379 lines
11 KiB
C
379 lines
11 KiB
C
/*---------------------------------------------------------------------------+
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| poly_sin.c |
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| Computation of an approximation of the sin function and the cosine |
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| function by a polynomial. |
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| Copyright (C) 1992,1993,1994,1997,1999 |
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| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
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| E-mail billm@melbpc.org.au |
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+---------------------------------------------------------------------------*/
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#include "exception.h"
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#include "reg_constant.h"
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#include "fpu_emu.h"
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#include "fpu_system.h"
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#include "control_w.h"
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#include "poly.h"
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#define N_COEFF_P 4
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#define N_COEFF_N 4
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static const unsigned long long pos_terms_l[N_COEFF_P] = {
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0xaaaaaaaaaaaaaaabLL,
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0x00d00d00d00cf906LL,
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0x000006b99159a8bbLL,
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0x000000000d7392e6LL
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};
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static const unsigned long long neg_terms_l[N_COEFF_N] = {
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0x2222222222222167LL,
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0x0002e3bc74aab624LL,
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0x0000000b09229062LL,
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0x00000000000c7973LL
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};
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#define N_COEFF_PH 4
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#define N_COEFF_NH 4
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static const unsigned long long pos_terms_h[N_COEFF_PH] = {
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0x0000000000000000LL,
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0x05b05b05b05b0406LL,
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0x000049f93edd91a9LL,
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0x00000000c9c9ed62LL
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};
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static const unsigned long long neg_terms_h[N_COEFF_NH] = {
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0xaaaaaaaaaaaaaa98LL,
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0x001a01a01a019064LL,
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0x0000008f76c68a77LL,
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0x0000000000d58f5eLL
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};
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/*--- poly_sine() -----------------------------------------------------------+
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+---------------------------------------------------------------------------*/
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void poly_sine(FPU_REG *st0_ptr)
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{
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int exponent, echange;
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Xsig accumulator, argSqrd, argTo4;
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unsigned long fix_up, adj;
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unsigned long long fixed_arg;
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FPU_REG result;
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exponent = exponent(st0_ptr);
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accumulator.lsw = accumulator.midw = accumulator.msw = 0;
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/* Split into two ranges, for arguments below and above 1.0 */
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/* The boundary between upper and lower is approx 0.88309101259 */
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if ((exponent < -1)
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|| ((exponent == -1) && (st0_ptr->sigh <= 0xe21240aa))) {
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/* The argument is <= 0.88309101259 */
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argSqrd.msw = st0_ptr->sigh;
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argSqrd.midw = st0_ptr->sigl;
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argSqrd.lsw = 0;
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mul64_Xsig(&argSqrd, &significand(st0_ptr));
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shr_Xsig(&argSqrd, 2 * (-1 - exponent));
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argTo4.msw = argSqrd.msw;
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argTo4.midw = argSqrd.midw;
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argTo4.lsw = argSqrd.lsw;
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mul_Xsig_Xsig(&argTo4, &argTo4);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
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N_COEFF_N - 1);
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mul_Xsig_Xsig(&accumulator, &argSqrd);
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negate_Xsig(&accumulator);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
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N_COEFF_P - 1);
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shr_Xsig(&accumulator, 2); /* Divide by four */
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accumulator.msw |= 0x80000000; /* Add 1.0 */
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mul64_Xsig(&accumulator, &significand(st0_ptr));
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mul64_Xsig(&accumulator, &significand(st0_ptr));
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mul64_Xsig(&accumulator, &significand(st0_ptr));
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/* Divide by four, FPU_REG compatible, etc */
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exponent = 3 * exponent;
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/* The minimum exponent difference is 3 */
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shr_Xsig(&accumulator, exponent(st0_ptr) - exponent);
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negate_Xsig(&accumulator);
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XSIG_LL(accumulator) += significand(st0_ptr);
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echange = round_Xsig(&accumulator);
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setexponentpos(&result, exponent(st0_ptr) + echange);
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} else {
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/* The argument is > 0.88309101259 */
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/* We use sin(st(0)) = cos(pi/2-st(0)) */
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fixed_arg = significand(st0_ptr);
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if (exponent == 0) {
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/* The argument is >= 1.0 */
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/* Put the binary point at the left. */
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fixed_arg <<= 1;
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}
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/* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
