/* l_stanh.s - Motorola 68040 FP hyperbolic tangent routines (LIB) *//* Copyright 1991-1993 Wind River Systems, Inc. */	.data	.globl	_copyright_wind_river	.long	_copyright_wind_river/*modification history--------------------01e,21jul93,kdl  added .text (SPR #2372).01d,23aug92,jcf  changed bxxx to jxx.01c,26may92,rrr  the tree shuffle01b,10jan92,kdl  added modification history; general cleanup.01a,15aug91,kdl  original version, from Motorola FPSP v2.0.*//*DESCRIPTION	stanhsa 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 __l_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.		Copyright (C) Motorola, Inc. 1990			All Rights Reserved	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA	The copyright notice above does not evidence any	actual or intended publication of such source code.STANH	idnt	2,1 Motorola 040 Floating Point Software Package	section	8NOMANUAL*/#include "fpsp040L.h"#define	X		FP_SCR5#define	XDCARE		X+2#define	XFRAC		X+4#define	SGN		L_SCR3#define	V		FP_SCR6BOUNDS1:	.long 0x3FD78000,0x3FFFDDCE |... 2^(-40), (5/2)LOG2|	xref	__l_t_frcinx|	xref	__l_t_extdnrm|	xref	__l_setox|	xref	__l_setoxm1	.text	.globl	__l_stanhd__l_stanhd:|--TANH(X) = X FOR DENORMALIZED X	jra 		__l_t_extdnrm	.globl	__l_stanh__l_stanh:	fmovex		a0@,fp0	|...lOAD INPUT	fmovex		fp0,a6@(X)	movel		a0@,d0	movew		a0@(4),d0	movel		d0,a6@(X)	andl		#0x7FFFFFFF,d0	cmp2l		pc@(BOUNDS1),d0		|...2**(-40) < |X| < (5/2)LOG2 ?	jcs 		TANHBORS|--THIS IS THE USUAL CASE|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).	movel		a6@(X),d0	movel		d0,a6@(SGN)	andl		#0x7FFF0000,d0	addl		#0x00010000,d0		|...EXPONENT OF 2|X|	movel		d0,a6@(X)	andl		#0x80000000,a6@(SGN)	fmovex		a6@(X),fp0		|...FP0 IS Y = 2|X|	movel		d1,a7@-	clrl		d1	fmovemx	fp0-fp0,a0@	bsrl		__l_setoxm1	 	|...FP0 IS Z = EXPM1(Y)	movel		a7@+,d1	fmovex		fp0,fp1	.long 0xf23c44a2,0x40000000		/* fadds  &0x40000000,fp1 */	movel		a6@(SGN),d0	fmovex		fp1,a6@(V)	eorl		d0,a6@(V)	fmovel		d1,fpcr			| restore users exceptions	fdivx		a6@(V),fp0	jra 		__l_t_frcinxTANHBORS:	cmpl		#0x3FFF8000,d0	jlt 		TANHSM	cmpl		#0x40048AA1,d0	jgt 		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].	movel		a6@(X),d0	movel		d0,a6@(SGN)	andl		#0x7FFF0000,d0	addl		#0x00010000,d0		|...EXPO OF 2|X|	movel		d0,a6@(X)		|...Y = 2|X|	andl		#0x80000000,a6@(SGN)	movel		a6@(SGN),d0	fmovex		a6@(X),fp0		|...Y = 2|X|	movel		d1,a7@-	clrl		d1	fmovemx	fp0-fp0,a0@	bsrl		__l_setox		|...FP0 IS EXP(Y)	movel		a7@+,d1	movel		a6@(SGN),d0	.long 0xf23c4422,0x3f800000	/*	fadds	&0x3F800000,fp0 */	eorl		#0xC0000000,d0		|...-SIGN(X)*2	fmoves		d0,fp1			|...-SIGN(X)*2 IN SGL FMT	fdivx		fp0,fp1	 		|...-SIGN(X)2 / [EXP(Y)+1 ]	movel		a6@(SGN),d0	orl		#0x3F800000,d0		|...SGN	fmoves		d0,fp0			|...SGN IN SGL FMT	fmovel		d1,fpcr			| restore users exceptions	faddx		fp1,fp0	jra 		__l_t_frcinxTANHSM:	movew		#0x0000,a6@(XDCARE)	fmovel		d1,fpcr			| restore users exceptions	fmovex		a6@(X),fp0		| last inst - possible exception set	jra 		__l_t_frcinxTANHHUGE:|---RETURN SGN(X) - SGN(X)EPS	movel		a6@(X),d0	andl		#0x80000000,d0	orl		#0x3F800000,d0	fmoves		d0,fp0	andl		#0x80000000,d0	eorl		#0x80800000,d0		|...-SIGN(X)*EPS	fmovel		d1,fpcr			| restore users exceptions	fadds		d0,fp0	jra 		__l_t_frcinx|	end