commit cc66165dd42e0e89cd641b9fb932b41060580ea7
parent 9bf293a5d5a75a52e37089e5f984a10845bb913e
Author: Sudipto Mallick <smlckz@disroot.org>
Date: Thu, 22 Jul 2021 16:12:10 +0000
strconv: implement Eisel-Lemire fast float parsing algorithm
Signed-off-by: Sudipto Mallick <smlckz@disroot.org>
Diffstat:
4 files changed, 1044 insertions(+), 139 deletions(-)
diff --git a/scripts/gen-stdlib b/scripts/gen-stdlib
@@ -680,6 +680,7 @@ gensrcs_strconv() {
numeric.ha \
ftos.ha \
stof.ha \
+ stof_data.ha \
$*
}
diff --git a/stdlib.mk b/stdlib.mk
@@ -1026,7 +1026,8 @@ stdlib_strconv_srcs= \
$(STDLIB)/strconv/stoi.ha \
$(STDLIB)/strconv/numeric.ha \
$(STDLIB)/strconv/ftos.ha \
- $(STDLIB)/strconv/stof.ha
+ $(STDLIB)/strconv/stof.ha \
+ $(STDLIB)/strconv/stof_data.ha
$(HARECACHE)/strconv/strconv.ssa: $(stdlib_strconv_srcs) $(stdlib_rt) $(stdlib_types) $(stdlib_strings) $(stdlib_ascii) $(stdlib_math)
@printf 'HAREC \t$@\n'
@@ -2231,6 +2232,7 @@ testlib_strconv_srcs= \
$(STDLIB)/strconv/numeric.ha \
$(STDLIB)/strconv/ftos.ha \
$(STDLIB)/strconv/stof.ha \
+ $(STDLIB)/strconv/stof_data.ha \
$(STDLIB)/strconv/+test/stou.ha \
$(STDLIB)/strconv/+test/stoi.ha
diff --git a/strconv/stof.ha b/strconv/stof.ha
@@ -1,12 +1,18 @@
+// Using the Eisel-Lemire algorithm [1] for fast parsing of floating-point
+// numbers, with Simple Decimal Conversion algorithm [2] as fallback.
+// [1]: https://nigeltao.github.io/blog/2020/eisel-lemire.html
+// [2]: https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html
+
use ascii;
-use bytes;
+use math;
use strings;
-const maxshift: u8 = 60, decimal_point_range: u16 = 2047;
+const maxshift: u8 = 60;
+const decimal_point_range: u16 = 2047;
type decimal = struct {
num_digits: size,
- decimal_point: int,
+ decimal_point: i32,
negative: bool,
truncated: bool,
digits: [800]u8,
@@ -19,88 +25,6 @@ fn trim(d: *decimal) void = {
};
};
-fn assign(d: *decimal, x: u64, negative: bool) void = {
- let sb = strings::toutf8(strconv::u64tos(x));
- let n = len(sb);
- for (let i = 0z; i < len(sb); i += 1) {
- sb[i] -= '0': u32: u8;
- };
- bytes::copy(d.digits[..n], sb[..n]);
- d.num_digits = n;
- d.negative = negative;
- d.truncated = false;
- trim(d);
-};
-
-const left_shift_table: [65]u16 = [
- 0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
- 0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
- 0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
- 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
- 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
- 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
- 0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
- 0x051C, 0x051C,
-];
-
-const pow5_table: [0x051C]u8 = [
- 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3,
- 9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8,
- 1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1,
- 0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8,
- 7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6,
- 9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5,
- 3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3,
- 1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0,
- 9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3,
- 9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1,
- 4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8,
- 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4,
- 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5,
- 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5,
- 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2,
