From 1681468efc719aae5dc5bd3c9ae389118c36d3fe Mon Sep 17 00:00:00 2001 From: PJ Fanning Date: Wed, 1 Feb 2023 21:45:43 +0100 Subject: [PATCH] Revert "backport schubfach changes from v2.15 (#854)" This reverts commit b110805081c3625e6bd911ae50072d12f02b4ebf. --- .../core/io/schubfach/DoubleToDecimal.java | 469 +++--- .../core/io/schubfach/FloatToDecimal.java | 459 +++--- .../jackson/core/io/schubfach/MathUtils.java | 1310 ++++++++--------- 3 files changed, 1242 insertions(+), 996 deletions(-) diff --git a/src/main/java/com/fasterxml/jackson/core/io/schubfach/DoubleToDecimal.java b/src/main/java/com/fasterxml/jackson/core/io/schubfach/DoubleToDecimal.java index 6d3f58d503..2b7778a316 100644 --- a/src/main/java/com/fasterxml/jackson/core/io/schubfach/DoubleToDecimal.java +++ b/src/main/java/com/fasterxml/jackson/core/io/schubfach/DoubleToDecimal.java @@ -1,132 +1,252 @@ /* - * Copyright (c) 2021, 2022, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * Copyright 2018-2020 Raffaello Giulietti * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). + * The above copyright notice and this permission notice shall be included in + * all copies or substantial portions of the Software. * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + * THE SOFTWARE. */ package com.fasterxml.jackson.core.io.schubfach; import java.io.IOException; -import static java.lang.Double.*; -import static java.lang.Long.*; -import static com.fasterxml.jackson.core.io.schubfach.MathUtils.*; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog10pow2; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog10threeQuartersPow2; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog2pow10; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.g0; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.g1; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.multiplyHigh; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.pow10; +import static java.lang.Double.doubleToRawLongBits; +import static java.lang.Long.numberOfLeadingZeros; /** * This class exposes a method to render a {@code double} as a string. + * + * @author Raffaello Giulietti */ final public class DoubleToDecimal { /* - * For full details about this code see the following references: - * - * [1] Giulietti, "The Schubfach way to render doubles", - * https://drive.google.com/file/d/1gp5xv4CAa78SVgCeWfGqqI4FfYYYuNFb - * - * [2] IEEE Computer Society, "IEEE Standard for Floating-Point Arithmetic" - * - * [3] Bouvier & Zimmermann, "Division-Free Binary-to-Decimal Conversion" - * - * Divisions are avoided altogether for the benefit of those architectures - * that do not provide specific machine instructions or where they are slow. - * This is discussed in section 10 of [1]. + For full details about this code see the following references: + + [1] Giulietti, "The Schubfach way to render doubles", + https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN + + [2] IEEE Computer Society, "IEEE Standard for Floating-Point Arithmetic" + + [3] Bouvier & Zimmermann, "Division-Free Binary-to-Decimal Conversion" + + Divisions are avoided altogether for the benefit of those architectures + that do not provide specific machine instructions or where they are slow. + This is discussed in section 10 of [1]. */ - /* The precision in bits */ + // Sources with the license are here: https://github.com/c4f7fcce9cb06515/Schubfach/blob/3c92d3c9b1fead540616c918cdfef432bca53dfa/todec/src/math/FloatToDecimal.java + + // The precision in bits. static final int P = 53; - /* Exponent width in bits */ + // Exponent width in bits. private static final int W = (Double.SIZE - 1) - (P - 1); - /* Minimum value of the exponent: -(2^(W-1)) - P + 3 */ - static final int Q_MIN = (-1 << (W - 1)) - P + 3; + // Minimum value of the exponent: -(2^(W-1)) - P + 3. + static final int Q_MIN = (-1 << W - 1) - P + 3; - /* Maximum value of the exponent: 2^(W-1) - P */ - static final int Q_MAX = (1 << (W - 1)) - P; + // Maximum value of the exponent: 2^(W-1) - P. + static final int Q_MAX = (1 << W - 1) - P; - /* 10^(E_MIN - 1) <= MIN_VALUE < 10^E_MIN */ + // 10^(E_MIN - 1) <= MIN_VALUE < 10^E_MIN static final int E_MIN = -323; - /* 10^(E_MAX - 1) <= MAX_VALUE < 10^E_MAX */ + // 10^(E_MAX - 1) <= MAX_VALUE < 10^E_MAX static final int E_MAX = 309; - /* Threshold to detect tiny values, as in section 8.2.1 of [1] */ + // Threshold to detect tiny values, as in section 8.1.1 of [1] static final long C_TINY = 3; - /* The minimum and maximum k, as in section 8 of [1] */ + // The minimum and maximum k, as in section 8 of [1] static final int K_MIN = -324; static final int K_MAX = 292; - /* H is as in section 8.1 of [1] */ + // H is as in section 8 of [1]. static final int H = 17; - /* Minimum value of the significand of a normal value: 2^(P-1) */ - private static final long C_MIN = 1L << (P - 1); + // Minimum value of the significand of a normal value: 2^(P-1). + private static final long C_MIN = 1L << P - 1; - /* Mask to extract the biased exponent */ + // Mask to extract the biased exponent. private static final int BQ_MASK = (1 << W) - 1; - /* Mask to extract the fraction bits */ - private static final long T_MASK = (1L << (P - 1)) - 1; + // Mask to extract the fraction bits. + private static final long T_MASK = (1L << P - 1) - 1; - /* Used in rop() */ + // Used in rop(). private static final long MASK_63 = (1L << 63) - 1; - /* Used for left-to-tight digit extraction */ + // Used for left-to-tight digit extraction. private static final int MASK_28 = (1 << 28) - 1; - private static final int NON_SPECIAL = 0; - private static final int PLUS_ZERO = 1; - private static final int MINUS_ZERO = 2; - private static final int PLUS_INF = 3; - private static final int MINUS_INF = 4; - private static final int NAN = 5; + private static final int NON_SPECIAL = 0; + private static final int PLUS_ZERO = 1; + private static final int MINUS_ZERO = 2; + private static final int PLUS_INF = 3; + private static final int MINUS_INF = 4; + private static final int NAN = 5; + + // For thread-safety, each thread gets its own instance of this class. + private static final ThreadLocal threadLocal = + ThreadLocal.withInitial(DoubleToDecimal::new); /* - * Room for the longer of the forms - * -ddddd.dddddddddddd H + 2 characters - * -0.00ddddddddddddddddd H + 5 characters - * -d.ddddddddddddddddE-eee H + 7 characters - * where there are H digits d + Room for the longer of the forms + -ddddd.dddddddddddd H + 2 characters + -0.00ddddddddddddddddd H + 5 characters + -d.ddddddddddddddddE-eee H + 7 characters + where there are H digits d */ - public static final int MAX_CHARS = H + 7; + public final int MAX_CHARS = H + 7; + // Numerical results are created here... private final byte[] bytes = new byte[MAX_CHARS]; - /* Index into bytes of rightmost valid character */ + // ... and copied here in appendTo() + private final char[] chars = new char[MAX_CHARS]; + + // Index into bytes of rightmost valid character. private int index; private DoubleToDecimal() { } /** - * Returns a string representation of the {@code double} - * argument. All characters mentioned below are ASCII characters. + * Returns a string rendering of the {@code double} argument. * - * @param v the {@code double} to be converted. - * @return a string representation of the argument. - * @see Double#toString(double) + *

The characters of the result are all drawn from the ASCII set. + *

+ * + *

A decimal is a number of the form + * d×10i + * for some (unique) integers d > 0 and i such that + * d is not a multiple of 10. + * These integers are the significand and + * the exponent, respectively, of the decimal. + * The length of the decimal is the (unique) + * integer n meeting + * 10n-1 ≤ d < 10n. + * + *

The decimal dv + * for a finite positive {@code v} is defined as follows: + *

+ * + *

The (uniquely) selected decimal dv + * is then formatted. + * + *

Let d, i and n be the significand, exponent and + * length of dv, respectively. + * Further, let e = n + i - 1 and let + * d1…dn + * be the usual decimal expansion of the significand. + * Note that d1 ≠ 0 ≠ dn. + *

+ * + * @param v the {@code double} to be rendered. + * @return a string rendering of the argument. */ public static String toString(double v) { - return new DoubleToDecimal().toDecimalString(v); + return threadLocalInstance().toDecimalString(v); } /** @@ -142,7 +262,11 @@ public static String toString(double v) { */ public static Appendable appendTo(double v, Appendable app) throws IOException { - return new DoubleToDecimal().appendDecimalTo(v, app); + return threadLocalInstance().appendDecimalTo(v, app); + } + + private static DoubleToDecimal threadLocalInstance() { + return threadLocal.get(); } private String toDecimalString(double v) { @@ -160,18 +284,17 @@ private Appendable appendDecimalTo(double v, Appendable app) throws IOException { switch (toDecimal(v)) { case NON_SPECIAL: - char[] chars = new char[index + 1]; - for (int i = 0; i < chars.length; ++i) { + for (int i = 0; i <= index; ++i) { chars[i] = (char) bytes[i]; } if (app instanceof StringBuilder) { - return ((StringBuilder) app).append(chars); + return ((StringBuilder) app).append(chars, 0, index + 1); } if (app instanceof StringBuffer) { - return ((StringBuffer) app).append(chars); + return ((StringBuffer) app).append(chars, 0, index + 1); } - for (char c : chars) { - app.append(c); + for (int i = 0; i <= index; ++i) { + app.append(chars[i]); } return app; case PLUS_ZERO: return app.append("0.0"); @@ -183,22 +306,22 @@ private Appendable appendDecimalTo(double v, Appendable app) } /* - * Returns - * PLUS_ZERO iff v is 0.0 - * MINUS_ZERO iff v is -0.0 - * PLUS_INF iff v is POSITIVE_INFINITY - * MINUS_INF iff v is NEGATIVE_INFINITY - * NAN iff v is NaN + Returns + PLUS_ZERO iff v is 0.0 + MINUS_ZERO iff v is -0.0 + PLUS_INF iff v is POSITIVE_INFINITY + MINUS_INF iff v is NEGATIVE_INFINITY + NAN iff v is NaN */ private int toDecimal(double v) { /* - * For full details see references [2] and [1]. - * - * For finite v != 0, determine integers c and q such that - * |v| = c 2^q and - * Q_MIN <= q <= Q_MAX and - * either 2^(P-1) <= c < 2^P (normal) - * or 0 < c < 2^(P-1) and q = Q_MIN (subnormal) + For full details see references [2] and [1]. + + For finite v != 0, determine integers c and q such that + |v| = c 2^q and + Q_MIN <= q <= Q_MAX and + either 2^(P-1) <= c < 2^P (normal) + or 0 < c < 2^(P-1) and q = Q_MIN (subnormal) */ long bits = doubleToRawLongBits(v); long t = bits & T_MASK; @@ -209,10 +332,10 @@ private int toDecimal(double v) { append('-'); } if (bq != 0) { - /* normal value. Here mq = -q */ + // normal value. Here mq = -q int mq = -Q_MIN + 1 - bq; long c = C_MIN | t; - /* The fast path discussed in section 8.3 of [1] */ + // The fast path discussed in section 8.2 of [1]. if (0 < mq & mq < P) { long f = c >> mq; if (f << mq == c) { @@ -222,7 +345,7 @@ private int toDecimal(double v) { return toDecimal(-mq, c, 0); } if (t != 0) { - /* subnormal value */ + // subnormal value return t < C_TINY ? toDecimal(Q_MIN, 10 * t, -1) : toDecimal(Q_MIN, t, 0); @@ -237,21 +360,21 @@ private int toDecimal(double v) { private int toDecimal(int q, long c, int dk) { /* - * The skeleton corresponds to figure 7 of [1]. - * The efficient computations are those summarized in figure 9. - * - * Here's a correspondence between Java names and names in [1], - * expressed as approximate LaTeX source code and informally. - * Other names are identical. - * cb: \bar{c} "c-bar" - * cbr: \bar{c}_r "c-bar-r" - * cbl: \bar{c}_l "c-bar-l" - * - * vb: \bar{v} "v-bar" - * vbr: \bar{v}_r "v-bar-r" - * vbl: \bar{v}_l "v-bar-l" - * - * rop: r_o' "r-o-prime" + The skeleton corresponds to figure 4 of [1]. + The efficient computations are those summarized in figure 7. + + Here's a correspondence between Java names and names in [1], + expressed as approximate LaTeX source code and informally. + Other names are identical. + cb: \bar{c} "c-bar" + cbr: \bar{c}_r "c-bar-r" + cbl: \bar{c}_l "c-bar-l" + + vb: \bar{v} "v-bar" + vbr: \bar{v}_r "v-bar-r" + vbl: \bar{v}_l "v-bar-l" + + rop: r_o' "r-o-prime" */ int out = (int) c & 0x1; long cb = c << 2; @@ -259,22 +382,22 @@ private int toDecimal(int q, long c, int dk) { long cbl; int k; /* - * flog10pow2(e) = floor(log_10(2^e)) - * flog10threeQuartersPow2(e) = floor(log_10(3/4 2^e)) - * flog2pow10(e) = floor(log_2(10^e)) + flog10pow2(e) = floor(log_10(2^e)) + flog10threeQuartersPow2(e) = floor(log_10(3/4 2^e)) + flog2pow10(e) = floor(log_2(10^e)) */ if (c != C_MIN | q == Q_MIN) { - /* regular spacing */ + // regular spacing cbl = cb - 2; k = flog10pow2(q); } else { - /* irregular spacing */ + // irregular spacing cbl = cb - 1; k = flog10threeQuartersPow2(q); } int h = q + flog2pow10(-k) + 2; - /* g1 and g0 are as in section 9.8.3 of [1], so g = g1 2^63 + g0 */ + // g1 and g0 are as in section 9.9.3 of [1], so g = g1 2^63 + g0 long g1 = g1(k); long g0 = g0(k); @@ -285,15 +408,15 @@ private int toDecimal(int q, long c, int dk) { long s = vb >> 2; if (s >= 100) { /* - * For n = 17, m = 1 the table in section 10 of [1] shows - * s' = floor(s / 10) = floor(s 115_292_150_460_684_698 / 2^60) - * = floor(s 115_292_150_460_684_698 2^4 / 2^64) - * - * sp10 = 10 s' - * tp10 = 10 t' - * upin iff u' = sp10 10^k in Rv - * wpin iff w' = tp10 10^k in Rv - * See section 9.3 of [1]. + For n = 17, m = 1 the table in section 10 of [1] shows + s' = floor(s / 10) = floor(s 115_292_150_460_684_698 / 2^60) + = floor(s 115_292_150_460_684_698 2^4 / 2^64) + + sp10 = 10 s' + tp10 = 10 t' + upin iff u' = sp10 10^k in Rv + wpin iff w' = tp10 10^k in Rv + See section 9.4 of [1]. */ long sp10 = 10 * multiplyHigh(s, 115_292_150_460_684_698L << 4); long tp10 = sp10 + 10; @@ -305,29 +428,29 @@ private int toDecimal(int q, long c, int dk) { } /* - * 10 <= s < 100 or s >= 100 and u', w' not in Rv - * uin iff u = s 10^k in Rv - * win iff w = t 10^k in Rv - * See section 9.3 of [1]. + 10 <= s < 100 or s >= 100 and u', w' not in Rv + uin iff u = s 10^k in Rv + win iff w = t 10^k in Rv + See section 9.4 of [1]. */ long t = s + 1; boolean uin = vbl + out <= s << 2; boolean win = (t << 2) + out <= vbr; if (uin != win) { - /* Exactly one of u or w lies in Rv */ + // Exactly one of u or w lies in Rv. return toChars(uin ? s : t, k + dk); } /* - * Both u and w lie in Rv: determine the one closest to v. - * See section 9.3 of [1]. + Both u and w lie in Rv: determine the one closest to v. + See section 9.4 of [1]. */ long cmp = vb - (s + t << 1); return toChars(cmp < 0 || cmp == 0 && (s & 0x1) == 0 ? s : t, k + dk); } /* - * Computes rop(cp g 2^(-127)), where g = g1 2^63 + g0 - * See section 9.9 and figure 8 of [1]. + Computes rop(cp g 2^(-127)), where g = g1 2^63 + g0 + See section 9.10 and figure 5 of [1]. */ private static long rop(long g1, long g0, long cp) { long x1 = multiplyHigh(g0, cp); @@ -339,14 +462,14 @@ private static long rop(long g1, long g0, long cp) { } /* - * Formats the decimal f 10^e. + Formats the decimal f 10^e. */ private int toChars(long f, int e) { /* - * For details not discussed here see section 10 of [1]. - * - * Determine len such that - * 10^(len-1) <= f < 10^len + For details not discussed here see section 10 of [1]. + + Determine len such that + 10^(len-1) <= f < 10^len */ int len = flog10pow2(Long.SIZE - numberOfLeadingZeros(f)); if (f >= pow10(len)) { @@ -354,27 +477,27 @@ private int toChars(long f, int e) { } /* - * Let fp and ep be the original f and e, respectively. - * Transform f and e to ensure - * 10^(H-1) <= f < 10^H - * fp 10^ep = f 10^(e-H) = 0.f 10^e + Let fp and ep be the original f and e, respectively. + Transform f and e to ensure + 10^(H-1) <= f < 10^H + fp 10^ep = f 10^(e-H) = 0.f 10^e */ f *= pow10(H - len); e += len; /* - * The toChars?() methods perform left-to-right digits extraction - * using ints, provided that the arguments are limited to 8 digits. - * Therefore, split the H = 17 digits of f into: - * h = the most significant digit of f - * m = the next 8 most significant digits of f - * l = the last 8, least significant digits of f - * - * For n = 17, m = 8 the table in section 10 of [1] shows - * floor(f / 10^8) = floor(193_428_131_138_340_668 f / 2^84) = - * floor(floor(193_428_131_138_340_668 f / 2^64) / 2^20) - * and for n = 9, m = 8 - * floor(hm / 10^8) = floor(1_441_151_881 hm / 2^57) + The toChars?() methods perform left-to-right digits extraction + using ints, provided that the arguments are limited to 8 digits. + Therefore, split the H = 17 digits of f into: + h = the most significant digit of f + m = the next 8 most significant digits of f + l = the last 8, least significant digits of f + + For n = 17, m = 8 the table in section 10 of [1] shows + floor(f / 10^8) = floor(193_428_131_138_340_668 f / 2^84) = + floor(floor(193_428_131_138_340_668 f / 2^64) / 2^20) + and for n = 9, m = 8 + floor(hm / 10^8) = floor(1_441_151_881 hm / 2^57) */ long hm = multiplyHigh(f, 193_428_131_138_340_668L) >>> 20; int l = (int) (f - 100_000_000L * hm); @@ -392,9 +515,9 @@ private int toChars(long f, int e) { private int toChars1(int h, int m, int l, int e) { /* - * 0 < e <= 7: plain format without leading zeroes. - * Left-to-right digits extraction: - * algorithm 1 in [3], with b = 10, k = 8, n = 28. + 0 < e <= 7: plain format without leading zeroes. + Left-to-right digits extraction: + algorithm 1 in [3], with b = 10, k = 8, n = 28. */ appendDigit(h); int y = y(m); @@ -416,7 +539,7 @@ private int toChars1(int h, int m, int l, int e) { } private int toChars2(int h, int m, int l, int e) { - /* -3 < e <= 0: plain format with leading zeroes */ + // -3 < e <= 0: plain format with leading zeroes. appendDigit(0); append('.'); for (; e < 0; ++e) { @@ -429,7 +552,7 @@ private int toChars2(int h, int m, int l, int e) { } private int toChars3(int h, int m, int l, int e) { - /* -3 >= e | e > 7: computerized scientific notation */ + // -3 >= e | e > 7: computerized scientific notation appendDigit(h); append('.'); append8Digits(m); @@ -447,8 +570,8 @@ private void lowDigits(int l) { private void append8Digits(int m) { /* - * Left-to-right digits extraction: - * algorithm 1 in [3], with b = 10, k = 8, n = 28. + Left-to-right digits extraction: + algorithm 1 in [3], with b = 10, k = 8, n = 28. */ int y = y(m); for (int i = 0; i < 8; ++i) { @@ -462,7 +585,7 @@ private void removeTrailingZeroes() { while (bytes[index] == '0') { --index; } - /* ... but do not remove the one directly to the right of '.' */ + // ... but do not remove the one directly to the right of '.' if (bytes[index] == '.') { ++index; } @@ -470,12 +593,12 @@ private void removeTrailingZeroes() { private int y(int a) { /* - * Algorithm 1 in [3] needs computation of - * floor((a + 1) 2^n / b^k) - 1 - * with a < 10^8, b = 10, k = 8, n = 28. - * Noting that - * (a + 1) 2^n <= 10^8 2^28 < 10^17 - * For n = 17, m = 8 the table in section 10 of [1] leads to: + Algorithm 1 in [3] needs computation of + floor((a + 1) 2^n / b^k) - 1 + with a < 10^8, b = 10, k = 8, n = 28. + Noting that + (a + 1) 2^n <= 10^8 2^28 < 10^17 + For n = 17, m = 8 the table in section 10 of [1] leads to: */ return (int) (multiplyHigh( (long) (a + 1) << 28, @@ -495,16 +618,16 @@ private void exponent(int e) { int d; if (e >= 100) { /* - * For n = 3, m = 2 the table in section 10 of [1] shows - * floor(e / 100) = floor(1_311 e / 2^17) + For n = 3, m = 2 the table in section 10 of [1] shows + floor(e / 100) = floor(1_311 e / 2^17) */ d = e * 1_311 >>> 17; appendDigit(d); e -= 100 * d; } /* - * For n = 2, m = 1 the table in section 10 of [1] shows - * floor(e / 10) = floor(103 e / 2^10) + For n = 2, m = 1 the table in section 10 of [1] shows + floor(e / 10) = floor(103 e / 2^10) */ d = e * 103 >>> 10; appendDigit(d); @@ -519,7 +642,7 @@ private void appendDigit(int d) { bytes[++index] = (byte) ('0' + d); } - /* Using the deprecated constructor enhances performance */ + // Using the deprecated constructor enhances performance. @SuppressWarnings("deprecation") private String charsToString() { return new String(bytes, 0, 0, index + 1); diff --git a/src/main/java/com/fasterxml/jackson/core/io/schubfach/FloatToDecimal.java b/src/main/java/com/fasterxml/jackson/core/io/schubfach/FloatToDecimal.java index 1cd886d23d..9ce9cc2b34 100644 --- a/src/main/java/com/fasterxml/jackson/core/io/schubfach/FloatToDecimal.java +++ b/src/main/java/com/fasterxml/jackson/core/io/schubfach/FloatToDecimal.java @@ -1,132 +1,251 @@ /* - * Copyright (c) 2021, 2022, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * Copyright 2018-2020 Raffaello Giulietti * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). + * The above copyright notice and this permission notice shall be included in + * all copies or substantial portions of the Software. * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + * THE SOFTWARE. */ package com.fasterxml.jackson.core.io.schubfach; import java.io.IOException; -import static java.lang.Float.*; -import static java.lang.Integer.*; -import static com.fasterxml.jackson.core.io.schubfach.MathUtils.*; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog10pow2; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog10threeQuartersPow2; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.flog2pow10; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.g1; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.multiplyHigh; +import static com.fasterxml.jackson.core.io.schubfach.MathUtils.pow10; +import static java.lang.Float.floatToRawIntBits; +import static java.lang.Integer.numberOfLeadingZeros; /** * This class exposes a method to render a {@code float} as a string. + * + * @author Raffaello Giulietti */ final public class FloatToDecimal { /* - * For full details about this code see the following references: - * - * [1] Giulietti, "The Schubfach way to render doubles", - * https://drive.google.com/file/d/1gp5xv4CAa78SVgCeWfGqqI4FfYYYuNFb - * - * [2] IEEE Computer Society, "IEEE Standard for Floating-Point Arithmetic" - * - * [3] Bouvier & Zimmermann, "Division-Free Binary-to-Decimal Conversion" - * - * Divisions are avoided altogether for the benefit of those architectures - * that do not provide specific machine instructions or where they are slow. - * This is discussed in section 10 of [1]. + For full details about this code see the following references: + + [1] Giulietti, "The Schubfach way to render doubles", + https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN + + [2] IEEE Computer Society, "IEEE Standard for Floating-Point Arithmetic" + + [3] Bouvier & Zimmermann, "Division-Free Binary-to-Decimal Conversion" + + Divisions are avoided altogether for the benefit of those architectures + that do not provide specific machine instructions or where they are slow. + This is discussed in section 10 of [1]. */ - /* The precision in bits */ + // Sources with the license are here: https://github.com/c4f7fcce9cb06515/Schubfach/blob/3c92d3c9b1fead540616c918cdfef432bca53dfa/todec/src/math/FloatToDecimal.java + + // The precision in bits. static final int P = 24; - /* Exponent width in bits */ + // Exponent width in bits. private static final int W = (Float.SIZE - 1) - (P - 1); - /* Minimum value of the exponent: -(2^(W-1)) - P + 3 */ - static final int Q_MIN = (-1 << (W - 1)) - P + 3; + // Minimum value of the exponent: -(2^(W-1)) - P + 3. + static final int Q_MIN = (-1 << W - 1) - P + 3; - /* Maximum value of the exponent: 2^(W-1) - P */ - static final int Q_MAX = (1 << (W - 1)) - P; + // Maximum value of the exponent: 2^(W-1) - P. + static final int Q_MAX = (1 << W - 1) - P; - /* 10^(E_MIN - 1) <= MIN_VALUE < 10^E_MIN */ + // 10^(E_MIN - 1) <= MIN_VALUE < 10^E_MIN static final int E_MIN = -44; - /* 10^(E_MAX - 1) <= MAX_VALUE < 10^E_MAX */ + // 10^(E_MAX - 1) <= MAX_VALUE < 10^E_MAX static final int E_MAX = 39; - /* Threshold to detect tiny values, as in section 8.2.1 of [1] */ + // Threshold to detect tiny values, as in section 8.1.1 of [1] static final int C_TINY = 8; - /* The minimum and maximum k, as in section 8 of [1] */ + // The minimum and maximum k, as in section 8 of [1] static final int K_MIN = -45; static final int K_MAX = 31; - /* H is as in section 8.1 of [1] */ + // H is as in section 8 of [1]. static final int H = 9; - /* Minimum value of the significand of a normal value: 2^(P-1) */ - private static final int C_MIN = 1 << (P - 1); + // Minimum value of the significand of a normal value: 2^(P-1). + private static final int C_MIN = 1 << P - 1; - /* Mask to extract the biased exponent */ + // Mask to extract the biased exponent. private static final int BQ_MASK = (1 << W) - 1; - /* Mask to extract the fraction bits */ - private static final int T_MASK = (1 << (P - 1)) - 1; + // Mask to extract the fraction bits. + private static final int T_MASK = (1 << P - 1) - 1; - /* Used in rop() */ + // Used in rop(). private static final long MASK_32 = (1L << 32) - 1; - /* Used for left-to-tight digit extraction */ + // Used for left-to-tight digit extraction. private static final int MASK_28 = (1 << 28) - 1; - private static final int NON_SPECIAL = 0; - private static final int PLUS_ZERO = 1; - private static final int MINUS_ZERO = 2; - private static final int PLUS_INF = 3; - private static final int MINUS_INF = 4; - private static final int NAN = 5; + private static final int NON_SPECIAL = 0; + private static final int PLUS_ZERO = 1; + private static final int MINUS_ZERO = 2; + private static final int PLUS_INF = 3; + private static final int MINUS_INF = 4; + private static final int NAN = 5; + + // For thread-safety, each thread gets its own instance of this class. + private static final ThreadLocal threadLocal = + ThreadLocal.withInitial(FloatToDecimal::new); /* - * Room for the longer of the forms - * -ddddd.dddd H + 2 characters - * -0.00ddddddddd H + 5 characters - * -d.ddddddddE-ee H + 6 characters - * where there are H digits d + Room for the longer of the forms + -ddddd.dddd H + 2 characters + -0.00ddddddddd H + 5 characters + -d.ddddddddE-ee H + 6 characters + where there are H digits d */ - public static final int MAX_CHARS = H + 6; + public final int MAX_CHARS = H + 6; + // Numerical results are created here... private final byte[] bytes = new byte[MAX_CHARS]; - /* Index into bytes of rightmost valid character */ + // ... and copied here in appendTo() + private final char[] chars = new char[MAX_CHARS]; + + // Index into buf of rightmost valid character. private int index; private FloatToDecimal() { } /** - * Returns a string representation of the {@code float} - * argument. All characters mentioned below are ASCII characters. + * Returns a string rendering of the {@code float} argument. + * + *

