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/*
* 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.
*
*
* $FreeBSD$
*
*/
#include <gnu/i386/fpemul/reg_constant.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() ------------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void
poly_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);
}
}
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