/* *  poly_tan.c * * Compute the tan of a FPU_REG, using a polynomial approximation. * * * Copyright (C) 1992,1993,1994 *                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163, *                       Australia.  E-mail   billm@vaxc.cc.monash.edu.au * All rights reserved. * * This copyright notice covers the redistribution and use of the * FPU emulator developed by W. Metzenthen. It covers only its use * in the 386BSD, FreeBSD and NetBSD operating systems. Any other * use is not permitted under this copyright. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright *    notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must include information specifying *    that source code for the emulator is freely available and include *    either: *      a) an offer to provide the source code for a nominal distribution *         fee, or *      b) list at least two alternative methods whereby the source *         can be obtained, e.g. a publically accessible bulletin board *         and an anonymous ftp site from which the software can be *         downloaded. * 3. All advertising materials specifically mentioning features or use of *    this emulator must acknowledge that it was developed by W. Metzenthen. * 4. The name of W. Metzenthen may not be used to endorse or promote *    products derived from this software without specific prior written *    permission. * * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY * AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL * W. METZENTHEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. * * * The purpose of this copyright, based upon the Berkeley copyright, is to * ensure that the covered software remains freely available to everyone. * * The software (with necessary differences) is also available, but under * the terms of the GNU copyleft, for the Linux operating system and for * the djgpp ms-dos extender. * * W. Metzenthen   June 1994. * * * $FreeBSD: src/sys/gnu/i386/fpemul/poly_tan.c,v 1.6.2.1 1999/09/05 08:09:48 peter Exp $ * */#include <gnu/i386/fpemul/exception.h>#include <gnu/i386/fpemul/reg_constant.h>#include <gnu/i386/fpemul/fpu_emu.h>#include <gnu/i386/fpemul/control_w.h>#define	HIPOWERop	3	/* odd poly, positive terms */static unsigned short oddplterms[HIPOWERop][4] ={	{0x846a, 0x42d1, 0xb544, 0x921f},	{0x6fb2, 0x0215, 0x95c0, 0x099c},	{0xfce6, 0x0cc8, 0x1c9a, 0x0000}};#define	HIPOWERon	2	/* odd poly, negative terms */static unsigned short oddnegterms[HIPOWERon][4] ={	{0x6906, 0xe205, 0x25c8, 0x8838},	{0x1dd7, 0x3fe3, 0x944e, 0x002c}};#define	HIPOWERep	2	/* even poly, positive terms */static unsigned short evenplterms[HIPOWERep][4] ={	{0xdb8f, 0x3761, 0x1432, 0x2acf},	{0x16eb, 0x13c1, 0x3099, 0x0003}};#define	HIPOWERen	2	/* even poly, negative terms */static unsigned short evennegterms[HIPOWERen][4] ={	{0x3a7c, 0xe4c5, 0x7f87, 0x2945},	{0x572b, 0x664c, 0xc543, 0x018c}};/*--- poly_tan() ------------------------------------------------------------+ |                                                                           | +---------------------------------------------------------------------------*/voidpoly_tan(FPU_REG * arg, FPU_REG * y_reg){	char    invert = 0;	short   exponent;	FPU_REG odd_poly, even_poly, pos_poly, neg_poly;	FPU_REG argSq;	long long arg_signif, argSqSq;	exponent = arg->exp - EXP_BIAS;	if (arg->tag == TW_Zero) {		/* Return 0.0 */		reg_move(&CONST_Z, y_reg);		return;	}	if (exponent >= -1) {		/* argument is in the range  [0.5 .. 