- 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5,
- 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5,
- 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5,
- 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2,
- 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0,
- 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2,
- 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1,
- 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6,
- 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7, 2,
- 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
- 0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7,
- 3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5,
- 6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9,
- 3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8,
- 0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0,
- 9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2,
- 5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2,
- 4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0,
- 0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7,
- 1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8,
- 9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4,
- 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1,
- 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5,
- 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9,
- 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4,
- 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4,
- 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4,
- 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1,
- 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5,
- 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1,
- 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1,
- 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9,
- 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0,
- 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6, 2,
- 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
- 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5,
- 1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2,
- 4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1,
- 7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5,
- 9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5,
-];
-
fn leftshift_newdigits(d: *decimal, shift: u32) u32 = {
shift &= 63;
let x_a = left_shift_table[shift]: u32;
@@ -123,7 +47,7 @@ fn leftshift_newdigits(d: *decimal, shift: u32) u32 = {
return nn;
};
-fn leftshift(d: *decimal, k: uint) void = {
+fn leftshift(d: *decimal, k: u32) void = {
assert(k <= maxshift);
if (d.num_digits == 0) return;
let nn = leftshift_newdigits(d, k);
@@ -155,11 +79,11 @@ fn leftshift(d: *decimal, k: uint) void = {
if (d.num_digits > len(d.digits)) {
d.num_digits = len(d.digits);
};
- d.decimal_point += nn: int;
+ d.decimal_point += nn: i32;
trim(d);
};
-fn rightshift(d: *decimal, k: uint) void = {
+fn rightshift(d: *decimal, k: u32) void = {
let r = 0z, w = 0z, n = 0u64;
for (n >> k == 0; r += 1) {
if (r >= d.num_digits) {
@@ -174,7 +98,11 @@ fn rightshift(d: *decimal, k: uint) void = {
};
n = n * 10 + d.digits[r];
};
- d.decimal_point -= r: int - 1;
+ d.decimal_point -= r: i32 - 1;
+ if (d.decimal_point < -(decimal_point_range: i32)) {
+ *d = decimal { ... };
+ return;
+ };
const mask = (1u64 << k) - 1;
for (r < d.num_digits; r += 1) {
const dig = n >> k;
@@ -203,15 +131,15 @@ fn decimal_shift(d: *decimal, k: int) void = {
