/*---------------------------------------------------------------------------+
| poly_2xm1.c |
| |
| Function to compute 2^x-1 by 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 "control_w.h"
#include "poly.h"
#define HIPOWER 11
static const unsigned long long lterms[HIPOWER] =
{
0x0000000000000000LL, /* This term done separately as 12 bytes */
0xf5fdeffc162c7543LL,
0x1c6b08d704a0bfa6LL,
0x0276556df749cc21LL,
0x002bb0ffcf14f6b8LL,
0x0002861225ef751cLL,
0x00001ffcbfcd5422LL,
0x00000162c005d5f1LL,
0x0000000da96ccb1bLL,
0x0000000078d1b897LL,
0x000000000422b029LL
};
static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);
/* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
*/
static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);
static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
&shiftterm2, &shiftterm3 };
/*--- poly_2xm1() -----------------------------------------------------------+
| Requires st(0) which is TAG_Valid and < 1. |
+---------------------------------------------------------------------------*/
int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
{
long int exponent, shift;
unsigned long long Xll;
Xsig accumulator, Denom, argSignif;
u_char tag;
exponent = exponent16(arg);
#ifdef PARANOID
if ( exponent >= 0 ) /* Don't want a |number| >= 1.0 */
{
/* Number negative, too large, or not Valid. */
EXCEPTION(EX_INTERNAL|0x127);
return 1;
}
#endif /* PARANOID */
argSignif.lsw = 0;
XSIG_LL(argSignif) = Xll = significand(arg);
if ( exponent == -1 )
{
shift = (argSignif.msw & 0x40000000) ? 3 : 2;
/* subtract 0.5 or 0.75 */
exponent -= 2;
XSIG_LL(argSignif) <<= 2;
Xll <<= 2;
}
else if ( exponent == -2 )
{
shift = 1;
/* subtract 0.25 */
exponent--;
XSIG_LL(argSignif) <<= 1;
Xll <<= 1;
}
else
shift = 0;
if ( exponent < -2 )
{
/* Shift the argument right by the required places. */
if ( FPU_shrx(&Xll, -2-exponent) >= 0x80000000U )
Xll++; /* round up */
}
accumulator.lsw = accumulator.midw = accumulator.msw = 0;
polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER-1);
mul_Xsig_Xsig(&accumulator, &argSignif);
shr_Xsig(&accumulator, 3);
mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */
add_two_Xsig(&accumulator, &argSignif, &exponent);
if ( shift )
{
/* The argument is large, use the identity:
f(x+a) = f(a) * (f(x) + 1) - 1;
*/
shr_Xsig(&accumulator, - exponent);
accumulator.msw |= 0x80000000; /* add 1.0 */
mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
accumulator.msw &= 0x3fffffff; /* subtract 1.0 */
exponent = 1;
}
if ( sign != SIGN_POS )
{
/* The argument is negative, use the identity:
f(-x) = -f(x) / (1 + f(x))
*/
Denom.lsw = accumulator.lsw;
XSIG_LL(Denom) = XSIG_LL(accumulator);
if ( exponent < 0 )
shr_Xsig(&Denom, - exponent);
else if ( exponent > 0 )
{
/* exponent must be 1 here */
XSIG_LL(Denom) <<= 1;
if ( Denom.lsw & 0x80000000 )
XSIG_LL(Denom) |= 1;
(Denom.lsw) <<= 1;
}
Denom.msw |= 0x80000000; /* add 1.0 */
div_Xsig(&accumulator, &Denom, &accumulator);
}
/* Convert to 64 bit signed-compatible */
exponent += round_Xsig(&accumulator);
result = &st(0);
significand(result) = XSIG_LL(accumulator);
setexponent16(result, exponent);
tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);
setsign(result, sign);
FPU_settag0(tag);
return 0;
}
