--- /dev/null
+/*---------------------------------------------------------------------------+
+ | poly_tan.c |
+ | |
+ | Compute the tan of a FPU_REG, using a polynomial approximation. |
+ | |
+ | 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 HiPOWERop 3 /* odd poly, positive terms */
+static const unsigned long long oddplterm[HiPOWERop] =
+{
+ 0x0000000000000000LL,
+ 0x0051a1cf08fca228LL,
+ 0x0000000071284ff7LL
+};
+
+#define HiPOWERon 2 /* odd poly, negative terms */
+static const unsigned long long oddnegterm[HiPOWERon] =
+{
+ 0x1291a9a184244e80LL,
+ 0x0000583245819c21LL
+};
+
+#define HiPOWERep 2 /* even poly, positive terms */
+static const unsigned long long evenplterm[HiPOWERep] =
+{
+ 0x0e848884b539e888LL,
+ 0x00003c7f18b887daLL
+};
+
+#define HiPOWERen 2 /* even poly, negative terms */
+static const unsigned long long evennegterm[HiPOWERen] =
+{
+ 0xf1f0200fd51569ccLL,
+ 0x003afb46105c4432LL
+};
+
+static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL;
+
+
+/*--- poly_tan() ------------------------------------------------------------+
+ | |
+ +---------------------------------------------------------------------------*/
+void poly_tan(FPU_REG *st0_ptr)
+{
+ long int exponent;
+ int invert;
+ Xsig argSq, argSqSq, accumulatoro, accumulatore, accum,
+ argSignif, fix_up;
+ unsigned long adj;
+
+ exponent = exponent(st0_ptr);
+
+#ifdef PARANOID
+ if ( signnegative(st0_ptr) ) /* Can't hack a number < 0.0 */
+ { arith_invalid(0); return; } /* Need a positive number */
+#endif /* PARANOID */
+
+ /* Split the problem into two domains, smaller and larger than pi/4 */
+ if ( (exponent == 0) || ((exponent == -1) && (st0_ptr->sigh > 0xc90fdaa2)) )
+ {
+ /* The argument is greater than (approx) pi/4 */
+ invert = 1;
+ accum.lsw = 0;
+ XSIG_LL(accum) = significand(st0_ptr);
+
+ 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);
+ /* This is a special case which arises due to rounding. */
+ if ( XSIG_LL(accum) == 0xffffffffffffffffLL )
+ {
+ FPU_settag0(TAG_Valid);
+ significand(st0_ptr) = 0x8a51e04daabda360LL;
+ setexponent16(st0_ptr, (0x41 + EXTENDED_Ebias) | SIGN_Negative);
+ return;
+ }
+
+ 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(st0_ptr);
+
+ if ( exponent < -1 )
+ {
+ /* shift the argument right by the required places */
+ if ( FPU_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 */
+ adj = mul_32_32(adj, adj); /* tan^2 */
+ }
+ else
+ adj = 0;
+ adj = mul_32_32(0x898cc517, adj); /* delta * tan^2 */
+
+ fix_up.msw += adj;
+ if ( !(fix_up.msw & 0x80000000) ) /* did fix_up overflow ? */
+ {
+ /* Yes, we need to add an msb */
+ shr_Xsig(&fix_up, 1);
+ fix_up.msw |= 0x80000000;
+ shr_Xsig(&fix_up, 64 + exponent);
+ }
+ else
+ shr_Xsig(&fix_up, 65 + exponent);
+
+ add_two_Xsig(&accum, &fix_up, &exponent);
+
+ /* accum now contains tan(pi/2 - arg).
+ Use tan(arg) = 1.0 / tan(pi/2 - arg)
+ */
+ accumulatoro.lsw = accumulatoro.midw = 0;
+ accumulatoro.msw = 0x80000000;
+ div_Xsig(&accumulatoro, &accum, &accum);
+ exponent = - exponent - 1;
+ }
+
+ /* Transfer the result */
+ round_Xsig(&accum);
+ FPU_settag0(TAG_Valid);
+ significand(st0_ptr) = XSIG_LL(accum);
+ setexponent16(st0_ptr, exponent + EXTENDED_Ebias); /* Result is positive. */
+
+}
git.openpandora.org / pandora-kernel.git / blobdiff