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authorDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-14 13:40:54 +0000
committerDaniel Baumann <daniel.baumann@progress-linux.org>2024-04-14 13:40:54 +0000
commit317c0644ccf108aa23ef3fd8358bd66c2840bfc0 (patch)
treec417b3d25c86b775989cb5ac042f37611b626c8a /deps/fpconv
parentInitial commit. (diff)
downloadredis-317c0644ccf108aa23ef3fd8358bd66c2840bfc0.tar.xz
redis-317c0644ccf108aa23ef3fd8358bd66c2840bfc0.zip
Adding upstream version 5:7.2.4.upstream/5%7.2.4
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to 'deps/fpconv')
-rw-r--r--deps/fpconv/LICENSE.txt23
-rw-r--r--deps/fpconv/Makefile27
-rw-r--r--deps/fpconv/README.md9
-rw-r--r--deps/fpconv/fpconv_dtoa.c373
-rw-r--r--deps/fpconv/fpconv_dtoa.h45
-rw-r--r--deps/fpconv/fpconv_powers.h133
6 files changed, 610 insertions, 0 deletions
diff --git a/deps/fpconv/LICENSE.txt b/deps/fpconv/LICENSE.txt
new file mode 100644
index 0000000..36b7cd9
--- /dev/null
+++ b/deps/fpconv/LICENSE.txt
@@ -0,0 +1,23 @@
+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.
diff --git a/deps/fpconv/Makefile b/deps/fpconv/Makefile
new file mode 100644
index 0000000..2654888
--- /dev/null
+++ b/deps/fpconv/Makefile
@@ -0,0 +1,27 @@
+STD=
+WARN= -Wall
+OPT= -Os
+
+R_CFLAGS= $(STD) $(WARN) $(OPT) $(DEBUG) $(CFLAGS)
+R_LDFLAGS= $(LDFLAGS)
+DEBUG= -g
+
+R_CC=$(CC) $(R_CFLAGS)
+R_LD=$(CC) $(R_LDFLAGS)
+
+AR= ar
+ARFLAGS= rcs
+
+libfpconv.a: fpconv_dtoa.o
+ $(AR) $(ARFLAGS) $@ $+
+
+fpconv_dtoa.o: fpconv_dtoa.h fpconv_dtoa.c
+
+.c.o:
+ $(R_CC) -c $<
+
+clean:
+ rm -f *.o
+ rm -f *.a
+
+
diff --git a/deps/fpconv/README.md b/deps/fpconv/README.md
new file mode 100644
index 0000000..d64ca68
--- /dev/null
+++ b/deps/fpconv/README.md
@@ -0,0 +1,9 @@
+libfpconv
+
+----------------------------------------------
+
+Fast and accurate double to string conversion based on Florian Loitsch's Grisu-algorithm[1].
+
+This port contains a subset of the 'C' version of Fast and accurate double to string conversion based on Florian Loitsch's Grisu-algorithm available at [github.com/night-shift/fpconv](https://github.com/night-shift/fpconv)).
+
+[1] https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf
diff --git a/deps/fpconv/fpconv_dtoa.c b/deps/fpconv/fpconv_dtoa.c
new file mode 100644
index 0000000..ad2f2de
--- /dev/null
+++ b/deps/fpconv/fpconv_dtoa.c
@@ -0,0 +1,373 @@
+/* fpconv_dtoa.c -- 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) 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 "fpconv_dtoa.h"
+
+#include "fpconv_powers.h"
+
+#include <stdbool.h>
+#include <string.h>
+
+#define fracmask 0x000FFFFFFFFFFFFFU
+#define expmask 0x7FF0000000000000U
+#define hiddenbit 0x0010000000000000U
+#define signmask 0x8000000000000000U
+#define expbias (1023 + 52)
+
+#define absv(n) ((n) < 0 ? -(n) : (n))
+#define minv(a, b) ((a) < (b) ? (a) : (b))
+
+static uint64_t tens[] = { 10000000000000000000U,
+ 1000000000000000000U,
+ 100000000000000000U,
+ 10000000000000000U,
+ 1000000000000000U,
+ 100000000000000U,
+ 10000000000000U,
+ 1000000000000U,
+ 100000000000U,
+ 10000000000U,
+ 1000000000U,
+ 100000000U,
+ 10000000U,
+ 1000000U,
+ 100000U,
+ 10000U,
+ 1000U,
+ 100U,
+ 10U,
+ 1U };
+
