380 lines
11 KiB
C
380 lines
11 KiB
C
// SPDX-License-Identifier: GPL-2.0
|
|
/*---------------------------------------------------------------------------+
|
|
| poly_sin.c |
|
|
| |
|
|
| Computation of an approximation of the sin function and the cosine |
|
|
| function by a polynomial. |
|
|
| |
|
|
| 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 N_COEFF_P 4
|
|
#define N_COEFF_N 4
|
|
|
|
static const unsigned long long pos_terms_l[N_COEFF_P] = {
|
|
0xaaaaaaaaaaaaaaabLL,
|
|
0x00d00d00d00cf906LL,
|
|
0x000006b99159a8bbLL,
|
|
0x000000000d7392e6LL
|
|
};
|
|
|
|
static const unsigned long long neg_terms_l[N_COEFF_N] = {
|
|
0x2222222222222167LL,
|
|
0x0002e3bc74aab624LL,
|
|
0x0000000b09229062LL,
|
|
0x00000000000c7973LL
|
|
};
|
|
|
|
#define N_COEFF_PH 4
|
|
#define N_COEFF_NH 4
|
|
static const unsigned long long pos_terms_h[N_COEFF_PH] = {
|
|
0x0000000000000000LL,
|
|
0x05b05b05b05b0406LL,
|
|
0x000049f93edd91a9LL,
|
|
0x00000000c9c9ed62LL
|
|
};
|
|
|
|
static const unsigned long long neg_terms_h[N_COEFF_NH] = {
|
|
0xaaaaaaaaaaaaaa98LL,
|
|
0x001a01a01a019064LL,
|
|
0x0000008f76c68a77LL,
|
|
0x0000000000d58f5eLL
|
|
};
|
|
|
|
/*--- poly_sine() -----------------------------------------------------------+
|
|
| |
|
|
+---------------------------------------------------------------------------*/
|
|
void poly_sine(FPU_REG *st0_ptr)
|
|
{
|
|
int exponent, echange;
|
|
Xsig accumulator, argSqrd, argTo4;
|
|
unsigned long fix_up, adj;
|
|
unsigned long long fixed_arg;
|
|
FPU_REG result;
|
|
|
|
exponent = exponent(st0_ptr);
|
|
|
|
accumulator.lsw = accumulator.midw = accumulator.msw = 0;
|
|
|
|
/* Split into two ranges, for arguments below and above 1.0 */
|
|
/* The boundary between upper and lower is approx 0.88309101259 */
|
|
if ((exponent < -1)
|
|
|| ((exponent == -1) && (st0_ptr->sigh <= 0xe21240aa))) {
|
|
/* The argument is <= 0.88309101259 */
|
|
|
|
argSqrd.msw = st0_ptr->sigh;
|
|
argSqrd.midw = st0_ptr->sigl;
|
|
argSqrd.lsw = 0;
|
|
mul64_Xsig(&argSqrd, &significand(st0_ptr));
|
|
shr_Xsig(&argSqrd, 2 * (-1 - exponent));
|
|
argTo4.msw = argSqrd.msw;
|
|
argTo4.midw = argSqrd.midw;
|
|
argTo4.lsw = argSqrd.lsw;
|
|
mul_Xsig_Xsig(&argTo4, &argTo4);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
|
|
N_COEFF_N - 1);
|
|
mul_Xsig_Xsig(&accumulator, &argSqrd);
|
|
negate_Xsig(&accumulator);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
|
|
N_COEFF_P - 1);
|
|
|
|
shr_Xsig(&accumulator, 2); /* Divide by four */
|
|
accumulator.msw |= 0x80000000; /* Add 1.0 */
|
|
|
|
mul64_Xsig(&accumulator, &significand(st0_ptr));
|
|
mul64_Xsig(&accumulator, &significand(st0_ptr));
|
|