The characters of the result are all drawn from the ASCII set. + *

    + *
  • Any NaN, whether quiet or signaling, is rendered as + * {@code "NaN"}, regardless of the sign bit. + *
  • The infinities +∞ and -∞ are rendered as + * {@code "Infinity"} and {@code "-Infinity"}, respectively. + *
  • The positive and negative zeroes are rendered as + * {@code "0.0"} and {@code "-0.0"}, respectively. + *
  • A finite negative {@code v} is rendered as the sign + * '{@code -}' followed by the rendering of the magnitude -{@code v}. + *
  • A finite positive {@code v} is rendered in two stages: + *
      + *
    • Selection of a decimal: A well-defined + * decimal dv is selected + * to represent {@code v}. + *
    • Formatting as a string: The decimal + * dv is formatted as a string, + * either in plain or in computerized scientific notation, + * depending on its value. + *
    + *
+ * + *

A decimal is a number of the form + * d×10i + * for some (unique) integers d > 0 and i such that + * d is not a multiple of 10. + * These integers are the significand and + * the exponent, respectively, of the decimal. + * The length of the decimal is the (unique) + * integer n meeting + * 10n-1 ≤ d < 10n. + * + *

The decimal dv + * for a finite positive {@code v} is defined as follows: + *

    + *
  • Let R be the set of all decimals that round to {@code v} + * according to the usual round-to-closest rule of + * IEEE 754 floating-point arithmetic. + *
  • Let m be the minimal length over all decimals in R. + *
  • When m ≥ 2, let T be the set of all decimals + * in R with length m. + * Otherwise, let T be the set of all decimals + * in R with length 1 or 2. + *
  • Define dv as + * the decimal in T that is closest to {@code v}. + * Or if there are two such decimals in T, + * select the one with the even significand (there is exactly one). + *
+ * + *

The (uniquely) selected decimal dv + * is then formatted. + * + *

Let d, i and n be the significand, exponent and + * length of dv, respectively. + * Further, let e = n + i - 1 and let + * d1…dn + * be the usual decimal expansion of the significand. + * Note that d1 ≠ 0 ≠ dn. + *

    + *
  • Case -3 ≤ e < 0: + * dv is formatted as + * 0.0…0d1…dn, + * where there are exactly -(n + i) zeroes between + * the decimal point and d1. + * For example, 123 × 10-4 is formatted as + * {@code 0.0123}. + *
  • Case 0 ≤ e < 7: + *
      + *
    • Subcase i ≥ 0: + * dv is formatted as + * d1…dn0…0.0, + * where there are exactly i zeroes + * between dn and the decimal point. + * For example, 123 × 102 is formatted as + * {@code 12300.0}. + *
    • Subcase i < 0: + * dv is formatted as + * d1…dn+i.dn+i+1…dn. + * There are exactly -i digits to the right of + * the decimal point. + * For example, 123 × 10-1 is formatted as + * {@code 12.3}. + *
    + *
  • Case e < -3 or e ≥ 7: + * computerized scientific notation is used to format + * dv. + * Here e is formatted as by {@link Integer#toString(int)}. + *
      + *
    • Subcase n = 1: + * dv is formatted as + * d1.0Ee. + * For example, 1 × 1023 is formatted as + * {@code 1.0E23}. + *
    • Subcase n > 1: + * dv is formatted as + * d1.d2…dnEe. + * For example, 123 × 10-21 is formatted as + * {@code 1.23E-19}. + *
    + *
* - * @param v the {@code float} to be converted. - * @return a string representation of the argument. - * @see Float#toString(float) + * @param v the {@code float} to be rendered. + * @return a string rendering of the argument. */ public static String toString(float v) { - return new FloatToDecimal().toDecimalString(v); + return threadLocalInstance().toDecimalString(v); } /** @@ -142,7 +261,11 @@ public static String toString(float v) { */ public static Appendable appendTo(float v, Appendable app) throws IOException { - return new FloatToDecimal().appendDecimalTo(v, app); + return threadLocalInstance().appendDecimalTo(v, app); + } + + private static FloatToDecimal threadLocalInstance() { + return threadLocal.get(); } private String toDecimalString(float v) { @@ -160,18 +283,17 @@ private Appendable appendDecimalTo(float v, Appendable app) throws IOException { switch (toDecimal(v)) { case NON_SPECIAL: - char[] chars = new char[index + 1]; - for (int i = 0; i < chars.length; ++i) { + for (int i = 0; i <= index; ++i) { chars[i] = (char) bytes[i]; } if (app instanceof StringBuilder) { - return ((StringBuilder) app).append(chars); + return ((StringBuilder) app).append(chars, 0, index + 1); } if (app instanceof StringBuffer) { - return ((StringBuffer) app).append(chars); + return ((StringBuffer) app).append(chars, 0, index + 1); } - for (char c : chars) { - app.append(c); + for (int i = 0; i <= index; ++i) { + app.append(chars[i]); } return app; case PLUS_ZERO: return app.append("0.0"); @@ -183,22 +305,22 @@ private Appendable appendDecimalTo(float v, Appendable app) } /* - * Returns - * PLUS_ZERO iff v is 0.0 - * MINUS_ZERO iff v is -0.0 - * PLUS_INF iff v is POSITIVE_INFINITY - * MINUS_INF iff v is NEGATIVE_INFINITY - * NAN iff v is NaN + Returns + PLUS_ZERO iff v is 0.0 + MINUS_ZERO iff v is -0.0 + PLUS_INF iff v is POSITIVE_INFINITY + MINUS_INF iff v is NEGATIVE_INFINITY + NAN iff v is NaN */ private int toDecimal(float v) { /* - * For full details see references [2] and [1]. - * - * For finite v != 0, determine integers c and q such that - * |v| = c 2^q and - * Q_MIN <= q <= Q_MAX and - * either 2^(P-1) <= c < 2^P (normal) - * or 0 < c < 2^(P-1) and q = Q_MIN (subnormal) + For full details see references [2] and [1]. + + For finite v != 0, determine integers c and q such that + |v| = c 2^q and + Q_MIN <= q <= Q_MAX and + either 2^(P-1) <= c < 2^P (normal) + or 0 < c < 2^(P-1) and q = Q_MIN (subnormal) */ int bits = floatToRawIntBits(v); int t = bits & T_MASK; @@ -209,10 +331,10 @@ private int toDecimal(float v) { append('-'); } if (bq != 0) { - /* normal value. Here mq = -q */ + // normal value. Here mq = -q int mq = -Q_MIN + 1 - bq; int c = C_MIN | t; - /* The fast path discussed in section 8.3 of [1] */ + // The fast path discussed in section 8.2 of [1]. if (0 < mq & mq < P) { int f = c >> mq; if (f << mq == c) { @@ -222,7 +344,7 @@ private int toDecimal(float v) { return toDecimal(-mq, c, 0); } if (t != 0) { - /* subnormal value */ + // subnormal value return t < C_TINY ? toDecimal(Q_MIN, 10 * t, -1) : toDecimal(Q_MIN, t, 0); @@ -237,22 +359,22 @@ private int toDecimal(float v) { private int toDecimal(int q, int c, int dk) { /* - * The skeleton corresponds to figure 7 of [1]. - * The efficient computations are those summarized in figure 9. - * Also check the appendix. - * - * Here's a correspondence between Java names and names in [1], - * expressed as approximate LaTeX source code and informally. - * Other names are identical. - * cb: \bar{c} "c-bar" - * cbr: \bar{c}_r "c-bar-r" - * cbl: \bar{c}_l "c-bar-l" - * - * vb: \bar{v} "v-bar" - * vbr: \bar{v}_r "v-bar-r" - * vbl: \bar{v}_l "v-bar-l" - * - * rop: r_o' "r-o-prime" + The skeleton corresponds to figure 4 of [1]. + The efficient computations are those summarized in figure 7. + Also check the appendix. + + Here's a correspondence between Java names and names in [1], + expressed as approximate LaTeX source code and informally. + Other names are identical. + cb: \bar{c} "c-bar" + cbr: \bar{c}_r "c-bar-r" + cbl: \bar{c}_l "c-bar-l" + + vb: \bar{v} "v-bar" + vbr: \bar{v}_r "v-bar-r" + vbl: \bar{v}_l "v-bar-l" + + rop: r_o' "r-o-prime" */ int out = c & 0x1; long cb = c << 2; @@ -260,22 +382,22 @@ private int toDecimal(int q, int c, int dk) { long cbl; int k; /* - * flog10pow2(e) = floor(log_10(2^e)) - * flog10threeQuartersPow2(e) = floor(log_10(3/4 2^e)) - * flog2pow10(e) = floor(log_2(10^e)) + flog10pow2(e) = floor(log_10(2^e)) + flog10threeQuartersPow2(e) = floor(log_10(3/4 2^e)) + flog2pow10(e) = floor(log_2(10^e)) */ if (c != C_MIN | q == Q_MIN) { - /* regular spacing */ + // regular spacing cbl = cb - 2; k = flog10pow2(q); } else { - /* irregular spacing */ + // irregular spacing0 cbl = cb - 1; k = flog10threeQuartersPow2(q); } int h = q + flog2pow10(-k) + 33; - /* g is as in the appendix */ + // g is as in the appendix long g = g1(k) + 1; int vb = rop(g, cb << h); @@ -285,14 +407,14 @@ private int toDecimal(int q, int c, int dk) { int s = vb >> 2; if (s >= 100) { /* - * For n = 9, m = 1 the table in section 10 of [1] shows - * s' = floor(s / 10) = floor(s 1_717_986_919 / 2^34) - * - * sp10 = 10 s' - * tp10 = 10 t' - * upin iff u' = sp10 10^k in Rv - * wpin iff w' = tp10 10^k in Rv - * See section 9.3 of [1]. + For n = 9, m = 1 the table in section 10 of [1] shows + s' = floor(s / 10) = floor(s 1_717_986_919 / 2^34) + + sp10 = 10 s' + tp10 = 10 t' + upin iff u' = sp10 10^k in Rv + wpin iff w' = tp10 10^k in Rv + See section 9.4 of [1]. */ int sp10 = 10 * (int) (s * 1_717_986_919L >>> 34); int tp10 = sp10 + 10; @@ -304,29 +426,29 @@ private int toDecimal(int q, int c, int dk) { } /* - * 10 <= s < 100 or s >= 100 and u', w' not in Rv - * uin iff u = s 10^k in Rv - * win iff w = t 10^k in Rv - * See section 9.3 of [1]. + 10 <= s < 100 or s >= 100 and u', w' not in Rv + uin iff u = s 10^k in Rv + win iff w = t 10^k in Rv + See section 9.4 of [1]. */ int t = s + 1; boolean uin = vbl + out <= s << 2; boolean win = (t << 2) + out <= vbr; if (uin != win) { - /* Exactly one of u or w lies in Rv */ + // Exactly one of u or w lies in Rv. return toChars(uin ? s : t, k + dk); } /* - * Both u and w lie in Rv: determine the one closest to v. - * See section 9.3 of [1]. + Both u and w lie in Rv: determine the one closest to v. + See section 9.4 of [1]. */ int cmp = vb - (s + t << 1); return toChars(cmp < 0 || cmp == 0 && (s & 0x1) == 0 ? s : t, k + dk); } /* - * Computes rop(cp g 2^(-95)) - * See appendix and figure 11 of [1]. + Computes rop(cp g 2^(-95)) + See appendix and figure 8 of [1]. */ private static int rop(long g, long cp) { long x1 = multiplyHigh(g, cp); @@ -335,14 +457,14 @@ private static int rop(long g, long cp) { } /* - * Formats the decimal f 10^e. + Formats the decimal f 10^e. */ private int toChars(int f, int e) { /* - * For details not discussed here see section 10 of [1]. - * - * Determine len such that - * 10^(len-1) <= f < 10^len + For details not discussed here see section 10 of [1]. + + Determine len such that + 10^(len-1) <= f < 10^len */ int len = flog10pow2(Integer.SIZE - numberOfLeadingZeros(f)); if (f >= pow10(len)) { @@ -350,23 +472,23 @@ private int toChars(int f, int e) { } /* - * Let fp and ep be the original f and e, respectively. - * Transform f and e to ensure - * 10^(H-1) <= f < 10^H - * fp 10^ep = f 10^(e-H) = 0.f 10^e + Let fp and ep be the original f and e, respectively. + Transform f and e to ensure + 10^(H-1) <= f < 10^H + fp 10^ep = f 10^(e-H) = 0.f 10^e */ - f *= (int)pow10(H - len); + f *= pow10(H - len); e += len; /* - * The toChars?() methods perform left-to-right digits extraction - * using ints, provided that the arguments are limited to 8 digits. - * Therefore, split the H = 9 digits of f into: - * h = the most significant digit of f - * l = the last 8, least significant digits of f - * - * For n = 9, m = 8 the table in section 10 of [1] shows - * floor(f / 10^8) = floor(1_441_151_881 f / 2^57) + The toChars?() methods perform left-to-right digits extraction + using ints, provided that the arguments are limited to 8 digits. + Therefore, split the H = 9 digits of f into: + h = the most significant digit of f + l = the last 8, least significant digits of f + + For n = 9, m = 8 the table in section 10 of [1] shows + floor(f / 10^8) = floor(1_441_151_881 f / 2^57) */ int h = (int) (f * 1_441_151_881L >>> 57); int l = f - 100_000_000 * h; @@ -382,9 +504,9 @@ private int toChars(int f, int e) { private int toChars1(int h, int l, int e) { /* - * 0 < e <= 7: plain format without leading zeroes. - * Left-to-right digits extraction: - * algorithm 1 in [3], with b = 10, k = 8, n = 28. + 0 < e <= 7: plain format without leading zeroes. + Left-to-right digits extraction: + algorithm 1 in [3], with b = 10, k = 8, n = 28. */ appendDigit(h); int y = y(l); @@ -406,7 +528,7 @@ private int toChars1(int h, int l, int e) { } private int toChars2(int h, int l, int e) { - /* -3 < e <= 0: plain format with leading zeroes */ + // -3 < e <= 0: plain format with leading zeroes. appendDigit(0); append('.'); for (; e < 0; ++e) { @@ -419,7 +541,7 @@ private int toChars2(int h, int l, int e) { } private int toChars3(int h, int l, int e) { - /* -3 >= e | e > 7: computerized scientific notation */ + // -3 >= e | e > 7: computerized scientific notation appendDigit(h); append('.'); append8Digits(l); @@ -430,8 +552,8 @@ private int toChars3(int h, int l, int e) { private void append8Digits(int m) { /* - * Left-to-right digits extraction: - * algorithm 1 in [3], with b = 10, k = 8, n = 28. + Left-to-right digits extraction: + algorithm 1 in [3], with b = 10, k = 8, n = 28. */ int y = y(m); for (int i = 0; i < 8; ++i) { @@ -445,7 +567,7 @@ private void removeTrailingZeroes() { while (bytes[index] == '0') { --index; } - /* ... but do not remove the one directly to the right of '.' */ + // ... but do not remove the one directly to the right of '.' if (bytes[index] == '.') { ++index; } @@ -453,12 +575,12 @@ private void removeTrailingZeroes() { private int y(int a) { /* - * Algorithm 1 in [3] needs computation of - * floor((a + 1) 2^n / b^k) - 1 - * with a < 10^8, b = 10, k = 8, n = 28. - * Noting that - * (a + 1) 2^n <= 10^8 2^28 < 10^17 - * For n = 17, m = 8 the table in section 10 of [1] leads to: + Algorithm 1 in [3] needs computation of + floor((a + 1) 2^n / b^k) - 1 + with a < 10^8, b = 10, k = 8, n = 28. + Noting that + (a + 1) 2^n <= 10^8 2^28 < 10^17 + For n = 17, m = 8 the table in section 10 of [1] leads to: */ return (int) (multiplyHigh( (long) (a + 1) << 28, @@ -476,8 +598,8 @@ private void exponent(int e) { return; } /* - * For n = 2, m = 1 the table in section 10 of [1] shows - * floor(e / 10) = floor(103 e / 2^10) + For n = 2, m = 1 the table in section 10 of [1] shows + floor(e / 10) = floor(103 e / 2^10) */ int d = e * 103 >>> 10; appendDigit(d); @@ -492,10 +614,11 @@ private void appendDigit(int d) { bytes[++index] = (byte) ('0' + d); } - /* Using the deprecated constructor enhances performance */ + // Using the deprecated constructor enhances performance. @SuppressWarnings("deprecation") private String charsToString() { return new String(bytes, 0, 0, index + 1); } } + diff --git a/src/main/java/com/fasterxml/jackson/core/io/schubfach/MathUtils.java b/src/main/java/com/fasterxml/jackson/core/io/schubfach/MathUtils.java index 28585748cc..c8e89d7c8b 100644 --- a/src/main/java/com/fasterxml/jackson/core/io/schubfach/MathUtils.java +++ b/src/main/java/com/fasterxml/jackson/core/io/schubfach/MathUtils.java @@ -1,26 +1,23 @@ /* - * Copyright (c) 2021, 2022, Oracle and/or its affiliates. All rights reserved. - * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * Copyright 2018-2020 Raffaello Giulietti * - * This code is free software; you can redistribute it and/or modify it - * under the terms of the GNU General Public License version 2 only, as - * published by the Free Software Foundation. Oracle designates this - * particular file as subject to the "Classpath" exception as provided - * by Oracle in the LICENSE file that accompanied this code. + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: * - * This code is distributed in the hope that it will be useful, but WITHOUT - * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or - * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License - * version 2 for more details (a copy is included in the LICENSE file that - * accompanied this code). + * The above copyright notice and this permission notice shall be included in + * all copies or substantial portions of the Software. * - * You should have received a copy of the GNU General Public License version - * 2 along with this work; if not, write to the Free Software Foundation, - * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. - * - * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA - * or visit www.oracle.com if you need additional information or have any - * questions. + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + * THE SOFTWARE. */ package com.fasterxml.jackson.core.io.schubfach; @@ -29,40 +26,43 @@ * This class exposes package private utilities for other classes. * Thus, all methods are assumed to be invoked with correct arguments, * so these are not checked at all. + * + * @author Raffaello Giulietti */ final class MathUtils { /* - * For full details about this code see the following reference: - * - * Giulietti, "The Schubfach way to render doubles", - * https://drive.google.com/file/d/1gp5xv4CAa78SVgCeWfGqqI4FfYYYuNFb + For full details about this code see the following reference: + + Giulietti, "The Schubfach way to render doubles", + https://drive.google.com/open?id=1luHhyQF9zKlM8yJ1nebU0OgVYhfC6CBN */ + // Sources with the license are here: https://github.com/c4f7fcce9cb06515/Schubfach/blob/3c92d3c9b1fead540616c918cdfef432bca53dfa/todec/src/math/FloatToDecimal.java + /* - * The boundaries for k in g0(int) and g1(int). - * K_MIN must be DoubleToDecimal.K_MIN or less. - * K_MAX must be DoubleToDecimal.K_MAX or more. + The boundaries for k in g0(int) and g1(int). + K_MIN must be DoubleToDecimal.K_MIN or less. + K_MAX must be DoubleToDecimal.K_MAX or more. */ static final int K_MIN = -324; static final int K_MAX = 292; - /* Must be DoubleToDecimal.H or more */ + // Must be DoubleToDecimal.H or more static final int H = 17; - /* C_10 = floor(log10(2) * 2^Q_10), A_10 = floor(log10(3/4) * 2^Q_10) */ + // C_10 = floor(log10(2) * 2^Q_10), A_10 = floor(log10(3/4) * 2^Q_10) private static final int Q_10 = 41; private static final long C_10 = 661_971_961_083L; private static final long A_10 = -274_743_187_321L; - /* C_2 = floor(log2(10) * 2^Q_2) */ + // C_2 = floor(log2(10) * 2^Q_2) private static final int Q_2 = 38; private static final long C_2 = 913_124_641_741L; private MathUtils() { - throw new RuntimeException("not supposed to be instantiated."); } - /* The first powers of 10. The last entry must be 10^(DoubleToDecimal.H) */ + // The first powers of 10. The last entry must be 10^H. private static final long[] pow10 = { 1L, 10L, @@ -100,11 +100,11 @@ static long pow10(int e) { * 10k ≤ 2{@code e} * < 10k+1. *

