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/*
* 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.
*
*
* $FreeBSD$
*
*/
#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;
}
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