/* 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. */
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;
}
/*--- poly_sine() -----------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void poly_sine(FPU_REG const *arg, FPU_REG *result)
{
short exponent;
FPU_REG fixed_arg, arg_sqrd, arg_to_4, accum, negaccum;
exponent = arg->exp - EXP_BIAS;
if ( arg->tag == TW_Zero )
{
/* Return 0.0 */
reg_move(&CONST_Z, result);
return;
}
#ifdef PARANOID
if ( arg->sign != 0 ) /* Can't hack a number < 0.0 */
{
EXCEPTION(EX_Invalid);
reg_move(&CONST_QNaN, result);
return;
}
if ( exponent >= 0 ) /* Can't hack a number > 1.0 */
{
if ( (exponent == 0) && (arg->sigl == 0) && (arg->sigh == 0x80000000) )
{
reg_move(&CONST_1, result);
return;
}
EXCEPTION(EX_Invalid);
reg_move(&CONST_QNaN, result);
return;
}
#endif PARANOID
fixed_arg.sigl = arg->sigl;
fixed_arg.sigh = arg->sigh;
if ( exponent < -1 )
{
/* shift the argument right by the required places */
if ( shrx(&(fixed_arg.sigl), -1-exponent) >= 0x80000000U )
significand(&fixed_arg)++; /* round up */
}
mul64(&significand(&fixed_arg), &significand(&fixed_arg),
&significand(&arg_sqrd));
mul64(&significand(&arg_sqrd), &significand(&arg_sqrd),
&significand(&arg_to_4));
/* will be a valid positive nr with expon = 0 */
*(short *)&(accum.sign) = 0;
accum.exp = 0;
/* Do the basic fixed point polynomial evaluation */
polynomial(&(accum.sigl), &(arg_to_4.sigl), lterms, HIPOWER-1);
/* will be a valid positive nr with expon = 0 */
*(short *)&(negaccum.sign) = 0;
negaccum.exp = 0;
/* Do the basic fixed point polynomial evaluation */
polynomial(&(negaccum.sigl), &(arg_to_4.sigl), negterms, HIPOWER-1);
mul64(&significand(&arg_sqrd), &significand(&negaccum),
&significand(&negaccum));
/* Subtract the mantissas */
significand(&accum) -= significand(&negaccum);
/* Convert to 64 bit signed-compatible */
accum.exp = EXP_BIAS - 1 + accum.exp;
reg_move(&accum, result);
normalize(result);
reg_mul(result, arg, result, FULL_PRECISION);
reg_u_add(result, arg, result, FULL_PRECISION);
if ( result->exp >= EXP_BIAS )
{
/* A small overflow may be possible... but an illegal result. */
if ( (result->exp > EXP_BIAS) /* Larger or equal 2.0 */
|| (result->sigl > 1) /* Larger than 1.0+msb */
|| (result->sigh != 0x80000000) /* Much > 1.0 */
)
{
#ifdef DEBUGGING
RE_ENTRANT_CHECK_OFF;
printk("\nEXP=%d, MS=%08x, LS=%08x\n", result->exp,
result->sigh, result->sigl);
RE_ENTRANT_CHECK_ON;
#endif DEBUGGING
EXCEPTION(EX_INTERNAL|0x103);
}
#ifdef DEBUGGING
RE_ENTRANT_CHECK_OFF;
printk("\n***CORRECTING ILLEGAL RESULT*** in poly_sin() computation\n");
printk("EXP=%d, MS=%08x, LS=%08x\n", result->exp,
result->sigh, result->sigl);
RE_ENTRANT_CHECK_ON;
#endif DEBUGGING
result->sigl = 0; /* Truncate the result to 1.00 */
}
}
/*--- 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(&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(&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);
}
/*--- poly_tan() ------------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void
poly_tan(FPU_REG * arg, FPU_REG * y_reg)
{
char invert = 0;
short exponent;
FPU_REG odd_poly, even_poly, pos_poly, neg_poly;
FPU_REG argSq;
long long arg_signif, argSqSq;
exponent = arg->exp - EXP_BIAS;
if (arg->tag == TW_Zero) {
/* Return 0.0 */
reg_move(&CONST_Z, y_reg);
return;
}
if (exponent >= -1) {
/* argument is in the range [0.5 .. 1.0] */
if (exponent >= 0) {
#ifdef PARANOID
if ((exponent == 0) &&
(arg->sigl == 0) && (arg->sigh == 0x80000000))