- * The result is correct when |{@code e}| ≤ 6_432_162. + * The result is correct when |{@code e}| ≤ 5_456_721. * Otherwise the result is undefined. * * @param e The exponent of 2, which should meet - * |{@code e}| ≤ 6_432_162 for safe results. + * |{@code e}| ≤ 5_456_721 for safe results. * @return ⌊log102{@code e}⌋. */ static int flog10pow2(int e) { @@ -117,11 +117,11 @@ static int flog10pow2(int e) { * < 10k+1. *

* The result is correct when - * -3_606_689 ≤ {@code e} ≤ 3_150_619. + * -2_956_395 ≤ {@code e} ≤ 2_500_325. * Otherwise the result is undefined. * * @param e The exponent of 2, which should meet - * -3_606_689 ≤ {@code e} ≤ 3_150_619 for safe results. + * -2_956_395 ≤ {@code e} ≤ 2_500_325 for safe results. * @return ⌊log10(3/4 · * 2{@code e})⌋. */ @@ -198,628 +198,628 @@ static long multiplyHigh(long x, long y) { } /* - * The precomputed values for g1(int) and g0(int). - * The first entry must be for an exponent of K_MIN or less. - * The last entry must be for an exponent of K_MAX or more. + The precomputed values for g1(int) and g0(int). + The first entry must be for an exponent of K_MIN or less. + The last entry must be for an exponent of K_MAX or more. */ private static final long[] g = { - 0x4F0C_EDC9_5A71_8DD4L, 0x5B01_E8B0_9AA0_D1B5L, // -324 - 0x7E7B_160E_F71C_1621L, 0x119C_A780_F767_B5EEL, // -323 - 0x652F_44D8_C5B0_11B4L, 0x0E16_EC67_2C52_F7F2L, // -322 - 0x50F2_9D7A_37C0_0E29L, 0x5812_56B8_F042_5FF5L, // -321 - 0x40C2_1794_F966_71BAL, 0x79A8_4560_C035_1991L, // -320 - 0x679C_F287_F570_B5F7L, 0x75DA_089A_CD21_C281L, // -319 - 0x52E3_F539_9126_F7F9L, 0x44AE_6D48_A41B_0201L, // -318 - 0x424F_F761_40EB_F994L, 0x36F1_F106_E9AF_34CDL, // -317 - 0x6A19_8BCE_CE46_5C20L, 0x57E9_81A4_A918_547BL, // -316 - 0x54E1_3CA5_71D1_E34DL, 0x2CBA_CE1D_5413_76C9L, // -315 - 0x43E7_63B7_8E41_82A4L, 0x23C8_A4E4_4342_C56EL, // -314 - 0x6CA5_6C58_E39C_043AL, 0x060D_D4A0_6B9E_08B0L, // -313 - 0x56EA_BD13_E949_9CFBL, 0x1E71_76E6_BC7E_6D59L, // -312 - 0x4588_9743_2107_B0C8L, 0x7EC1_2BEB_C9FE_BDE1L, // -311 - 0x6F40_F205_01A5_E7A7L, 0x7E01_DFDF_A997_9635L, // -310 - 0x5900_C19D_9AEB_1FB9L, 0x4B34_B319_5479_44F7L, // -309 - 0x4733_CE17_AF22_7FC7L, 0x55C3_C27A_A9FA_9D93L, // -308 - 0x71EC_7CF2_B1D0_CC72L, 0x5606_03F7_765D_C8EAL, // -307 - 0x5B23_9728_8E40_A38EL, 0x7804_CFF9_2B7E_3A55L, // -306 - 0x48E9_45BA_0B66_E93FL, 0x1337_0CC7_55FE_9511L, // -305 - 0x74A8_6F90_123E_41FEL, 0x51F1_AE0B_BCCA_881BL, // -304 - 0x5D53_8C73_41CB_67FEL, 0x74C1_5809_63D5_39AFL, // -303 - 0x4AA9_3D29_016F_8665L, 0x43CD_E007_8310_FAF3L, // -302 - 0x7775_2EA8_024C_0A3CL, 0x0616_333F_381B_2B1EL, // -301 - 0x5F90_F220_01D6_6E96L, 0x3811_C298_F9AF_55B1L, // -300 - 0x4C73_F4E6_67DE_BEDEL, 0x600E_3547_2E25_DE28L, // -299 - 0x7A53_2170_A631_3164L, 0x3349_EED8_49D6_303FL, // -298 - 0x61DC_1AC0_84F4_2783L, 0x42A1_8BE0_3B11_C033L, // -297 - 0x4E49_AF00_6A5C_EC69L, 0x1BB4_6FE6_95A7_CCF5L, // -296 - 0x7D42_B19A_43C7_E0A8L, 0x2C53_E63D_BC3F_AE55L, // -295 - 0x6435_5AE1_CFD3_1A20L, 0x2376_51CA_FCFF_BEAAL, // -294 - 0x502A_AF1B_0CA8_E1B3L, 0x35F8_416F_30CC_9888L, // -293 - 0x4022_25AF_3D53_E7C2L, 0x5E60_3458_F3D6_E06DL, // -292 - 0x669D_0918_621F_D937L, 0x4A33_86F4_B957_CD7BL, // -291 - 0x5217_3A79_E819_7A92L, 0x6E8F_9F2A_2DDF_D796L, // -290 - 0x41AC_2EC7_ECE1_2EDBL, 0x720C_7F54_F17F_DFABL, // -289 - 0x6913_7E0C_AE35_17C6L, 0x1CE0_CBBB_1BFF_CC45L, // -288 - 0x540F_980A_24F7_4638L, 0x171A_3C95_AFFF_D69EL, // -287 - 0x433F_ACD4_EA5F_6B60L, 0x127B_63AA_F333_1218L, // -286 - 0x6B99_1487_DD65_7899L, 0x6A5F_05DE_51EB_5026L, // -285 - 0x5614_106C_B11D_FA14L, 0x5518_D17E_A7EF_7352L, // -284 - 0x44DC_D9F0_8DB1_94DDL, 0x2A7A_4132_1FF2_C2A8L, // -283 - 0x6E2E_2980_E2B5_BAFBL, 0x5D90_6850_331E_043FL, // -282 - 0x5824_EE00_B55E_2F2FL, 0x6473_86A6_8F4B_3699L, // -281 - 0x4683_F19A_2AB1_BF59L, 0x36C2_D21E_D908_F87BL, // -280 - 0x70D3_1C29_DDE9_3228L, 0x579E_1CFE_280E_5A5DL, // -279 - 0x5A42_7CEE_4B20_F4EDL, 0x2C7E_7D98_200B_7B7EL, // -278 - 0x4835_30BE_A280_C3F1L, 0x09FE_CAE0_19A2_C932L, // -277 - 0x7388_4DFD_D0CE_064EL, 0x4331_4499_C29E_0EB6L, // -276 - 0x5C6D_0B31_73D8_050BL, 0x4F5A_9D47_CEE4_D891L, // -275 - 0x49F0_D5C1_2979_9DA2L, 0x72AE_E439_7250_AD41L, // -274 - 0x764E_22CE_A8C2_95D1L, 0x377E_39F5_83B4_4868L, // -273 - 0x5EA4_E8A5_53CE_DE41L, 0x12CB_6191_3629_D387L, // -272 - 0x4BB7_2084_430B_E500L, 0x756F_8140_F821_7605L, // -271 - 0x7925_00D3_9E79_6E67L, 0x6F18_CECE_59CF_233CL, // -270 - 0x60EA_670F_B1FA_BEB9L, 0x3F47_0BD8_47D8_E8FDL, // -269 - 0x4D88_5272_F4C8_9894L, 0x329F_3CAD_0647_20CAL, // -268 - 0x7C0D_50B7_EE0D_C0EDL, 0x3765_2DE1_A3A5_0143L, // -267 - 0x633D_DA2C_BE71_6724L, 0x2C50_F181_4FB7_3436L, // -266 - 0x4F64_AE8A_31F4_5283L, 0x3D0D_8E01_0C92_902BL, // -265 - 0x7F07_7DA9_E986_EA6BL, 0x7B48_E334_E0EA_8045L, // -264 - 0x659F_97BB_2138_BB89L, 0x4907_1C2A_4D88_669DL, // -263 - 0x514C_7962_80FA_2FA1L, 0x20D2_7CEE_A46D_1EE4L, // -262 - 0x4109_FAB5_33FB_594DL, 0x670E_CA58_838A_7F1DL, // -261 - 0x680F_F788_532B_C216L, 0x0B4A_DD5A_6C10_CB62L, // -260 - 0x533F_F939_DC23_01ABL, 0x22A2_4AAE_BCDA_3C4EL, // -259 - 0x4299_942E_49B5_9AEFL, 0x354E_A225_63E1_C9D8L, // -258 - 0x6A8F_537D_42BC_2B18L, 0x554A_9D08_9FCF_A95AL, // -257 - 0x553F_75FD_CEFC_EF46L, 0x776E_E406_E63F_BAAEL, // -256 - 0x4432_C4CB_0BFD_8C38L, 0x5F8B_E99F_1E99_6225L, // -255 - 0x6D1E_07AB_4662_79F4L, 0x3279_75CB_6428_9D08L, // -254 - 0x574B_3955_D1E8_6190L, 0x2861_2B09_1CED_4A6DL, // -253 - 0x45D5_C777_DB20_4E0DL, 0x06B4_226D_B0BD_D524L, // -252 - 0x6FBC_7259_5E9A_167BL, 0x2453_6A49_1AC9_5506L, // -251 - 0x5963_8EAD_E548_11FCL, 0x1D0F_883A_7BD4_4405L, // -250 - 0x4782_D88B_1DD3_4196L, 0x4A72_D361_FCA9_D004L, // -249 - 0x726A_F411_C952_028AL, 0x43EA_EBCF_FAA9_4CD3L, // -248 - 0x5B88_C341_6DDB_353BL, 0x4FEF_230C_C887_70A9L, // -247 - 0x493A_35CD_F17C_2A96L, 0x0CBF_4F3D_6D39_26EEL, // -246 - 0x7529_EFAF_E8C6_AA89L, 0x6132_1862_485B_717CL, // -245 - 0x5DBB_2626_53D2_2207L, 0x675B_46B5_06AF_8DFDL, // -244 - 0x4AFC_1E85_0FDB_4E6CL, 0x52AF_6BC4_0559_3E64L, // -243 - 0x77F9_CA6E_7FC5_4A47L, 0x377F_12D3_3BC1_FD6DL, // -242 - 0x5FFB_0858_6637_6E9FL, 0x45FF_4242_9634_CABDL, // -241 - 0x4CC8_D379_EB5F_8BB2L, 0x6B32_9B68_782A_3BCBL, // -240 - 0x7ADA_EBF6_4565_AC51L, 0x2B84_2BDA_59DD_2C77L, // -239 - 0x6248_BCC5_0451_56A7L, 0x3C69_BCAE_AE4A_89F9L, // -238 - 0x4EA0_9704_0374_4552L, 0x6387_CA25_583B_A194L, // -237 - 0x7DCD_BE6C_D253_A21EL, 0x05A6_103B_C05F_68EDL, // -236 - 0x64A4_9857_0EA9_4E7EL, 0x37B8_0CFC_99E5_ED8AL, // -235 - 0x5083_AD12_7221_0B98L, 0x2C93_3D96_E184_BE08L, // -234 - 0x4069_5741_F4E7_3C79L, 0x7075_CADF_1AD0_9807L, // -233 - 0x670E_F203_2171_FA5CL, 0x4D89_4498_2AE7_59A4L, // -232 - 0x5272_5B35_B45B_2EB0L, 0x3E07_6A13_5585_E150L, // -231 - 0x41F5_15C4_9048_F226L, 0x64D2_BB42_AAD1_810DL, // -230 - 0x6988_22D4_1A0E_503EL, 0x07B7_9204_4482_6815L, // -229 - 0x546C_E8A9_AE71_D9CBL, 0x1FC6_0E69_D068_5344L, // -228 - 0x438A_53BA_F1F4_AE3CL, 0x196B_3EBB_0D20_429DL, // -227 - 0x6C10_85F7_E987_7D2DL, 0x0F11_FDF8_1500_6A94L, // -226 - 0x5673_9E5F_EE05_FDBDL, 0x58DB_3193_4400_5543L, // -225 - 0x4529_4B7F_F19E_6497L, 0x60AF_5ADC_3666_AA9CL, // -224 - 0x6EA8_78CC_B5CA_3A8CL, 0x344B_C493_8A3D_DDC7L, // -223 - 0x5886_C70A_2B08_2ED6L, 0x5D09_6A0F_A1CB_17D2L, // -222 - 0x46D2_38D4_EF39_BF12L, 0x173A_BB3F_B4A2_7975L, // -221 - 0x7150_5AEE_4B8F_981DL, 0x0B91_2B99_2103_F588L, // -220 - 0x5AA6_AF25_093F_ACE4L, 0x0940_EFAD_B403_2AD3L, // -219 - 0x4885_58EA_6DCC_8A50L, 0x0767_2624_9002_88A9L, // -218 - 0x7408_8E43_E2E0_DD4CL, 0x723E_A36D_B337_410EL, // -217 - 0x5CD3_A503_1BE7_1770L, 0x5B65_4F8A_F5C5_CDA5L, // -216 - 0x4A42_EA68_E31F_45F3L, 0x62B7_72D5_916B_0AEBL, // -215 - 0x76D1_770E_3832_0986L, 0x0458_B7BC_1BDE_77DDL, // -214 - 0x5F0D_F8D8_2CF4_D46BL, 0x1D13_C630_164B_9318L, // -213 - 0x4C0B_2D79_BD90_A9EFL, 0x30DC_9E8C_DEA2_DC13L, // -212 - 0x79AB_7BF5_FC1A_A97FL, 0x0160_FDAE_3104_9351L, // -211 - 0x6155_FCC4_C9AE_EDFFL, 0x1AB3_FE24_F403_A90EL, // -210 - 0x4DDE_63D0_A158_BE65L, 0x6229_981D_9002_EDA5L, // -209 - 0x7C97_061A_9BC1_30A2L, 0x69DC_2695_B337_E2A1L, // -208 - 0x63AC_04E2_1634_26E8L, 0x54B0_1EDE_28F9_821BL, // -207 - 0x4FBC_D0B4_DE90_1F20L, 0x43C0_18B1_BA61_34E2L, // -206 - 0x7F94_8121_6419_CB67L, 0x1F99_C11C_5D68_549DL, // -205 - 0x6610_674D_E9AE_3C52L, 0x4C7B_00E3_7DED_107EL, // -204 - 0x51A6_B90B_2158_3042L, 0x09FC_00B5_FE57_4065L, // -203 - 0x4152_2DA2_8113_59CEL, 0x3B30_0091_9845_CD1DL, // -202 - 0x6883_7C37_34EB_C2E3L, 0x784C_CDB5_C06F_AE95L, // -201 - 0x539C_635F_5D89_68B6L, 0x2D0A_3E2B_0059_5877L, // -200 - 0x42E3_82B2_B13A_BA2BL, 0x3DA1_CB55_99E1_1393L, // -199 - 0x6B05_9DEA_B52A_C378L, 0x629C_7888_F634_EC1EL, // -198 - 0x559E_17EE_F755_692DL, 0x3549_FA07_2B5D_89B1L, // -197 - 0x447E_798B_F911_20F1L, 0x1107_FB38_EF7E_07C1L, // -196 - 0x6D97_28DF_F4E8_34B5L, 0x01A6_5EC1_7F30_0C68L, // -195 - 0x57AC_20B3_2A53_5D5DL, 0x4E1E_B234_65C0_09EDL, // -194 - 0x4623_4D5C_21DC_4AB1L, 0x24E5_5B5D_1E33_3B24L, // -193 - 0x7038_7BC6_9C93_AAB5L, 0x216E_F894_FD1E_C506L, // -192 - 0x59C6_C96B_B076_222AL, 0x4DF2_6077_30E5_6A6CL, // -191 - 0x47D2_3ABC_8D2B_4E88L, 0x3E5B_805F_5A51_21F0L, // -190 - 0x72E9_F794_1512_1740L, 0x63C5_9A32_2A1B_697FL, // -189 - 0x5BEE_5FA9_AA74_DF67L, 0x0304_7B5B_54E2_BACCL, // -188 - 0x498B_7FBA_EEC3_E5ECL, 0x0269_FC49_10B5_623DL, // -187 - 0x75AB_FF91_7E06_3CACL, 0x6A43_2D41_B455_69FBL, // -186 - 0x5E23_32DA_CB38_308AL, 0x21CF_5767_C377_87FCL, // -185 - 0x4B4F_5BE2_3C2C_F3A1L, 0x67D9_12B9_692C_6CCAL, // -184 - 0x787E_F969_F9E1_85CFL, 0x595B_5128_A847_1476L, // -183 - 0x6065_9454_C7E7_9E3FL, 0x6115_DA86_ED05_A9F8L, // -182 - 0x4D1E_1043_D31F_B1CCL, 0x4DAB_1538_BD9E_2193L, // -181 - 0x7B63_4D39_51CC_4FADL, 0x62AB_5527_95C9_CF52L, // -180 - 0x62B5_D761_0E3D_0C8BL, 0x0222_AA86_116E_3F75L, // -179 - 0x4EF7_DF80_D830_D6D5L, 0x4E82_2204_DABE_992AL, // -178 - 0x7E59_659A_F381_57BCL, 0x1736_9CD4_9130_F510L, // -177 - 0x6514_5148_C2CD_DFC9L, 0x5F5E_E3DD_40F3_F740L, // -176 - 0x50DD_0DD3_CF0B_196EL, 0x1918_B64A_9A5C_C5CDL, // -175 - 0x40B0_D7DC_A5A2_7ABEL, 0x4746_F83B_AEB0_9E3EL, // -174 - 0x6781_5961_0903_F797L, 0x253E_59F9_1780_FD2FL, // -173 - 0x52CD_E11A_6D9C_C612L, 0x50FE_AE60_DF9A_6426L, // -172 - 0x423E_4DAE_BE17_04DBL, 0x5A65_584D_7FAE_B685L, // -171 - 0x69FD_4917_968B_3AF9L, 0x10A2_26E2_65E4_573BL, // -170 - 0x54CA_A0DF_ABA2_9594L, 0x0D4E_8581_EB1D_1295L, // -169 - 0x43D5_4D7F_BC82_1143L, 0x243E_D134_BC17_4211L, // -168 - 0x6C88_7BFF_9403_4ED2L, 0x06CA_E854_6025_3682L, // -167 - 0x56D3_9666_1002_A574L, 0x6BD5_86A9_E684_2B9BL, // -166 - 0x4576_11EB_4002_1DF7L, 0x0977_9EEE_5203_5616L, // -165 - 0x6F23_4FDE_CCD0_2FF1L, 0x5BF2_97E3_B66B_BCEFL, // -164 - 0x58E9_0CB2_3D73_598EL, 0x165B_ACB6_2B89_63F3L, // -163 - 0x4720_D6F4_FDF5_E13EL, 0x4516_23C4_EFA1_1CC2L, // -162 - 0x71CE_24BB_2FEF_CECAL, 0x3B56_9FA1_7F68_2E03L, // -161 - 0x5B0B_5095_BFF3_0BD5L, 0x15DE_E61A_CC53_5803L, // -160 - 0x48D5_DA11_665C_0977L, 0x2B18_B815_7042_ACCFL, // -159 - 0x7489_5CE8_A3C6_758BL, 0x5E8D_F355_806A_AE18L, // -158 - 0x5D3A_B0BA_1C9E_C46FL, 0x653E_5C44_66BB_BE7AL, // -157 - 0x4A95_5A2E_7D4B_D059L, 0x3765_169D_1EFC_9861L, // -156 - 0x7755_5D17_2EDF_B3C2L, 0x256E_8A94_FE60_F3CFL, // -155 - 0x5F77_7DAC_257F_C301L, 0x6ABE_D543_FEB3_F63FL, // -154 - 0x4C5F_97BC_EACC_9C01L, 0x3BCB_DDCF_FEF6_5E99L, // -153 - 0x7A32_8C61_77AD_C668L, 0x5FAC_9619_97F0_975BL, // -152 - 0x61C2_09E7_92F1_6B86L, 0x7FBD_44E1_465A_12AFL, // -151 - 0x4E34_D4B9_425A_BC6BL, 0x7FCA_9D81_0514_DBBFL, // -150 - 0x7D21_545B_9D5D_FA46L, 0x32DD_C8CE_6E87_C5FFL, // -149 - 0x641A_A9E2_E44B_2E9EL, 0x5BE4_A0A5_2539_6B32L, // -148 - 0x5015_54B5_836F_587EL, 0x7CB6_E6EA_842D_EF5CL, // -147 - 0x4011_1091_35F2_AD32L, 0x3092_5255_368B_25E3L, // -146 - 0x6681_B41B_8984_4850L, 0x4DB6_EA21_F0DE_A304L, // -145 - 0x5201_5CE2_D469_D373L, 0x57C5_881B_2718_826AL, // -144 - 0x419A_B0B5_76BB_0F8FL, 0x5FD1_39AF_527A_01EFL, // -143 - 0x68F7_8122_5791_B27FL, 0x4C81_F5E5_50C3_364AL, // -142 - 0x53F9_341B_7941_5B99L, 0x239B_2B1D_DA35_C508L, // -141 - 0x432D_C349_2DCD_E2E1L, 0x02E2_88E4_AE91_6A6DL, // -140 - 0x6B7C_6BA8_4949_6B01L, 0x516A_74A1_174F_10AEL, // -139 - 0x55FD_22ED_076D_EF34L, 0x4121_F6E7_45D8_DA25L, // -138 - 0x44CA_8257_3924_BF5DL, 0x1A81_9252_9E47_14EBL, // -137 - 0x6E10_D08B_8EA1_322EL, 0x5D9C_1D50_FD3E_87DDL, // -136 - 0x580D_73A2_D880_F4F2L, 0x17B0_1773_FDCB_9FE4L, // -135 - 0x4671_294F_139A_5D8EL, 