332 lines
7.6 KiB
C
332 lines
7.6 KiB
C
/* Copyright (C) 2007-2017 Free Software Foundation, Inc.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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#ifndef _SQRT_MACROS_H_
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#define _SQRT_MACROS_H_
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#define FENCE __fence
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#if DOUBLE_EXTENDED_ON
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extern BINARY80 SQRT80 (BINARY80);
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__BID_INLINE__ UINT64
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short_sqrt128 (UINT128 A10) {
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BINARY80 lx, ly, l64;
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int_float f64;
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// 2^64
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f64.i = 0x5f800000;
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l64 = (BINARY80) f64.d;
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lx = (BINARY80) A10.w[1] * l64 + (BINARY80) A10.w[0];
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ly = SQRT80 (lx);
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return (UINT64) ly;
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}
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__BID_INLINE__ void
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long_sqrt128 (UINT128 * pCS, UINT256 C256) {
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UINT256 C4;
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UINT128 CS;
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UINT64 X;
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SINT64 SE;
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BINARY80 l64, lm64, l128, lxL, lx, ly, lS, lSH, lSL, lE, l3, l2,
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l1, l0, lp, lCl;
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int_float fx, f64, fm64;
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int *ple = (int *) &lx;
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// 2^64
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f64.i = 0x5f800000;
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l64 = (BINARY80) f64.d;
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l128 = l64 * l64;
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lx = l3 = (BINARY80) C256.w[3] * l64 * l128;
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l2 = (BINARY80) C256.w[2] * l128;
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lx = FENCE (lx + l2);
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l1 = (BINARY80) C256.w[1] * l64;
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lx = FENCE (lx + l1);
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l0 = (BINARY80) C256.w[0];
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lx = FENCE (lx + l0);
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// sqrt(C256)
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lS = SQRT80 (lx);
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// get coefficient
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// 2^(-64)
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fm64.i = 0x1f800000;
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lm64 = (BINARY80) fm64.d;
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CS.w[1] = (UINT64) (lS * lm64);
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CS.w[0] = (UINT64) (lS - (BINARY80) CS.w[1] * l64);
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///////////////////////////////////////
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// CAUTION!
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// little endian code only
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// add solution for big endian
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//////////////////////////////////////
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lSH = lS;
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*((UINT64 *) & lSH) &= 0xffffffff00000000ull;
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// correction for C256 rounding
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lCl = FENCE (l3 - lx);
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lCl = FENCE (lCl + l2);
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lCl = FENCE (lCl + l1);
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lCl = FENCE (lCl + l0);
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lSL = lS - lSH;
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//////////////////////////////////////////
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// Watch for compiler re-ordering
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//
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/////////////////////////////////////////
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// C256-S^2
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lxL = FENCE (lx - lSH * lSH);
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lp = lSH * lSL;
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lp += lp;
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lxL = FENCE (lxL - lp);
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lSL *= lSL;
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lxL = FENCE (lxL - lSL);
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lCl += lxL;
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// correction term
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lE = lCl / (lS + lS);
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// get low part of coefficient
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X = CS.w[0];
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if (lCl >= 0) {
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SE = (SINT64) (lE);
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CS.w[0] += SE;
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if (CS.w[0] < X)
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CS.w[1]++;
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} else {
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SE = (SINT64) (-lE);
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CS.w[0] -= SE;
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if (CS.w[0] > X)
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CS.w[1]--;
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}
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pCS->w[0] = CS.w[0];
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pCS->w[1] = CS.w[1];
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}
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#else
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extern double sqrt (double);
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__BID_INLINE__ UINT64
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short_sqrt128 (UINT128 A10) {
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UINT256 ARS, ARS0, AE0, AE, S;
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UINT64 MY, ES, CY;
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double lx, l64;
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int_double f64, ly;
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int ey, k;
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// 2^64
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f64.i = 0x43f0000000000000ull;
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l64 = f64.d;
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lx = (double) A10.w[1] * l64 + (double) A10.w[0];
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ly.d = 1.0 / sqrt (lx);
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MY = (ly.i & 0x000fffffffffffffull) | 0x0010000000000000ull;
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ey = 0x3ff - (ly.i >> 52);
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// A10*RS^2
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__mul_64x128_to_192 (ARS0, MY, A10);
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__mul_64x192_to_256 (ARS, MY, ARS0);
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// shr by 2*ey+40, to get a 64-bit value
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k = (ey << 1) + 104 - 64;
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if (k >= 128) {
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if (k > 128)
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ES = (ARS.w[2] >> (k - 128)) | (ARS.w[3] << (192 - k));
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else
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ES = ARS.w[2];
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} else {
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if (k >= 64) {
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ARS.w[0] = ARS.w[1];
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ARS.w[1] = ARS.w[2];
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k -= 64;
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}
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if (k) {
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__shr_128 (ARS, ARS, k);
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}
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ES = ARS.w[0];
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}
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ES = ((SINT64) ES) >> 1;
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if (((SINT64) ES) < 0) {
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ES = -ES;