1.0] */		if (exponent >= 0) {#ifdef PARANOID			if ((exponent == 0) &&			    (arg->sigl == 0) && (arg->sigh == 0x80000000))#endif				/* PARANOID */			{				arith_overflow(y_reg);				return;			}#ifdef PARANOID			EXCEPTION(EX_INTERNAL | 0x104);	/* There must be a logic							 * error */			return;#endif				/* PARANOID */		}		/* The argument is in the range  [0.5 .. 1.0) */		/* Convert the argument to a number in the range  (0.0 .. 0.5] */		*((long long *) (&arg->sigl)) = -*((long long *) (&arg->sigl));		normalize(arg);	/* Needed later */		exponent = arg->exp - EXP_BIAS;		invert = 1;	}#ifdef PARANOID	if (arg->sign != 0) {	/* Can't hack a number < 0.0 */		arith_invalid(y_reg);		return;	}			/* Need a positive number */#endif				/* PARANOID */	*(long long *) &arg_signif = *(long long *) &(arg->sigl);	if (exponent < -1) {		/* shift the argument right by the required places */		if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)			arg_signif++;	/* round up */	}	mul64(&arg_signif, &arg_signif, (long long *) (&argSq.sigl));	mul64((long long *) (&argSq.sigl), (long long *) (&argSq.sigl), &argSqSq);	/* will be a valid positive nr with expon = 0 */	*(short *) &(pos_poly.sign) = 0;	pos_poly.exp = EXP_BIAS;	/* Do the basic fixed point polynomial evaluation */	polynomial((u_int *) &pos_poly.sigl, (unsigned *) &argSqSq, oddplterms, HIPOWERop - 1);	/* will be a valid positive nr with expon = 0 */	*(short *) &(neg_poly.sign) = 0;	neg_poly.exp = EXP_BIAS;	/* Do the basic fixed point polynomial evaluation */	polynomial((u_int *) &neg_poly.sigl, (unsigned *) &argSqSq, oddnegterms, HIPOWERon - 1);	mul64((long long *) (&argSq.sigl), (long long *) (&neg_poly.sigl),	    (long long *) (&neg_poly.sigl));	/* Subtract the mantissas */	*((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl));	/* Convert to 64 bit signed-compatible */	pos_poly.exp -= 1;	reg_move(&pos_poly, &odd_poly);	normalize(&odd_poly);	reg_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION);	reg_u_add(&odd_poly, arg, &odd_poly, FULL_PRECISION);	/* This is just the odd								 * polynomial */	/* will be a valid positive nr with expon = 0 */	*(short *) &(pos_poly.sign) = 0;	pos_poly.exp = EXP_BIAS;	/* Do the basic fixed point polynomial evaluation */	polynomial((u_int *) &pos_poly.sigl, (unsigned *) &argSqSq, evenplterms, HIPOWERep - 1);	mul64((long long *) (&argSq.sigl),	    (long long *) (&pos_poly.sigl), (long long *) (&pos_poly.sigl));	/* will be a valid positive nr with expon = 0 */	*(short *) &(neg_poly.sign) = 0;	neg_poly.exp = EXP_BIAS;	/* Do the basic fixed point polynomial evaluation */	polynomial((u_int *) &neg_poly.sigl, (unsigned *) &argSqSq, evennegterms, HIPOWERen - 1);	/* Subtract the mantissas */	*((long long *) (&neg_poly.sigl)) -= *((long long *) (&pos_poly.sigl));	/* and multiply by argSq */	/* Convert argSq to a valid reg number */	*(short *) &(argSq.sign) = 0;	argSq.exp = EXP_BIAS - 1;	normalize(&argSq);	/* Convert to 64 bit signed-compatible */	neg_poly.exp -= 1;	reg_move(&neg_poly, &even_poly);	normalize(&even_poly);	reg_mul(&even_poly, &argSq, &even_poly, FULL_PRECISION);	reg_add(&even_poly, &argSq, &even_poly, FULL_PRECISION);	reg_sub(&CONST_1, &even_poly, &even_poly, FULL_PRECISION);	/* This is just the even									 * polynomial */	/* Now ready to copy the results */	if (invert) {		reg_div(&even_poly, &odd_poly, y_reg, FULL_PRECISION);	} else {		reg_div(&odd_poly, &even_poly, y_reg, FULL_PRECISION);	}}