0x4626_7929_97D6_1984L, // -134 - 0x70B5_0EE4_EC2A_2F4AL, 0x3D0A_5B75_BFBC_F59FL, // -133 - 0x5A2A_7250_BCEE_8C3BL, 0x4A6E_AF91_6630_C47FL, // -132 - 0x4821_F50D_63F2_09C9L, 0x21F2_260D_EB5A_36CCL, // -131 - 0x7369_8815_6CB6_760EL, 0x6983_7016_455D_247AL, // -130 - 0x5C54_6CDD_F091_F80BL, 0x6E02_C011_D117_5062L, // -129 - 0x49DD_23E4_C074_C66FL, 0x719B_CCDB_0DAC_404EL, // -128 - 0x762E_9FD4_6721_3D7FL, 0x68F9_47C4_E2AD_33B0L, // -127 - 0x5E8B_B310_5280_FDFFL, 0x6D94_396A_4EF0_F627L, // -126 - 0x4BA2_F5A6_A867_3199L, 0x3E10_2DEE_A58D_91B9L, // -125 - 0x7904_BC3D_DA3E_B5C2L, 0x3019_E317_6F48_E927L, // -124 - 0x60D0_9697_E1CB_C49BL, 0x4014_B5AC_5907_20ECL, // -123 - 0x4D73_ABAC_B4A3_03AFL, 0x4CDD_5E23_7A6C_1A57L, // -122 - 0x7BEC_45E1_2104_D2B2L, 0x47C8_969F_2A46_908AL, // -121 - 0x6323_6B1A_80D0_A88EL, 0x6CA0_787F_5505_406FL, // -120 - 0x4F4F_88E2_00A6_ED3FL, 0x0A19_F9FF_7737_66BFL, // -119 - 0x7EE5_A7D0_010B_1531L, 0x5CF6_5CCB_F1F2_3DFEL, // -118 - 0x6584_8640_00D5_AA8EL, 0x172B_7D6F_F4C1_CB32L, // -117 - 0x5136_D1CC_CD77_BBA4L, 0x78EF_978C_C3CE_3C28L, // -116 - 0x40F8_A7D7_0AC6_2FB7L, 0x13F2_DFA3_CFD8_3020L, // -115 - 0x67F4_3FBE_77A3_7F8BL, 0x3984_9906_1959_E699L, // -114 - 0x5329_CC98_5FB5_FFA2L, 0x6136_E0D1_ADE1_8548L, // -113 - 0x4287_D6E0_4C91_994FL, 0x00F8_B3DA_F181_376DL, // -112 - 0x6A72_F166_E0E8_F54BL, 0x1B27_862B_1C01_F247L, // -111 - 0x5528_C11F_1A53_F76FL, 0x2F52_D1BC_1667_F506L, // -110 - 0x4420_9A7F_4843_2C59L, 0x0C42_4163_451F_F738L, // -109 - 0x6D00_F732_0D38_46F4L, 0x7A03_9BD2_0833_2526L, // -108 - 0x5733_F8F4_D760_38C3L, 0x7B36_1641_A028_EA85L, // -107 - 0x45C3_2D90_AC4C_FA36L, 0x2F5E_7834_8020_BB9EL, // -106 - 0x6F9E_AF4D_E07B_29F0L, 0x4BCA_59ED_99CD_F8FCL, // -105 - 0x594B_BF71_8062_87F3L, 0x563B_7B24_7B0B_2D96L, // -104 - 0x476F_CC5A_CD1B_9FF6L, 0x11C9_2F50_626F_57ACL, // -103 - 0x724C_7A2A_E1C5_CCBDL, 0x02DB_7EE7_03E5_5912L, // -102 - 0x5B70_61BB_E7D1_7097L, 0x1BE2_CBEC_031D_E0DCL, // -101 - 0x4926_B496_530D_F3ACL, 0x164F_0989_9C17_E716L, // -100 - 0x750A_BA8A_1E7C_B913L, 0x3D4B_4275_C68C_A4F0L, // -99 - 0x5DA2_2ED4_E530_940FL, 0x4AA2_9B91_6BA3_B726L, // -98 - 0x4AE8_2577_1DC0_7672L, 0x6EE8_7C74_561C_9285L, // -97 - 0x77D9_D58B_62CD_8A51L, 0x3173_FA53_BCFA_8408L, // -96 - 0x5FE1_77A2_B571_3B74L, 0x278F_FB76_30C8_69A0L, // -95 - 0x4CB4_5FB5_5DF4_2F90L, 0x1FA6_62C4_F3D3_87B3L, // -94 - 0x7ABA_32BB_C986_B280L, 0x32A3_D13B_1FB8_D91FL, // -93 - 0x622E_8EFC_A138_8ECDL, 0x0EE9_742F_4C93_E0E6L, // -92 - 0x4E8B_A596_E760_723DL, 0x58BA_C359_0A0F_E71EL, // -91 - 0x7DAC_3C24_A567_1D2FL, 0x412A_D228_1019_71C9L, // -90 - 0x6489_C9B6_EAB8_E426L, 0x00EF_0E86_7347_8E3BL, // -89 - 0x506E_3AF8_BBC7_1CEBL, 0x1A58_D86B_8F6C_71C9L, // -88 - 0x4058_2F2D_6305_B0BCL, 0x1513_E056_0C56_C16EL, // -87 - 0x66F3_7EAF_04D5_E793L, 0x3B53_0089_AD57_9BE2L, // -86 - 0x525C_6558_D0AB_1FA9L, 0x15DC_006E_2446_164FL, // -85 - 0x41E3_8447_0D55_B2EDL, 0x5E49_99F1_B69E_783FL, // -84 - 0x696C_06D8_1555_EB15L, 0x7D42_8FE9_2430_C065L, // -83 - 0x5456_6BE0_1111_88DEL, 0x3102_0CBA_835A_3384L, // -82 - 0x4378_564C_DA74_6D7EL, 0x5A68_0A2E_CF7B_5C69L, // -81 - 0x6BF3_BD47_C3ED_7BFDL, 0x770C_DD17_B25E_FA42L, // -80 - 0x565C_976C_9CBD_FCCBL, 0x1270_B0DF_C1E5_9502L, // -79 - 0x4516_DF8A_16FE_63D5L, 0x5B8D_5A4C_9B1E_10CEL, // -78 - 0x6E8A_FF43_57FD_6C89L, 0x127B_C3AD_C4FC_E7B0L, // -77 - 0x586F_329C_4664_56D4L, 0x0EC9_6957_D0CA_52F3L, // -76 - 0x46BF_5BB0_3850_4576L, 0x3F07_8779_73D5_0F29L, // -75 - 0x7132_2C4D_26E6_D58AL, 0x31A5_A58F_1FBB_4B75L, // -74 - 0x5A8E_89D7_5252_446EL, 0x5AEA_EAD8_E62F_6F91L, // -73 - 0x4872_07DF_750E_9D25L, 0x2F22_557A_51BF_8C74L, // -72 - 0x73E9_A632_54E4_2EA2L, 0x1836_EF2A_1C65_AD86L, // -71 - 0x5CBA_EB5B_771C_F21BL, 0x2CF8_BF54_E384_8AD2L, // -70 - 0x4A2F_22AF_927D_8E7CL, 0x23FA_32AA_4F9D_3BDBL, // -69 - 0x76B1_D118_EA62_7D93L, 0x5329_EAAA_18FB_92F8L, // -68 - 0x5EF4_A747_21E8_6476L, 0x0F54_BBBB_472F_A8C6L, // -67 - 0x4BF6_EC38_E7ED_1D2BL, 0x25DD_62FC_38F2_ED6CL, // -66 - 0x798B_138E_3FE1_C845L, 0x22FB_D193_8E51_7BDFL, // -65 - 0x613C_0FA4_FFE7_D36AL, 0x4F2F_DADC_71DA_C97FL, // -64 - 0x4DC9_A61D_9986_42BBL, 0x58F3_157D_27E2_3ACCL, // -63 - 0x7C75_D695_C270_6AC5L, 0x74B8_2261_D969_F7ADL, // -62 - 0x6391_7877_CEC0_556BL, 0x1093_4EB4_ADEE_5FBEL, // -61 - 0x4FA7_9393_0BCD_1122L, 0x4075_D890_8B25_1965L, // -60 - 0x7F72_85B8_12E1_B504L, 0x00BC_8DB4_11D4_F56EL, // -59 - 0x65F5_37C6_7581_5D9CL, 0x66FD_3E29_A7DD_9125L, // -58 - 0x5190_F96B_9134_4AE3L, 0x6BFD_CB54_864A_DA84L, // -57 - 0x4140_C789_40F6_A24FL, 0x6FFE_3C43_9EA2_486AL, // -56 - 0x6867_A5A8_67F1_03B2L, 0x7FFD_2D38_FDD0_73DCL, // -55 - 0x5386_1E20_5327_3628L, 0x6664_242D_97D9_F64AL, // -54 - 0x42D1_B1B3_75B8_F820L, 0x51E9_B68A_DFE1_91D5L, // -53 - 0x6AE9_1C52_55F4_C034L, 0x1CA9_2411_6635_B621L, // -52 - 0x5587_49DB_77F7_0029L, 0x63BA_8341_1E91_5E81L, // -51 - 0x446C_3B15_F992_6687L, 0x6962_029A_7EDA_B201L, // -50 - 0x6D79_F823_28EA_3DA6L, 0x0F03_375D_97C4_5001L, // -49 - 0x5794_C682_8721_CAEBL, 0x259C_2C4A_DFD0_4001L, // -48 - 0x4610_9ECE_D281_6F22L, 0x5149_BD08_B30D_0001L, // -47 - 0x701A_97B1_50CF_1837L, 0x3542_C80D_EB48_0001L, // -46 - 0x59AE_DFC1_0D72_79C5L, 0x7768_A00B_22A0_0001L, // -45 - 0x47BF_1967_3DF5_2E37L, 0x7920_8008_E880_0001L, // -44 - 0x72CB_5BD8_6321_E38CL, 0x5B67_3341_7400_0001L, // -43 - 0x5BD5_E313_8281_82D6L, 0x7C52_8F67_9000_0001L, // -42 - 0x4977_E8DC_6867_9BDFL, 0x16A8_72B9_4000_0001L, // -41 - 0x758C_A7C7_0D72_92FEL, 0x5773_EAC2_0000_0001L, // -40 - 0x5E0A_1FD2_7128_7598L, 0x45F6_5568_0000_0001L, // -39 - 0x4B3B_4CA8_5A86_C47AL, 0x04C5_1120_0000_0001L, // -38 - 0x785E_E10D_5DA4_6D90L, 0x07A1_B500_0000_0001L, // -37 - 0x604B_E73D_E483_8AD9L, 0x52E7_C400_0000_0001L, // -36 - 0x4D09_85CB_1D36_08AEL, 0x0F1F_D000_0000_0001L, // -35 - 0x7B42_6FAB_61F0_0DE3L, 0x31CC_8000_0000_0001L, // -34 - 0x629B_8C89_1B26_7182L, 0x5B0A_0000_0000_0001L, // -33 - 0x4EE2_D6D4_15B8_5ACEL, 0x7C08_0000_0000_0001L, // -32 - 0x7E37_BE20_22C0_914BL, 0x1340_0000_0000_0001L, // -31 - 0x64F9_64E6_8233_A76FL, 0x2900_0000_0000_0001L, // -30 - 0x50C7_83EB_9B5C_85F2L, 0x5400_0000_0000_0001L, // -29 - 0x409F_9CBC_7C4A_04C2L, 0x1000_0000_0000_0001L, // -28 - 0x6765_C793_FA10_079DL, 0x0000_0000_0000_0001L, // -27 - 0x52B7_D2DC_C80C_D2E4L, 0x0000_0000_0000_0001L, // -26 - 0x422C_A8B0_A00A_4250L, 0x0000_0000_0000_0001L, // -25 - 0x69E1_0DE7_6676_D080L, 0x0000_0000_0000_0001L, // -24 - 0x54B4_0B1F_852B_DA00L, 0x0000_0000_0000_0001L, // -23 - 0x43C3_3C19_3756_4800L, 0x0000_0000_0000_0001L, // -22 - 0x6C6B_935B_8BBD_4000L, 0x0000_0000_0000_0001L, // -21 - 0x56BC_75E2_D631_0000L, 0x0000_0000_0000_0001L, // -20 - 0x4563_9182_44F4_0000L, 0x0000_0000_0000_0001L, // -19 - 0x6F05_B59D_3B20_0000L, 0x0000_0000_0000_0001L, // -18 - 0x58D1_5E17_6280_0000L, 0x0000_0000_0000_0001L, // -17 - 0x470D_E4DF_8200_0000L, 0x0000_0000_0000_0001L, // -16 - 0x71AF_D498_D000_0000L, 0x0000_0000_0000_0001L, // -15 - 0x5AF3_107A_4000_0000L, 0x0000_0000_0000_0001L, // -14 - 0x48C2_7395_0000_0000L, 0x0000_0000_0000_0001L, // -13 - 0x746A_5288_0000_0000L, 0x0000_0000_0000_0001L, // -12 - 0x5D21_DBA0_0000_0000L, 0x0000_0000_0000_0001L, // -11 - 0x4A81_7C80_0000_0000L, 0x0000_0000_0000_0001L, // -10 - 0x7735_9400_0000_0000L, 0x0000_0000_0000_0001L, // -9 - 0x5F5E_1000_0000_0000L, 0x0000_0000_0000_0001L, // -8 - 0x4C4B_4000_0000_0000L, 0x0000_0000_0000_0001L, // -7 - 0x7A12_0000_0000_0000L, 0x0000_0000_0000_0001L, // -6 - 0x61A8_0000_0000_0000L, 0x0000_0000_0000_0001L, // -5 - 0x4E20_0000_0000_0000L, 0x0000_0000_0000_0001L, // -4 - 0x7D00_0000_0000_0000L, 0x0000_0000_0000_0001L, // -3 - 0x6400_0000_0000_0000L, 0x0000_0000_0000_0001L, // -2 - 0x5000_0000_0000_0000L, 0x0000_0000_0000_0001L, // -1 - 0x4000_0000_0000_0000L, 0x0000_0000_0000_0001L, // 0 - 0x6666_6666_6666_6666L, 0x3333_3333_3333_3334L, // 1 - 0x51EB_851E_B851_EB85L, 0x0F5C_28F5_C28F_5C29L, // 2 - 0x4189_374B_C6A7_EF9DL, 0x5916_872B_020C_49BBL, // 3 - 0x68DB_8BAC_710C_B295L, 0x74F0_D844_D013_A92BL, // 4 - 0x53E2_D623_8DA3_C211L, 0x43F3_E037_0CDC_8755L, // 5 - 0x431B_DE82_D7B6_34DAL, 0x698F_E692_70B0_6C44L, // 6 - 0x6B5F_CA6A_F2BD_215EL, 0x0F4C_A41D_811A_46D4L, // 7 - 0x55E6_3B88_C230_E77EL, 0x3F70_834A_CDAE_9F10L, // 8 - 0x44B8_2FA0_9B5A_52CBL, 0x4C5A_02A2_3E25_4C0DL, // 9 - 0x6DF3_7F67_5EF6_EADFL, 0x2D5C_D103_96A2_1347L, // 10 - 0x57F5_FF85_E592_557FL, 0x3DE3_DA69_454E_75D3L, // 11 - 0x465E_6604_B7A8_4465L, 0x7E4F_E1ED_D10B_9175L, // 12 - 0x7097_09A1_25DA_0709L, 0x4A19_697C_81AC_1BEFL, // 13 - 0x5A12_6E1A_84AE_6C07L, 0x54E1_2130_67BC_E326L, // 14 - 0x480E_BE7B_9D58_566CL, 0x43E7_4DC0_52FD_8285L, // 15 - 0x734A_CA5F_6226_F0ADL, 0x530B_AF9A_1E62_6A6DL, // 16 - 0x5C3B_D519_1B52_5A24L, 0x426F_BFAE_7EB5_21F1L, // 17 - 0x49C9_7747_490E_AE83L, 0x4EBF_CC8B_9890_E7F4L, // 18 - 0x760F_253E_DB4A_B0D2L, 0x4ACC_7A78_F41B_0CBAL, // 19 - 0x5E72_8432_4908_8D75L, 0x223D_2EC7_29AF_3D62L, // 20 - 0x4B8E_D028_3A6D_3DF7L, 0x34FD_BF05_BAF2_9781L, // 21 - 0x78E4_8040_5D7B_9658L, 0x54C9_31A2_C4B7_58CFL, // 22 - 0x60B6_CD00_4AC9_4513L, 0x5D6D_C14F_03C5_E0A5L, // 23 - 0x4D5F_0A66_A23A_9DA9L, 0x3124_9AA5_9C9E_4D51L, // 24 - 0x7BCB_43D7_69F7_62A8L, 0x4EA0_F76F_60FD_4882L, // 25 - 0x6309_0312_BB2C_4EEDL, 0x254D_92BF_80CA_A068L, // 26 - 0x4F3A_68DB_C8F0_3F24L, 0x1DD7_A899_33D5_4D20L, // 27 - 0x7EC3_DAF9_4180_6506L, 0x62F2_A75B_8622_1500L, // 28 - 0x6569_7BFA_9ACD_1D9FL, 0x025B_B916_04E8_10CDL, // 29 - 0x5121_2FFB_AF0A_7E18L, 0x6849_60DE_6A53_40A4L, // 30 - 0x40E7_5996_25A1_FE7AL, 0x203A_B3E5_21DC_33B6L, // 31 - 0x67D8_8F56_A29C_CA5DL, 0x19F7_863B_6960_52BDL, // 32 - 0x5313_A5DE_E87D_6EB0L, 0x7B2C_6B62_BAB3_7564L, // 33 - 0x4276_1E4B_ED31_255AL, 0x2F56_BC4E_FBC2_C450L, // 34 - 0x6A56_96DF_E1E8_3BC3L, 0x6557_93B1_92D1_3A1AL, // 35 - 0x5512_124C_B4B9_C969L, 0x3779_42F4_7574_2E7BL, // 36 - 0x440E_750A_2A2E_3ABAL, 0x5F94_3590_5DF6_8B96L, // 37 - 0x6CE3_EE76_A9E3_912AL, 0x65B9_EF4D_6324_1289L, // 38 - 0x571C_BEC5_54B6_0DBBL, 0x6AFB_25D7_8283_4207L, // 39 - 0x45B0_989D_DD5E_7163L, 0x08C8_EB12_CECF_6806L, // 40 - 0x6F80_F42F_C897_1BD1L, 0x5ADB_11B7_B14B_D9A3L, // 41 - 0x5933_F68C_A078_E30EL, 0x157C_0E2C_8DD6_47B5L, // 42 - 0x475C_C53D_4D2D_8271L, 0x5DFC_D823_A4AB_6C91L, // 43 - 0x722E_0862_1515_9D82L, 0x632E_269F_6DDF_141BL, // 44 - 0x5B58_06B4_DDAA_E468L, 0x4F58_1EE5_F17F_4349L, // 45 - 0x4913_3890_B155_8386L, 0x72AC_E584_C132_9C3BL, // 46 - 0x74EB_8DB4_4EEF_38D7L, 0x6AAE_3C07_9B84_2D2AL, // 47 - 0x5D89_3E29_D8BF_60ACL, 0x5558_3006_1603_5755L, // 48 - 0x4AD4_31BB_13CC_4D56L, 0x7779_C004_DE69_12ABL, // 49 - 0x77B9_E92B_52E0_7BBEL, 0x258F_99A1_63DB_5111L, // 50 - 0x5FC7_EDBC_424D_2FCBL, 0x37A6_1481_1CAF_740DL, // 51 - 0x4C9F_F163_683D_BFD5L, 0x7951_AA00_E3BF_900BL, // 52 - 0x7A99_8238_A6C9_32EFL, 0x754F_7667_D2CC_19ABL, // 53 - 0x6214_682D_523A_8F26L, 0x2AA5_F853_0F09_AE22L, // 54 - 0x4E76_B9BD_DB62_0C1EL, 0x5551_9375_A5A1_581BL, // 55 - 0x7D8A_C2C9_5F03_4697L, 0x3BB5_B8BC_3C35_59C5L, // 56 - 0x646F_023A_B269_0545L, 0x7C91_6096_9691_149EL, // 57 - 0x5058_CE95_5B87_376BL, 0x16DA_B3AB_ABA7_43B2L, // 58 - 0x4047_0BAA_AF9F_5F88L, 0x78AE_F622_EFB9_02F5L, // 59 - 0x66D8_12AA_B298_98DBL, 0x0DE4_BD04_B2C1_9E54L, // 60 - 0x5246_7555_5BAD_4715L, 0x57EA_30D0_8F01_4B76L, // 61 - 0x41D1_F777_7C8A_9F44L, 0x4654_F3DA_0C01_092CL, // 62 - 0x694F_F258_C744_3207L, 0x23BB_1FC3_4668_0EACL, // 63 - 0x543F_F513_D29C_F4D2L, 0x4FC8_E635_D1EC_D88AL, // 64 - 0x4366_5DA9_754A_5D75L, 0x263A_51C4_A7F0_AD3BL, // 65 - 0x6BD6_FC42_5543_C8BBL, 0x56C3_B607_731A_AEC4L, // 66 - 0x5645_969B_7769_6D62L, 0x789C_919F_8F48_8BD0L, // 67 - 0x4504_787C_5F87_8AB5L, 0x46E3_A7B2_D906_D640L, // 68 - 0x6E6D_8D93_CC0C_1122L, 0x3E39_0C51_5B3E_239AL, // 69 - 0x5857_A476_3CD6_741BL, 0x4B60_D6A7_7C31_B615L, // 70 - 0x46AC_8391_CA45_29AFL, 0x55E7_121F_968E_2B44L, // 71 - 0x7114_05B6_106E_A919L, 0x0971_B698_F0E3_786DL, // 72 - 0x5A76_6AF8_0D25_5414L, 0x078E_2BAD_8D82_C6BDL, // 73 - 0x485E_BBF9_A41D_DCDCL, 0x6C71_BC8A_D79B_D231L, // 74 - 0x73CA_C65C_39C9_6161L, 0x2D82_C744_8C2C_8382L, // 75 - 0x5CA2_3849_C7D4_4DE7L, 0x3E02_3903_A356_CF9BL, // 76 - 0x4A1B_603B_0643_7185L, 0x7E68_2D9C_82AB_D949L, // 77 - 0x7692_3391_A39F_1C09L, 0x4A40_48FA_6AAC_8EDBL, // 78 - 0x5EDB_5C74_82E5_B007L, 0x5500_3A61_EEF0_7249L, // 79 - 0x4BE2_B05D_3584_8CD2L, 0x7733_61E7_F259_F507L, // 80 - 0x796A_B3C8_55A0_E151L, 0x3EB8_9CA6_508F_EE71L, // 81 - 0x6122_296D_114D_810DL, 0x7EFA_16EB_73A6_585BL, // 