#endif /* PARANOID */
{
arith_overflow(y_reg);
return;
}
#ifdef PARANOID
EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic
* error */
return;
#endif /* PARANOID */
}
/* The argument is in the range [0.5 .. 1.0) */
/* Convert the argument to a number in the range (0.0 .. 0.5] */
*((long long *) (&arg->sigl)) = -*((long long *) (&arg->sigl));
normalize(arg); /* Needed later */
exponent = arg->exp - EXP_BIAS;
invert = 1;
}
#ifdef PARANOID
if (arg->sign != 0) { /* Can't hack a number < 0.0 */
arith_invalid(y_reg);
return;
} /* Need a positive number */
#endif /* PARANOID */
*(long long *) &arg_signif = *(long long *) &(arg->sigl);
if (exponent < -1) {
/* shift the argument right by the required places */
if (shrx(&arg_signif, -1 - exponent) >= (unsigned)0x80000000)
arg_signif++; /* round up */
}
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, oddplterms, HIPOWERop - 1);
/* 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, oddnegterms, HIPOWERon - 1);
mul64((long long *) (&argSq.sigl), (long long *) (&neg_poly.sigl),
(long long *) (&neg_poly.sigl));
/* Subtract the mantissas */
*((long long *) (&pos_poly.sigl)) -= *((long long *) (&neg_poly.sigl));
/* Convert to 64 bit signed-compatible */
pos_poly.exp -= 1;
reg_move(&pos_poly, &odd_poly);
normalize(&odd_poly);
reg_mul(&odd_poly, arg, &odd_poly, FULL_PRECISION);
reg_u_add(&odd_poly, arg, &odd_poly, FULL_PRECISION); /* This is just the odd
* polynomial */
/* 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, evenplterms, HIPOWERep - 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, evennegterms, HIPOWERen - 1);
/* Subtract the mantissas */
*((long long *) (&neg_poly.sigl)) -= *((long long *) (&pos_poly.sigl));
/* and multiply by argSq */
/* Convert argSq to a valid reg number */
*(short *) &(argSq.sign) = 0;
argSq.exp = EXP_BIAS - 1;
normalize(&argSq);
/* Convert to 64 bit signed-compatible */
neg_poly.exp -= 1;
reg_move(&neg_poly, &even_poly);
normalize(&even_poly);
reg_mul(&even_poly, &argSq, &even_poly, FULL_PRECISION);
reg_add(&even_poly, &argSq, &even_poly, FULL_PRECISION);
reg_sub(&CONST_1, &even_poly, &even_poly, FULL_PRECISION); /* This is just the even
* polynomial */
/* Now ready to copy the results */
if (invert) {
reg_div(&even_poly, &odd_poly, y_reg, FULL_PRECISION);
} else {
reg_div(&odd_poly, &even_poly, y_reg, FULL_PRECISION);
}
}
/*--- poly_tan() ------------------------------------------------------------+
| |
+---------------------------------------------------------------------------*/
void poly_tan(FPU_REG const *arg, FPU_REG *result)
{
long int exponent;
int invert;
Xsig argSq, argSqSq, accumulatoro, accumulatore, accum,
argSignif, fix_up;
unsigned long adj;
exponent = arg->exp - EXP_BIAS;
#ifdef PARANOID
if ( arg->sign != 0 ) /* Can't hack a number < 0.0 */
{ arith_invalid(result); return; } /* Need a positive number */
#endif PARANOID
/* Split the problem into two domains, smaller and larger than pi/4 */
if ( (exponent == 0) || ((exponent == -1) && (arg->sigh > 0xc90fdaa2)) )
{
/* The argument is greater than (approx) pi/4 */
invert = 1;
accum.lsw = 0;
XSIG_LL(accum) = significand(arg);
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);
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(arg);
if ( exponent < -1 )
{
/* shift the argument right by the required places */
if ( 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 */
mul_32_32(adj, adj, &adj); /* tan^2 */
}
else