+static inline uint64_t get_dbits(double d) {
+ union
+ {
+ double dbl;
+ uint64_t i;
+ } dbl_bits = { d };
+
+ return dbl_bits.i;
+}
+
+static Fp build_fp(double d) {
+ uint64_t bits = get_dbits(d);
+
+ Fp fp;
+ fp.frac = bits & fracmask;
+ fp.exp = (bits & expmask) >> 52;
+
+ if (fp.exp) {
+ fp.frac += hiddenbit;
+ fp.exp -= expbias;
+
+ } else {
+ fp.exp = -expbias + 1;
+ }
+
+ return fp;
+}
+
+static void normalize(Fp *fp) {
+ while ((fp->frac & hiddenbit) == 0) {
+ fp->frac <<= 1;
+ fp->exp--;
+ }
+
+ int shift = 64 - 52 - 1;
+ fp->frac <<= shift;
+ fp->exp -= shift;
+}
+
+static void get_normalized_boundaries(Fp *fp, Fp *lower, Fp *upper) {
+ upper->frac = (fp->frac << 1) + 1;
+ upper->exp = fp->exp - 1;
+
+ while ((upper->frac & (hiddenbit << 1)) == 0) {
+ upper->frac <<= 1;
+ upper->exp--;
+ }
+
+ int u_shift = 64 - 52 - 2;
+
+ upper->frac <<= u_shift;
+ upper->exp = upper->exp - u_shift;
+
+ int l_shift = fp->frac == hiddenbit ? 2 : 1;
+
+ lower->frac = (fp->frac << l_shift) - 1;
+ lower->exp = fp->exp - l_shift;
+
+ lower->frac <<= lower->exp - upper->exp;
+ lower->exp = upper->exp;
+}
+
+static Fp multiply(Fp *a, Fp *b) {
+ const uint64_t lomask = 0x00000000FFFFFFFF;
+
+ uint64_t ah_bl = (a->frac >> 32) * (b->frac & lomask);
+ uint64_t al_bh = (a->frac & lomask) * (b->frac >> 32);
+ uint64_t al_bl = (a->frac & lomask) * (b->frac & lomask);
+ uint64_t ah_bh = (a->frac >> 32) * (b->frac >> 32);
+
+ uint64_t tmp = (ah_bl & lomask) + (al_bh & lomask) + (al_bl >> 32);
+ /* round up */
+ tmp += 1U << 31;
+
+ Fp fp = { ah_bh + (ah_bl >> 32) + (al_bh >> 32) + (tmp >> 32), a->exp + b->exp + 64 };
+
+ return fp;
+}
+
+static void round_digit(char *digits,
+ int ndigits,
+ uint64_t delta,
+ uint64_t rem,
+ uint64_t kappa,
+ uint64_t frac) {
+ while (rem < frac && delta - rem >= kappa &&
+ (rem + kappa < frac || frac - rem > rem + kappa - frac)) {
+ digits[ndigits - 1]--;
+ rem += kappa;
+ }
+}
+
+static int generate_digits(Fp *fp, Fp *upper, Fp *lower, char *digits, int *K) {
+ uint64_t wfrac = upper->frac - fp->frac;
+ uint64_t delta = upper->frac - lower->frac;
+
+ Fp one;
+ one.frac = 1ULL << -upper->exp;
+ one.exp = upper->exp;
+
+ uint64_t part1 = upper->frac >> -one.exp;
+ uint64_t part2 = upper->frac & (one.frac - 1);
+
+ int idx = 0, kappa = 10;
+ uint64_t *divp;
+ /* 1000000000 */
+ for (divp = tens + 10; kappa > 0; divp++) {
+ uint64_t div = *divp;
+ unsigned digit = part1 / div;
+
+ if (digit || idx) {
+ digits[idx++] = digit + '0';
+ }
+
+ part1 -= digit * div;
+ kappa--;
+
+ uint64_t tmp = (part1 << -one.exp) + part2;
+ if (tmp <= delta) {
+ *K += kappa;
+ round_digit(digits, idx, delta, tmp, div << -one.exp, wfrac);
+
+ return idx;
+ }
+ }
+
+ /* 10 */
+ uint64_t *unit = tens + 18;
+
+ while (true) {
+ part2 *= 10;
+ delta *= 10;
+ kappa--;
+
+ unsigned digit = part2 >> -one.exp;
+ if (digit || idx) {
+ digits[idx++] = digit + '0';
+ }
+
+ part2 &= one.frac - 1;
+ if (part2 < delta) {
+ *K += kappa;
+ round_digit(digits, idx, delta, part2, one.frac, wfrac * *unit);
+
+ return idx;
+ }
+
+ unit--;
+ }
+}
+
+static int grisu2(double d, char *digits, int *K) {
+ Fp w = build_fp(d);
+
+ Fp lower, upper;
+ get_normalized_boundaries(&w, &lower, &upper);
+
+ normalize(&w);
+
+ int k;