82 - 0x4DB4_EDF0_DAA4_673EL, 0x3261_ABEF_8FB8_46AFL, // 83 - 0x7C54_AFE7_C43A_3ECAL, 0x1D69_1318_E5F3_A44BL, // 84 - 0x6376_F31F_D02E_98A1L, 0x6454_0F47_1E5C_836FL, // 85 - 0x4F92_5C19_7358_7A1BL, 0x0376_729F_4B7D_35F3L, // 86 - 0x7F50_935B_EBC0_C35EL, 0x38BD_8432_1261_EFEBL, // 87 - 0x65DA_0F7C_BC9A_35E5L, 0x13CA_D028_0EB4_BFEFL, // 88 - 0x517B_3F96_FD48_2B1DL, 0x5CA2_4020_0BC3_CCBFL, // 89 - 0x412F_6612_6439_BC17L, 0x63B5_0019_A303_0A33L, // 90 - 0x684B_D683_D38F_9359L, 0x1F88_0029_04D1_A9EAL, // 91 - 0x536F_DECF_DC72_DC47L, 0x32D3_3354_03DA_EE55L, // 92 - 0x42BF_E573_16C2_49D2L, 0x5BDC_2910_0315_8B77L, // 93 - 0x6ACC_A251_BE03_A951L, 0x12F9_DB4C_D1BC_1258L, // 94 - 0x5570_81DA_FE69_5440L, 0x7594_AF70_A7C9_A847L, // 95 - 0x445A_017B_FEBA_A9CDL, 0x4476_F2C0_863A_ED06L, // 96 - 0x6D5C_CF2C_CAC4_42E2L, 0x3A57_EACD_A391_7B3CL, // 97 - 0x577D_728A_3BD0_3581L, 0x7B79_88A4_82DA_C8FDL, // 98 - 0x45FD_F53B_630C_F79BL, 0x15FA_D3B6_CF15_6D97L, // 99 - 0x6FFC_BB92_3814_BF5EL, 0x565E_1F8A_E4EF_15BEL, // 100 - 0x5996_FC74_F9AA_32B2L, 0x11E4_E608_B725_AAFFL, // 101 - 0x47AB_FD2A_6154_F55BL, 0x27EA_51A0_9284_88CCL, // 102 - 0x72AC_C843_CEEE_555EL, 0x7310_829A_8407_4146L, // 103 - 0x5BBD_6D03_0BF1_DDE5L, 0x4273_9BAE_D005_CDD2L, // 104 - 0x4964_5735_A327_E4B7L, 0x4EC2_E2F2_4004_A4A8L, // 105 - 0x756D_5855_D1D9_6DF2L, 0x4AD1_6B1D_333A_A10CL, // 106 - 0x5DF1_1377_DB14_57F5L, 0x2241_227D_C295_4DA3L, // 107 - 0x4B27_42C6_48DD_132AL, 0x4E9A_81FE_3544_3E1CL, // 108 - 0x783E_D13D_4161_B844L, 0x175D_9CC9_EED3_9694L, // 109 - 0x6032_40FD_CDE7_C69CL, 0x7917_B0A1_8BDC_7876L, // 110 - 0x4CF5_00CB_0B1F_D217L, 0x1412_F3B4_6FE3_9392L, // 111 - 0x7B21_9ADE_7832_E9BEL, 0x5351_85ED_7FD2_85B6L, // 112 - 0x6281_48B1_F9C2_5498L, 0x42A7_9E57_9975_37C5L, // 113 - 0x4ECD_D3C1_949B_76E0L, 0x3552_E512_E12A_9304L, // 114 - 0x7E16_1F9C_20F8_BE33L, 0x6EEB_081E_3510_EB39L, // 115 - 0x64DE_7FB0_1A60_9829L, 0x3F22_6CE4_F740_BC2EL, // 116 - 0x50B1_FFC0_151A_1354L, 0x3281_F0B7_2C33_C9BEL, // 117 - 0x408E_6633_4414_DC43L, 0x4201_8D5F_568F_D498L, // 118 - 0x674A_3D1E_D354_939FL, 0x1CCF_4898_8A7F_BA8DL, // 119 - 0x52A1_CA7F_0F76_DC7FL, 0x30A5_D3AD_3B99_620BL, // 120 - 0x421B_0865_A5F8_B065L, 0x73B7_DC8A_9614_4E6FL, // 121 - 0x69C4_DA3C_3CC1_1A3CL, 0x52BF_C744_2353_B0B1L, // 122 - 0x549D_7B63_63CD_AE96L, 0x7566_3903_4F76_26F4L, // 123 - 0x43B1_2F82_B63E_2545L, 0x4451_C735_D92B_525DL, // 124 - 0x6C4E_B26A_BD30_3BA2L, 0x3A1C_71EF_C1DE_EA2EL, // 125 - 0x56A5_5B88_9759_C94EL, 0x61B0_5B26_34B2_54F2L, // 126 - 0x4551_1606_DF7B_0772L, 0x1AF3_7C1E_908E_AA5BL, // 127 - 0x6EE8_233E_325E_7250L, 0x2B1F_2CFD_B417_76F8L, // 128 - 0x58B9_B5CB_5B7E_C1D9L, 0x6F4C_23FE_29AC_5F2DL, // 129 - 0x46FA_F7D5_E2CB_CE47L, 0x72A3_4FFE_87BD_18F1L, // 130 - 0x7191_8C89_6ADF_B073L, 0x0438_7FFD_A5FB_5B1BL, // 131 - 0x5ADA_D6D4_557F_C05CL, 0x0360_6664_84C9_15AFL, // 132 - 0x48AF_1243_7799_66B0L, 0x02B3_851D_3707_448CL, // 133 - 0x744B_506B_F28F_0AB3L, 0x1DEC_082E_BE72_0746L, // 134 - 0x5D09_0D23_2872_6EF5L, 0x64BC_D358_985B_3905L, // 135 - 0x4A6D_A41C_205B_8BF7L, 0x6A30_A913_AD15_C738L, // 136 - 0x7715_D360_33C5_ACBFL, 0x5D1A_A81F_7B56_0B8CL, // 137 - 0x5F44_A919_C304_8A32L, 0x7DAE_ECE5_FC44_D609L, // 138 - 0x4C36_EDAE_359D_3B5BL, 0x7E25_8A51_969D_7808L, // 139 - 0x79F1_7C49_EF61_F893L, 0x16A2_76E8_F0FB_F33FL, // 140 - 0x618D_FD07_F2B4_C6DCL, 0x121B_9253_F3FC_C299L, // 141 - 0x4E0B_30D3_2890_9F16L, 0x41AF_A843_2997_0214L, // 142 - 0x7CDE_B485_0DB4_31BDL, 0x4F7F_739E_A8F1_9CEDL, // 143 - 0x63E5_5D37_3E29_C164L, 0x3F99_294B_BA5A_E3F1L, // 144 - 0x4FEA_B0F8_FE87_CDE9L, 0x7FAD_BAA2_FB7B_E98DL, // 145 - 0x7FDD_E7F4_CA72_E30FL, 0x7F7C_5DD1_925F_DC15L, // 146 - 0x664B_1FF7_085B_E8D9L, 0x4C63_7E41_41E6_49ABL, // 147 - 0x51D5_B32C_06AF_ED7AL, 0x704F_9834_34B8_3AEFL, // 148 - 0x4177_C289_9EF3_2462L, 0x26A6_135C_F6F9_C8BFL, // 149 - 0x68BF_9DA8_FE51_D3D0L, 0x3DD6_8561_8B29_4132L, // 150 - 0x53CC_7E20_CB74_A973L, 0x4B12_044E_08ED_CDC2L, // 151 - 0x4309_FE80_A2C3_BAC2L, 0x6F41_9D0B_3A57_D7CEL, // 152 - 0x6B43_30CD_D139_2AD1L, 0x3202_94DE_C3BF_BFB0L, // 153 - 0x55CF_5A3E_40FA_88A7L, 0x419B_AA4B_CFCC_995AL, // 154 - 0x44A5_E1CB_672E_D3B9L, 0x1AE2_EEA3_0CA3_ADE1L, // 155 - 0x6DD6_3612_3EB1_52C1L, 0x77D1_7DD1_ADD2_AFCFL, // 156 - 0x57DE_91A8_3227_7567L, 0x7974_64A7_BE42_263FL, // 157 - 0x464B_A7B9_C1B9_2AB9L, 0x4790_5086_31CE_84FFL, // 158 - 0x7079_0C5C_6928_445CL, 0x0C1A_1A70_4FB0_D4CCL, // 159 - 0x59FA_7049_EDB9_D049L, 0x567B_4859_D95A_43D6L, // 160 - 0x47FB_8D07_F161_736EL, 0x11FC_39E1_7AAE_9CABL, // 161 - 0x732C_14D9_8235_857DL, 0x032D_2968_C44A_9445L, // 162 - 0x5C23_43E1_34F7_9DFDL, 0x4F57_5453_D03B_A9D1L, // 163 - 0x49B5_CFE7_5D92_E4CAL, 0x72AC_4376_402F_BB0EL, // 164 - 0x75EF_B30B_C8EB_07ABL, 0x0446_D256_CD19_2B49L, // 165 - 0x5E59_5C09_6D88_D2EFL, 0x1D05_7512_3DAD_BC3AL, // 166 - 0x4B7A_B007_8AD3_DBF2L, 0x4A6A_C40E_97BE_302FL, // 167 - 0x78C4_4CD8_DE1F_C650L, 0x7711_39B0_F2C9_E6B1L, // 168 - 0x609D_0A47_1819_6B73L, 0x78DA_948D_8F07_EBC1L, // 169 - 0x4D4A_6E9F_467A_BC5CL, 0x60AE_DD3E_0C06_5634L, // 170 - 0x7BAA_4A98_70C4_6094L, 0x344A_FB96_79A3_BD20L, // 171 - 0x62EE_A213_8D69_E6DDL, 0x103B_FC78_614F_CA80L, // 172 - 0x4F25_4E76_0ABB_1F17L, 0x2696_6393_810C_A200L, // 173 - 0x7EA2_1723_445E_9825L, 0x2423_D285_9B47_6999L, // 174 - 0x654E_78E9_037E_E01DL, 0x69B6_4204_7C39_2148L, // 175 - 0x510B_93ED_9C65_8017L, 0x6E2B_6803_9694_1AA0L, // 176 - 0x40D6_0FF1_49EA_CCDFL, 0x71BC_5336_1210_154DL, // 177 - 0x67BC_E64E_DCAA_E166L, 0x1C60_8523_5019_BBAEL, // 178 - 0x52FD_850B_E3BB_E784L, 0x7D1A_041C_4014_9625L, // 179 - 0x4264_6A6F_E963_1F9DL, 0x4A7B_367D_0010_781DL, // 180 - 0x6A3A_43E6_4238_3295L, 0x5D91_F0C8_001A_59C8L, // 181 - 0x54FB_6985_01C6_8EDEL, 0x17A7_F3D3_3348_47D4L, // 182 - 0x43FC_546A_67D2_0BE4L, 0x7953_2975_C2A0_3976L, // 183 - 0x6CC6_ED77_0C83_463BL, 0x0EEB_7589_3766_C256L, // 184 - 0x5705_8AC5_A39C_382FL, 0x2589_2AD4_2C52_3512L, // 185 - 0x459E_089E_1C7C_F9BFL, 0x37A0_EF10_2374_F742L, // 186 - 0x6F63_40FC_FA61_8F98L, 0x5901_7E80_38BB_2536L, // 187 - 0x591C_33FD_951A_D946L, 0x7A67_9866_93C8_EA91L, // 188 - 0x4749_C331_4415_7A9FL, 0x151F_AD1E_DCA0_BBA8L, // 189 - 0x720F_9EB5_39BB_F765L, 0x0832_AE97_C767_92A5L, // 190 - 0x5B3F_B22A_9496_5F84L, 0x068E_F213_05EC_7551L, // 191 - 0x48FF_C1BB_AA11_E603L, 0x1ED8_C1A8_D189_F774L, // 192 - 0x74CC_692C_434F_D66BL, 0x4AF4_690E_1C0F_F253L, // 193 - 0x5D70_5423_690C_AB89L, 0x225D_20D8_1673_2843L, // 194 - 0x4AC0_434F_873D_5607L, 0x3517_4D79_AB8F_5369L, // 195 - 0x779A_054C_0B95_5672L, 0x21BE_E25C_45B2_1F0EL, // 196 - 0x5FAE_6AA3_3C77_785BL, 0x3498_B516_9E28_18D8L, // 197 - 0x4C8B_8882_96C5_F9E2L, 0x5D46_F745_4B53_4713L, // 198 - 0x7A78_DA6A_8AD6_5C9DL, 0x7BA4_BED5_4552_0B52L, // 199 - 0x61FA_4855_3BDE_B07EL, 0x2FB6_FF11_0441_A2A8L, // 200 - 0x4E61_D377_6318_8D31L, 0x72F8_CC0D_9D01_4EEDL, // 201 - 0x7D69_5258_9E8D_AEB6L, 0x1E5A_E015_C802_17E1L, // 202 - 0x6454_41E0_7ED7_BEF8L, 0x1848_B344_A001_ACB4L, // 203 - 0x5043_67E6_CBDF_CBF9L, 0x603A_2903_B334_8A2AL, // 204 - 0x4035_ECB8_A319_6FFBL, 0x002E_8736_28F6_D4EEL, // 205 - 0x66BC_ADF4_3828_B32BL, 0x19E4_0B89_DB24_87E3L, // 206 - 0x5230_8B29_C686_F5BCL, 0x14B6_6FA1_7C1D_3983L, // 207 - 0x41C0_6F54_9ED2_5E30L, 0x1091_F2E7_967D_C79CL, // 208 - 0x6933_E554_3150_96B3L, 0x341C_B7D8_F0C9_3F5FL, // 209 - 0x5429_8443_5AA6_DEF5L, 0x767D_5FE0_C0A0_FF80L, // 210 - 0x4354_69CF_7BB8_B25EL, 0x2B97_7FE7_0080_CC66L, // 211 - 0x6BBA_42E5_92C1_1D63L, 0x5F58_CCA4_CD9A_E0A3L, // 212 - 0x562E_9BEA_DBCD_B11CL, 0x4C47_0A1D_7148_B3B6L, // 213 - 0x44F2_1655_7CA4_8DB0L, 0x3D05_A1B1_276D_5C92L, // 214 - 0x6E50_23BB_FAA0_E2B3L, 0x7B3C_35E8_3F15_60E9L, // 215 - 0x5840_1C96_621A_4EF6L, 0x2F63_5E53_65AA_B3EDL, // 216 - 0x4699_B078_4E7B_725EL, 0x591C_4B75_EAEE_F658L, // 217 - 0x70F5_E726_E3F8_B6FDL, 0x74FA_1256_44B1_8A26L, // 218 - 0x5A5E_5285_832D_5F31L, 0x43FB_41DE_9D5A_D4EBL, // 219 - 0x484B_7537_9C24_4C27L, 0x4FFC_34B2_177B_DD89L, // 220 - 0x73AB_EEBF_603A_1372L, 0x4CC6_BAB6_8BF9_6274L, // 221 - 0x5C89_8BCC_4CFB_42C2L, 0x0A38_955E_D661_1B90L, // 222 - 0x4A07_A309_D72F_689BL, 0x21C6_DDE5_784D_AFA7L, // 223 - 0x7672_9E76_2518_A75EL, 0x693E_2FD5_8D49_190BL, // 224 - 0x5EC2_185E_8413_B918L, 0x5431_BFDE_0AA0_E0D5L, // 225 - 0x4BCE_79E5_3676_2DADL, 0x29C1_664B_3BB3_E711L, // 226 - 0x794A_5CA1_F0BD_15E2L, 0x0F9B_D6DE_C5EC_A4E8L, // 227 - 0x6108_4A1B_26FD_AB1BL, 0x2616_457F_04BD_50BAL, // 228 - 0x4DA0_3B48_EBFE_227CL, 0x1E78_3798_D097_73C8L, // 229 - 0x7C33_920E_4663_6A60L, 0x30C0_58F4_80F2_52D9L, // 230 - 0x635C_74D8_384F_884DL, 0x0D66_AD90_6728_4247L, // 231 - 0x4F7D_2A46_9372_D370L, 0x711E_F140_5286_9B6CL, // 232 - 0x7F2E_AA0A_8584_8581L, 0x34FE_4ECD_50D7_5F14L, // 233 - 0x65BE_EE6E_D136_D134L, 0x2A65_0BD7_73DF_7F43L, // 234 - 0x5165_8B8B_DA92_40F6L, 0x551D_A312_C319_329CL, // 235 - 0x411E_093C_AEDB_672BL, 0x5DB1_4F42_35AD_C217L, // 236 - 0x6830_0EC7_7E2B_D845L, 0x7C4E_E536_BC49_368AL, // 237 - 0x5359_A56C_64EF_E037L, 0x7D0B_EA92_303A_9208L, // 238 - 0x42AE_1DF0_50BF_E693L, 0x173C_BBA8_2695_41A0L, // 239 - 0x6AB0_2FE6_E799_70EBL, 0x3EC7_92A6_A422_029AL, // 240 - 0x5559_BFEB_EC7A_C0BCL, 0x3239_421E_E9B4_CEE1L, // 241 - 0x4447_CCBC_BD2F_0096L, 0x5B61_01B2_5490_A581L, // 242 - 0x6D3F_ADFA_C84B_3424L, 0x2BCE_691D_541A_A268L, // 243 - 0x5766_24C8_A03C_29B6L, 0x563E_BA7D_DCE2_1B87L, // 244 - 0x45EB_50A0_8030_215EL, 0x7832_2ECB_171B_4939L, // 245 - 0x6FDE_E767_3380_3564L, 0x59E9_E478_24F8_7527L, // 246 - 0x597F_1F85_C2CC_F783L, 0x6187_E9F9_B72D_2A86L, // 247 - 0x4798_E604_9BD7_2C69L, 0x346C_BB2E_2C24_2205L, // 248 - 0x728E_3CD4_2C8B_7A42L, 0x20AD_F849_E039_D007L, // 249 - 0x5BA4_FD76_8A09_2E9BL, 0x33BE_603B_19C7_D99FL, // 250 - 0x4950_CAC5_3B3A_8BAFL, 0x42FE_B362_7B06_47B3L, // 251 - 0x754E_113B_91F7_45E5L, 0x5197_856A_5E70_72B8L, // 252 - 0x5DD8_0DC9_4192_9E51L, 0x27AC_6ABB_7EC0_5BC6L, // 253 - 0x4B13_3E3A_9ADB_B1DAL, 0x52F0_5562_CBCD_1638L, // 254 - 0x781E_C9F7_5E2C_4FC4L, 0x1E4D_556A_DFAE_89F3L, // 255 - 0x6018_A192_B1BD_0C9CL, 0x7EA4_4455_7FBE_D4C3L, // 256 - 0x4CE0_8142_27CA_707DL, 0x4BB6_9D11_32FF_109CL, // 257 - 0x7B00_CED0_3FAA_4D95L, 0x5F8A_94E8_5198_1A93L, // 258 - 0x6267_0BD9_CC88_3E11L, 0x32D5_43ED_0E13_4875L, // 259 - 0x4EB8_D647_D6D3_64DAL, 0x5BDD_CFF0_D80F_6D2BL, // 260 - 0x7DF4_8A0C_8AEB_D491L, 0x12FC_7FE7_C018_AEABL, // 261 - 0x64C3_A1A3_A256_43A7L, 0x28C9_FFEC_99AD_5889L, // 262 - 0x509C_814F_B511_CFB9L, 0x0707_FFF0_7AF1_13A1L, // 263 - 0x407D_343F_C40E_3FC7L, 0x1F39_998D_2F27_42E7L, // 264 - 0x672E_B9FF_A016_CC71L, 0x7EC2_8F48_4B72_04A4L, // 265 - 0x528B_C7FF_B345_705BL, 0x189B_A5D3_6F8E_6A1DL, // 266 - 0x4209_6CCC_8F6A_C048L, 0x7A16_1E42_BFA5_21B1L, // 267 - 0x69A8_AE14_18AA_CD41L, 0x4356_96D1_32A1_CF81L, // 268 - 0x5486_F1A9_AD55_7101L, 0x1C45_4574_2881_72CEL, // 269 - 0x439F_27BA_F111_2734L, 0x169D_D129_BA01_28A5L, // 270 - 0x6C31_D92B_1B4E_A520L, 0x242F_B50F_9001_DAA1L, // 271 - 0x568E_4755_AF72_1DB3L, 0x368C_90D9_4001_7BB4L, // 272 - 0x453E_9F77_BF8E_7E29L, 0x120A_0D7A_999A_C95DL, // 273 - 0x6ECA_98BF_98E3_FD0EL, 0x5010_1590_F5C4_7561L, // 274 - 0x58A2_13CC_7A4F_FDA5L, 0x2673_4473_F7D0_5DE8L, // 275 - 0x46E8_0FD6_C83F_FE1DL, 0x6B8F_69F6_5FD9_E4B9L, // 276 - 0x7173_4C8A_D9FF_FCFCL, 0x45B2_4323_CC8F_D45CL, // 277 - 0x5AC2_A3A2_47FF_FD96L, 0x6AF5_0283_0A0C_A9E3L, // 278 - 0x489B_B61B_6CCC_CADFL, 0x08C4_0202_6E70_87E9L, // 279 - 0x742C_5692_47AE_1164L, 0x746C_D003_E3E7_3FDBL, // 280 - 0x5CF0_4541_D2F1_A783L, 0x76BD_7336_4FEC_3315L, // 281 - 0x4A59_D101_758E_1F9CL, 0x5EFD_F5C5_0CBC_F5ABL, // 282 - 0x76F6_1B35_88E3_65C7L, 0x4B2F_EFA1_ADFB_22ABL, // 283 - 0x5F2B_48F7_A0B5_EB06L, 0x08F3_261A_F195_B555L, // 284 - 0x4C22_A0C6_1A2B_226BL, 0x20C2_84E2_5ADE_2AABL, // 285 - 0x79D1_013C_F6AB_6A45L, 0x1AD0_D49D_5E30_4444L, // 286 - 0x6174_00FD_9222_BB6AL, 0x48A7_107D_E4F3_69D0L, // 287 - 0x4DF6_6731_41B5_62BBL, 0x53B8_D9FE_50C2_BB0DL, // 288 - 0x7CBD_71E8_6922_3792L, 0x52C1_5CCA_1AD1_2B48L, // 289 - 0x63CA_C186_BA81_C60EL, 0x7567_7D6E_7BDA_8906L, // 290 - 0x4FD5_679E_FB9B_04D8L, 0x5DEC_6458_6315_3A6CL, // 291 - 0x7FBB_D8FE_5F5E_6E27L, 0x497A_3A27_04EE_C3DFL, // 292 + /* -324 */ 0x4F0C_EDC9_5A71_8DD4L, 0x5B01_E8B0_9AA0_D1B5L, + /* -323 */ 0x7E7B_160E_F71C_1621L, 0x119C_A780_F767_B5EEL, + /* -322 */ 0x652F_44D8_C5B0_11B4L, 0x0E16_EC67_2C52_F7F2L, + /* -321 */ 0x50F2_9D7A_37C0_0E29L, 0x5812_56B8_F042_5FF5L, + /* -320 */ 0x40C2_1794_F966_71BAL, 0x79A8_4560_C035_1991L, + /* -319 */ 0x679C_F287_F570_B5F7L, 0x75DA_089A_CD21_C281L, + /* -318 */ 0x52E3_F539_9126_F7F9L, 0x44AE_6D48_A41B_0201L, + /* -317 */ 0x424F_F761_40EB_F994L, 0x36F1_F106_E9AF_34CDL, + /* -316 */ 0x6A19_8BCE_CE46_5C20L, 0x57E9_81A4_A918_547BL, + /* -315 */ 0x54E1_3CA5_71D1_E34DL, 0x2CBA_CE1D_5413_76C9L, + /* -314 */ 0x43E7_63B7_8E41_82A4L, 0x23C8_A4E4_4342_C56EL, + /* -313 */ 0x6CA5_6C58_E39C_043AL, 0x060D_D4A0_6B9E_08B0L, + /* -312 */ 0x56EA_BD13_E949_9CFBL, 0x1E71_76E6_BC7E_6D59L, + /* -311 */ 0x4588_9743_2107_B0C8L, 0x7EC1_2BEB_C9FE_BDE1L, + /* -310 */ 0x6F40_F205_01A5_E7A7L, 0x7E01_DFDF_A997_9635L, + /* -309 */ 0x5900_C19D_9AEB_1FB9L, 0x4B34_B319_5479_44F7L, + /* -308 */ 0x4733_CE17_AF22_7FC7L, 0x55C3_C27A_A9FA_9D93L, + /* -307 */ 0x71EC_7CF2_B1D0_CC72L, 0x5606_03F7_765D_C8EAL, + /* -306 */ 0x5B23_9728_8E40_A38EL, 0x7804_CFF9_2B7E_3A55L, + /* -305 */ 0x48E9_45BA_0B66_E93FL, 0x1337_0CC7_55FE_9511L, + /* -304 */ 0x74A8_6F90_123E_41FEL, 0x51F1_AE0B_BCCA_881BL, + /* -303 */ 0x5D53_8C73_41CB_67FEL, 0x74C1_5809_63D5_39AFL, + /* -302 */ 0x4AA9_3D29_016F_8665L, 0x43CD_E007_8310_FAF3L, + /* -301 */ 0x7775_2EA8_024C_0A3CL, 0x0616_333F_381B_2B1EL, + /* -300 */ 0x5F90_F220_01D6_6E96L, 0x3811_C298_F9AF_55B1L, + /* -299 */ 0x4C73_F4E6_67DE_BEDEL, 0x600E_3547_2E25_DE28L, + /* -298 */ 0x7A53_2170_A631_3164L, 0x3349_EED8_49D6_303FL, + /* -297 */ 0x61DC_1AC0_84F4_2783L, 0x42A1_8BE0_3B11_C033L, + /* -296 */ 0x4E49_AF00_6A5C_EC69L, 0x1BB4_6FE6_95A7_CCF5L, + /* -295 */ 0x7D42_B19A_43C7_E0A8L, 0x2C53_E63D_BC3F_AE55L, + /* -294 */ 0x6435_5AE1_CFD3_1A20L, 0x2376_51CA_FCFF_BEAAL, + /* -293 */ 0x502A_AF1B_0CA8_E1B3L, 0x35F8_416F_30CC_9888L, + /* -292 */ 0x4022_25AF_3D53_E7C2L, 0x5E60_3458_F3D6_E06DL, + /* -291 */ 0x669D_0918_621F_D937L, 0x4A33_86F4_B957_CD7BL, + /* -290 */ 0x5217_3A79_E819_7A92L, 0x6E8F_9F2A_2DDF_D796L, + /* -289 */ 0x41AC_2EC7_ECE1_2EDBL, 0x720C_7F54_F17F_DFABL, + /* -288 */ 0x6913_7E0C_AE35_17C6L, 0x1CE0_CBBB_1BFF_CC45L, + /* -287 */ 0x540F_980A_24F7_4638L, 0x171A_3C95_AFFF_D69EL, + /* -286 */ 0x433F_ACD4_EA5F_6B60L, 0x127B_63AA_F333_1218L, + /* -285 */ 0x6B99_1487_DD65_7899L, 0x6A5F_05DE_51EB_5026L, + /* -284 */ 0x5614_106C_B11D_FA14L, 0x5518_D17E_A7EF_7352L, + /* -283 */ 0x44DC_D9F0_8DB1_94DDL, 0x2A7A_4132_1FF2_C2A8L, + /* -282 */ 0x6E2E_2980_E2B5_BAFBL, 0x5D90_6850_331E_043FL, + /* -281 */ 0x5824_EE00_B55E_2F2FL, 0x6473_86A6_8F4B_3699L, + /* -280 */ 0x4683_F19A_2AB1_BF59L, 0x36C2_D21E_D908_F87BL, + /* -279 */ 0x70D3_1C29_DDE9_3228L, 0x579E_1CFE_280E_5A5DL, + /* -278 */ 0x5A42_7CEE_4B20_F4EDL, 0x2C7E_7D98_200B_7B7EL, + /* -277 */ 0x4835_30BE_A280_C3F1L, 0x09FE_CAE0_19A2_C932L, + /* -276 */ 0x7388_4DFD_D0CE_064EL, 0x4331_4499_C29E_0EB6L, + /* -275 */ 0x5C6D_0B31_73D8_050BL, 0x4F5A_9D47_CEE4_D891L, + /* -274 */ 0x49F0_D5C1_2979_9DA2L, 0x72AE_E439_7250_AD41L, + /* -273 */ 0x764E_22CE_A8C2_95D1L, 0x377E_39F5_83B4_4868L, + /* -272 */ 0x5EA4_E8A5_53CE_DE41L, 0x12CB_6191_3629_D387L, + /* -271 */ 0x4BB7_2084_430B_E500L, 0x756F_8140_F821_7605L, + /* -270 */ 0x7925_00D3_9E79_6E67L, 0x6F18_CECE_59CF_233CL, + /* -269 */ 0x60EA_670F_B1FA_BEB9L, 0x3F47_0BD8_47D8_E8FDL, + /* -268 */ 0x4D88_5272_F4C8_9894L, 0x329F_3CAD_0647_20CAL, + /* -267 */ 0x7C0D_50B7_EE0D_C0EDL, 0x3765_2DE1_A3A5_0143L, + /* -266 */ 0x633D_DA2C_BE71_6724L, 0x2C50_F181_4FB7_3436L, + /* -265 */ 0x4F64_AE8A_31F4_5283L, 0x3D0D_8E01_0C92_902BL, + /* -264 */ 0x7F07_7DA9_E986_EA6BL, 0x7B48_E334_E0EA_8045L, + /* -263 */ 0x659F_97BB_2138_BB89L, 0x4907_1C2A_4D88_669DL, + /* -262 */ 0x514C_7962_80FA_2FA1L, 0x20D2_7CEE_A46D_1EE4L, + /* -261 */ 0x4109_FAB5_33FB_594DL, 0x670E_CA58_838A_7F1DL, + /* -260 */ 0x680F_F788_532B_C216L, 0x0B4A_DD5A_6C10_CB62L, + /* -259 */ 0x533F_F939_DC23_01ABL, 0x22A2_4AAE_BCDA_3C4EL, + /* -258 */ 0x4299_942E_49B5_9AEFL, 0x354E_A225_63E1_C9D8L, + /* -257 */ 0x6A8F_537D_42BC_2B18L, 0x554A_9D08_9FCF_A95AL, + /* -256 */ 0x553F_75FD_CEFC_EF46L, 0x776E_E406_E63F_BAAEL, + /* -255 */ 0x4432_C4CB_0BFD_8C38L, 0x5F8B_E99F_1E99_6225L, + /* -254 */ 0x6D1E_07AB_4662_79F4L, 0x3279_75CB_6428_9D08L, + /* -253 */ 0x574B_3955_D1E8_6190L, 0x2861_2B09_1CED_4A6DL, + /* -252 */ 0x45D5_C777_DB20_4E0DL, 0x06B4_226D_B0BD_D524L, + /* -251 */ 0x6FBC_7259_5E9A_167BL, 0x2453_6A49_1AC9_5506L, + /* -250 */ 0x5963_8EAD_E548_11FCL, 0x1D0F_883A_7BD4_4405L, + /* -249 */ 0x4782_D88B_1DD3_4196L, 0x4A72_D361_FCA9_D004L, + /* -248 */ 0x726A_F411_C952_028AL, 0x43EA_EBCF_FAA9_4CD3L, + /* -247 */ 0x5B88_C341_6DDB_353BL, 0x4FEF_230C_C887_70A9L, + /* -246 */ 0x493A_35CD_F17C_2A96L, 0x0CBF_4F3D_6D39_26EEL, + /* -245 */ 0x7529_EFAF_E8C6_AA89L, 0x6132_1862_485B_717CL, + /* -244 */ 0x5DBB_2626_53D2_2207L, 0x675B_46B5_06AF_8DFDL, + /* -243 */ 0x4AFC_1E85_0FDB_4E6CL, 0x52AF_6BC4_0559_3E64L, + /* -242 */ 0x77F9_CA6E_7FC5_4A47L, 0x377F_12D3_3BC1_FD6DL, + /* -241 */ 0x5FFB_0858_6637_6E9FL, 0x45FF_4242_9634_CABDL, + /* -240 */ 0x4CC8_D379_EB5F_8BB2L, 0x6B32_9B68_782A_3BCBL, + /* -239 */ 0x7ADA_EBF6_4565_AC51L, 0x2B84_2BDA_59DD_2C77L, + /* -238 */ 0x6248_BCC5_0451_56A7L, 0x3C69_BCAE_AE4A_89F9L, + /* -237 */ 0x4EA0_9704_0374_4552L, 0x6387_CA25_583B_A194L, + /* -236 */ 0x7DCD_BE6C_D253_A21EL, 0x05A6_103B_C05F_68EDL, + /* -235 */ 0x64A4_9857_0EA9_4E7EL, 0x37B8_0CFC_99E5_ED8AL, + /* -234 */ 0x5083_AD12_7221_0B98L, 0x2C93_3D96_E184_BE08L, + /* -233 */ 0x4069_5741_F4E7_3C79L, 0x7075_CADF_1AD0_9807L, + /* -232 */ 0x670E_F203_2171_FA5CL, 0x4D89_4498_2AE7_59A4L, + /* -231 */ 0x5272_5B35_B45B_2EB0L, 0x3E07_6A13_5585_E150L, + /* -230 */ 0x41F5_15C4_9048_F226L, 0x64D2_BB42_AAD1_810DL, + /* -229 */ 0x6988_22D4_1A0E_503EL, 0x07B7_9204_4482_6815L, + /* -228 */ 0x546C_E8A9_AE71_D9CBL, 0x1FC6_0E69_D068_5344L, + /* -227 */ 0x438A_53BA_F1F4_AE3CL, 0x196B_3EBB_0D20_429DL, + /* -226 */ 0x6C10_85F7_E987_7D2DL, 0x0F11_FDF8_1500_6A94L, + /* -225 */ 0x5673_9E5F_EE05_FDBDL, 0x58DB_3193_4400_5543L, + /* -224 */ 0x4529_4B7F_F19E_6497L, 0x60AF_5ADC_3666_AA9CL, + /* -223 */ 0x6EA8_78CC_B5CA_3A8CL, 0x344B_C493_8A3D_DDC7L, + /* -222 */ 0x5886_C70A_2B08_2ED6L, 0x5D09_6A0F_A1CB_17D2L, + /* -221 */ 0x46D2_38D4_EF39_BF12L, 0x173A_BB3F_B4A2_7975L, + /* -220 */ 0x7150_5AEE_4B8F_981DL, 0x0B91_2B99_2103_F588L, + /* -219 */ 0x5AA6_AF25_093F_ACE4L, 0x0940_EFAD_B403_2AD3L, + /* -218 */ 0x4885_58EA_6DCC_8A50L, 0x0767_2624_9002_88A9L, + /* -217 */ 0x7408_8E43_E2E0_DD4CL, 0x723E_A36D_B337_410EL, + /* -216 */ 0x5CD3_A503_1BE7_1770L, 0x5B65_4F8A_F5C5_CDA5L, + /* -215 */ 0x4A42_EA68_E31F_45F3L, 0x62B7_72D5_916B_0AEBL, + /* -214 */ 0x76D1_770E_3832_0986L, 0x0458_B7BC_1BDE_77DDL, + /* -213 */ 0x5F0D_F8D8_2CF4_D46BL, 0x1D13_C630_164B_9318L, + /* -212 */ 0x4C0B_2D79_BD90_A9EFL, 0x30DC_9E8C_DEA2_DC13L, + /* -211 */ 0x79AB_7BF5_FC1A_A97FL, 0x0160_FDAE_3104_9351L, + /* -210 */ 0x6155_FCC4_C9AE_EDFFL, 0x1AB3_FE24_F403_A90EL, + /* -209 */ 0x4DDE_63D0_A158_BE65L, 0x6229_981D_9002_EDA5L, + /* -208 */ 0x7C97_061A_9BC1_30A2L, 0x69DC_2695_B337_E2A1L, + /* -207 */ 0x63AC_04E2_1634_26E8L, 0x54B0_1EDE_28F9_821BL, + /* -206 */ 0x4FBC_D0B4_DE90_1F20L, 0x43C0_18B1_BA61_34E2L, + /* -205 */ 0x7F94_8121_6419_CB67L, 0x1F99_C11C_5D68_549DL, + /* -204 */ 0x6610_674D_E9AE_3C52L, 0x4C7B_00E3_7DED_107EL, + /* -203 */ 0x51A6_B90B_2158_3042L, 0x09FC_00B5_FE57_4065L, + /* -202 */ 0x4152_2DA2_8113_59CEL, 0x3B30_0091_9845_CD1DL, + /* -201 */ 0x6883_7C37_34EB_C2E3L, 0x784C_CDB5_C06F_AE95L, + /* -200 */ 0x539C_635F_5D89_68B6L, 0x2D0A_3E2B_0059_5877L, + /* -199 */ 0x42E3_82B2_B13A_BA2BL, 0x3DA1_CB55_99E1_1393L, + /* -198 */ 0x6B05_9DEA_B52A_C378L, 0x629C_7888_F634_EC1EL, + /* -197 */ 0x559E_17EE_F755_692DL, 0x3549_FA07_2B5D_89B1L, + /* -196 */ 0x447E_798B_F911_20F1L, 0x1107_FB38_EF7E_07C1L, + /* -195 */ 0x6D97_28DF_F4E8_34B5L, 0x01A6_5EC1_7F30_0C68L, + /* -194 */ 0x57AC_20B3_2A53_5D5DL, 0x4E1E_B234_65C0_09EDL, + /* -193 */ 0x4623_4D5C_21DC_4AB1L, 0x24E5_5B5D_1E33_3B24L, + /* -192 */ 0x7038_7BC6_9C93_AAB5L, 0x216E_F894_FD1E_C506L, + /* -191 */ 0x59C6_C96B_B076_222AL, 0x4DF2_6077_30E5_6A6CL, + /* -190 */ 0x47D2_3ABC_8D2B_4E88L, 0x3E5B_805F_5A51_21F0L, + /* -189 */ 0x72E9_F794_1512_1740L, 0x63C5_9A32_2A1B_697FL, + /* -188 */ 0x5BEE_5FA9_AA74_DF67L, 0x0304_7B5B_54E2_BACCL, + /* -187 */ 0x498B_7FBA_EEC3_E5ECL, 0x0269_FC49_10B5_623DL, + /* -186 */ 0x75AB_FF91_7E06_3CACL, 0x6A43_2D41_B455_69FBL, + /* -185 */ 0x5E23_32DA_CB38_308AL, 0x21CF_5767_C377_87FCL, + /* -184 */ 0x4B4F_5BE2_3C2C_F3A1L, 0x67D9_12B9_692C_6CCAL, + /* -183 */ 0x787E_F969_F9E1_85CFL, 0x595B_5128_A847_1476L, + /* -182 */ 0x6065_9454_C7E7_9E3FL, 0x6115_DA86_ED05_A9F8L, + /* -181 */ 0x4D1E_1043_D31F_B1CCL, 0x4DAB_1538_BD9E_2193L, + /* -180 */ 0x7B63_4D39_51CC_4FADL, 0x62AB_5527_95C9_CF52L, + /* -179 */ 0x62B5_D761_0E3D_0C8BL, 0x0222_AA86_116E_3F75L, + /* -178 */ 0x4EF7_DF80_D830_D6D5L, 0x4E82_2204_DABE_992AL, + /* -177 */ 0x7E59_659A_F381_57BCL, 0x1736_9CD4_9130_F510L, + /* -176 */ 0x6514_5148_C2CD_DFC9L, 0x5F5E_E3DD_40F3_F740L, + /* -175 */ 0x50DD_0DD3_CF0B_196EL, 0x1918_B64A_9A5C_C5CDL, + /* -174 */ 0x40B0_D7DC_A5A2_7ABEL, 0x4746_F83B_AEB0_9E3EL, + /* -173 */ 0x6781_5961_0903_F797L, 0x253E_59F9_1780_FD2FL, + /* -172 */ 0x52CD_E11A_6D9C_C612L, 0x50FE_AE60_DF9A_6426L, + /* -171 */ 0x423E_4DAE_BE17_04DBL, 0x5A65_584D_7FAE_B685L, + /* -170 */ 0x69FD_4917_968B_3AF9L, 0x10A2_26E2_65E4_573BL, + /* -169 */ 0x54CA_A0DF_ABA2_9594L, 0x0D4E_8581_EB1D_1295L, + /* -168 */ 0x43D5_4D7F_BC82_1143L, 0x243E_D134_BC17_4211L, + /* -167 */ 0x6C88_7BFF_9403_4ED2L, 0x06CA_E854_6025_3682L, + /* -166 */ 0x56D3_9666_1002_A574L, 0x6BD5_86A9_E684_2B9BL, + /* -165 */ 0x4576_11EB_4002_1DF7L, 0x0977_9EEE_5203_5616L, + /* -164 */ 0x6F23_4FDE_CCD0_2FF1L, 0x5BF2_97E3_B66B_BCEFL, + /* -163 */ 0x58E9_0CB2_3D73_598EL, 0x165B_ACB6_2B89_63F3L, + /* -162 */ 0x4720_D6F4_FDF5_E13EL, 0x4516_23C4_EFA1_1CC2L, + /* -161 */ 0x71CE_24BB_2FEF_CECAL, 0x3B56_9FA1_7F68_2E03L, + /* -160 */ 0x5B0B_5095_BFF3_0BD5L, 0x15DE_E61A_CC53_5803L, + /* -159 */ 0x48D5_DA11_665C_0977L, 0x2B18_B815_7042_ACCFL, + /* -158 */ 0x7489_5CE8_A3C6_758BL, 0x5E8D_F355_806A_AE18L, + /* -157 */ 0x5D3A_B0BA_1C9E_C46FL, 0x653E_5C44_66BB_BE7AL, + /* -156 */ 0x4A95_5A2E_7D4B_D059L, 0x3765_169D_1EFC_9861L, + /* -155 */ 0x7755_5D17_2EDF_B3C2L, 0x256E_8A94_FE60_F3CFL, + /* -154 */ 0x5F77_7DAC_257F_C301L, 0x6ABE_D543_FEB3_F63FL, + /* -153 */ 0x4C5F_97BC_EACC_9C01L, 0x3BCB_DDCF_FEF6_5E99L, + /* -152 */ 0x7A32_8C61_77AD_C668L, 0x5FAC_9619_97F0_975BL, + /* -151 */ 0x61C2_09E7_92F1_6B86L, 0x7FBD_44E1_465A_12AFL, + /* -150 */ 0x4E34_D4B9_425A_BC6BL, 0x7FCA_9D81_0514_DBBFL, + /* -149 */ 0x7D21_545B_9D5D_FA46L, 0x32DD_C8CE_6E87_C5FFL, + /* -148 */ 0x641A_A9E2_E44B_2E9EL, 0x5BE4_A0A5_2539_6B32L, + /* -147 */ 0x5015_54B5_836F_587EL, 0x7CB6_E6EA_842D_EF5CL, + /* -146 */ 0x4011_1091_35F2_AD32L, 0x3092_5255_368B_25E3L, + /* -145 */ 0x6681_B41B_8984_4850L, 0x4DB6_EA21_F0DE_A304L, + /* -144 */ 0x5201_5CE2_D469_D373L, 0x57C5_881B_2718_826AL, + /* -143 */ 0x419A_B0B5_76BB_0F8FL, 0x5FD1_39AF_527A_01EFL, + /* -142 */ 0x68F7_8122_5791_B27FL, 0x4C81_F5E5_50C3_364AL, + /* -141 */ 0x53F9_341B_7941_5B99L, 0x239B_2B1D_DA35_C508L, + /* -140 */ 0x432D_C349_2DCD_E2E1L, 0x02E2_88E4_AE91_6A6DL, + /* -139 */ 0x6B7C_6BA8_4949_6B01L, 0x516A_74A1_174F_10AEL, + /* -138 */ 0x55FD_22ED_076D_EF34L, 0x4121_F6E7_45D8_DA25L, + /* -137 */ 0x44CA_8257_3924_BF5DL, 0x1A81_9252_9E47_14EBL, + /* -136 */ 0x6E10_D08B_8EA1_322EL, 0x5D9C_1D50_FD3E_87DDL, + /* -135 */ 0x580D_73A2_D880_F4F2L, 0x17B0_1773_FDCB_9FE4L, + /* -134 */ 0x4671_294F_139A_5D8EL, 0x4626_7929_97D6_1984L, + /* -133 */ 0x70B5_0EE4_EC2A_2F4AL, 0x3D0A_5B75_BFBC_F59FL, + /* -132 */ 0x5A2A_7250_BCEE_8C3BL, 0x4A6E_AF91_6630_C47FL, + /* -131 */ 0x4821_F50D_63F2_09C9L, 0x21F2_260D_EB5A_36CCL, + /* -130 */ 0x7369_8815_6CB6_760EL, 0x6983_7016_455D_247AL, + /* -129 */ 0x5C54_6CDD_F091_F80BL, 0x6E02_C011_D117_5062L, + /* -128 */ 0x49DD_23E4_C074_C66FL, 0x719B_CCDB_0DAC_404EL, + /* -127 */ 0x762E_9FD4_6721_3D7FL, 0x68F9_47C4_E2AD_33B0L, + /* -126 */ 0x5E8B_B310_5280_FDFFL, 0x6D94_396A_4EF0_F627L, + /* -125 */ 0x4BA2_F5A6_A867_3199L, 0x3E10_2DEE_A58D_91B9L, + /* -124 */ 0x7904_BC3D_DA3E_B5C2L, 0x3019_E317_6F48_E927L, + /* -123 */ 0x60D0_9697_E1CB_C49BL, 0x4014_B5AC_5907_20ECL, + /* -122 */ 0x4D73_ABAC_B4A3_03AFL, 0x4CDD_5E23_7A6C_1A57L, + /* -121 */ 0x7BEC_45E1_2104_D2B2L, 0x47C8_969F_2A46_908AL, + /* -120 */ 0x6323_6B1A_80D0_A88EL, 0x6CA0_787F_5505_406FL, + /* -119 */ 0x4F4F_88E2_00A6_ED3FL, 0x0A19_F9FF_7737_66BFL, + /* -118 */ 