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+/* fpconv_powers.h -- floating point conversion utilities.
+ *
+ * Fast and accurate double to string conversion based on Florian Loitsch's
+ * Grisu-algorithm[1].
+ *
+ * [1] https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf
+ * ----------------------------------------------------------------------------
+ *
+ * Copyright (c) 2021, Redis Labs
+ * Copyright (c) 2013-2019, night-shift <as.smljk at gmail dot com>
+ * Copyright (c) 2009, Florian Loitsch < florian.loitsch at inria dot fr >
+ * All rights reserved.
+ *
+ * Boost Software License - Version 1.0 - August 17th, 2003
+ *
+ * Permission is hereby granted, free of charge, to any person or organization
+ * obtaining a copy of the software and accompanying documentation covered by
+ * this license (the "Software") to use, reproduce, display, distribute,
+ * execute, and transmit the Software, and to prepare derivative works of the
+ * Software, and to permit third-parties to whom the Software is furnished to
+ * do so, all subject to the following:
+ *
+ * The copyright notices in the Software and this entire statement, including
+ * the above license grant, this restriction and the following disclaimer,
+ * must be included in all copies of the Software, in whole or in part, and
+ * all derivative works of the Software, unless such copies or derivative
+ * works are solely in the form of machine-executable object code generated by
+ * a source language processor.
+ *
+ * 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, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+ * SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+ * FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ */
+
+#include <stdint.h>
+
+#define npowers 87
+#define steppowers 8
+#define firstpower -348 /* 10 ^ -348 */
+
+#define expmax -32
+#define expmin -60
+
+
+typedef struct Fp {
+ uint64_t frac;
+ int exp;
+} Fp;
+
+static Fp powers_ten[] = {
+ { 18054884314459144840U, -1220 }, { 13451937075301367670U, -1193 },
+ { 10022474136428063862U, -1166 }, { 14934650266808366570U, -1140 },
+ { 11127181549972568877U, -1113 }, { 16580792590934885855U, -1087 },
+ { 12353653155963782858U, -1060 }, { 18408377700990114895U, -1034 },
+ { 13715310171984221708U, -1007 }, { 10218702384817765436U, -980 },
+ { 15227053142812498563U, -954 }, { 11345038669416679861U, -927 },
+ { 16905424996341287883U, -901 }, { 12595523146049147757U, -874 },
+ { 9384396036005875287U, -847 }, { 13983839803942852151U, -821 },
+ { 10418772551374772303U, -794 }, { 15525180923007089351U, -768 },
+ { 11567161174868858868U, -741 }, { 17236413322193710309U, -715 },
+ { 12842128665889583758U, -688 }, { 9568131466127621947U, -661 },
+ { 14257626930069360058U, -635 }, { 10622759856335341974U, -608 },
+ { 15829145694278690180U, -582 }, { 11793632577567316726U, -555 },
+ { 17573882009934360870U, -529 }, { 13093562431584567480U, -502 },
+ { 9755464219737475723U, -475 }, { 14536774485912137811U, -449 },
+ { 10830740992659433045U, -422 }, { 16139061738043178685U, -396 },
+ { 12024538023802026127U, -369 }, { 17917957937422433684U, -343 },
+ { 13349918974505688015U, -316 }, { 9946464728195732843U, -289 },
+ { 14821387422376473014U, -263 }, { 11042794154864902060U, -236 },
+ { 16455045573212060422U, -210 }, { 12259964326927110867U, -183 },
+ { 18268770466636286478U, -157 }, { 13611294676837538539U, -130 },
+ { 10141204801825835212U, -103 }, { 15111572745182864684U, -77 },
+ { 11258999068426240000U, -50 }, { 16777216000000000000U, -24 },
+ { 12500000000000000000U, 3 }, { 9313225746154785156U, 30 },
+ { 13877787807814456755U, 56 }, { 10339757656912845936U, 83 },
+ { 15407439555097886824U, 109 }, { 11479437019748901445U, 136 },
+ { 17105694144590052135U, 162 }, { 12744735289059618216U, 189 },
+ { 9495567745759798747U, 216 }, { 14149498560666738074U, 242 },
+ { 10542197943230523224U, 269 }, { 15709099088952724970U, 295 },
+ { 11704190886730495818U, 322 }, { 17440603504673385349U, 348 },
+ { 12994262207056124023U, 375 }, { 9681479787123295682U, 402 },
+ { 14426529090290212157U, 428 }, { 10748601772107342003U, 455 },
+ { 16016664761464807395U, 481 }, { 11933345169920330789U, 508 },
+ { 17782069995880619868U, 534 }, { 13248674568444952270U, 561 },
+ { 9871031767461413346U, 588 }, { 14708983551653345445U, 614 },
+ { 10959046745042015199U, 641 }, { 16330252207878254650U, 667 },
+ { 12166986024289022870U, 694 }, { 18130221999122236476U, 720 },
+ { 13508068024458167312U, 747 }, { 10064294952495520794U, 774 },
+ { 14996968138956309548U, 800 }, { 11173611982879273257U, 827 },
+ { 16649979327439178909U, 853 }, { 12405201291620119593U, 880 },
+ { 9242595204427927429U, 907 }, { 13772540099066387757U, 933 },
+ { 10261342003245940623U, 960 }, { 15290591125556738113U, 986 },
+ { 11392378155556871081U, 1013 }, { 16975966327722178521U, 1039 },
+ { 12648080533535911531U, 1066 }
+};
+
+/**
+ * Grisu needs a cache of precomputed powers-of-ten.
+ * This function, given an exponent and an integer k
+ * return the normalized floating-point approximation of the power of 10.
+ * @param exp
+ * @param k
+ * @return
+ */
+static Fp find_cachedpow10(int exp, int* k)
+{
+ const double one_log_ten = 0.30102999566398114;
+
+ const int approx = -(exp + npowers) * one_log_ten;
+ int idx = (approx - firstpower) / steppowers;
+
+ while(1) {
+ int current = exp + powers_ten[idx].exp + 64;
+
+ if(current < expmin) {
+ idx++;
+ continue;
+ }
+
+ if(current > expmax) {
+ idx--;
+ continue;
+ }
+
+ *k = (firstpower + idx * steppowers);
+
+ return powers_ten[idx];
+ }
+}