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// A*RS*eps (scaled by 2^64)
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__mul_64x192_to_256 (AE0, ES, ARS0);
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AE.w[0] = AE0.w[1];
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AE.w[1] = AE0.w[2];
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AE.w[2] = AE0.w[3];
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__add_carry_out (S.w[0], CY, ARS0.w[0], AE.w[0]);
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__add_carry_in_out (S.w[1], CY, ARS0.w[1], AE.w[1], CY);
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S.w[2] = ARS0.w[2] + AE.w[2] + CY;
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} else {
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// A*RS*eps (scaled by 2^64)
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__mul_64x192_to_256 (AE0, ES, ARS0);
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AE.w[0] = AE0.w[1];
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AE.w[1] = AE0.w[2];
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AE.w[2] = AE0.w[3];
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__sub_borrow_out (S.w[0], CY, ARS0.w[0], AE.w[0]);
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__sub_borrow_in_out (S.w[1], CY, ARS0.w[1], AE.w[1], CY);
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S.w[2] = ARS0.w[2] - AE.w[2] - CY;
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}
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k = ey + 51;
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if (k >= 64) {
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if (k >= 128) {
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S.w[0] = S.w[2];
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S.w[1] = 0;
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k -= 128;
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} else {
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S.w[0] = S.w[1];
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S.w[1] = S.w[2];
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}
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k -= 64;
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}
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if (k) {
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__shr_128 (S, S, k);
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}
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return (UINT64) ((S.w[0] + 1) >> 1);
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}
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__BID_INLINE__ void
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long_sqrt128 (UINT128 * pCS, UINT256 C256) {
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UINT512 ARS0, ARS;
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UINT256 ARS00, AE, AE2, S;
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UINT128 ES, ES2, ARS1;
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UINT64 ES32, CY, MY;
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double l64, l128, lx, l2, l1, l0;
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int_double f64, ly;
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int ey, k, k2;
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// 2^64
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f64.i = 0x43f0000000000000ull;
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l64 = f64.d;
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l128 = l64 * l64;
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lx = (double) C256.w[3] * l64 * l128;
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l2 = (double) C256.w[2] * l128;
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lx = FENCE (lx + l2);
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l1 = (double) C256.w[1] * l64;
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lx = FENCE (lx + l1);
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l0 = (double) C256.w[0];
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lx = FENCE (lx + l0);
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// sqrt(C256)
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ly.d = 1.0 / sqrt (lx);
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MY = (ly.i & 0x000fffffffffffffull) | 0x0010000000000000ull;
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ey = 0x3ff - (ly.i >> 52);
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// A10*RS^2, scaled by 2^(2*ey+104)
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__mul_64x256_to_320 (ARS0, MY, C256);
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__mul_64x320_to_384 (ARS, MY, ARS0);
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// shr by k=(2*ey+104)-128
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// expect k is in the range (192, 256) if result in [10^33, 10^34)
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// apply an additional signed shift by 1 at the same time (to get eps=eps0/2)
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k = (ey << 1) + 104 - 128 - 192;
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k2 = 64 - k;
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ES.w[0] = (ARS.w[3] >> (k + 1)) | (ARS.w[4] << (k2 - 1));
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ES.w[1] = (ARS.w[4] >> k) | (ARS.w[5] << k2);
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ES.w[1] = ((SINT64) ES.w[1]) >> 1;
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// A*RS >> 192 (for error term computation)
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ARS1.w[0] = ARS0.w[3];
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ARS1.w[1] = ARS0.w[4];
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// A*RS>>64
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ARS00.w[0] = ARS0.w[1];
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ARS00.w[1] = ARS0.w[2];
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ARS00.w[2] = ARS0.w[3];
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ARS00.w[3] = ARS0.w[4];
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if (((SINT64) ES.w[1]) < 0) {
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ES.w[0] = -ES.w[0];
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ES.w[1] = -ES.w[1];
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if (ES.w[0])
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ES.w[1]--;
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// A*RS*eps
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__mul_128x128_to_256 (AE, ES, ARS1);
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__add_carry_out (S.w[0], CY, ARS00.w[0], AE.w[0]);
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__add_carry_in_out (S.w[1], CY, ARS00.w[1], AE.w[1], CY);
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__add_carry_in_out (S.w[2], CY, ARS00.w[2], AE.w[2], CY);
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S.w[3] = ARS00.w[3] + AE.w[3] + CY;
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} else {
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// A*RS*eps
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__mul_128x128_to_256 (AE, ES, ARS1);
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__sub_borrow_out (S.w[0], CY, ARS00.w[0], AE.w[0]);
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__sub_borrow_in_out (S.w[1], CY, ARS00.w[1], AE.w[1], CY);
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__sub_borrow_in_out (S.w[2], CY, ARS00.w[2], AE.w[2], CY);
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S.w[3] = ARS00.w[3] - AE.w[3] - CY;
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}
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// 3/2*eps^2, scaled by 2^128
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ES32 = ES.w[1] + (ES.w[1] >> 1);
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__mul_64x64_to_128 (ES2, ES32, ES.w[1]);
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// A*RS*3/2*eps^2
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__mul_128x128_to_256 (AE2, ES2, ARS1);
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// result, scaled by 2^(ey+52-64)
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__add_carry_out (S.w[0], CY, S.w[0], AE2.w[0]);
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__add_carry_in_out (S.w[1], CY, S.w[1], AE2.w[1], CY);
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__add_carry_in_out (S.w[2], CY, S.w[2], AE2.w[2], CY);
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S.w[3] = S.w[3] + AE2.w[3] + CY;
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// k in (0, 64)
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k = ey + 51 - 128;
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k2 = 64 - k;
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S.w[0] = (S.w[1] >> k) | (S.w[2] << k2);
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S.w[1] = (S.w[2] >> k) | (S.w[3] << k2);
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// round to nearest
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S.w[0]++;
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if (!S.w[0])
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S.w[1]++;
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pCS->w[0] = (S.w[1] << 63) | (S.w[0] >> 1);
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pCS->w[1] = S.w[1] >> 1;
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}
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#endif
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#endif
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