0x7EE5_A7D0_010B_1531L, 0x5CF6_5CCB_F1F2_3DFEL, + /* -117 */ 0x6584_8640_00D5_AA8EL, 0x172B_7D6F_F4C1_CB32L, + /* -116 */ 0x5136_D1CC_CD77_BBA4L, 0x78EF_978C_C3CE_3C28L, + /* -115 */ 0x40F8_A7D7_0AC6_2FB7L, 0x13F2_DFA3_CFD8_3020L, + /* -114 */ 0x67F4_3FBE_77A3_7F8BL, 0x3984_9906_1959_E699L, + /* -113 */ 0x5329_CC98_5FB5_FFA2L, 0x6136_E0D1_ADE1_8548L, + /* -112 */ 0x4287_D6E0_4C91_994FL, 0x00F8_B3DA_F181_376DL, + /* -111 */ 0x6A72_F166_E0E8_F54BL, 0x1B27_862B_1C01_F247L, + /* -110 */ 0x5528_C11F_1A53_F76FL, 0x2F52_D1BC_1667_F506L, + /* -109 */ 0x4420_9A7F_4843_2C59L, 0x0C42_4163_451F_F738L, + /* -108 */ 0x6D00_F732_0D38_46F4L, 0x7A03_9BD2_0833_2526L, + /* -107 */ 0x5733_F8F4_D760_38C3L, 0x7B36_1641_A028_EA85L, + /* -106 */ 0x45C3_2D90_AC4C_FA36L, 0x2F5E_7834_8020_BB9EL, + /* -105 */ 0x6F9E_AF4D_E07B_29F0L, 0x4BCA_59ED_99CD_F8FCL, + /* -104 */ 0x594B_BF71_8062_87F3L, 0x563B_7B24_7B0B_2D96L, + /* -103 */ 0x476F_CC5A_CD1B_9FF6L, 0x11C9_2F50_626F_57ACL, + /* -102 */ 0x724C_7A2A_E1C5_CCBDL, 0x02DB_7EE7_03E5_5912L, + /* -101 */ 0x5B70_61BB_E7D1_7097L, 0x1BE2_CBEC_031D_E0DCL, + /* -100 */ 0x4926_B496_530D_F3ACL, 0x164F_0989_9C17_E716L, + /* -99 */ 0x750A_BA8A_1E7C_B913L, 0x3D4B_4275_C68C_A4F0L, + /* -98 */ 0x5DA2_2ED4_E530_940FL, 0x4AA2_9B91_6BA3_B726L, + /* -97 */ 0x4AE8_2577_1DC0_7672L, 0x6EE8_7C74_561C_9285L, + /* -96 */ 0x77D9_D58B_62CD_8A51L, 0x3173_FA53_BCFA_8408L, + /* -95 */ 0x5FE1_77A2_B571_3B74L, 0x278F_FB76_30C8_69A0L, + /* -94 */ 0x4CB4_5FB5_5DF4_2F90L, 0x1FA6_62C4_F3D3_87B3L, + /* -93 */ 0x7ABA_32BB_C986_B280L, 0x32A3_D13B_1FB8_D91FL, + /* -92 */ 0x622E_8EFC_A138_8ECDL, 0x0EE9_742F_4C93_E0E6L, + /* -91 */ 0x4E8B_A596_E760_723DL, 0x58BA_C359_0A0F_E71EL, + /* -90 */ 0x7DAC_3C24_A567_1D2FL, 0x412A_D228_1019_71C9L, + /* -89 */ 0x6489_C9B6_EAB8_E426L, 0x00EF_0E86_7347_8E3BL, + /* -88 */ 0x506E_3AF8_BBC7_1CEBL, 0x1A58_D86B_8F6C_71C9L, + /* -87 */ 0x4058_2F2D_6305_B0BCL, 0x1513_E056_0C56_C16EL, + /* -86 */ 0x66F3_7EAF_04D5_E793L, 0x3B53_0089_AD57_9BE2L, + /* -85 */ 0x525C_6558_D0AB_1FA9L, 0x15DC_006E_2446_164FL, + /* -84 */ 0x41E3_8447_0D55_B2EDL, 0x5E49_99F1_B69E_783FL, + /* -83 */ 0x696C_06D8_1555_EB15L, 0x7D42_8FE9_2430_C065L, + /* -82 */ 0x5456_6BE0_1111_88DEL, 0x3102_0CBA_835A_3384L, + /* -81 */ 0x4378_564C_DA74_6D7EL, 0x5A68_0A2E_CF7B_5C69L, + /* -80 */ 0x6BF3_BD47_C3ED_7BFDL, 0x770C_DD17_B25E_FA42L, + /* -79 */ 0x565C_976C_9CBD_FCCBL, 0x1270_B0DF_C1E5_9502L, + /* -78 */ 0x4516_DF8A_16FE_63D5L, 0x5B8D_5A4C_9B1E_10CEL, + /* -77 */ 0x6E8A_FF43_57FD_6C89L, 0x127B_C3AD_C4FC_E7B0L, + /* -76 */ 0x586F_329C_4664_56D4L, 0x0EC9_6957_D0CA_52F3L, + /* -75 */ 0x46BF_5BB0_3850_4576L, 0x3F07_8779_73D5_0F29L, + /* -74 */ 0x7132_2C4D_26E6_D58AL, 0x31A5_A58F_1FBB_4B75L, + /* -73 */ 0x5A8E_89D7_5252_446EL, 0x5AEA_EAD8_E62F_6F91L, + /* -72 */ 0x4872_07DF_750E_9D25L, 0x2F22_557A_51BF_8C74L, + /* -71 */ 0x73E9_A632_54E4_2EA2L, 0x1836_EF2A_1C65_AD86L, + /* -70 */ 0x5CBA_EB5B_771C_F21BL, 0x2CF8_BF54_E384_8AD2L, + /* -69 */ 0x4A2F_22AF_927D_8E7CL, 0x23FA_32AA_4F9D_3BDBL, + /* -68 */ 0x76B1_D118_EA62_7D93L, 0x5329_EAAA_18FB_92F8L, + /* -67 */ 0x5EF4_A747_21E8_6476L, 0x0F54_BBBB_472F_A8C6L, + /* -66 */ 0x4BF6_EC38_E7ED_1D2BL, 0x25DD_62FC_38F2_ED6CL, + /* -65 */ 0x798B_138E_3FE1_C845L, 0x22FB_D193_8E51_7BDFL, + /* -64 */ 0x613C_0FA4_FFE7_D36AL, 0x4F2F_DADC_71DA_C97FL, + /* -63 */ 0x4DC9_A61D_9986_42BBL, 0x58F3_157D_27E2_3ACCL, + /* -62 */ 0x7C75_D695_C270_6AC5L, 0x74B8_2261_D969_F7ADL, + /* -61 */ 0x6391_7877_CEC0_556BL, 0x1093_4EB4_ADEE_5FBEL, + /* -60 */ 0x4FA7_9393_0BCD_1122L, 0x4075_D890_8B25_1965L, + /* -59 */ 0x7F72_85B8_12E1_B504L, 0x00BC_8DB4_11D4_F56EL, + /* -58 */ 0x65F5_37C6_7581_5D9CL, 0x66FD_3E29_A7DD_9125L, + /* -57 */ 0x5190_F96B_9134_4AE3L, 0x6BFD_CB54_864A_DA84L, + /* -56 */ 0x4140_C789_40F6_A24FL, 0x6FFE_3C43_9EA2_486AL, + /* -55 */ 0x6867_A5A8_67F1_03B2L, 0x7FFD_2D38_FDD0_73DCL, + /* -54 */ 0x5386_1E20_5327_3628L, 0x6664_242D_97D9_F64AL, + /* -53 */ 0x42D1_B1B3_75B8_F820L, 0x51E9_B68A_DFE1_91D5L, + /* -52 */ 0x6AE9_1C52_55F4_C034L, 0x1CA9_2411_6635_B621L, + /* -51 */ 0x5587_49DB_77F7_0029L, 0x63BA_8341_1E91_5E81L, + /* -50 */ 0x446C_3B15_F992_6687L, 0x6962_029A_7EDA_B201L, + /* -49 */ 0x6D79_F823_28EA_3DA6L, 0x0F03_375D_97C4_5001L, + /* -48 */ 0x5794_C682_8721_CAEBL, 0x259C_2C4A_DFD0_4001L, + /* -47 */ 0x4610_9ECE_D281_6F22L, 0x5149_BD08_B30D_0001L, + /* -46 */ 0x701A_97B1_50CF_1837L, 0x3542_C80D_EB48_0001L, + /* -45 */ 0x59AE_DFC1_0D72_79C5L, 0x7768_A00B_22A0_0001L, + /* -44 */ 0x47BF_1967_3DF5_2E37L, 0x7920_8008_E880_0001L, + /* -43 */ 0x72CB_5BD8_6321_E38CL, 0x5B67_3341_7400_0001L, + /* -42 */ 0x5BD5_E313_8281_82D6L, 0x7C52_8F67_9000_0001L, + /* -41 */ 0x4977_E8DC_6867_9BDFL, 0x16A8_72B9_4000_0001L, + /* -40 */ 0x758C_A7C7_0D72_92FEL, 0x5773_EAC2_0000_0001L, + /* -39 */ 0x5E0A_1FD2_7128_7598L, 0x45F6_5568_0000_0001L, + /* -38 */ 0x4B3B_4CA8_5A86_C47AL, 0x04C5_1120_0000_0001L, + /* -37 */ 0x785E_E10D_5DA4_6D90L, 0x07A1_B500_0000_0001L, + /* -36 */ 0x604B_E73D_E483_8AD9L, 0x52E7_C400_0000_0001L, + /* -35 */ 0x4D09_85CB_1D36_08AEL, 0x0F1F_D000_0000_0001L, + /* -34 */ 0x7B42_6FAB_61F0_0DE3L, 0x31CC_8000_0000_0001L, + /* -33 */ 0x629B_8C89_1B26_7182L, 0x5B0A_0000_0000_0001L, + /* -32 */ 0x4EE2_D6D4_15B8_5ACEL, 0x7C08_0000_0000_0001L, + /* -31 */ 0x7E37_BE20_22C0_914BL, 0x1340_0000_0000_0001L, + /* -30 */ 0x64F9_64E6_8233_A76FL, 0x2900_0000_0000_0001L, + /* -29 */ 0x50C7_83EB_9B5C_85F2L, 0x5400_0000_0000_0001L, + /* -28 */ 0x409F_9CBC_7C4A_04C2L, 0x1000_0000_0000_0001L, + /* -27 */ 0x6765_C793_FA10_079DL, 0x0000_0000_0000_0001L, + /* -26 */ 0x52B7_D2DC_C80C_D2E4L, 0x0000_0000_0000_0001L, + /* -25 */ 0x422C_A8B0_A00A_4250L, 0x0000_0000_0000_0001L, + /* -24 */ 0x69E1_0DE7_6676_D080L, 0x0000_0000_0000_0001L, + /* -23 */ 0x54B4_0B1F_852B_DA00L, 0x0000_0000_0000_0001L, + /* -22 */ 0x43C3_3C19_3756_4800L, 0x0000_0000_0000_0001L, + /* -21 */ 0x6C6B_935B_8BBD_4000L, 0x0000_0000_0000_0001L, + /* -20 */ 0x56BC_75E2_D631_0000L, 0x0000_0000_0000_0001L, + /* -19 */ 0x4563_9182_44F4_0000L, 0x0000_0000_0000_0001L, + /* -18 */ 0x6F05_B59D_3B20_0000L, 0x0000_0000_0000_0001L, + /* -17 */ 0x58D1_5E17_6280_0000L, 0x0000_0000_0000_0001L, + /* -16 */ 0x470D_E4DF_8200_0000L, 0x0000_0000_0000_0001L, + /* -15 */ 0x71AF_D498_D000_0000L, 0x0000_0000_0000_0001L, + /* -14 */ 0x5AF3_107A_4000_0000L, 0x0000_0000_0000_0001L, + /* -13 */ 0x48C2_7395_0000_0000L, 0x0000_0000_0000_0001L, + /* -12 */ 0x746A_5288_0000_0000L, 0x0000_0000_0000_0001L, + /* -11 */ 0x5D21_DBA0_0000_0000L, 0x0000_0000_0000_0001L, + /* -10 */ 0x4A81_7C80_0000_0000L, 0x0000_0000_0000_0001L, + /* -9 */ 0x7735_9400_0000_0000L, 0x0000_0000_0000_0001L, + /* -8 */ 0x5F5E_1000_0000_0000L, 0x0000_0000_0000_0001L, + /* -7 */ 0x4C4B_4000_0000_0000L, 0x0000_0000_0000_0001L, + /* -6 */ 0x7A12_0000_0000_0000L, 0x0000_0000_0000_0001L, + /* -5 */ 0x61A8_0000_0000_0000L, 0x0000_0000_0000_0001L, + /* -4 */ 0x4E20_0000_0000_0000L, 0x0000_0000_0000_0001L, + /* -3 */ 0x7D00_0000_0000_0000L, 0x0000_0000_0000_0001L, + /* -2 */ 0x6400_0000_0000_0000L, 0x0000_0000_0000_0001L, + /* -1 */ 0x5000_0000_0000_0000L, 0x0000_0000_0000_0001L, + /* 0 */ 0x4000_0000_0000_0000L, 0x0000_0000_0000_0001L, + /* 1 */ 0x6666_6666_6666_6666L, 0x3333_3333_3333_3334L, + /* 2 */ 0x51EB_851E_B851_EB85L, 0x0F5C_28F5_C28F_5C29L, + /* 3 */ 0x4189_374B_C6A7_EF9DL, 0x5916_872B_020C_49BBL, + /* 4 */ 0x68DB_8BAC_710C_B295L, 0x74F0_D844_D013_A92BL, + /* 5 */ 0x53E2_D623_8DA3_C211L, 0x43F3_E037_0CDC_8755L, + /* 6 */ 0x431B_DE82_D7B6_34DAL, 0x698F_E692_70B0_6C44L, + /* 7 */ 0x6B5F_CA6A_F2BD_215EL, 0x0F4C_A41D_811A_46D4L, + /* 8 */ 0x55E6_3B88_C230_E77EL, 0x3F70_834A_CDAE_9F10L, + /* 9 */ 0x44B8_2FA0_9B5A_52CBL, 0x4C5A_02A2_3E25_4C0DL, + /* 10 */ 0x6DF3_7F67_5EF6_EADFL, 0x2D5C_D103_96A2_1347L, + /* 11 */ 0x57F5_FF85_E592_557FL, 0x3DE3_DA69_454E_75D3L, + /* 12 */ 0x465E_6604_B7A8_4465L, 0x7E4F_E1ED_D10B_9175L, + /* 13 */ 0x7097_09A1_25DA_0709L, 0x4A19_697C_81AC_1BEFL, + /* 14 */ 0x5A12_6E1A_84AE_6C07L, 0x54E1_2130_67BC_E326L, + /* 15 */ 0x480E_BE7B_9D58_566CL, 0x43E7_4DC0_52FD_8285L, + /* 16 */ 0x734A_CA5F_6226_F0ADL, 0x530B_AF9A_1E62_6A6DL, + /* 17 */ 0x5C3B_D519_1B52_5A24L, 0x426F_BFAE_7EB5_21F1L, + /* 18 */ 0x49C9_7747_490E_AE83L, 0x4EBF_CC8B_9890_E7F4L, + /* 19 */ 0x760F_253E_DB4A_B0D2L, 0x4ACC_7A78_F41B_0CBAL, + /* 20 */ 0x5E72_8432_4908_8D75L, 0x223D_2EC7_29AF_3D62L, + /* 21 */ 0x4B8E_D028_3A6D_3DF7L, 0x34FD_BF05_BAF2_9781L, + /* 22 */ 0x78E4_8040_5D7B_9658L, 0x54C9_31A2_C4B7_58CFL, + /* 23 */ 0x60B6_CD00_4AC9_4513L, 0x5D6D_C14F_03C5_E0A5L, + /* 24 */ 0x4D5F_0A66_A23A_9DA9L, 0x3124_9AA5_9C9E_4D51L, + /* 25 */ 0x7BCB_43D7_69F7_62A8L, 0x4EA0_F76F_60FD_4882L, + /* 26 */ 0x6309_0312_BB2C_4EEDL, 0x254D_92BF_80CA_A068L, + /* 27 */ 0x4F3A_68DB_C8F0_3F24L, 0x1DD7_A899_33D5_4D20L, + /* 28 */ 0x7EC3_DAF9_4180_6506L, 0x62F2_A75B_8622_1500L, + /* 29 */ 0x6569_7BFA_9ACD_1D9FL, 0x025B_B916_04E8_10CDL, + /* 30 */ 0x5121_2FFB_AF0A_7E18L, 0x6849_60DE_6A53_40A4L, + /* 31 */ 0x40E7_5996_25A1_FE7AL, 0x203A_B3E5_21DC_33B6L, + /* 32 */ 0x67D8_8F56_A29C_CA5DL, 0x19F7_863B_6960_52BDL, + /* 33 */ 0x5313_A5DE_E87D_6EB0L, 0x7B2C_6B62_BAB3_7564L, + /* 34 */ 0x4276_1E4B_ED31_255AL, 0x2F56_BC4E_FBC2_C450L, + /* 35 */ 0x6A56_96DF_E1E8_3BC3L, 0x6557_93B1_92D1_3A1AL, + /* 36 */ 0x5512_124C_B4B9_C969L, 0x3779_42F4_7574_2E7BL, + /* 37 */ 0x440E_750A_2A2E_3ABAL, 0x5F94_3590_5DF6_8B96L, + /* 38 */ 0x6CE3_EE76_A9E3_912AL, 0x65B9_EF4D_6324_1289L, + /* 39 */ 0x571C_BEC5_54B6_0DBBL, 0x6AFB_25D7_8283_4207L, + /* 40 */ 0x45B0_989D_DD5E_7163L, 0x08C8_EB12_CECF_6806L, + /* 41 */ 0x6F80_F42F_C897_1BD1L, 0x5ADB_11B7_B14B_D9A3L, + /* 42 */ 0x5933_F68C_A078_E30EL, 0x157C_0E2C_8DD6_47B5L, + /* 43 */ 0x475C_C53D_4D2D_8271L, 0x5DFC_D823_A4AB_6C91L, + /* 44 */ 0x722E_0862_1515_9D82L, 0x632E_269F_6DDF_141BL, + /* 45 */ 0x5B58_06B4_DDAA_E468L, 0x4F58_1EE5_F17F_4349L, + /* 46 */ 0x4913_3890_B155_8386L, 0x72AC_E584_C132_9C3BL, + /* 47 */ 0x74EB_8DB4_4EEF_38D7L, 0x6AAE_3C07_9B84_2D2AL, + /* 48 */ 0x5D89_3E29_D8BF_60ACL, 0x5558_3006_1603_5755L, + /* 49 */ 0x4AD4_31BB_13CC_4D56L, 0x7779_C004_DE69_12ABL, + /* 50 */ 0x77B9_E92B_52E0_7BBEL, 0x258F_99A1_63DB_5111L, + /* 51 */ 0x5FC7_EDBC_424D_2FCBL, 0x37A6_1481_1CAF_740DL, + /* 52 */ 0x4C9F_F163_683D_BFD5L, 0x7951_AA00_E3BF_900BL, + /* 53 */ 0x7A99_8238_A6C9_32EFL, 0x754F_7667_D2CC_19ABL, + /* 54 */ 0x6214_682D_523A_8F26L, 0x2AA5_F853_0F09_AE22L, + /* 55 */ 0x4E76_B9BD_DB62_0C1EL, 0x5551_9375_A5A1_581BL, + /* 56 */ 0x7D8A_C2C9_5F03_4697L, 0x3BB5_B8BC_3C35_59C5L, + /* 57 */ 0x646F_023A_B269_0545L, 0x7C91_6096_9691_149EL, + /* 58 */ 0x5058_CE95_5B87_376BL, 0x16DA_B3AB_ABA7_43B2L, + /* 59 */ 0x4047_0BAA_AF9F_5F88L, 0x78AE_F622_EFB9_02F5L, + /* 60 */ 0x66D8_12AA_B298_98DBL, 0x0DE4_BD04_B2C1_9E54L, + /* 61 */ 0x5246_7555_5BAD_4715L, 0x57EA_30D0_8F01_4B76L, + /* 62 */ 0x41D1_F777_7C8A_9F44L, 0x4654_F3DA_0C01_092CL, + /* 63 */ 0x694F_F258_C744_3207L, 0x23BB_1FC3_4668_0EACL, + /* 64 */ 0x543F_F513_D29C_F4D2L, 0x4FC8_E635_D1EC_D88AL, + /* 65 */ 0x4366_5DA9_754A_5D75L, 0x263A_51C4_A7F0_AD3BL, + /* 66 */ 0x6BD6_FC42_5543_C8BBL, 0x56C3_B607_731A_AEC4L, + /* 67 */ 0x5645_969B_7769_6D62L, 0x789C_919F_8F48_8BD0L, + /* 68 */ 0x4504_787C_5F87_8AB5L, 0x46E3_A7B2_D906_D640L, + /* 69 */ 0x6E6D_8D93_CC0C_1122L, 0x3E39_0C51_5B3E_239AL, + /* 70 */ 0x5857_A476_3CD6_741BL, 0x4B60_D6A7_7C31_B615L, + /* 71 */ 0x46AC_8391_CA45_29AFL, 0x55E7_121F_968E_2B44L, + /* 72 */ 0x7114_05B6_106E_A919L, 0x0971_B698_F0E3_786DL, + /* 73 */ 0x5A76_6AF8_0D25_5414L, 0x078E_2BAD_8D82_C6BDL, + /* 74 */ 0x485E_BBF9_A41D_DCDCL, 0x6C71_BC8A_D79B_D231L, + /* 75 */ 0x73CA_C65C_39C9_6161L, 0x2D82_C744_8C2C_8382L, + /* 76 */ 0x5CA2_3849_C7D4_4DE7L, 0x3E02_3903_A356_CF9BL, + /* 77 */ 0x4A1B_603B_0643_7185L, 0x7E68_2D9C_82AB_D949L, + /* 78 */ 0x7692_3391_A39F_1C09L, 0x4A40_48FA_6AAC_8EDBL, + /* 79 */ 0x5EDB_5C74_82E5_B007L, 0x5500_3A61_EEF0_7249L, + /* 80 */ 0x4BE2_B05D_3584_8CD2L, 0x7733_61E7_F259_F507L, + /* 81 */ 0x796A_B3C8_55A0_E151L, 0x3EB8_9CA6_508F_EE71L, + /* 82 */ 0x6122_296D_114D_810DL, 0x7EFA_16EB_73A6_585BL, + /* 83 */ 0x4DB4_EDF0_DAA4_673EL, 0x3261_ABEF_8FB8_46AFL, + /* 84 */ 0x7C54_AFE7_C43A_3ECAL, 0x1D69_1318_E5F3_A44BL, + /* 85 */ 0x6376_F31F_D02E_98A1L, 0x6454_0F47_1E5C_836FL, + /* 86 */ 0x4F92_5C19_7358_7A1BL, 0x0376_729F_4B7D_35F3L, + /* 87 */ 0x7F50_935B_EBC0_C35EL, 0x38BD_8432_1261_EFEBL, + /* 88 */ 