1994-10-26 10:48:18 +03:00
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* $NetBSD: scosh.sa,v 1.2 1994/10/26 07:49:39 cgd Exp $
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1994-07-05 21:50:24 +04:00
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* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
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* M68000 Hi-Performance Microprocessor Division
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* M68040 Software Package
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*
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* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
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* All rights reserved.
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*
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* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
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* To the maximum extent permitted by applicable law,
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* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
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* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
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* PARTICULAR PURPOSE and any warranty against infringement with
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* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
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* and any accompanying written materials.
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*
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* To the maximum extent permitted by applicable law,
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* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
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* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
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* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
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* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
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* SOFTWARE. Motorola assumes no responsibility for the maintenance
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* and support of the SOFTWARE.
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*
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* You are hereby granted a copyright license to use, modify, and
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* distribute the SOFTWARE so long as this entire notice is retained
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* without alteration in any modified and/or redistributed versions,
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* and that such modified versions are clearly identified as such.
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* No licenses are granted by implication, estoppel or otherwise
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* under any patents or trademarks of Motorola, Inc.
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*
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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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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 DC.L $40C62D38,$D3D64634 ... 16381 LOG2 LEAD
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T2 DC.L $3D6F90AE,$B1E75CC7 ... 16381 LOG2 TRAIL
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TWO16380 DC.L $7FFB0000,$80000000,$00000000,$00000000
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xdef scoshd
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scoshd:
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*--COSH(X) = 1 FOR DENORMALIZED X
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FMOVE.S #:3F800000,FP0
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FMOVE.L d1,FPCR
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FADD.S #:00800000,FP0
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bra t_frcinx
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xdef scosh
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scosh:
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FMOVE.X (a0),FP0 ...LOAD INPUT
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move.l (a0),d0
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move.w 4(a0),d0
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ANDI.L #$7FFFFFFF,d0
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CMPI.L #$400CB167,d0
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BGT.B 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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FABS.X FP0 ...|X|
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move.l d1,-(sp)
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clr.l d1
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fmovem.x fp0,(a0) ;pass parameter to setox
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bsr setox ...FP0 IS EXP(|X|)
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FMUL.S #:3F000000,FP0 ...(1/2)EXP(|X|)
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move.l (sp)+,d1
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FMOVE.S #:3E800000,FP1 ...(1/4)
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FDIV.X FP0,FP1 ...1/(2 EXP(|X|))
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FMOVE.L d1,FPCR
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FADD.X fp1,FP0
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bra t_frcinx
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COSHBIG:
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CMPI.L #$400CB2B3,d0
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BGT.B COSHHUGE
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FABS.X FP0
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FSUB.D T1(pc),FP0 ...(|X|-16381LOG2_LEAD)
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FSUB.D T2(pc),FP0 ...|X| - 16381 LOG2, ACCURATE
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move.l d1,-(sp)
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clr.l d1
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fmovem.x fp0,(a0)
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bsr setox
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fmove.l (sp)+,fpcr
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FMUL.X TWO16380(pc),FP0
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bra t_frcinx
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COSHHUGE:
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fmove.l #0,fpsr ;clr N bit if set by source
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bclr.b #7,(a0) ;always return positive value
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fmovem.x (a0),fp0
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bra t_ovfl
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end
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