mul64_Xsig(&accumulator, &significand(st0_ptr));
|
|
|
|
/* Divide by four, FPU_REG compatible, etc */
|
|
exponent = 3 * exponent;
|
|
|
|
/* The minimum exponent difference is 3 */
|
|
shr_Xsig(&accumulator, exponent(st0_ptr) - exponent);
|
|
|
|
negate_Xsig(&accumulator);
|
|
XSIG_LL(accumulator) += significand(st0_ptr);
|
|
|
|
echange = round_Xsig(&accumulator);
|
|
|
|
setexponentpos(&result, exponent(st0_ptr) + echange);
|
|
} else {
|
|
/* The argument is > 0.88309101259 */
|
|
/* We use sin(st(0)) = cos(pi/2-st(0)) */
|
|
|
|
fixed_arg = significand(st0_ptr);
|
|
|
|
if (exponent == 0) {
|
|
/* The argument is >= 1.0 */
|
|
|
|
/* Put the binary point at the left. */
|
|
fixed_arg <<= 1;
|
|
}
|
|
/* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
|
|
fixed_arg = 0x921fb54442d18469LL - fixed_arg;
|
|
/* There is a special case which arises due to rounding, to fix here. */
|
|
if (fixed_arg == 0xffffffffffffffffLL)
|
|
fixed_arg = 0;
|
|
|
|
XSIG_LL(argSqrd) = fixed_arg;
|
|
argSqrd.lsw = 0;
|
|
mul64_Xsig(&argSqrd, &fixed_arg);
|
|
|
|
XSIG_LL(argTo4) = XSIG_LL(argSqrd);
|
|
argTo4.lsw = argSqrd.lsw;
|
|
mul_Xsig_Xsig(&argTo4, &argTo4);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
|
|
N_COEFF_NH - 1);
|
|
mul_Xsig_Xsig(&accumulator, &argSqrd);
|
|
negate_Xsig(&accumulator);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
|
|
N_COEFF_PH - 1);
|
|
negate_Xsig(&accumulator);
|
|
|
|
mul64_Xsig(&accumulator, &fixed_arg);
|
|
mul64_Xsig(&accumulator, &fixed_arg);
|
|
|
|
shr_Xsig(&accumulator, 3);
|
|
negate_Xsig(&accumulator);
|
|
|
|
add_Xsig_Xsig(&accumulator, &argSqrd);
|
|
|
|
shr_Xsig(&accumulator, 1);
|
|
|
|
accumulator.lsw |= 1; /* A zero accumulator here would cause problems */
|
|
negate_Xsig(&accumulator);
|
|
|
|
/* The basic computation is complete. Now fix the answer to
|
|
compensate for the error due to the approximation used for
|
|
pi/2
|
|
*/
|
|
|
|
/* This has an exponent of -65 */
|
|
fix_up = 0x898cc517;
|
|
/* The fix-up needs to be improved for larger args */
|
|
if (argSqrd.msw & 0xffc00000) {
|
|
/* Get about 32 bit precision in these: */
|
|
fix_up -= mul_32_32(0x898cc517, argSqrd.msw) / 6;
|
|
}
|
|
fix_up = mul_32_32(fix_up, LL_MSW(fixed_arg));
|
|
|
|
adj = accumulator.lsw; /* temp save */
|
|
accumulator.lsw -= fix_up;
|
|
if (accumulator.lsw > adj)
|
|
XSIG_LL(accumulator)--;
|
|
|
|
echange = round_Xsig(&accumulator);
|
|
|
|
setexponentpos(&result, echange - 1);
|
|
}
|
|
|
|
significand(&result) = XSIG_LL(accumulator);
|
|
setsign(&result, getsign(st0_ptr));
|
|
FPU_copy_to_reg0(&result, TAG_Valid);
|
|
|
|
#ifdef PARANOID
|
|
if ((exponent(&result) >= 0)
|
|
