228 lines
7.6 KiB
C
228 lines
7.6 KiB
C
/*
|
|
* 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);
|
|
}
|
|
|
|
}
|