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|
/*---------------------------------------------------------------------------+
| poly_tan.c |
| |
| Compute the tan of a FPU_REG, using a polynomial approximation. |
| |
| Copyright (C) 1992,1993,1994,1997,1999 |
| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, |
| Australia. E-mail billm@melbpc.org.au |
| |
| |
+---------------------------------------------------------------------------*/
#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "fpu_system.h"
#include "control_w.h"
#include "poly.h"
#define HiPOWERop 3 /* odd poly, positive terms */
static const unsigned long long oddplterm[HiPOWERop] = {
0x0000000000000000LL,
0x0051a1cf08fca228LL,
0x0000000071284ff7LL
};
#define HiPOWERon 2 /* odd poly, negative terms */
static const unsigned long long oddnegterm[HiPOWERon] = {
0x1291a9a184244e80LL,
0x0000583245819c21LL
};
#define HiPOWERep 2 /* even poly, positive terms */
static const unsigned long long evenplterm[HiPOWERep] = {
0x0e848884b539e888LL,
0x00003c7f18b887daLL
};
#define HiPOWERen 2 /* even poly, negative terms */
static const unsigned long long evennegterm[HiPOWERen] = {
0xf1f0200fd51569ccLL,
0x003afb46105c4432LL
};
static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL;
/*--- poly_tan() ------------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void poly_tan(FPU_REG *st0_ptr)
{
long int exponent;
int invert;
Xsig argSq, argSqSq, accumulatoro, accumulatore, accum,
argSignif, fix_up;
unsigned long adj;
exponent = exponent(st0_ptr);
#ifdef PARANOID
if (signnegative(st0_ptr)) { /* Can't hack a number < 0.0 */
arith_invalid(0);
return;
} /* Need a positive number */
#endif /* PARANOID */
/* Split the problem into two domains, smaller and larger than pi/4 */
if ((exponent == 0)
|| ((exponent == -1) && (st0_ptr->sigh > 0xc90fdaa2))) {
/* The argument is greater than (approx) pi/4 */
invert = 1;
accum.lsw = 0;
XSIG_LL(accum) = significand(st0_ptr);
if (exponent == 0) {
/* The argument is >= 1.0 */
/* Put the binary point at the left. */
XSIG_LL(accum) <<= 1;
}
/* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
XSIG_LL(accum) = 0x921fb54442d18469LL - XSIG_LL(accum);
/* This is a special case which arises due to rounding. */
if (XSIG_LL(accum) == 0xffffffffffffffffLL) {
FPU_settag0(TAG_Valid);
significand(st0_ptr) = 0x8a51e04daabda360LL;
setexponent16(st0_ptr,
(0x41 + EXTENDED_Ebias) | SIGN_Negative);
return;
}
argSignif.lsw = accum.lsw;
XSIG_LL(argSignif) = XSIG_LL(accum);
exponent = -1 + norm_Xsig(&argSignif);
} else {
invert = 0;
argSignif.lsw = 0;
XSIG_LL(accum) = XSIG_LL(argSignif) = significand(st0_ptr);
if (exponent < -1) {
/* shift the argument right by the required places */
if (FPU_shrx(&XSIG_LL(accum), -1 - exponent) >=
0x80000000U)
XSIG_LL(accum)++; /* round up */
}
}
XSIG_LL(argSq) = XSIG_LL(accum);
argSq.lsw = accum.lsw;
mul_Xsig_Xsig(&argSq, &argSq);
XSIG_LL(argSqSq) = XSIG_LL(argSq);
argSqSq.lsw = argSq.lsw;
mul_Xsig_Xsig(&argSqSq, &argSqSq);
/* Compute the negative terms for the numerator polynomial */
accumulatoro.msw = accumulatoro.midw = accumulatoro.lsw = 0;
polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddnegterm,
HiPOWERon - 1);
mul_Xsig_Xsig(&accumulatoro, &argSq);
negate_Xsig(&accumulatoro);
/* Add the positive terms */
polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddplterm,
HiPOWERop - 1);
/* Compute the positive terms for the denominator polynomial */
accumulatore.msw = accumulatore.midw = accumulatore.lsw = 0;
polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evenplterm,
HiPOWERep - 1);
mul_Xsig_Xsig(&accumulatore, &argSq);
negate_Xsig(&accumulatore);
/* Add the negative terms */
polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evennegterm,
HiPOWERen - 1);
/* Multiply by arg^2 */
mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
/* de-normalize and divide by 2 */
shr_Xsig(&accumulatore, -2 * (1 + exponent) + 1);
negate_Xsig(&accumulatore); /* This does 1 - accumulator */
/* Now find the ratio. */
if (accumulatore.msw == 0) {
/* accumulatoro must contain 1.0 here, (actually, 0) but it
really doesn't matter what value we use because it will
have negligible effect in later calculations
*/
XSIG_LL(accum) = 0x8000000000000000LL;
accum.lsw = 0;
} else {
div_Xsig(&accumulatoro, &accumulatore, &accum);
}
/* Multiply by 1/3 * arg^3 */
mul64_Xsig(&accum, &XSIG_LL(argSignif));
mul64_Xsig(&accum, &XSIG_LL(argSignif));
mul64_Xsig(&accum, &XSIG_LL(argSignif));
mul64_Xsig(&accum, &twothirds);
shr_Xsig(&accum, -2 * (exponent + 1));
/* tan(arg) = arg + accum */
add_two_Xsig(&accum, &argSignif, &exponent);
if (invert) {
/* We now have the value of tan(pi_2 - arg) where pi_2 is an
approximation for pi/2
*/
/* The next step is to fix the answer to compensate for the
error due to the approximation used for pi/2
*/
/* This is (approx) delta, the error in our approx for pi/2
(see above). It has an exponent of -65
*/
XSIG_LL(fix_up) = 0x898cc51701b839a2LL;
fix_up.lsw = 0;
if (exponent == 0)
adj = 0xffffffff; /* We want approx 1.0 here, but
this is close enough. */
else if (exponent > -30) {
adj = accum.msw >> -(exponent + 1); /* tan */
adj = mul_32_32(adj, adj); /* tan^2 */
} else
adj = 0;
adj = mul_32_32(0x898cc517, adj); /* delta * tan^2 */
fix_up.msw += adj;
if (!(fix_up.msw & 0x80000000)) { /* did fix_up overflow ? */
/* Yes, we need to add an msb */
shr_Xsig(&fix_up, 1);
fix_up.msw |= 0x80000000;
shr_Xsig(&fix_up, 64 + exponent);
} else
shr_Xsig(&fix_up, 65 + exponent);
add_two_Xsig(&accum, &fix_up, &exponent);
/* accum now contains tan(pi/2 - arg).
Use tan(arg) = 1.0 / tan(pi/2 - arg)
*/
accumulatoro.lsw = accumulatoro.midw = 0;
accumulatoro.msw = 0x80000000;
div_Xsig(&accumulatoro, &accum, &accum);
exponent = -exponent - 1;
}
/* Transfer the result */
round_Xsig(&accum);
FPU_settag0(TAG_Valid);
significand(st0_ptr) = XSIG_LL(accum);
setexponent16(st0_ptr, exponent + EXTENDED_Ebias); /* Result is positive. */
}
|