&& (significand(&result) > 0x8000000000000000LL)) {
|
|
EXCEPTION(EX_INTERNAL | 0x150);
|
|
}
|
|
#endif /* PARANOID */
|
|
|
|
}
|
|
|
|
/*--- poly_cos() ------------------------------------------------------------+
|
|
| |
|
|
+---------------------------------------------------------------------------*/
|
|
void poly_cos(FPU_REG *st0_ptr)
|
|
{
|
|
FPU_REG result;
|
|
long int exponent, exp2, echange;
|
|
Xsig accumulator, argSqrd, fix_up, argTo4;
|
|
unsigned long long fixed_arg;
|
|
|
|
#ifdef PARANOID
|
|
if ((exponent(st0_ptr) > 0)
|
|
|| ((exponent(st0_ptr) == 0)
|
|
&& (significand(st0_ptr) > 0xc90fdaa22168c234LL))) {
|
|
EXCEPTION(EX_Invalid);
|
|
FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
|
|
return;
|
|
}
|
|
#endif /* PARANOID */
|
|
|
|
exponent = exponent(st0_ptr);
|
|
|
|
accumulator.lsw = accumulator.midw = accumulator.msw = 0;
|
|
|
|
if ((exponent < -1)
|
|
|| ((exponent == -1) && (st0_ptr->sigh <= 0xb00d6f54))) {
|
|
/* arg is < 0.687705 */
|
|
|
|
argSqrd.msw = st0_ptr->sigh;
|
|
argSqrd.midw = st0_ptr->sigl;
|
|
argSqrd.lsw = 0;
|
|
mul64_Xsig(&argSqrd, &significand(st0_ptr));
|
|
|
|
if (exponent < -1) {
|
|
/* shift the argument right by the required places */
|
|
shr_Xsig(&argSqrd, 2 * (-1 - exponent));
|
|
}
|
|
|
|
argTo4.msw = argSqrd.msw;
|
|
argTo4.midw = argSqrd.midw;
|
|
argTo4.lsw = argSqrd.lsw;
|
|
mul_Xsig_Xsig(&argTo4, &argTo4);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
|
|
N_COEFF_NH - 1);
|
|
mul_Xsig_Xsig(&accumulator, &argSqrd);
|
|
negate_Xsig(&accumulator);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
|
|
N_COEFF_PH - 1);
|
|
negate_Xsig(&accumulator);
|
|
|
|
mul64_Xsig(&accumulator, &significand(st0_ptr));
|
|
mul64_Xsig(&accumulator, &significand(st0_ptr));
|
|
shr_Xsig(&accumulator, -2 * (1 + exponent));
|
|
|
|
shr_Xsig(&accumulator, 3);
|
|
negate_Xsig(&accumulator);
|
|
|
|
add_Xsig_Xsig(&accumulator, &argSqrd);
|
|
|
|
shr_Xsig(&accumulator, 1);
|
|
|
|
/* It doesn't matter if accumulator is all zero here, the
|
|
following code will work ok */
|
|
negate_Xsig(&accumulator);
|
|
|
|
if (accumulator.lsw & 0x80000000)
|
|
XSIG_LL(accumulator)++;
|
|
if (accumulator.msw == 0) {
|
|
/* The result is 1.0 */
|
|
FPU_copy_to_reg0(&CONST_1, TAG_Valid);
|
|
return;
|
|
} else {
|
|
significand(&result) = XSIG_LL(accumulator);
|
|
|
|
/* will be a valid positive nr with expon = -1 */
|
|
setexponentpos(&result, -1);
|
|
}
|
|
} else {
|
|
fixed_arg = significand(st0_ptr);
|
|
|
|
if (exponent == 0) {
|
|
/* The argument is >= 1.0 */
|
|
|
|
/* Put the binary point at the left. */
|
|
fixed_arg <<= 1;
|
|
}
|
|
/* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
