--- /dev/null
+/*---------------------------------------------------------------------------+
+ | 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 */
+
+}
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