// SPDX-License-Identifier: GPL-2.0
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/*---------------------------------------------------------------------------+
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| poly_atan.c |
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| Compute the arctan of a FPU_REG, using a polynomial approximation. |
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| Copyright (C) 1992,1993,1994,1997 |
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| W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
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| E-mail billm@suburbia.net |
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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 "status_w.h"
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#include "control_w.h"
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#include "poly.h"
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#define HIPOWERon 6 /* odd poly, negative terms */
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static const unsigned long long oddnegterms[HIPOWERon] = {
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0x0000000000000000LL, /* Dummy (not for - 1.0) */
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0x015328437f756467LL,
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0x0005dda27b73dec6LL,
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0x0000226bf2bfb91aLL,
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0x000000ccc439c5f7LL,
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0x0000000355438407LL
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};
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#define HIPOWERop 6 /* odd poly, positive terms */
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static const unsigned long long oddplterms[HIPOWERop] = {
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/* 0xaaaaaaaaaaaaaaabLL, transferred to fixedpterm[] */
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0x0db55a71875c9ac2LL,
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0x0029fce2d67880b0LL,
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0x0000dfd3908b4596LL,
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0x00000550fd61dab4LL,
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0x0000001c9422b3f9LL,
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0x000000003e3301e1LL
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};
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static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL;
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static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa);
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static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b);
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/*--- poly_atan() -----------------------------------------------------------+
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+---------------------------------------------------------------------------*/
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void poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
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FPU_REG *st1_ptr, u_char st1_tag)
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{
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u_char transformed, inverted, sign1, sign2;
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int exponent;
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long int dummy_exp;
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Xsig accumulator, Numer, Denom, accumulatore, argSignif, argSq, argSqSq;
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u_char tag;
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sign1 = getsign(st0_ptr);
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sign2 = getsign(st1_ptr);
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if (st0_tag == TAG_Valid) {
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exponent = exponent(st0_ptr);
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} else {
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/* This gives non-compatible stack contents... */
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FPU_to_exp16(st0_ptr, st0_ptr);
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exponent = exponent16(st0_ptr);
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}
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if (st1_tag == TAG_Valid) {
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exponent -= exponent(st1_ptr);
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} else {
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/* This gives non-compatible stack contents... */
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FPU_to_exp16(st1_ptr, st1_ptr);
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exponent -= exponent16(st1_ptr);
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}
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if ((exponent < 0) || ((exponent == 0) &&
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((st0_ptr->sigh < st1_ptr->sigh) ||
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((st0_ptr->sigh == st1_ptr->sigh) &&
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(st0_ptr->sigl < st1_ptr->sigl))))) {
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inverted = 1;
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Numer.lsw = Denom.lsw = 0;
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XSIG_LL(Numer) = significand(st0_ptr);
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XSIG_LL(Denom) = significand(st1_ptr);
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} else {
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inverted = 0;
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exponent = -exponent;
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Numer.lsw = Denom.lsw = 0;
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XSIG_LL(Numer) = significand(st1_ptr);
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XSIG_LL(Denom) = significand(st0_ptr);
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}
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div_Xsig(&Numer, &Denom, &argSignif);
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exponent += norm_Xsig(&argSignif);
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if ((exponent >= -1)
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|| ((exponent == -2) && (argSignif.msw > 0xd413ccd0))) {
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/* The argument is greater than sqrt(2)-1 (=0.414213562...) */
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/* Convert the argument by an identity for atan */
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transformed = 1;
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if (exponent >= 0) {
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#ifdef PARANOID
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if (!((exponent == 0) &&
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(argSignif.lsw == 0) && (argSignif.midw == 0) &&
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(argSignif.msw == 0x80000000))) {
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EXCEPTION(EX_INTERNAL | 0x104); /* There must be a logic error */
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return;
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}
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#endif /* PARANOID */
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argSignif.msw = 0; /* Make the transformed arg -> 0.0 */
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} else {
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Numer.lsw = Denom.lsw = argSignif.lsw;
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XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);
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if (exponent < -1)
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shr_Xsig(&Numer, -1 - exponent);
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negate_Xsig(&Numer);
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shr_Xsig(&Denom, -exponent);
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Denom.msw |= 0x80000000;
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div_Xsig(&Numer, &Denom, &argSignif);
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exponent = -1 + norm_Xsig(&argSignif);
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}
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} else {
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transformed = 0;
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}
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argSq.lsw = argSignif.lsw;
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argSq.midw = argSignif.midw;
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argSq.msw = argSignif.msw;
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mul_Xsig_Xsig(&argSq, &argSq);
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argSqSq.lsw = argSq.lsw;
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argSqSq.midw = argSq.midw;
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argSqSq.msw = argSq.msw;
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mul_Xsig_Xsig(&argSqSq, &argSqSq);
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accumulatore.lsw = argSq.lsw;
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XSIG_LL(accumulatore) = XSIG_LL(argSq);
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shr_Xsig(&argSq, 2 * (-1 - exponent - 1));
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shr_Xsig(&argSqSq, 4 * (-1 - exponent - 1));
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/* Now have argSq etc with binary point at the left
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.1xxxxxxxx */
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/* Do the basic fixed point polynomial evaluation */
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accumulator.msw = accumulator.midw = accumulator.lsw = 0;
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polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
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oddplterms, HIPOWERop - 1);
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mul64_Xsig(&accumulator, &XSIG_LL(argSq));
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negate_Xsig(&accumulator);
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polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms,
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HIPOWERon - 1);
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negate_Xsig(&accumulator);
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add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);
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mul64_Xsig(&accumulatore, &denomterm);
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shr_Xsig(&accumulatore, 1 + 2 * (-1 - exponent));
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accumulatore.msw |= 0x80000000;
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div_Xsig(&accumulator, &accumulatore, &accumulator);
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mul_Xsig_Xsig(&accumulator, &argSignif);
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mul_Xsig_Xsig(&accumulator, &argSq);
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shr_Xsig(&accumulator, 3);
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negate_Xsig(&accumulator);
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add_Xsig_Xsig(&accumulator, &argSignif);
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if (transformed) {
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/* compute pi/4 - accumulator */
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shr_Xsig(&accumulator, -1 - exponent);
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negate_Xsig(&accumulator);
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add_Xsig_Xsig(&accumulator, &pi_signif);
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exponent = -1;
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}
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if (inverted) {
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/* compute pi/2 - accumulator */
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shr_Xsig(&accumulator, -exponent);
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negate_Xsig(&accumulator);
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add_Xsig_Xsig(&accumulator, &pi_signif);
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exponent = 0;
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}
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if (sign1) {
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/* compute pi - accumulator */
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shr_Xsig(&accumulator, 1 - exponent);
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negate_Xsig(&accumulator);
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add_Xsig_Xsig(&accumulator, &pi_signif);
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exponent = 1;
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}
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exponent += round_Xsig(&accumulator);
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significand(st1_ptr) = XSIG_LL(accumulator);
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setexponent16(st1_ptr, exponent);
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tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
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FPU_settagi(1, tag);
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set_precision_flag_up(); /* We do not really know if up or down,
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use this as the default. */
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}
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