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209 lines
6.3 KiB
209 lines
6.3 KiB
// 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 [email protected] | |
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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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