any modified and/or redistributed versions,
* and that such modified versions are clearly identified as such.
* No licenses are granted by implication, estoppel or otherwise
* under any patents or trademarks of Motorola, Inc.
*
* 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.
*
SSINH IDNT 2,1 Motorola 040 Floating Point Software Package
section 8
T1 DC.L $40C62D38,$D3D64634 ... 16381 LOG2 LEAD
T2 DC.L $3D6F90AE,$B1E75CC7 ... 16381 LOG2 TRAIL
xref t_frcinx
xref t_ovfl
xref t_extdnrm
xref setox
xref setoxm1
xdef ssinhd
ssinhd:
*--SINH(X) = X FOR DENORMALIZED X
bra t_extdnrm
xdef ssinh
ssinh:
FMOVE.x (a0),FP0 ...LOAD INPUT
move.l (a0),d0
move.w 4(a0),d0
move.l d0,a1 save a copy of original (compacted) operand
AND.L #$7FFFFFFF,D0
CMP.L #$400CB167,D0
BGT.B SINHBIG
*--THIS IS THE USUAL CASE, |X| < 16380 LOG2
*--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
FABS.X FP0 ...Y = |X|
movem.l a1/d1,-(sp)
fmovem.x fp0,(a0)
clr.l d1
bsr setoxm1 ...FP0 IS Z = EXPM1(Y)
fmove.l #0,fpcr
movem.l (sp)+,a1/d1
FMOVE.X FP0,FP1
FADD.S #:3F800000,FP1 ...1+Z
FMOVE.X FP0,-(sp)
FDIV.X FP1,FP0 ...Z/(1+Z)
MOVE.L a1,d0
AND.L #$80000000,D0
OR.L #$3F000000,D0
FADD.X (sp)+,FP0
MOVE.L D0,-(sp)
fmove.l d1,fpcr
fmul.s (sp)+,fp0 ;last fp inst - possible exceptions set
bra t_frcinx
SINHBIG:
cmp.l #$400CB2B3,D0
bgt t_ovfl
FABS.X FP0
FSUB.D T1(pc),FP0 ...(|X|-16381LOG2_LEAD)
clr.l -(sp)
move.l #$80000000,-(sp)
move.l a1,d0
AND.L #$80000000,D0
OR.L #$7FFB0000,D0
MOVE.L D0,-(sp) ...EXTENDED FMT
FSUB.D T2(pc),FP0 ...|X| - 16381 LOG2, ACCURATE
move.l d1,-(sp)
clr.l d1
fmovem.x fp0,(a0)
bsr setox
fmove.l (sp)+,fpcr
fmul.x (sp)+,fp0 ;possible exception
bra t_frcinx
end
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