// SPDX-License-Identifier: GPL-2.0
/*---------------------------------------------------------------------------+
 |  poly_atan.c                                                              |
 |                                                                           |
 | Compute the arctan of a FPU_REG, using a polynomial approximation.        |
 |                                                                           |
 | Copyright (C) 1992,1993,1994,1997                                         |
 |                  W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
 |                  E-mail   billm@suburbia.net                              |
 |                                                                           |
 |                                                                           |
 +---------------------------------------------------------------------------*/

#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "fpu_system.h"
#include "status_w.h"
#include "control_w.h"
#include "poly.h"

#define HIPOWERon       6       /* odd poly, negative terms */
static const unsigned long long oddnegterms[HIPOWERon] = {
        0x0000000000000000LL,   /* Dummy (not for - 1.0) */
        0x015328437f756467LL,
        0x0005dda27b73dec6LL,
        0x0000226bf2bfb91aLL,
        0x000000ccc439c5f7LL,
        0x0000000355438407LL
};

#define HIPOWERop       6       /* odd poly, positive terms */
static const unsigned long long oddplterms[HIPOWERop] = {
/*  0xaaaaaaaaaaaaaaabLL,  transferred to fixedpterm[] */
        0x0db55a71875c9ac2LL,
        0x0029fce2d67880b0LL,
        0x0000dfd3908b4596LL,
        0x00000550fd61dab4LL,
        0x0000001c9422b3f9LL,
        0x000000003e3301e1LL
};

static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL;

static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa);

static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b);

/*--- poly_atan() -----------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
               FPU_REG *st1_ptr, u_char st1_tag)
{
        u_char transformed, inverted, sign1, sign2;
        int exponent;
        long int dummy_exp;
        Xsig accumulator, Numer, Denom, accumulatore, argSignif, argSq, argSqSq;
        u_char tag;

        sign1 = getsign(st0_ptr);
        sign2 = getsign(st1_ptr);
        if (st0_tag == TAG_Valid) {
                exponent = exponent(st0_ptr);
        } else {
                /* This gives non-compatible stack contents... */
                FPU_to_exp16(st0_ptr, st0_ptr);
                exponent = exponent16(st0_ptr);
        }
        if (st1_tag == TAG_Valid) {
                exponent -= exponent(st1_ptr);
        } else {
                /* This gives non-compatible stack contents... */
                FPU_to_exp16(st1_ptr, st1_ptr);
                exponent -= exponent16(st1_ptr);
        }

        if ((exponent < 0) || ((exponent == 0) &&
                               ((st0_ptr->sigh < st1_ptr->sigh) ||
                                ((st0_ptr->sigh == st1_ptr->sigh) &&
                                 (st0_ptr->sigl < st1_ptr->sigl))))) {
                inverted = 1;
                Numer.lsw = Denom.lsw = 0;
                XSIG_LL(Numer) = significand(st0_ptr);
                XSIG_LL(Denom) = significand(st1_ptr);
        } else {
                inverted = 0;
                exponent = -exponent;
                Numer.lsw = Denom.lsw = 0;
                XSIG_LL(Numer) = significand(st1_ptr);
                XSIG_LL(Denom) = significand(st0_ptr);
        }
        div_Xsig(&Numer, &Denom, &argSignif);
        exponent += norm_Xsig(&argSignif);

        if ((exponent >= -1)
            || ((exponent == -2) && (argSignif.msw > 0xd413ccd0))) {
                /* The argument is greater than sqrt(2)-1 (=0.414213562...) */
                /* Convert the argument by an identity for atan */
                transformed = 1;

                if (exponent >= 0) {
#ifdef PARANOID
                        if (!((exponent == 0) &&
                              (argSignif.lsw == 0) && (argSignif.midw == 0) &&
                              (argSignif.msw == 0x80000000))) {
                                EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic error */
                                return;
                        }
#endif /* PARANOID */
                        argSignif.msw = 0;      /* Make the transformed arg -> 0.0 */
                } else {
                        Numer.lsw = Denom.lsw = argSignif.lsw;
                        XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);

                        if (exponent < -1)
                                shr_Xsig(&Numer, -1 - exponent);
                        negate_Xsig(&Numer);

                        shr_Xsig(&Denom, -exponent);
                        Denom.msw |= 0x80000000;

                        div_Xsig(&Numer, &Denom, &argSignif);

                        exponent = -1 + norm_Xsig(&argSignif);
                }
        } else {
                transformed = 0;
        }

        argSq.lsw = argSignif.lsw;
        argSq.midw = argSignif.midw;
        argSq.msw = argSignif.msw;
        mul_Xsig_Xsig(&argSq, &argSq);

        argSqSq.lsw = argSq.lsw;
        argSqSq.midw = argSq.midw;
        argSqSq.msw = argSq.msw;
        mul_Xsig_Xsig(&argSqSq, &argSqSq);

        accumulatore.lsw = argSq.lsw;
        XSIG_LL(accumulatore) = XSIG_LL(argSq);

        shr_Xsig(&argSq, 2 * (-1 - exponent - 1));
        shr_Xsig(&argSqSq, 4 * (-1 - exponent - 1));

        /* Now have argSq etc with binary point at the left
           .1xxxxxxxx */

        /* Do the basic fixed point polynomial evaluation */
        accumulator.msw = accumulator.midw = accumulator.lsw = 0;
        polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
                        oddplterms, HIPOWERop - 1);
        mul64_Xsig(&accumulator, &XSIG_LL(argSq));
        negate_Xsig(&accumulator);
        polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms,
                        HIPOWERon - 1);
        negate_Xsig(&accumulator);
        add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);

        mul64_Xsig(&accumulatore, &denomterm);
        shr_Xsig(&accumulatore, 1 + 2 * (-1 - exponent));
        accumulatore.msw |= 0x80000000;

        div_Xsig(&accumulator, &accumulatore, &accumulator);

        mul_Xsig_Xsig(&accumulator, &argSignif);
        mul_Xsig_Xsig(&accumulator, &argSq);

        shr_Xsig(&accumulator, 3);
        negate_Xsig(&accumulator);
        add_Xsig_Xsig(&accumulator, &argSignif);

        if (transformed) {
                /* compute pi/4 - accumulator */
                shr_Xsig(&accumulator, -1 - exponent);
                negate_Xsig(&accumulator);
                add_Xsig_Xsig(&accumulator, &pi_signif);
                exponent = -1;
        }

        if (inverted) {
                /* compute pi/2 - accumulator */
                shr_Xsig(&accumulator, -exponent);
                negate_Xsig(&accumulator);
                add_Xsig_Xsig(&accumulator, &pi_signif);
                exponent = 0;
        }

        if (sign1) {
                /* compute pi - accumulator */
                shr_Xsig(&accumulator, 1 - exponent);
                negate_Xsig(&accumulator);
                add_Xsig_Xsig(&accumulator, &pi_signif);
                exponent = 1;
        }

        exponent += round_Xsig(&accumulator);

        significand(st1_ptr) = XSIG_LL(accumulator);
        setexponent16(st1_ptr, exponent);

        tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
        FPU_settagi(1, tag);

        set_precision_flag_up();        /* We do not really know if up or down,
                                           use this as the default. */

}