if (k > 0) {
for (k > maxshift: int) {
leftshift(d, maxshift);
- k -= maxshift: int;
+ k -= maxshift: i32;
};
- leftshift(d, k: uint);
+ leftshift(d, k: u32);
} else if (k < 0) {
for (k < -(maxshift: int)) {
rightshift(d, maxshift);
- k += maxshift: int;
+ k += maxshift: i32;
};
- rightshift(d, (-k): uint);
+ rightshift(d, (-k): u32);
};
};
@@ -222,8 +150,34 @@ fn should_round_up(d: *decimal, nd: uint) bool = if (nd < d.num_digits) {
} else return d.digits[nd] >= 5;
} else false;
+fn round(d: *decimal, nd: uint) void = {
+ if (nd >= d.num_digits) return;
+ if (should_round_up(d, nd)) roundup(d, nd)
+ else rounddown(d, nd);
+};
+
+fn rounddown(d: *decimal, nd: uint) void = {
+ if (nd >= d.num_digits) return;
+ d.num_digits = nd;
+ trim(d);
+};
+
+fn roundup(d: *decimal, nd: uint) void = {
+ if (nd >= d.num_digits) return;
+ for (let i = nd: int - 1; i >= 0; i -= 1) {
+ if (d.digits[i] < 9) {
+ d.digits[i] += 1;
+ d.num_digits = i: size + 1;
+ return;
+ };
+ };
+ d.digits[0] = 1;
+ d.num_digits = 1;
+ d.decimal_point += 1;
+};
+
fn decimal_round(d: *decimal) u64 = {
- if (d.num_digits == 0 && d.decimal_point < 0) return 0;
+ if (d.num_digits == 0 || d.decimal_point < 0) return 0;
if (d.decimal_point > 18) return ~0u64;
let i = 0z, n: u64 = 0;
for (i < d.decimal_point: uint && i < d.num_digits; i += 1) {
@@ -238,18 +192,96 @@ fn decimal_round(d: *decimal) u64 = {
return n;
};
-fn parse(s: str) (decimal | invalid) = {
+type fast_parsed_float = struct {
+ mantissa: u64,
+ exponent: i32,
+ negative: bool,
+ truncated: bool,
+};
+
+fn fast_parse(s: str) (fast_parsed_float | void | invalid) = {
+ if (len(s) == 0 || len(s) > 256) {
+ return;
+ };
+ let buf = strings::toutf8(s);
+ let i = 0z, neg = false, trunc = false;
+ if (buf[i] == '-': u32: u8) {
+ neg = true;
+ i += 1;
+ } else if (buf[i] == '+': u32: u8) {
+ i += 1;
+ };
+ let sawdot = false, sawdigits = false;
+ let nd = 0, ndmant = 0, dp = 0;
+ let mant = 0u64, exp = 0i32;
+ for (i < len(s); i += 1) {
+ if (buf[i] == '.': u32: u8) {
+ if (sawdot) return i: invalid;
+ sawdot = true;
+ dp = nd;
+ } else if (ascii::isdigit(buf[i]: u32: rune)) {
+ sawdigits = true;
+ if (buf[i] == '0': u32: u8 && nd == 0) {
+ dp -= 1;
+ continue;
+ };
+ nd += 1;
+ if (ndmant < 19) {
+ mant = mant * 10 + buf[i] - '0': u32: u8;
+ ndmant += 1;
+ } else if (buf[i] != '0': u32: u8) {
+ trunc = true;
+ };
+ } else break;
+ };
+ if (!sawdigits) return i: invalid;
+ if (!sawdot) {
+ dp = nd;
+ };
+ if (i < len(s) && (buf[i] == 'e': u32: u8 || buf[i] == 'E': u32: u8)) {
+ i += 1;
+ if (i >= len(s)) return i: invalid;
+ let expsign: int = 1;
+ if (buf[i] == '+': u32: u8) {
+ i += 1;
+ } else if (buf[i] == '-': u32: u8) {
+ expsign = -1;
+ i += 1;
+ };
+ if (i >= len(s) || !ascii::isdigit(buf[i]: u32: rune))
+ return i: invalid;
+ let e: int = 0;
+ for (i < len(s) && ascii::isdigit(buf[i]: u32: rune); i += 1) {
+ if (e < 10000) {
+ e = e * 10 + buf[i]: int - '0': u32: int;
+ };
+ };
+ dp += e * expsign;
+ };
+ if (i != len(s)) return i: invalid;
+ if (mant != 0) {
+ exp = dp - ndmant;
+ };
+ return fast_parsed_float {
+ mantissa = mant,
+ exponent = exp,
+ negative = neg,
+ truncated = trunc,
+ };
+};
+
+fn decimal_parse(d: *decimal, s: str) (void | invalid) = {
let i = 0z;
- let d = decimal { ... };
if (len(s) == 0) return 0: invalid;
const buf = strings::toutf8(s);
- d.negative = if (buf[0] == '+': u32: u8) {
+ d.negative = false;
+ d.truncated = false;
+ if (buf[0] == '+': u32: u8) {
i += 1;
- false;
} else if (buf[0] == '-': u32: u8) {