|
|
fixed_arg = 0x921fb54442d18469LL - fixed_arg;
|
|
/* There is a special case which arises due to rounding, to fix here. */
|
|
if (fixed_arg == 0xffffffffffffffffLL)
|
|
fixed_arg = 0;
|
|
|
|
exponent = -1;
|
|
exp2 = -1;
|
|
|
|
/* A shift is needed here only for a narrow range of arguments,
|
|
i.e. for fixed_arg approx 2^-32, but we pick up more... */
|
|
if (!(LL_MSW(fixed_arg) & 0xffff0000)) {
|
|
fixed_arg <<= 16;
|
|
exponent -= 16;
|
|
exp2 -= 16;
|
|
}
|
|
|
|
XSIG_LL(argSqrd) = fixed_arg;
|
|
argSqrd.lsw = 0;
|
|
mul64_Xsig(&argSqrd, &fixed_arg);
|
|
|
|
if (exponent < -1) {
|
|
/* shift the argument right by the required places */
|
|
shr_Xsig(&argSqrd, 2 * (-1 - exponent));
|
|
}
|
|
|
|
argTo4.msw = argSqrd.msw;
|
|
argTo4.midw = argSqrd.midw;
|
|
argTo4.lsw = argSqrd.lsw;
|
|
mul_Xsig_Xsig(&argTo4, &argTo4);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
|
|
N_COEFF_N - 1);
|
|
mul_Xsig_Xsig(&accumulator, &argSqrd);
|
|
negate_Xsig(&accumulator);
|
|
|
|
polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
|
|
N_COEFF_P - 1);
|
|
|
|
shr_Xsig(&accumulator, 2); /* Divide by four */
|
|
accumulator.msw |= 0x80000000; /* Add 1.0 */
|
|
|
|
mul64_Xsig(&accumulator, &fixed_arg);
|
|
mul64_Xsig(&accumulator, &fixed_arg);
|
|
mul64_Xsig(&accumulator, &fixed_arg);
|
|
|
|
/* Divide by four, FPU_REG compatible, etc */
|
|
exponent = 3 * exponent;
|
|
|
|
/* The minimum exponent difference is 3 */
|
|
shr_Xsig(&accumulator, exp2 - exponent);
|
|
|
|
negate_Xsig(&accumulator);
|
|
XSIG_LL(accumulator) += fixed_arg;
|
|
|
|
/* The basic computation is complete. Now fix the answer to
|
|
compensate for the error due to the approximation used for
|
|
pi/2
|
|
*/
|
|
|
|
/* This has an exponent of -65 */
|
|
XSIG_LL(fix_up) = 0x898cc51701b839a2ll;
|
|
fix_up.lsw = 0;
|
|
|
|
/* The fix-up needs to be improved for larger args */
|
|
if (argSqrd.msw & 0xffc00000) {
|
|
/* Get about 32 bit precision in these: */
|
|
fix_up.msw -= mul_32_32(0x898cc517, argSqrd.msw) / 2;
|
|
fix_up.msw += mul_32_32(0x898cc517, argTo4.msw) / 24;
|
|
}
|
|
|
|
exp2 += norm_Xsig(&accumulator);
|
|
shr_Xsig(&accumulator, 1); /* Prevent overflow */
|
|
exp2++;
|
|
shr_Xsig(&fix_up, 65 + exp2);
|
|
|
|
add_Xsig_Xsig(&accumulator, &fix_up);
|
|
|
|
echange = round_Xsig(&accumulator);
|
|
|
|
setexponentpos(&result, exp2 + echange);
|
|
significand(&result) = XSIG_LL(accumulator);
|
|
}
|
|
|
|
FPU_copy_to_reg0(&result, TAG_Valid);
|
|
|
|
#ifdef PARANOID
|
|
if ((exponent(&result) >= 0)
|
|
&& (significand(&result) > 0x8000000000000000LL)) {
|
|
EXCEPTION(EX_INTERNAL | 0x151);
|
|
}
|
|
#endif /* PARANOID */
|
|
|
|
}
|