0x65DA_0F7C_BC9A_35E5L, 0x13CA_D028_0EB4_BFEFL, + /* 89 */ 0x517B_3F96_FD48_2B1DL, 0x5CA2_4020_0BC3_CCBFL, + /* 90 */ 0x412F_6612_6439_BC17L, 0x63B5_0019_A303_0A33L, + /* 91 */ 0x684B_D683_D38F_9359L, 0x1F88_0029_04D1_A9EAL, + /* 92 */ 0x536F_DECF_DC72_DC47L, 0x32D3_3354_03DA_EE55L, + /* 93 */ 0x42BF_E573_16C2_49D2L, 0x5BDC_2910_0315_8B77L, + /* 94 */ 0x6ACC_A251_BE03_A951L, 0x12F9_DB4C_D1BC_1258L, + /* 95 */ 0x5570_81DA_FE69_5440L, 0x7594_AF70_A7C9_A847L, + /* 96 */ 0x445A_017B_FEBA_A9CDL, 0x4476_F2C0_863A_ED06L, + /* 97 */ 0x6D5C_CF2C_CAC4_42E2L, 0x3A57_EACD_A391_7B3CL, + /* 98 */ 0x577D_728A_3BD0_3581L, 0x7B79_88A4_82DA_C8FDL, + /* 99 */ 0x45FD_F53B_630C_F79BL, 0x15FA_D3B6_CF15_6D97L, + /* 100 */ 0x6FFC_BB92_3814_BF5EL, 0x565E_1F8A_E4EF_15BEL, + /* 101 */ 0x5996_FC74_F9AA_32B2L, 0x11E4_E608_B725_AAFFL, + /* 102 */ 0x47AB_FD2A_6154_F55BL, 0x27EA_51A0_9284_88CCL, + /* 103 */ 0x72AC_C843_CEEE_555EL, 0x7310_829A_8407_4146L, + /* 104 */ 0x5BBD_6D03_0BF1_DDE5L, 0x4273_9BAE_D005_CDD2L, + /* 105 */ 0x4964_5735_A327_E4B7L, 0x4EC2_E2F2_4004_A4A8L, + /* 106 */ 0x756D_5855_D1D9_6DF2L, 0x4AD1_6B1D_333A_A10CL, + /* 107 */ 0x5DF1_1377_DB14_57F5L, 0x2241_227D_C295_4DA3L, + /* 108 */ 0x4B27_42C6_48DD_132AL, 0x4E9A_81FE_3544_3E1CL, + /* 109 */ 0x783E_D13D_4161_B844L, 0x175D_9CC9_EED3_9694L, + /* 110 */ 0x6032_40FD_CDE7_C69CL, 0x7917_B0A1_8BDC_7876L, + /* 111 */ 0x4CF5_00CB_0B1F_D217L, 0x1412_F3B4_6FE3_9392L, + /* 112 */ 0x7B21_9ADE_7832_E9BEL, 0x5351_85ED_7FD2_85B6L, + /* 113 */ 0x6281_48B1_F9C2_5498L, 0x42A7_9E57_9975_37C5L, + /* 114 */ 0x4ECD_D3C1_949B_76E0L, 0x3552_E512_E12A_9304L, + /* 115 */ 0x7E16_1F9C_20F8_BE33L, 0x6EEB_081E_3510_EB39L, + /* 116 */ 0x64DE_7FB0_1A60_9829L, 0x3F22_6CE4_F740_BC2EL, + /* 117 */ 0x50B1_FFC0_151A_1354L, 0x3281_F0B7_2C33_C9BEL, + /* 118 */ 0x408E_6633_4414_DC43L, 0x4201_8D5F_568F_D498L, + /* 119 */ 0x674A_3D1E_D354_939FL, 0x1CCF_4898_8A7F_BA8DL, + /* 120 */ 0x52A1_CA7F_0F76_DC7FL, 0x30A5_D3AD_3B99_620BL, + /* 121 */ 0x421B_0865_A5F8_B065L, 0x73B7_DC8A_9614_4E6FL, + /* 122 */ 0x69C4_DA3C_3CC1_1A3CL, 0x52BF_C744_2353_B0B1L, + /* 123 */ 0x549D_7B63_63CD_AE96L, 0x7566_3903_4F76_26F4L, + /* 124 */ 0x43B1_2F82_B63E_2545L, 0x4451_C735_D92B_525DL, + /* 125 */ 0x6C4E_B26A_BD30_3BA2L, 0x3A1C_71EF_C1DE_EA2EL, + /* 126 */ 0x56A5_5B88_9759_C94EL, 0x61B0_5B26_34B2_54F2L, + /* 127 */ 0x4551_1606_DF7B_0772L, 0x1AF3_7C1E_908E_AA5BL, + /* 128 */ 0x6EE8_233E_325E_7250L, 0x2B1F_2CFD_B417_76F8L, + /* 129 */ 0x58B9_B5CB_5B7E_C1D9L, 0x6F4C_23FE_29AC_5F2DL, + /* 130 */ 0x46FA_F7D5_E2CB_CE47L, 0x72A3_4FFE_87BD_18F1L, + /* 131 */ 0x7191_8C89_6ADF_B073L, 0x0438_7FFD_A5FB_5B1BL, + /* 132 */ 0x5ADA_D6D4_557F_C05CL, 0x0360_6664_84C9_15AFL, + /* 133 */ 0x48AF_1243_7799_66B0L, 0x02B3_851D_3707_448CL, + /* 134 */ 0x744B_506B_F28F_0AB3L, 0x1DEC_082E_BE72_0746L, + /* 135 */ 0x5D09_0D23_2872_6EF5L, 0x64BC_D358_985B_3905L, + /* 136 */ 0x4A6D_A41C_205B_8BF7L, 0x6A30_A913_AD15_C738L, + /* 137 */ 0x7715_D360_33C5_ACBFL, 0x5D1A_A81F_7B56_0B8CL, + /* 138 */ 0x5F44_A919_C304_8A32L, 0x7DAE_ECE5_FC44_D609L, + /* 139 */ 0x4C36_EDAE_359D_3B5BL, 0x7E25_8A51_969D_7808L, + /* 140 */ 0x79F1_7C49_EF61_F893L, 0x16A2_76E8_F0FB_F33FL, + /* 141 */ 0x618D_FD07_F2B4_C6DCL, 0x121B_9253_F3FC_C299L, + /* 142 */ 0x4E0B_30D3_2890_9F16L, 0x41AF_A843_2997_0214L, + /* 143 */ 0x7CDE_B485_0DB4_31BDL, 0x4F7F_739E_A8F1_9CEDL, + /* 144 */ 0x63E5_5D37_3E29_C164L, 0x3F99_294B_BA5A_E3F1L, + /* 145 */ 0x4FEA_B0F8_FE87_CDE9L, 0x7FAD_BAA2_FB7B_E98DL, + /* 146 */ 0x7FDD_E7F4_CA72_E30FL, 0x7F7C_5DD1_925F_DC15L, + /* 147 */ 0x664B_1FF7_085B_E8D9L, 0x4C63_7E41_41E6_49ABL, + /* 148 */ 0x51D5_B32C_06AF_ED7AL, 0x704F_9834_34B8_3AEFL, + /* 149 */ 0x4177_C289_9EF3_2462L, 0x26A6_135C_F6F9_C8BFL, + /* 150 */ 0x68BF_9DA8_FE51_D3D0L, 0x3DD6_8561_8B29_4132L, + /* 151 */ 0x53CC_7E20_CB74_A973L, 0x4B12_044E_08ED_CDC2L, + /* 152 */ 0x4309_FE80_A2C3_BAC2L, 0x6F41_9D0B_3A57_D7CEL, + /* 153 */ 0x6B43_30CD_D139_2AD1L, 0x3202_94DE_C3BF_BFB0L, + /* 154 */ 0x55CF_5A3E_40FA_88A7L, 0x419B_AA4B_CFCC_995AL, + /* 155 */ 0x44A5_E1CB_672E_D3B9L, 0x1AE2_EEA3_0CA3_ADE1L, + /* 156 */ 0x6DD6_3612_3EB1_52C1L, 0x77D1_7DD1_ADD2_AFCFL, + /* 157 */ 0x57DE_91A8_3227_7567L, 0x7974_64A7_BE42_263FL, + /* 158 */ 0x464B_A7B9_C1B9_2AB9L, 0x4790_5086_31CE_84FFL, + /* 159 */ 0x7079_0C5C_6928_445CL, 0x0C1A_1A70_4FB0_D4CCL, + /* 160 */ 0x59FA_7049_EDB9_D049L, 0x567B_4859_D95A_43D6L, + /* 161 */ 0x47FB_8D07_F161_736EL, 0x11FC_39E1_7AAE_9CABL, + /* 162 */ 0x732C_14D9_8235_857DL, 0x032D_2968_C44A_9445L, + /* 163 */ 0x5C23_43E1_34F7_9DFDL, 0x4F57_5453_D03B_A9D1L, + /* 164 */ 0x49B5_CFE7_5D92_E4CAL, 0x72AC_4376_402F_BB0EL, + /* 165 */ 0x75EF_B30B_C8EB_07ABL, 0x0446_D256_CD19_2B49L, + /* 166 */ 0x5E59_5C09_6D88_D2EFL, 0x1D05_7512_3DAD_BC3AL, + /* 167 */ 0x4B7A_B007_8AD3_DBF2L, 0x4A6A_C40E_97BE_302FL, + /* 168 */ 0x78C4_4CD8_DE1F_C650L, 0x7711_39B0_F2C9_E6B1L, + /* 169 */ 0x609D_0A47_1819_6B73L, 0x78DA_948D_8F07_EBC1L, + /* 170 */ 0x4D4A_6E9F_467A_BC5CL, 0x60AE_DD3E_0C06_5634L, + /* 171 */ 0x7BAA_4A98_70C4_6094L, 0x344A_FB96_79A3_BD20L, + /* 172 */ 0x62EE_A213_8D69_E6DDL, 0x103B_FC78_614F_CA80L, + /* 173 */ 0x4F25_4E76_0ABB_1F17L, 0x2696_6393_810C_A200L, + /* 174 */ 0x7EA2_1723_445E_9825L, 0x2423_D285_9B47_6999L, + /* 175 */ 0x654E_78E9_037E_E01DL, 0x69B6_4204_7C39_2148L, + /* 176 */ 0x510B_93ED_9C65_8017L, 0x6E2B_6803_9694_1AA0L, + /* 177 */ 0x40D6_0FF1_49EA_CCDFL, 0x71BC_5336_1210_154DL, + /* 178 */ 0x67BC_E64E_DCAA_E166L, 0x1C60_8523_5019_BBAEL, + /* 179 */ 0x52FD_850B_E3BB_E784L, 0x7D1A_041C_4014_9625L, + /* 180 */ 0x4264_6A6F_E963_1F9DL, 0x4A7B_367D_0010_781DL, + /* 181 */ 0x6A3A_43E6_4238_3295L, 0x5D91_F0C8_001A_59C8L, + /* 182 */ 0x54FB_6985_01C6_8EDEL, 0x17A7_F3D3_3348_47D4L, + /* 183 */ 0x43FC_546A_67D2_0BE4L, 0x7953_2975_C2A0_3976L, + /* 184 */ 0x6CC6_ED77_0C83_463BL, 0x0EEB_7589_3766_C256L, + /* 185 */ 0x5705_8AC5_A39C_382FL, 0x2589_2AD4_2C52_3512L, + /* 186 */ 0x459E_089E_1C7C_F9BFL, 0x37A0_EF10_2374_F742L, + /* 187 */ 0x6F63_40FC_FA61_8F98L, 0x5901_7E80_38BB_2536L, + /* 188 */ 0x591C_33FD_951A_D946L, 0x7A67_9866_93C8_EA91L, + /* 189 */ 0x4749_C331_4415_7A9FL, 0x151F_AD1E_DCA0_BBA8L, + /* 190 */ 0x720F_9EB5_39BB_F765L, 0x0832_AE97_C767_92A5L, + /* 191 */ 0x5B3F_B22A_9496_5F84L, 0x068E_F213_05EC_7551L, + /* 192 */ 0x48FF_C1BB_AA11_E603L, 0x1ED8_C1A8_D189_F774L, + /* 193 */ 0x74CC_692C_434F_D66BL, 0x4AF4_690E_1C0F_F253L, + /* 194 */ 0x5D70_5423_690C_AB89L, 0x225D_20D8_1673_2843L, + /* 195 */ 0x4AC0_434F_873D_5607L, 0x3517_4D79_AB8F_5369L, + /* 196 */ 0x779A_054C_0B95_5672L, 0x21BE_E25C_45B2_1F0EL, + /* 197 */ 0x5FAE_6AA3_3C77_785BL, 0x3498_B516_9E28_18D8L, + /* 198 */ 0x4C8B_8882_96C5_F9E2L, 0x5D46_F745_4B53_4713L, + /* 199 */ 0x7A78_DA6A_8AD6_5C9DL, 0x7BA4_BED5_4552_0B52L, + /* 200 */ 0x61FA_4855_3BDE_B07EL, 0x2FB6_FF11_0441_A2A8L, + /* 201 */ 0x4E61_D377_6318_8D31L, 0x72F8_CC0D_9D01_4EEDL, + /* 202 */ 0x7D69_5258_9E8D_AEB6L, 0x1E5A_E015_C802_17E1L, + /* 203 */ 0x6454_41E0_7ED7_BEF8L, 0x1848_B344_A001_ACB4L, + /* 204 */ 0x5043_67E6_CBDF_CBF9L, 0x603A_2903_B334_8A2AL, + /* 205 */ 0x4035_ECB8_A319_6FFBL, 0x002E_8736_28F6_D4EEL, + /* 206 */ 0x66BC_ADF4_3828_B32BL, 0x19E4_0B89_DB24_87E3L, + /* 207 */ 0x5230_8B29_C686_F5BCL, 0x14B6_6FA1_7C1D_3983L, + /* 208 */ 0x41C0_6F54_9ED2_5E30L, 0x1091_F2E7_967D_C79CL, + /* 209 */ 0x6933_E554_3150_96B3L, 0x341C_B7D8_F0C9_3F5FL, + /* 210 */ 0x5429_8443_5AA6_DEF5L, 0x767D_5FE0_C0A0_FF80L, + /* 211 */ 0x4354_69CF_7BB8_B25EL, 0x2B97_7FE7_0080_CC66L, + /* 212 */ 0x6BBA_42E5_92C1_1D63L, 0x5F58_CCA4_CD9A_E0A3L, + /* 213 */ 0x562E_9BEA_DBCD_B11CL, 0x4C47_0A1D_7148_B3B6L, + /* 214 */ 0x44F2_1655_7CA4_8DB0L, 0x3D05_A1B1_276D_5C92L, + /* 215 */ 0x6E50_23BB_FAA0_E2B3L, 0x7B3C_35E8_3F15_60E9L, + /* 216 */ 0x5840_1C96_621A_4EF6L, 0x2F63_5E53_65AA_B3EDL, + /* 217 */ 0x4699_B078_4E7B_725EL, 0x591C_4B75_EAEE_F658L, + /* 218 */ 0x70F5_E726_E3F8_B6FDL, 0x74FA_1256_44B1_8A26L, + /* 219 */ 0x5A5E_5285_832D_5F31L, 0x43FB_41DE_9D5A_D4EBL, + /* 220 */ 0x484B_7537_9C24_4C27L, 0x4FFC_34B2_177B_DD89L, + /* 221 */ 0x73AB_EEBF_603A_1372L, 0x4CC6_BAB6_8BF9_6274L, + /* 222 */ 0x5C89_8BCC_4CFB_42C2L, 0x0A38_955E_D661_1B90L, + /* 223 */ 0x4A07_A309_D72F_689BL, 0x21C6_DDE5_784D_AFA7L, + /* 224 */ 0x7672_9E76_2518_A75EL, 0x693E_2FD5_8D49_190BL, + /* 225 */ 0x5EC2_185E_8413_B918L, 0x5431_BFDE_0AA0_E0D5L, + /* 226 */ 0x4BCE_79E5_3676_2DADL, 0x29C1_664B_3BB3_E711L, + /* 227 */ 0x794A_5CA1_F0BD_15E2L, 0x0F9B_D6DE_C5EC_A4E8L, + /* 228 */ 0x6108_4A1B_26FD_AB1BL, 0x2616_457F_04BD_50BAL, + /* 229 */ 0x4DA0_3B48_EBFE_227CL, 0x1E78_3798_D097_73C8L, + /* 230 */ 0x7C33_920E_4663_6A60L, 0x30C0_58F4_80F2_52D9L, + /* 231 */ 0x635C_74D8_384F_884DL, 0x0D66_AD90_6728_4247L, + /* 232 */ 0x4F7D_2A46_9372_D370L, 0x711E_F140_5286_9B6CL, + /* 233 */ 0x7F2E_AA0A_8584_8581L, 0x34FE_4ECD_50D7_5F14L, + /* 234 */ 0x65BE_EE6E_D136_D134L, 0x2A65_0BD7_73DF_7F43L, + /* 235 */ 0x5165_8B8B_DA92_40F6L, 0x551D_A312_C319_329CL, + /* 236 */ 0x411E_093C_AEDB_672BL, 0x5DB1_4F42_35AD_C217L, + /* 237 */ 0x6830_0EC7_7E2B_D845L, 0x7C4E_E536_BC49_368AL, + /* 238 */ 0x5359_A56C_64EF_E037L, 0x7D0B_EA92_303A_9208L, + /* 239 */ 0x42AE_1DF0_50BF_E693L, 0x173C_BBA8_2695_41A0L, + /* 240 */ 0x6AB0_2FE6_E799_70EBL, 0x3EC7_92A6_A422_029AL, + /* 241 */ 0x5559_BFEB_EC7A_C0BCL, 0x3239_421E_E9B4_CEE1L, + /* 242 */ 0x4447_CCBC_BD2F_0096L, 0x5B61_01B2_5490_A581L, + /* 243 */ 0x6D3F_ADFA_C84B_3424L, 0x2BCE_691D_541A_A268L, + /* 244 */ 0x5766_24C8_A03C_29B6L, 0x563E_BA7D_DCE2_1B87L, + /* 245 */ 0x45EB_50A0_8030_215EL, 0x7832_2ECB_171B_4939L, + /* 246 */ 0x6FDE_E767_3380_3564L, 0x59E9_E478_24F8_7527L, + /* 247 */ 0x597F_1F85_C2CC_F783L, 0x6187_E9F9_B72D_2A86L, + /* 248 */ 0x4798_E604_9BD7_2C69L, 0x346C_BB2E_2C24_2205L, + /* 249 */ 0x728E_3CD4_2C8B_7A42L, 0x20AD_F849_E039_D007L, + /* 250 */ 0x5BA4_FD76_8A09_2E9BL, 0x33BE_603B_19C7_D99FL, + /* 251 */ 0x4950_CAC5_3B3A_8BAFL, 0x42FE_B362_7B06_47B3L, + /* 252 */ 0x754E_113B_91F7_45E5L, 0x5197_856A_5E70_72B8L, + /* 253 */ 0x5DD8_0DC9_4192_9E51L, 0x27AC_6ABB_7EC0_5BC6L, + /* 254 */ 0x4B13_3E3A_9ADB_B1DAL, 0x52F0_5562_CBCD_1638L, + /* 255 */ 0x781E_C9F7_5E2C_4FC4L, 0x1E4D_556A_DFAE_89F3L, + /* 256 */ 0x6018_A192_B1BD_0C9CL, 0x7EA4_4455_7FBE_D4C3L, + /* 257 */ 0x4CE0_8142_27CA_707DL, 0x4BB6_9D11_32FF_109CL, + /* 258 */ 0x7B00_CED0_3FAA_4D95L, 0x5F8A_94E8_5198_1A93L, + /* 259 */ 0x6267_0BD9_CC88_3E11L, 0x32D5_43ED_0E13_4875L, + /* 260 */ 0x4EB8_D647_D6D3_64DAL, 0x5BDD_CFF0_D80F_6D2BL, + /* 261 */ 0x7DF4_8A0C_8AEB_D491L, 0x12FC_7FE7_C018_AEABL, + /* 262 */ 0x64C3_A1A3_A256_43A7L, 0x28C9_FFEC_99AD_5889L, + /* 263 */ 0x509C_814F_B511_CFB9L, 0x0707_FFF0_7AF1_13A1L, + /* 264 */ 0x407D_343F_C40E_3FC7L, 0x1F39_998D_2F27_42E7L, + /* 265 */ 0x672E_B9FF_A016_CC71L, 0x7EC2_8F48_4B72_04A4L, + /* 266 */ 0x528B_C7FF_B345_705BL, 0x189B_A5D3_6F8E_6A1DL, + /* 267 */ 0x4209_6CCC_8F6A_C048L, 0x7A16_1E42_BFA5_21B1L, + /* 268 */ 0x69A8_AE14_18AA_CD41L, 0x4356_96D1_32A1_CF81L, + /* 269 */ 0x5486_F1A9_AD55_7101L, 0x1C45_4574_2881_72CEL, + /* 270 */ 0x439F_27BA_F111_2734L, 0x169D_D129_BA01_28A5L, + /* 271 */ 0x6C31_D92B_1B4E_A520L, 0x242F_B50F_9001_DAA1L, + /* 272 */ 0x568E_4755_AF72_1DB3L, 0x368C_90D9_4001_7BB4L, + /* 273 */ 0x453E_9F77_BF8E_7E29L, 0x120A_0D7A_999A_C95DL, + /* 274 */ 0x6ECA_98BF_98E3_FD0EL, 0x5010_1590_F5C4_7561L, + /* 275 */ 0x58A2_13CC_7A4F_FDA5L, 0x2673_4473_F7D0_5DE8L, + /* 276 */ 0x46E8_0FD6_C83F_FE1DL, 0x6B8F_69F6_5FD9_E4B9L, + /* 277 */ 0x7173_4C8A_D9FF_FCFCL, 0x45B2_4323_CC8F_D45CL, + /* 278 */ 0x5AC2_A3A2_47FF_FD96L, 0x6AF5_0283_0A0C_A9E3L, + /* 279 */ 0x489B_B61B_6CCC_CADFL, 0x08C4_0202_6E70_87E9L, + /* 280 */ 0x742C_5692_47AE_1164L, 0x746C_D003_E3E7_3FDBL, + /* 281 */ 0x5CF0_4541_D2F1_A783L, 0x76BD_7336_4FEC_3315L, + /* 282 */ 0x4A59_D101_758E_1F9CL, 0x5EFD_F5C5_0CBC_F5ABL, + /* 283 */ 0x76F6_1B35_88E3_65C7L, 0x4B2F_EFA1_ADFB_22ABL, + /* 284 */ 0x5F2B_48F7_A0B5_EB06L, 0x08F3_261A_F195_B555L, + /* 285 */ 0x4C22_A0C6_1A2B_226BL, 0x20C2_84E2_5ADE_2AABL, + /* 286 */ 0x79D1_013C_F6AB_6A45L, 0x1AD0_D49D_5E30_4444L, + /* 287 */ 0x6174_00FD_9222_BB6AL, 0x48A7_107D_E4F3_69D0L, + /* 288 */ 0x4DF6_6731_41B5_62BBL, 0x53B8_D9FE_50C2_BB0DL, + /* 289 */ 0x7CBD_71E8_6922_3792L, 0x52C1_5CCA_1AD1_2B48L, + /* 290 */ 0x63CA_C186_BA81_C60EL, 0x7567_7D6E_7BDA_8906L, + /* 291 */ 0x4FD5_679E_FB9B_04D8L, 0x5DEC_6458_6315_3A6CL, + /* 292 */ 0x7FBB_D8FE_5F5E_6E27L, 0x497A_3A27_04EE_C3DFL, }; }