1994-10-26 10:48:18 +03:00
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* $NetBSD: satanh.sa,v 1.2 1994/10/26 07:49:33 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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* satanh.sa 3.3 12/19/90
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*
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* The entry point satanh computes the inverse
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* hyperbolic tangent of
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* an input argument; satanhd 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 arctanh(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 satanh takes approximately 270 cycles.
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*
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* Algorithm:
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*
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* ATANH
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* 1. If |X| >= 1, go to 3.
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*
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* 2. (|X| < 1) Calculate atanh(X) by
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* sgn := sign(X)
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* y := |X|
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* z := 2y/(1-y)
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* atanh(X) := sgn * (1/2) * logp1(z)
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* Exit.
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*
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* 3. If |X| > 1, go to 5.
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*
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* 4. (|X| = 1) Generate infinity with an appropriate sign and
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* divide-by-zero by
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* sgn := sign(X)
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* atan(X) := sgn / (+0).
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* Exit.
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*
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* 5. (|X| > 1) Generate an invalid operation by 0 * infinity.
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* Exit.
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*
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satanh IDNT 2,1 Motorola 040 Floating Point Software Package
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section 8
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xref t_dz
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xref t_operr
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xref t_frcinx
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xref t_extdnrm
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xref slognp1
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xdef satanhd
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satanhd:
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*--ATANH(X) = X FOR DENORMALIZED X
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bra t_extdnrm
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xdef satanh
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satanh:
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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 #$3FFF8000,D0
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BGE.B ATANHBIG
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*--THIS IS THE USUAL CASE, |X| < 1
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*--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
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FABS.X (a0),FP0 ...Y = |X|
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FMOVE.X FP0,FP1
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FNEG.X FP1 ...-Y
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FADD.X FP0,FP0 ...2Y
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FADD.S #:3F800000,FP1 ...1-Y
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FDIV.X FP1,FP0 ...2Y/(1-Y)
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move.l (a0),d0
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ANDI.L #$80000000,D0
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ORI.L #$3F000000,D0 ...SIGN(X)*HALF
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move.l d0,-(sp)
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fmovem.x fp0,(a0) ...overwrite input
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move.l d1,-(sp)
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clr.l d1
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bsr slognp1 ...LOG1P(Z)
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fmove.l (sp)+,fpcr
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FMUL.S (sp)+,FP0
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bra t_frcinx
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ATANHBIG:
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FABS.X (a0),FP0 ...|X|
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FCMP.S #:3F800000,FP0
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fbgt t_operr
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bra t_dz
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end
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