196 lines
6.5 KiB
C
196 lines
6.5 KiB
C
/*
|
|
* poly_sin.c
|
|
*
|
|
* Computation of an approximation of the sin function by a polynomial
|
|
*
|
|
*
|
|
* 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.
|
|
*
|
|
*
|
|
* $Id: poly_sin.c,v 1.8 1997/02/22 09:29:18 peter Exp $
|
|
*
|
|
*/
|
|
|
|
#ifdef DEBUG
|
|
#include <sys/types.h>
|
|
#include <sys/systm.h> /* for printf() in EXCEPTION() */
|
|
#endif
|
|
|
|
#include <gnu/i386/fpemul/exception.h>
|
|
#include <gnu/i386/fpemul/reg_constant.h>
|
|
#include <gnu/i386/fpemul/control_w.h>
|
|
|
|
|
|
#define HIPOWER 5
|
|
static unsigned short lterms[HIPOWER][4] =
|
|
{
|
|
{0x846a, 0x42d1, 0xb544, 0x921f},
|
|
{0xe110, 0x75aa, 0xbc67, 0x1466},
|
|
{0x503d, 0xa43f, 0x83c1, 0x000a},
|
|
{0x8f9d, 0x7a19, 0x00f4, 0x0000},
|
|
{0xda03, 0x06aa, 0x0000, 0x0000},
|
|
};
|
|
|
|
static unsigned short negterms[HIPOWER][4] =
|
|
{
|
|
{0x95ed, 0x2df2, 0xe731, 0xa55d},
|
|
{0xd159, 0xe62b, 0xd2cc, 0x0132},
|
|
{0x6342, 0xe9fb, 0x3c60, 0x0000},
|
|
{0x6256, 0xdf5a, 0x0002, 0x0000},
|
|
{0xf279, 0x000b, 0x0000, 0x0000},
|
|
};
|
|
|
|
|
|
/*--- poly_sine() -----------------------------------------------------------+
|
|
| |
|
|
+---------------------------------------------------------------------------*/
|
|
void
|
|
poly_sine(FPU_REG * arg, FPU_REG * result)
|
|
{
|
|
short exponent;
|
|
FPU_REG Xx, Xx2, Xx4, accum, negaccum;
|
|
|
|
|
|
exponent = arg->exp - EXP_BIAS;
|
|
|
|
if (arg->tag == TW_Zero) {
|
|
/* Return 0.0 */
|
|
reg_move(&CONST_Z, result);
|
|
return;
|
|
}
|
|
#ifdef PARANOID
|
|
if (arg->sign != 0) { /* Can't hack a number < 0.0 */
|
|
EXCEPTION(EX_Invalid);
|
|
reg_move(&CONST_QNaN, result);
|
|
return;
|
|
}
|
|
if (exponent >= 0) { /* Can't hack a number > 1.0 */
|
|
if ((exponent == 0) && (arg->sigl == 0) && (arg->sigh == 0x80000000)) {
|
|
reg_move(&CONST_1, result);
|
|
return;
|
|
}
|
|
EXCEPTION(EX_Invalid);
|
|
reg_move(&CONST_QNaN, result);
|
|
return;
|
|
}
|
|
#endif /* PARANOID */
|
|
|
|
Xx.sigl = arg->sigl;
|
|
Xx.sigh = arg->sigh;
|
|
if (exponent < -1) {
|
|
/* shift the argument right by the required places */
|
|
if (shrx(&(Xx.sigl), -1 - exponent) >= (unsigned)0x80000000)
|
|
(*((long long *) (&(Xx.sigl))))++; /* round up */
|
|
}
|
|
mul64((long long *) &(Xx.sigl), (long long *) &(Xx.sigl),
|
|
(long long *) &(Xx2.sigl));
|
|
mul64((long long *) &(Xx2.sigl), (long long *) &(Xx2.sigl),
|
|
(long long *) &(Xx4.sigl));
|
|
|
|
/* will be a valid positive nr with expon = 0 */
|
|
*(short *) &(accum.sign) = 0;
|
|
accum.exp = 0;
|
|
|
|
/* Do the basic fixed point polynomial evaluation */
|
|
polynomial((u_int *) &(accum.sigl), (u_int *)&(Xx4.sigl), lterms, HIPOWER - 1);
|
|
|
|
/* will be a valid positive nr with expon = 0 */
|
|
*(short *) &(negaccum.sign) = 0;
|
|
negaccum.exp = 0;
|
|
|
|
/* Do the basic fixed point polynomial evaluation */
|
|
polynomial((u_int *) &(negaccum.sigl), (u_int *)&(Xx4.sigl), negterms, HIPOWER - 1);
|
|
mul64((long long *) &(Xx2.sigl), (long long *) &(negaccum.sigl),
|
|
(long long *) &(negaccum.sigl));
|
|
|
|
/* Subtract the mantissas */
|
|
*((long long *) (&(accum.sigl))) -= *((long long *) (&(negaccum.sigl)));
|
|
|
|
/* Convert to 64 bit signed-compatible */
|
|
accum.exp = EXP_BIAS - 1 + accum.exp;
|
|
|
|
*(short *) &(result->sign) = *(short *) &(accum.sign);
|
|
result->exp = accum.exp;
|
|
result->sigl = accum.sigl;
|
|
result->sigh = accum.sigh;
|
|
|
|
normalize(result);
|
|
|
|
reg_mul(result, arg, result, FULL_PRECISION);
|
|
reg_u_add(result, arg, result, FULL_PRECISION);
|
|
|
|
/* A small overflow may be possible... but an illegal result. */
|
|
if (result->exp >= EXP_BIAS) {
|
|
if ((result->exp > EXP_BIAS) /* Larger or equal 2.0 */
|
|
||(result->sigl > 1) /* Larger than 1.0+msb */
|
|
||(result->sigh != 0x80000000) /* Much > 1.0 */
|
|
) {
|
|
#ifdef DEBUGGING
|
|
RE_ENTRANT_CHECK_OFF
|
|
printk("\nEXP=%d, MS=%08x, LS=%08x\n", result->exp,
|
|
result->sigh, result->sigl);
|
|
RE_ENTRANT_CHECK_ON
|
|
#endif /* DEBUGGING */
|
|
EXCEPTION(EX_INTERNAL | 0x103);
|
|
}
|
|
#ifdef DEBUGGING
|
|
RE_ENTRANT_CHECK_OFF
|
|
printk("\n***CORRECTING ILLEGAL RESULT*** in poly_sin() computation\n");
|
|
printk("EXP=%d, MS=%08x, LS=%08x\n", result->exp,
|
|
result->sigh, result->sigl);
|
|
RE_ENTRANT_CHECK_ON
|
|
#endif /* DEBUGGING */
|
|
|
|
result->sigl = 0; /* Truncate the result to 1.00 */
|
|
}
|
|
}
|