+ d.negative = true;
i += 1;
- true;
- } else false;
+ };
let sawdot = false, sawdigits = false;
let nd: u32 = 0, dp: i32 = 0;
for (i < len(s); i += 1) {
@@ -278,14 +310,15 @@ fn parse(s: str) (decimal | invalid) = {
if (i < len(s) && (buf[i] == 'e': u32: u8 || buf[i] == 'E': u32: u8)) {
i += 1;
if (i >= len(s)) return i: invalid;
- const expsign: int = if (buf[i] == '+': u32: u8) {
+ let expsign: int = 1;
+ if (buf[i] == '+': u32: u8) {
i += 1;
- 1;
} else if (buf[i] == '-': u32: u8) {
+ expsign = -1;
i += 1;
- -1;
- } else 1;
- if (i >= len(s) || !ascii::isdigit(buf[i]: u32: rune)) return i: invalid;
+ };
+ if (i >= len(s) || !ascii::isdigit(buf[i]: u32: rune))
+ return i: invalid;
let e: int = 0;
for (i < len(s) && ascii::isdigit(buf[i]: u32: rune); i += 1) {
if (e < 10000) {
@@ -295,80 +328,259 @@ fn parse(s: str) (decimal | invalid) = {
d.decimal_point += e * expsign;
};
if (i != len(s)) return i: invalid;
- return d;
};
-const powtab: [19]i8 = [
- 1, 3, 6, 9, 13, 16, 19, 23, 26, 29, 33, 36, 39, 43, 46, 49, 53, 56, 59,
-];
+fn leading_zeroes(n: u64) uint = {
+ assert(n > 0);
+ let b = 0u;
+ if ((n & 0b1111111111111111111111111111111100000000000000000000000000000000u64) > 0) {
+ n >>= 32;
+ b |= 32;
+ };
+ if ((n & 0b11111111111111110000000000000000u64) > 0) {
+ n >>= 16;
+ b |= 16;
+ };
+ if ((n & 0b1111111100000000u64) > 0) {
+ n >>= 8;
+ b |= 8;
+ };
+ if ((n & 0b11110000) > 0) {
+ n >>= 4;
+ b |= 4;
+ };
+ if ((n & 0b1100) > 0) {
+ n >>= 2;
+ b |= 2;
+ };
+ if ((n & 0b10) > 0) {
+ n >>= 1;
+ b |= 1;
+ };
+ return 63 - b;
+};
-fn floatbits(d: decimal, mbits: u8, ebits: u8, ebias: i16) (u64 | overflow) = {
- let e: int = 0, m: u64 = 0, z = 1u64 << (mbits + ebits);
- if (d.num_digits == 0 || d.decimal_point < -326) {
- return if (d.negative) z else 0;
+fn eisel_lemire(
+ mantissa: u64,
+ exp10: i32,
+ neg: bool,
+ f: *math::floatinfo
+) (u64 | void) = {
+ if (mantissa == 0 || exp10 > 288 || exp10 < -307) return;
+ const po10 = powers_of_ten[exp10 + 307];
+ const clz = leading_zeroes(mantissa);
+ mantissa <<= clz;
+ let shift = 64 - f.mantbits - 3, mask = (1 << shift) - 1;
+ // log(10) / log(2) ≈ 217706 / 65536; x / 65536 = x >> 16
+ let exp = (217706 * exp10) >> 16;
+ let e2 = (exp + f.expbias: i32 + 64): u64 - clz: u64;
+ let x = u128mul(mantissa, po10[1]);
+ if ((x.hi & mask) == mask && ((x.lo + mantissa) < mantissa)) {
+ const y = u128mul(mantissa, po10[0]);
+ let merged = r128 { hi = x.hi, lo = x.lo + y.hi };
+ if (merged.lo < x.lo) {
+ merged.hi += 1;
+ };
+ if (((merged.hi & mask) == mask) && ((merged.lo + 1) == 0) &&
+ (y.lo + mantissa < mantissa)) {
+ return;
+ };
+ x = merged;
+ };
+ let msb = x.hi >> 63, mant = x.hi >> (msb + shift);
+ e2 -= 1 ^ msb;
+ if (x.lo == 0 && (x.hi & mask == 0) && (mant & 3 == 1)) {
+ return;
+ };
+ mant += mant & 1;
+ mant >>= 1;
+ if ((mant >> (f.mantbits + 1)) > 0) {
+ mant >>= 1;
+ e2 += 1;
};
- if (d.decimal_point > 310) {
+ if (e2 <= 0 || e2 >= (1 << f.expbits) - 1) {
+ return;
+ };
+ return mkfloat(mant, e2: uint, neg, f);
+};
+
+fn floatbits(d: *decimal, f: *math::floatinfo) (u64 | overflow) = {
+ let e: int = 0, m: u64 = 0;
+ const powtab: [19]i8 = [
+ 0, 3, 6, 9, 13, 16, 19, 23, 26, 29,
+ 33, 36, 39, 43, 46, 49, 53, 56, 59,
+ ];
+ if (d.num_digits == 0 || d.decimal_point < -326) {
+ return if (d.negative) mkfloat(0, 0, d.negative, f)
+ else 0;
+ } else if (d.decimal_point > 310) {
return overflow;
};
+ if (d.num_digits <= 19) {
+ let mant = 0u64;
+ for (let i = 0z; i < d.num_digits; i += 1) {
+ mant = (10 * mant) + d.digits[i];
