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* $OpenBSD: stanh.sa,v 1.2 1996/05/29 21:05:43 niklas Exp $
* $NetBSD: stanh.sa,v 1.3 1994/10/26 07:50:12 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.
*
* stanh.sa 3.1 12/10/90
*
* The entry point sTanh computes the hyperbolic tangent of
* an input argument; sTanhd does the same except for denormalized
* input.
*
* Input: Double-extended number X in location pointed to
* by address register a0.
*
* Output: The value tanh(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 stanh takes approximately 270 cycles.
*
* Algorithm:
*
* TANH
* 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
*
* 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
* sgn := sign(X), y := 2|X|, z := expm1(Y), and
* tanh(X) = sgn*( z/(2+z) ).
* Exit.
*
* 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
* go to 7.
*
* 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
*
* 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
* sgn := sign(X), y := 2|X|, z := exp(Y),
* tanh(X) = sgn - [ sgn*2/(1+z) ].
* Exit.
*
* 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
* calculate Tanh(X) by
* sgn := sign(X), Tiny := 2**(-126),
* tanh(X) := sgn - sgn*Tiny.
* Exit.
*
* 7. (|X| < 2**(-40)). Tanh(X) = X. Exit.
*
STANH IDNT 2,1 Motorola 040 Floating Point Software Package
section 8
include fpsp.h
X equ FP_SCR5
XDCARE equ X+2
XFRAC equ X+4
SGN equ L_SCR3
V equ FP_SCR6
BOUNDS1 DC.L $3FD78000,$3FFFDDCE ... 2^(-40), (5/2)LOG2
xref t_frcinx
xref t_extdnrm
xref setox
xref setoxm1
xdef stanhd
stanhd:
*--TANH(X) = X FOR DENORMALIZED X
bra t_extdnrm
xdef stanh
stanh:
FMOVE.X (a0),FP0 ...LOAD INPUT
FMOVE.X FP0,X(a6)
move.l (a0),d0
move.w 4(a0),d0
MOVE.L D0,X(a6)
AND.L #$7FFFFFFF,D0
CMP2.L BOUNDS1(pc),D0 ...2**(-40) < |X| < (5/2)LOG2 ?
BCS.B TANHBORS
*--THIS IS THE USUAL CASE
*--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
MOVE.L X(a6),D0
MOVE.L D0,SGN(a6)
AND.L #$7FFF0000,D0
ADD.L #$00010000,D0 ...EXPONENT OF 2|X|
MOVE.L D0,X(a6)
AND.L #$80000000,SGN(a6)
FMOVE.X X(a6),FP0 ...FP0 IS Y = 2|X|
move.l d1,-(a7)
clr.l d1
fmovem.x fp0,(a0)
bsr setoxm1 ...FP0 IS Z = EXPM1(Y)
move.l (a7)+,d1
FMOVE.X FP0,FP1
FADD.S #:40000000,FP1 ...Z+2
MOVE.L SGN(a6),D0
FMOVE.X FP1,V(a6)
EOR.L D0,V(a6)
FMOVE.L d1,FPCR ;restore users exceptions
FDIV.X V(a6),FP0
bra t_frcinx
TANHBORS:
CMP.L #$3FFF8000,D0
BLT.W TANHSM
CMP.L #$40048AA1,D0
BGT.W TANHHUGE
*-- (5/2) LOG2 < |X| < 50 LOG2,
*--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
*--TANH(X) = SGN - SGN*2/[EXP(Y)+1].
MOVE.L X(a6),D0
MOVE.L D0,SGN(a6)
AND.L #$7FFF0000,D0
ADD.L #$00010000,D0 ...EXPO OF 2|X|
MOVE.L D0,X(a6) ...Y = 2|X|
AND.L #$80000000,SGN(a6)
MOVE.L SGN(a6),D0
FMOVE.X X(a6),FP0 ...Y = 2|X|
move.l d1,-(a7)
clr.l d1
fmovem.x fp0,(a0)
bsr setox ...FP0 IS EXP(Y)
move.l (a7)+,d1
move.l SGN(a6),d0
FADD.S #:3F800000,FP0 ...EXP(Y)+1
EOR.L #$C0000000,D0 ...-SIGN(X)*2
FMOVE.S d0,FP1 ...-SIGN(X)*2 IN SGL FMT
FDIV.X FP0,FP1 ...-SIGN(X)2 / [EXP(Y)+1 ]
MOVE.L SGN(a6),D0
OR.L #$3F800000,D0 ...SGN
FMOVE.S d0,FP0 ...SGN IN SGL FMT
FMOVE.L d1,FPCR ;restore users exceptions
FADD.X fp1,FP0
bra t_frcinx
TANHSM:
CLR.W XDCARE(a6)
FMOVE.L d1,FPCR ;restore users exceptions
FMOVE.X X(a6),FP0 ;last inst - possible exception set
bra t_frcinx
TANHHUGE:
*---RETURN SGN(X) - SGN(X)EPS
MOVE.L X(a6),D0
AND.L #$80000000,D0
OR.L #$3F800000,D0
FMOVE.S d0,FP0
AND.L #$80000000,D0
EOR.L #$80800000,D0 ...-SIGN(X)*EPS
FMOVE.L d1,FPCR ;restore users exceptions
FADD.S d0,FP0
bra t_frcinx
end
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