+ Fp cp = find_cachedpow10(upper.exp, &k);
+
+ w = multiply(&w, &cp);
+ upper = multiply(&upper, &cp);
+ lower = multiply(&lower, &cp);
+
+ lower.frac++;
+ upper.frac--;
+
+ *K = -k;
+
+ return generate_digits(&w, &upper, &lower, digits, K);
+}
+
+static int emit_digits(char *digits, int ndigits, char *dest, int K, bool neg) {
+ int exp = absv(K + ndigits - 1);
+
+ /* write plain integer */
+ if (K >= 0 && (exp < (ndigits + 7))) {
+ memcpy(dest, digits, ndigits);
+ memset(dest + ndigits, '0', K);
+
+ return ndigits + K;
+ }
+
+ /* write decimal w/o scientific notation */
+ if (K < 0 && (K > -7 || exp < 4)) {
+ int offset = ndigits - absv(K);
+ /* fp < 1.0 -> write leading zero */
+ if (offset <= 0) {
+ offset = -offset;
+ dest[0] = '0';
+ dest[1] = '.';
+ memset(dest + 2, '0', offset);
+ memcpy(dest + offset + 2, digits, ndigits);
+
+ return ndigits + 2 + offset;
+
+ /* fp > 1.0 */
+ } else {
+ memcpy(dest, digits, offset);
+ dest[offset] = '.';
+ memcpy(dest + offset + 1, digits + offset, ndigits - offset);
+
+ return ndigits + 1;
+ }
+ }
+
+ /* write decimal w/ scientific notation */
+ ndigits = minv(ndigits, 18 - neg);
+
+ int idx = 0;
+ dest[idx++] = digits[0];
+
+ if (ndigits > 1) {
+ dest[idx++] = '.';
+ memcpy(dest + idx, digits + 1, ndigits - 1);
+ idx += ndigits - 1;
+ }
+
+ dest[idx++] = 'e';
+
+ char sign = K + ndigits - 1 < 0 ? '-' : '+';
+ dest[idx++] = sign;
+
+ int cent = 0;
+
+ if (exp > 99) {
+ cent = exp / 100;
+ dest[idx++] = cent + '0';
+ exp -= cent * 100;
+ }
+ if (exp > 9) {
+ int dec = exp / 10;
+ dest[idx++] = dec + '0';
+ exp -= dec * 10;
+
+ } else if (cent) {
+ dest[idx++] = '0';
+ }
+
+ dest[idx++] = exp % 10 + '0';
+
+ return idx;
+}
+
+static int filter_special(double fp, char *dest) {
+ if (fp == 0.0) {
+ dest[0] = '0';
+ return 1;
+ }
+
+ uint64_t bits = get_dbits(fp);
+
+ bool nan = (bits & expmask) == expmask;
+
+ if (!nan) {
+ return 0;
+ }
+
+ if (bits & fracmask) {
+ dest[0] = 'n';
+ dest[1] = 'a';
+ dest[2] = 'n';
+
+ } else {
+ dest[0] = 'i';
+ dest[1] = 'n';
+ dest[2] = 'f';
+ }
+
+ return 3;
+}
+
+int fpconv_dtoa(double d, char dest[24]) {
+ char digits[18];
+
+ int str_len = 0;
+ bool neg = false;
+
+ if (get_dbits(d) & signmask) {
+ dest[0] = '-';
+ str_len++;
+ neg = true;
+ }
+
+ int spec = filter_special(d, dest + str_len);
+
+ if (spec) {
+ return str_len + spec;
+ }
+
+ int K = 0;
+ int ndigits = grisu2(d, digits, &K);
+
+ str_len += emit_digits(digits, ndigits, dest + str_len, K, neg);
+
+ return str_len;
+}
diff --git a/deps/fpconv/fpconv_dtoa.h b/deps/fpconv/fpconv_dtoa.h
new file mode 100644
index 0000000..328ed83
--- /dev/null
+++ b/deps/fpconv/fpconv_dtoa.h
@@ -0,0 +1,45 @@
+/* fpconv_dtoa.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) 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.
+ */
+
+#ifndef FPCONV_DTOA_H
+#define FPCONV_DTOA_H
+
+int fpconv_dtoa(double fp, char dest[24]);
+
+#endif
+
+/* [1] http://florian.loitsch.com/publications/dtoa-pldi2010.pdf */
diff --git a/deps/fpconv/fpconv_powers.h b/deps/fpconv/fpconv_powers.h
new file mode 100644
index 0000000..bc488f6
--- /dev/null
+++ b/deps/fpconv/fpconv_powers.h
@@ -0,0 +1,133 @@
+/* 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];
+ }
+}