254 lines
7.9 KiB
C
254 lines
7.9 KiB
C
/*
|
|
* p_atan.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.
|
|
*
|
|
*
|
|
* $Id$
|
|
*
|
|
*/
|
|
|
|
#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 HIPOWERon 6 /* odd poly, negative terms */
|
|
static unsigned oddnegterms[HIPOWERon][2] =
|
|
{
|
|
{0x00000000, 0x00000000}, /* for + 1.0 */
|
|
{0x763b6f3d, 0x1adc4428},
|
|
{0x20f0630b, 0x0502909d},
|
|
{0x4e825578, 0x0198ce38},
|
|
{0x22b7cb87, 0x008da6e3},
|
|
{0x9b30ca03, 0x00239c79}
|
|
};
|
|
#define HIPOWERop 6 /* odd poly, positive terms */
|
|
static unsigned oddplterms[HIPOWERop][2] =
|
|
{
|
|
{0xa6f67cb8, 0x94d910bd},
|
|
{0xa02ffab4, 0x0a43cb45},
|
|
{0x04265e6b, 0x02bf5655},
|
|
{0x0a728914, 0x00f280f7},
|
|
{0x6d640e01, 0x004d6556},
|
|
{0xf1dd2dbf, 0x000a530a}
|
|
};
|
|
|
|
|
|
static unsigned denomterm[2] =
|
|
{0xfc4bd208, 0xea2e6612};
|
|
|
|
|
|
static void poly_add_1(FPU_REG * src);
|
|
|
|
/*--- poly_atan() -----------------------------------------------------------+
|
|
| |
|
|
+---------------------------------------------------------------------------*/
|
|
void
|
|
poly_atan(FPU_REG * arg)
|
|
{
|
|
char recursions = 0;
|
|
short exponent;
|
|
FPU_REG odd_poly, even_poly, pos_poly, neg_poly;
|
|
FPU_REG argSq;
|
|
long long arg_signif, argSqSq;
|
|
|
|
|
|
#ifdef PARANOID
|
|
if (arg->sign != 0) { /* Can't hack a number < 0.0 */
|
|
arith_invalid(arg);
|
|
return;
|
|
} /* Need a positive number */
|
|
#endif /* PARANOID */
|
|
|
|
exponent = arg->exp - EXP_BIAS;
|
|
|
|
if (arg->tag == TW_Zero) {
|
|
/* Return 0.0 */
|
|
reg_move(&CONST_Z, arg);
|
|
return;
|
|
}
|
|
if (exponent >= -2) {
|
|
/* argument is in the range [0.25 .. 1.0] */
|
|
if (exponent >= 0) {
|
|
#ifdef PARANOID
|
|
if ((exponent == 0) &&
|
|
(arg->sigl == 0) && (arg->sigh == 0x80000000))
|
|
#endif /* PARANOID */
|
|
{
|
|
reg_move(&CONST_PI4, arg);
|
|
return;
|
|
}
|
|
#ifdef PARANOID
|
|
EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic
|
|
* error */
|
|
#endif /* PARANOID */
|
|
}
|
|
/* If the argument is greater than sqrt(2)-1 (=0.414213562...) */
|
|
/* convert the argument by an identity for atan */
|
|
if ((exponent >= -1) || (arg->sigh > 0xd413ccd0)) {
|
|
FPU_REG numerator, denom;
|
|
|
|
recursions++;
|
|
|
|
arg_signif = *(long long *) &(arg->sigl);
|
|
if (exponent < -1) {
|
|
if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
|
|
arg_signif++; /* round up */
|
|
}
|
|
*(long long *) &(numerator.sigl) = -arg_signif;
|
|
numerator.exp = EXP_BIAS - 1;
|
|
normalize(&numerator); /* 1 - arg */
|
|
|
|
arg_signif = *(long long *) &(arg->sigl);
|
|
if (shrx(&arg_signif, -exponent) >= (unsigned)0x80000000)
|
|
arg_signif++; /* round up */
|
|
*(long long *) &(denom.sigl) = arg_signif;
|
|
denom.sigh |= 0x80000000; /* 1 + arg */
|
|
|
|
arg->exp = numerator.exp;
|
|
reg_u_div(&numerator, &denom, arg, FULL_PRECISION);
|
|
|
|
exponent = arg->exp - EXP_BIAS;
|
|
}
|
|
}
|
|
*(long long *) &arg_signif = *(long long *) &(arg->sigl);
|
|
|
|
#ifdef PARANOID
|
|
/* This must always be true */
|
|
if (exponent >= -1) {
|
|
EXCEPTION(EX_INTERNAL | 0x120); /* There must be a logic error */
|
|
}
|
|
#endif /* PARANOID */
|
|
|
|
/* shift the argument right by the required places */
|
|
if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
|
|
arg_signif++; /* round up */
|
|
|
|
/* Now have arg_signif with binary point at the left .1xxxxxxxx */
|
|
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,
|
|
(unsigned short (*)[4]) oddplterms, HIPOWERop - 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,
|
|
(unsigned short (*)[4]) oddnegterms, HIPOWERon - 1);
|
|
|
|
/* Subtract the mantissas */
|
|
*((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl));
|
|
|
|
reg_move(&pos_poly, &odd_poly);
|
|
poly_add_1(&odd_poly);
|
|
|
|
/* The complete odd polynomial */
|
|
reg_u_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION);
|
|
|
|
/* will be a valid positive nr with expon = 0 */
|
|
*(short *) &(even_poly.sign) = 0;
|
|
|
|
mul64((long long *) (&argSq.sigl),
|
|
(long long *) (&denomterm), (long long *) (&even_poly.sigl));
|
|
|
|
poly_add_1(&even_poly);
|
|
|
|
reg_div(&odd_poly, &even_poly, arg, FULL_PRECISION);
|
|
|
|
if (recursions)
|
|
reg_sub(&CONST_PI4, arg, arg, FULL_PRECISION);
|
|
}
|
|
|
|
|
|
/* The argument to this function must be polynomial() compatible,
|
|
i.e. have an exponent (not checked) of EXP_BIAS-1 but need not
|
|
be normalized.
|
|
This function adds 1.0 to the (assumed positive) argument. */
|
|
static void
|
|
poly_add_1(FPU_REG * src)
|
|
{
|
|
/* Rounding in a consistent direction produces better results
|
|
for the use of this function in poly_atan. Simple truncation
|
|
is used here instead of round-to-nearest. */
|
|
|
|
#ifdef OBSOLETE
|
|
char round = (src->sigl & 3) == 3;
|
|
#endif /* OBSOLETE */
|
|
|
|
shrx(&src->sigl, 1);
|
|
|
|
#ifdef OBSOLETE
|
|
if (round)
|
|
(*(long long *) &src->sigl)++; /* Round to even */
|
|
#endif /* OBSOLETE */
|
|
|
|
src->sigh |= 0x80000000;
|
|
|
|
src->exp = EXP_BIAS;
|
|
|
|
}
|