+ };
+ const exp10 = d.decimal_point - d.num_digits: i32;
+ const r = eisel_lemire(mant, exp10, d.negative, f);
+ if (r is u64) {
+ return r: u64;
+ };
+ };
for (d.decimal_point > 0) {
const n: int = if (d.decimal_point: uint >= len(powtab))
maxshift: int
else powtab[d.decimal_point];
- decimal_shift(&d, -n);
+ decimal_shift(d, -n);
e += n;
};
for (d.decimal_point <= 0) {
const n: int = if (d.decimal_point == 0) {
if (d.digits[0] >= 5) break;
if (d.digits[0] < 2) 2 else 1;
- } else if (-d.decimal_point >= len(powtab): int)
+ } else if (-d.decimal_point >= len(powtab): i32)
maxshift: int
else powtab[-d.decimal_point];
- decimal_shift(&d, n);
+ decimal_shift(d, n);
e -= n;
};
e -= 1;
- if (e < -ebias + 1) {
- const n = -ebias - e + 1;
- decimal_shift(&d, -n);
+ if (e <= -f.expbias + 1) {
+ const n = -f.expbias - e + 1;
+ decimal_shift(d, -n);
e += n;
};
- if (e + ebias >= (1 << ebits: int) - 1) {
+ if (e + f.expbias >= (1 << f.expbits: int) - 1) {
return overflow;
};
- decimal_shift(&d, mbits: int + 1);
- m = decimal_round(&d);
- if (m == 2 << mbits) {
+ decimal_shift(d, f.mantbits: int + 1);
+ m = decimal_round(d);
+ if (m == 2 << f.mantbits) {
m >>= 1;
e += 1;
- if (e + ebias >= (1 << ebits: int) - 1) {
+ if (e + f.expbias >= (1 << f.expbits: int) - 1) {
return overflow;
};
};
- if (m & (1u64 << mbits) == 0) {
- e = -ebias;
+ if (m & (1 << f.mantbits) == 0) {
+ e = -f.expbias;
};
- return mkf(m, (e + ebias): uint, mbits, ebits, d.negative);
+ return mkfloat(m, (e + f.expbias): uint, d.negative, f);
};
-fn mkf(m: u64, e: uint, mbits: u8, ebits: u8, negative: bool) u64 = {
- let n: u64 = m & ((1u64 << mbits) - 1);
- n |= (e & ((1u64 << ebits) - 1)) << mbits;
+fn mkfloat(m: u64, e: uint, negative: bool, f: *math::floatinfo) u64 = {
+ let n: u64 = m & ((1 << f.mantbits) - 1);
+ n |= (e & ((1 << f.expbits) - 1)) << f.mantbits;
if (negative) {
- n |= 1u64 << (mbits + ebits);
+ n |= 1 << (f.mantbits + f.expbits);
+ };
+ return n;
+};
+
+const f64pow10: [_]f64 = [
+ 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5, 1.0e6, 1.0e7, 1.0e8, 1.0e9,
+ 1.0e10, 1.0e11, 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17, 1.0e18,
+ 1.0e19, 1.0e20, 1.0e21, 1.0e22
+];
+
+fn stof64exact(mant: u64, exp: i32, neg: bool) (f64 | void) = {
+ if (mant >> math::F64_MANTISSA_BITS != 0) return;
+ let n = mant: i64: f64; // XXX: ARCH
+ if (neg) {
+ n = -n;
};
+ if (exp == 0) {
+ return n;
+ };
+ if (-22 <= exp && exp <= 22) {
+ if (exp >= 0) {
+ n *= f64pow10[exp];
+ } else {
+ n /= f64pow10[-exp];
+ };
+ } else return;
+ return n;
+};
+
+const f32pow10: [_]f32 = [
+ 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5, 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10
+];
+
+fn stof32exact(mant: u32, exp: i32, neg: bool) (f32 | void) = {
+ if (mant >> math::F32_MANTISSA_BITS != 0) return;
+ let n = mant: i32: f32; // XXX: ARCH
+ if (neg) {
+ n = -n;
+ };
+ if (exp == 0) {
+ return n;
+ };
+ if (-10 <= exp && exp <= 10) {
+ if (exp >= 0) {
+ n *= f32pow10[exp];
+ } else {
+ n /= f64pow10[-exp];
+ };
+ } else return;
return n;
};
// Converts a string to a f64. If the string is not syntactically well-formed
// floating-point number in base 10, [[strconv::invalid]] is returned. If the
// string represents a floating-point number that is larger than the largest
-// finite f64 number, [[strconv::overflow]] is returned. Zero with is returned
-// if the string represents a floating-point number that is smaller than the f64
-// number nearest to zero with respective sign.
