/*--- 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 */
}
}
void reg_add(FPU_REG *a, FPU_REG *b, FPU_REG *dest, int control_w)
{
int diff;
if ( !(a->tag | b->tag) )
{
/* Both registers are valid */
if (!(a->sign ^ b->sign))
{
/* signs are the same */
reg_u_add(a, b, dest, control_w);
dest->sign = a->sign;
return;
}
/* The signs are different, so do a subtraction */
diff = a->exp - b->exp;
if (!diff)
{
diff = a->sigh - b->sigh; /* Works only if ms bits are identical */
if (!diff)
{
diff = a->sigl > b->sigl;
if (!diff)
diff = -(a->sigl < b->sigl);
}
}
if (diff > 0)
{
reg_u_sub(a, b, dest, control_w);
dest->sign = a->sign;
}
else if ( diff == 0 )
{
reg_move(&CONST_Z, dest);
/* sign depends upon rounding mode */
dest->sign = ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG;
}
else
{
reg_u_sub(b, a, dest, control_w);
dest->sign = b->sign;
}
return;
}
else
{
if ( (a->tag == TW_NaN) || (b->tag == TW_NaN) )
{
real_2op_NaN(a, b, dest);
return;
}
else if (a->tag == TW_Zero)
{
if (b->tag == TW_Zero)
{
char different_signs = a->sign ^ b->sign;
/* Both are zero, result will be zero. */
reg_move(a, dest);
if (different_signs)
{
/* Signs are different. */
/* Sign of answer depends upon rounding mode. */
dest->sign = ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG;
}
}
else
reg_move(b, dest);
return;
}
else if (b->tag == TW_Zero)
{
reg_move(a, dest);
return;
}
else if (a->tag == TW_Infinity)
{
if (b->tag != TW_Infinity)
{
reg_move(a, dest);
return;
}
/* They are both + or - infinity */
if (a->sign == b->sign)
{
reg_move(a, dest);
return;
}
reg_move(&CONST_QNaN, dest); /* inf - inf is undefined. */
return;
}
else if (b->tag == TW_Infinity)
{
reg_move(b, dest);
return;
}
}
#ifdef PARANOID
EXCEPTION(EX_INTERNAL|0x101);
#endif
}
/*--- 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);
}
}
/* Subtract b from a. (a-b) -> dest */
void reg_sub(FPU_REG *a, FPU_REG *b, FPU_REG *dest, int control_w)
{
int diff;
if ( !(a->tag | b->tag) )
{
/* Both registers are valid */
diff = a->exp - b->exp;
if (!diff)
{
diff = a->sigh - b->sigh; /* Works only if ms bits are identical */
if (!diff)
{
diff = a->sigl > b->sigl;
if (!diff)
diff = -(a->sigl < b->sigl);
}
}
switch (a->sign*2 + b->sign)
{
case 0: /* P - P */
case 3: /* N - N */
if (diff > 0)
{
reg_u_sub(a, b, dest, control_w);
dest->sign = a->sign;
}
else if ( diff == 0 )
{
reg_move(&CONST_Z, dest);
/* sign depends upon rounding mode */
dest->sign = ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG;
}
else
{
reg_u_sub(b, a, dest, control_w);
dest->sign = a->sign ^ SIGN_POS^SIGN_NEG;
}
return;
case 1: /* P - N */
reg_u_add(a, b, dest, control_w);
dest->sign = SIGN_POS;
return;
case 2: /* N - P */
reg_u_add(a, b, dest, control_w);
dest->sign = SIGN_NEG;
return;
}
}
else
{
if ( (a->tag == TW_NaN) || (b->tag == TW_NaN) )
{
real_2op_NaN(a, b, dest);
return;
}
else if (b->tag == TW_Zero)
{
if (a->tag == TW_Zero)
{
char same_signs = !(a->sign ^ b->sign);
/* Both are zero, result will be zero. */
reg_move(a, dest); /* Answer for different signs. */
if (same_signs)
{
/* Sign depends upon rounding mode */
dest->sign = ((control_w & CW_RC) != RC_DOWN)
? SIGN_POS : SIGN_NEG;
}
}
else
reg_move(a, dest);
return;
}
else if (a->tag == TW_Zero)
{
reg_move(b, dest);
dest->sign ^= SIGN_POS^SIGN_NEG;
return;
}
else if (a->tag == TW_Infinity)
{
if (b->tag != TW_Infinity)
{
reg_move(a, dest);
return;
}
if (a->sign == b->sign)
{
reg_move(&CONST_QNaN, dest);
return;
}
reg_move(a, dest);
return;
}
else if (b->tag == TW_Infinity)
{
reg_move(b, dest);
dest->sign ^= SIGN_POS^SIGN_NEG;
return;
}
}
#ifdef PARANOID
EXCEPTION(EX_INTERNAL|0x110);
#endif
}