1994-10-26 10:48:18 +03:00
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* $NetBSD: ssinh.sa,v 1.3 1994/10/26 07:50:05 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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* 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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SSINH IDNT 2,1 Motorola 040 Floating Point Software Package
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section 8
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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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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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xdef 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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xdef ssinh
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ssinh:
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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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move.l d0,a1 save a copy of original (compacted) operand
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AND.L #$7FFFFFFF,D0
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CMP.L #$400CB167,D0
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BGT.B 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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FABS.X FP0 ...Y = |X|
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movem.l a1/d1,-(sp)
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fmovem.x fp0,(a0)
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clr.l d1
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bsr setoxm1 ...FP0 IS Z = EXPM1(Y)
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fmove.l #0,fpcr
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movem.l (sp)+,a1/d1
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FMOVE.X FP0,FP1
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FADD.S #:3F800000,FP1 ...1+Z
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FMOVE.X FP0,-(sp)
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FDIV.X FP1,FP0 ...Z/(1+Z)
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MOVE.L a1,d0
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AND.L #$80000000,D0
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OR.L #$3F000000,D0
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FADD.X (sp)+,FP0
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MOVE.L D0,-(sp)
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fmove.l d1,fpcr
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fmul.s (sp)+,fp0 ;last fp inst - possible exceptions set
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bra t_frcinx
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SINHBIG:
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cmp.l #$400CB2B3,D0
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bgt t_ovfl
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FABS.X FP0
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FSUB.D T1(pc),FP0 ...(|X|-16381LOG2_LEAD)
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1994-07-05 21:56:52 +04:00
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clr.l -(sp)
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1994-07-05 21:50:24 +04:00
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move.l #$80000000,-(sp)
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move.l a1,d0
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AND.L #$80000000,D0
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OR.L #$7FFB0000,D0
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MOVE.L D0,-(sp) ...EXTENDED FMT
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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 (sp)+,fp0 ;possible exception
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bra t_frcinx
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end
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