+// finite f64 number, [[strconv::overflow]] is returned. Zero is returned if the
+// string represents a floating-point number that is smaller than the f64 number
+// nearest to zero with respective sign.
export fn stof64(s: str) (f64 | invalid | overflow) = {
- const n = floatbits(parse(s)?, 52, 11, 1023)?;
- return *(&n: *f64);
+ const p = fast_parse(s)?;
+ if (p is fast_parsed_float) {
+ const p = p: fast_parsed_float;
+ if (!p.truncated) {
+ let n = stof64exact(p.mantissa, p.exponent,
+ p.negative);
+ if (n is f64) {
+ return n: f64;
+ };
+ let n = eisel_lemire(p.mantissa, p.exponent,
+ p.negative, &math::f64info);
+ if (n is u64) {
+ return math::f64frombits(n: u64);
+ };
+ };
+ };
+ let d = decimal { ... };
+ decimal_parse(&d, s)?;
+ const n = floatbits(&d, &math::f64info)?;
+ return math::f64frombits(n);
+};
+
+// Converts a string to a f32. If the string is not syntactically well-formed
+// floating-point number in base 10, [[strconv::invalid]] is returned. If the
+// string represents a floating-point number that is larger than the largest
+// finite f64 number, [[strconv::overflow]] is returned. Zero is returned if the
+// string represents a floating-point number that is smaller than the f32 number
+// nearest to zero with respective sign.
+export fn stof32(s: str) (f32 | invalid | overflow) = {
+ const p = fast_parse(s)?;
+ if (p is fast_parsed_float) {
+ const p = p: fast_parsed_float;
+ if (!p.truncated) {
+ let n = stof32exact(p.mantissa: u32, p.exponent,
+ p.negative);
+ if (n is f32) {
+ return n: f32;
+ };
+ let n = eisel_lemire(p.mantissa, p.exponent,
+ p.negative, &math::f32info);
+ if (n is u64) {
+ return math::f32frombits(n: u64: u32);
+ };
+ };
+ };
+ let d = decimal { ... };
+ decimal_parse(&d, s)?;
+ const n = floatbits(&d, &math::f32info)?: u32;
+ return math::f32frombits(n);
};
@test fn stof64() void = {
@@ -379,11 +591,33 @@ export fn stof64(s: str) (f64 | invalid | overflow) = {
assert(stof64("3.14"): f64 == 3.14);
assert(stof64("2.99792458E+8"): f64 == 299792458.0);
assert(stof64("6.022e23"): f64 == 6.022e23);
+ assert(stof64("1e310") is overflow);
+ assert(stof64("9007199254740991"): f64 == 9007199254740991.0);
+ assert(stof64("90071992547409915"): f64 == 90071992547409920.0);
+ assert(stof64("90071992547409925"): f64 == 90071992547409920.0);
assert(stof64("2.2250738585072014e-308"): f64 == 2.2250738585072014e-308);
assert(stof64("-1e-324"): f64 == -0.0);
- assert(stof64("1e309") is overflow);
+ assert(stof64("5e-324"): f64 == 5.0e-324);
assert(stof64(""): invalid: size == 0);
assert(stof64("0ZO"): invalid: size == 1);
assert(stof64("1.23ezz"): invalid: size == 5);
};
+@test fn stof32() void = {
+ assert(stof32("0"): f32 == 0.0);
+ assert(stof32("1e10"): f32 == 1.0e10);
+ assert(stof32("299792458"): f32 == 299792458.0);
+ assert(stof32("6.022e23"): f32 == 6.022e23);
+ assert(stof32("1e40") is overflow);
+ assert(stof32("16777215"): f32 == 16777215.0);
+ assert(stof32("167772155"): f32 == 167772160.0);
+ assert(stof32("167772145"): f32 == 167772140.0);
+ assert(stof32("6.62607015e-34"): f32 == 6.62607015e-34);
+ assert(stof32("1.1754944e-38"): f32 == 1.1754944e-38);
+ assert(stof32("-1e-50"): f32 == -0.0);
+ assert(stof32("1e-45"): f32 == 1.0e-45);
+ assert(stof32(""): invalid: size == 0);
+ assert(stof32("0ZO"): invalid: size == 1);
+ assert(stof32("1.23e-zz"): invalid: size == 6);
+};
+
diff --git a/strconv/stof_data.ha b/strconv/stof_data.ha
@@ -0,0 +1,668 @@
+const left_shift_table: [65]u16 = [
+ 0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
+ 0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
+ 0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
+ 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
+ 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
+ 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
+ 0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
+ 0x051C, 0x051C,
+];
+
+const pow5_table: [0x051C]u8 = [
+ 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3,
+ 9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8,
+ 1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1,
+ 0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8,
+ 7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6,
+ 9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5,