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fixed_arg = 0x921fb54442d18469LL - fixed_arg;
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/* There is a special case which arises due to rounding, to fix here. */
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if (fixed_arg == 0xffffffffffffffffLL)
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fixed_arg = 0;
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XSIG_LL(argSqrd) = fixed_arg;
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argSqrd.lsw = 0;
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mul64_Xsig(&argSqrd, &fixed_arg);
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XSIG_LL(argTo4) = XSIG_LL(argSqrd);
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argTo4.lsw = argSqrd.lsw;
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mul_Xsig_Xsig(&argTo4, &argTo4);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
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N_COEFF_NH - 1);
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mul_Xsig_Xsig(&accumulator, &argSqrd);
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negate_Xsig(&accumulator);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
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N_COEFF_PH - 1);
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negate_Xsig(&accumulator);
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mul64_Xsig(&accumulator, &fixed_arg);
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mul64_Xsig(&accumulator, &fixed_arg);
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shr_Xsig(&accumulator, 3);
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negate_Xsig(&accumulator);
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add_Xsig_Xsig(&accumulator, &argSqrd);
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shr_Xsig(&accumulator, 1);
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accumulator.lsw |= 1; /* A zero accumulator here would cause problems */
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negate_Xsig(&accumulator);
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/* The basic computation is complete. Now fix the answer to
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compensate for the error due to the approximation used for
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pi/2
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*/
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/* This has an exponent of -65 */
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fix_up = 0x898cc517;
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/* The fix-up needs to be improved for larger args */
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if (argSqrd.msw & 0xffc00000) {
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/* Get about 32 bit precision in these: */
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fix_up -= mul_32_32(0x898cc517, argSqrd.msw) / 6;
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}
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fix_up = mul_32_32(fix_up, LL_MSW(fixed_arg));
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adj = accumulator.lsw; /* temp save */
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accumulator.lsw -= fix_up;
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if (accumulator.lsw > adj)
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XSIG_LL(accumulator)--;
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echange = round_Xsig(&accumulator);
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setexponentpos(&result, echange - 1);
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}
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significand(&result) = XSIG_LL(accumulator);
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setsign(&result, getsign(st0_ptr));
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FPU_copy_to_reg0(&result, TAG_Valid);
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#ifdef PARANOID
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if ((exponent(&result) >= 0)
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&& (significand(&result) > 0x8000000000000000LL)) {
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EXCEPTION(EX_INTERNAL | 0x150);
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}
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#endif /* PARANOID */
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}
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/*--- poly_cos() ------------------------------------------------------------+
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+---------------------------------------------------------------------------*/
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void poly_cos(FPU_REG *st0_ptr)
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{
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FPU_REG result;
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long int exponent, exp2, echange;
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Xsig accumulator, argSqrd, fix_up, argTo4;
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unsigned long long fixed_arg;
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#ifdef PARANOID
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if ((exponent(st0_ptr) > 0)
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|| ((exponent(st0_ptr) == 0)
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&& (significand(st0_ptr) > 0xc90fdaa22168c234LL))) {
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EXCEPTION(EX_Invalid);
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FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
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return;
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}
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#endif /* PARANOID */
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exponent = exponent(st0_ptr);
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accumulator.lsw = accumulator.midw = accumulator.msw = 0;
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if ((exponent < -1)
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|| ((exponent == -1) && (st0_ptr->sigh <= 0xb00d6f54))) {
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/* arg is < 0.687705 */
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argSqrd.msw = st0_ptr->sigh;
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argSqrd.midw = st0_ptr->sigl;
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argSqrd.lsw = 0;
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mul64_Xsig(&argSqrd, &significand(st0_ptr));
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if (exponent < -1) {
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/* shift the argument right by the required places */
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shr_Xsig(&argSqrd, 2 * (-1 - exponent));
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}
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argTo4.msw = argSqrd.msw;
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argTo4.midw = argSqrd.midw;
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argTo4.lsw = argSqrd.lsw;
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mul_Xsig_Xsig(&argTo4, &argTo4);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
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N_COEFF_NH - 1);
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mul_Xsig_Xsig(&accumulator, &argSqrd);
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negate_Xsig(&accumulator);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
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N_COEFF_PH - 1);
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negate_Xsig(&accumulator);
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mul64_Xsig(&accumulator, &significand(st0_ptr));
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mul64_Xsig(&accumulator, &significand(st0_ptr));
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shr_Xsig(&accumulator, -2 * (1 + exponent));
