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|
/*---------------------------------------------------------------------------+
| poly_atan.c |
| |
| Compute the arctan of a FPU_REG, using a polynomial approximation. |
| |
| Copyright (C) 1992,1993,1994,1997 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
| E-mail billm@suburbia.net |
| |
| |
+---------------------------------------------------------------------------*/
#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "fpu_system.h"
#include "status_w.h"
#include "control_w.h"
#include "poly.h"
#define HIPOWERon 6 /* odd poly, negative terms */
static const unsigned long long oddnegterms[HIPOWERon] =
{
0x0000000000000000LL, /* Dummy (not for - 1.0) */
0x015328437f756467LL,
0x0005dda27b73dec6LL,
0x0000226bf2bfb91aLL,
0x000000ccc439c5f7LL,
0x0000000355438407LL
} ;
#define HIPOWERop 6 /* odd poly, positive terms */
static const unsigned long long oddplterms[HIPOWERop] =
{
/* 0xaaaaaaaaaaaaaaabLL, transferred to fixedpterm[] */
0x0db55a71875c9ac2LL,
0x0029fce2d67880b0LL,
0x0000dfd3908b4596LL,
0x00000550fd61dab4LL,
0x0000001c9422b3f9LL,
0x000000003e3301e1LL
};
static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL;
static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa);
static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b);
/*--- poly_atan() -----------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
FPU_REG *st1_ptr, u_char st1_tag)
{
u_char transformed, inverted,
sign1, sign2;
int exponent;
long int dummy_exp;
Xsig accumulator, Numer, Denom, accumulatore, argSignif,
argSq, argSqSq;
u_char tag;
sign1 = getsign(st0_ptr);
sign2 = getsign(st1_ptr);
if ( st0_tag == TAG_Valid )
{
exponent = exponent(st0_ptr);
}
else
{
/* This gives non-compatible stack contents... */
FPU_to_exp16(st0_ptr, st0_ptr);
exponent = exponent16(st0_ptr);
}
if ( st1_tag == TAG_Valid )
{
exponent -= exponent(st1_ptr);
}
else
{
/* This gives non-compatible stack contents... */
FPU_to_exp16(st1_ptr, st1_ptr);
exponent -= exponent16(st1_ptr);
}
if ( (exponent < 0) || ((exponent == 0) &&
((st0_ptr->sigh < st1_ptr->sigh) ||
((st0_ptr->sigh == st1_ptr->sigh) &&
(st0_ptr->sigl < st1_ptr->sigl))) ) )
{
inverted = 1;
Numer.lsw = Denom.lsw = 0;
XSIG_LL(Numer) = significand(st0_ptr);
XSIG_LL(Denom) = significand(st1_ptr);
}
else
{
inverted = 0;
exponent = -exponent;
Numer.lsw = Denom.lsw = 0;
XSIG_LL(Numer) = significand(st1_ptr);
XSIG_LL(Denom) = significand(st0_ptr);
}
div_Xsig(&Numer, &Denom, &argSignif);
exponent += norm_Xsig(&argSignif);
if ( (exponent >= -1)
|| ((exponent == -2) && (argSignif.msw > 0xd413ccd0)) )
{
/* The argument is greater than sqrt(2)-1 (=0.414213562...) */
/* Convert the argument by an identity for atan */
transformed = 1;
if ( exponent >= 0 )
{
#ifdef PARANOID
if ( !( (exponent == 0) &&
(argSignif.lsw == 0) && (argSignif.midw == 0) &&
(argSignif.msw == 0x80000000) ) )
{
EXCEPTION(EX_INTERNAL|0x104); /* There must be a logic error */
return;
}
#endif /* PARANOID */
argSignif.msw = 0; /* Make the transformed arg -> 0.0 */
}
else
{
Numer.lsw = Denom.lsw = argSignif.lsw;
XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);
if ( exponent < -1 )
shr_Xsig(&Numer, -1-exponent);
negate_Xsig(&Numer);
shr_Xsig(&Denom, -exponent);
Denom.msw |= 0x80000000;
div_Xsig(&Numer, &Denom, &argSignif);
exponent = -1 + norm_Xsig(&argSignif);
}
}
else
{
transformed = 0;
}
argSq.lsw = argSignif.lsw; argSq.midw = argSignif.midw;
argSq.msw = argSignif.msw;
mul_Xsig_Xsig(&argSq, &argSq);
argSqSq.lsw = argSq.lsw; argSqSq.midw = argSq.midw; argSqSq.msw = argSq.msw;
mul_Xsig_Xsig(&argSqSq, &argSqSq);
accumulatore.lsw = argSq.lsw;
XSIG_LL(accumulatore) = XSIG_LL(argSq);
shr_Xsig(&argSq, 2*(-1-exponent-1));
shr_Xsig(&argSqSq, 4*(-1-exponent-1));
/* Now have argSq etc with binary point at the left
.1xxxxxxxx */
/* Do the basic fixed point polynomial evaluation */
accumulator.msw = accumulator.midw = accumulator.lsw = 0;
polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
oddplterms, HIPOWERop-1);
mul64_Xsig(&accumulator, &XSIG_LL(argSq));
negate_Xsig(&accumulator);
polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms, HIPOWERon-1);
negate_Xsig(&accumulator);
add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);
mul64_Xsig(&accumulatore, &denomterm);
shr_Xsig(&accumulatore, 1 + 2*(-1-exponent));
accumulatore.msw |= 0x80000000;
div_Xsig(&accumulator, &accumulatore, &accumulator);
mul_Xsig_Xsig(&accumulator, &argSignif);
mul_Xsig_Xsig(&accumulator, &argSq);
shr_Xsig(&accumulator, 3);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &argSignif);
if ( transformed )
{
/* compute pi/4 - accumulator */
shr_Xsig(&accumulator, -1-exponent);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &pi_signif);
exponent = -1;
}
if ( inverted )
{
/* compute pi/2 - accumulator */
shr_Xsig(&accumulator, -exponent);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &pi_signif);
exponent = 0;
}
if ( sign1 )
{
/* compute pi - accumulator */
shr_Xsig(&accumulator, 1 - exponent);
negate_Xsig(&accumulator);
add_Xsig_Xsig(&accumulator, &pi_signif);
exponent = 1;
}
exponent += round_Xsig(&accumulator);
significand(st1_ptr) = XSIG_LL(accumulator);
setexponent16(st1_ptr, exponent);
tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
FPU_settagi(1, tag);
set_precision_flag_up(); /* We do not really know if up or down,
use this as the default. */
}
|