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shr_Xsig(&accumulator, 3);
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negate_Xsig(&accumulator);
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add_Xsig_Xsig(&accumulator, &argSqrd);
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shr_Xsig(&accumulator, 1);
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/* It doesn't matter if accumulator is all zero here, the
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following code will work ok */
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negate_Xsig(&accumulator);
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if (accumulator.lsw & 0x80000000)
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XSIG_LL(accumulator)++;
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if (accumulator.msw == 0) {
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/* The result is 1.0 */
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FPU_copy_to_reg0(&CONST_1, TAG_Valid);
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return;
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} else {
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significand(&result) = XSIG_LL(accumulator);
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/* will be a valid positive nr with expon = -1 */
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setexponentpos(&result, -1);
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}
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} else {
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fixed_arg = significand(st0_ptr);
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if (exponent == 0) {
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/* The argument is >= 1.0 */
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/* Put the binary point at the left. */
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fixed_arg <<= 1;
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}
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/* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
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fixed_arg = 0x921fb54442d18469LL - fixed_arg;
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/* There is a special case which arises due to rounding, to fix here. */
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if (fixed_arg == 0xffffffffffffffffLL)
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fixed_arg = 0;
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exponent = -1;
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exp2 = -1;
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/* A shift is needed here only for a narrow range of arguments,
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i.e. for fixed_arg approx 2^-32, but we pick up more... */
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if (!(LL_MSW(fixed_arg) & 0xffff0000)) {
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fixed_arg <<= 16;
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exponent -= 16;
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exp2 -= 16;
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}
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XSIG_LL(argSqrd) = fixed_arg;
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argSqrd.lsw = 0;
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mul64_Xsig(&argSqrd, &fixed_arg);
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if (exponent < -1) {
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/* shift the argument right by the required places */
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shr_Xsig(&argSqrd, 2 * (-1 - exponent));
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}
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argTo4.msw = argSqrd.msw;
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argTo4.midw = argSqrd.midw;
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argTo4.lsw = argSqrd.lsw;
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mul_Xsig_Xsig(&argTo4, &argTo4);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
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N_COEFF_N - 1);
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mul_Xsig_Xsig(&accumulator, &argSqrd);
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negate_Xsig(&accumulator);
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polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
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N_COEFF_P - 1);
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shr_Xsig(&accumulator, 2); /* Divide by four */
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accumulator.msw |= 0x80000000; /* Add 1.0 */
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mul64_Xsig(&accumulator, &fixed_arg);
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mul64_Xsig(&accumulator, &fixed_arg);
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mul64_Xsig(&accumulator, &fixed_arg);
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/* Divide by four, FPU_REG compatible, etc */
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exponent = 3 * exponent;
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/* The minimum exponent difference is 3 */
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shr_Xsig(&accumulator, exp2 - exponent);
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negate_Xsig(&accumulator);
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XSIG_LL(accumulator) += fixed_arg;
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/* The basic computation is complete. Now fix the answer to
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compensate for the error due to the approximation used for
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pi/2
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*/
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/* This has an exponent of -65 */
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XSIG_LL(fix_up) = 0x898cc51701b839a2ll;
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fix_up.lsw = 0;
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/* The fix-up needs to be improved for larger args */
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if (argSqrd.msw & 0xffc00000) {
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/* Get about 32 bit precision in these: */
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fix_up.msw -= mul_32_32(0x898cc517, argSqrd.msw) / 2;
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fix_up.msw += mul_32_32(0x898cc517, argTo4.msw) / 24;
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}
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exp2 += norm_Xsig(&accumulator);
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shr_Xsig(&accumulator, 1); /* Prevent overflow */
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exp2++;
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shr_Xsig(&fix_up, 65 + exp2);
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add_Xsig_Xsig(&accumulator, &fix_up);
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echange = round_Xsig(&accumulator);
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setexponentpos(&result, exp2 + echange);
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significand(&result) = XSIG_LL(accumulator);
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}
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FPU_copy_to_reg0(&result, TAG_Valid);
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#ifdef PARANOID
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if ((exponent(&result) >= 0)
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&& (significand(&result) > 0x8000000000000000LL)) {
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EXCEPTION(EX_INTERNAL | 0x151);
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}
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#endif /* PARANOID */
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}
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