+ 3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3,
+ 1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0,
+ 9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3,
+ 9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1,
+ 4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8,
+ 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4,
+ 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5,
+ 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5,
+ 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2,
+ 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5,
+ 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5,
+ 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5,
+ 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2,
+ 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0,
+ 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2,
+ 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1,
+ 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6,
+ 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7, 2,
+ 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
+ 0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7,
+ 3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5,
+ 6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9,
+ 3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8,
+ 0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0,
+ 9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2,
+ 5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2,
+ 4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0,
+ 0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7,
+ 1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8,
+ 9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4,
+ 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1,
+ 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5,
+ 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9,
+ 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4,
+ 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4,
+ 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4,
+ 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1,
+ 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5,
+ 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1,
+ 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1,
+ 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9,
+ 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0,
+ 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6, 2,
+ 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
+ 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5,
+ 1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2,
+ 4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1,
+ 7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5,
+ 9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5,
+];
+
+const powers_of_ten: [596][2]u64 = [
+ [0xA5D3B6D479F8E056, 0x8FD0C16206306BAB], // 1e-307
+ [0x8F48A4899877186C, 0xB3C4F1BA87BC8696], // 1e-306
+ [0x331ACDABFE94DE87, 0xE0B62E2929ABA83C], // 1e-305
+ [0x9FF0C08B7F1D0B14, 0x8C71DCD9BA0B4925], // 1e-304
+ [0x07ECF0AE5EE44DD9, 0xAF8E5410288E1B6F], // 1e-303
+ [0xC9E82CD9F69D6150, 0xDB71E91432B1A24A], // 1e-302
+ [0xBE311C083A225CD2, 0x892731AC9FAF056E], // 1e-301
+ [0x6DBD630A48AAF406, 0xAB70FE17C79AC6CA], // 1e-300
+ [0x092CBBCCDAD5B108, 0xD64D3D9DB981787D], // 1e-299
+ [0x25BBF56008C58EA5, 0x85F0468293F0EB4E], // 1e-298
+ [0xAF2AF2B80AF6F24E, 0xA76C582338ED2621], // 1e-297
+ [0x1AF5AF660DB4AEE1, 0xD1476E2C07286FAA], // 1e-296
+ [0x50D98D9FC890ED4D, 0x82CCA4DB847945CA], // 1e-295
+ [0xE50FF107BAB528A0, 0xA37FCE126597973C], // 1e-294
+ [0x1E53ED49A96272C8, 0xCC5FC196FEFD7D0C], // 1e-293
+ [0x25E8E89C13BB0F7A, 0xFF77B1FCBEBCDC4F], // 1e-292
+ [0x77B191618C54E9AC, 0x9FAACF3DF73609B1], // 1e-291
+ [0xD59DF5B9EF6A2417, 0xC795830D75038C1D], // 1e-290
+ [0x4B0573286B44AD1D, 0xF97AE3D0D2446F25], // 1e-289
+ [0x4EE367F9430AEC32, 0x9BECCE62836AC577], // 1e-288
+ [0x229C41F793CDA73F, 0xC2E801FB244576D5], // 1e-287
+ [0x6B43527578C1110F, 0xF3A20279ED56D48A], // 1e-286
+ [0x830A13896B78AAA9, 0x9845418C345644D6], // 1e-285
+ [0x23CC986BC656D553, 0xBE5691EF416BD60C], // 1e-284
+ [0x2CBFBE86B7EC8AA8, 0xEDEC366B11C6CB8F], // 1e-283
+ [0x7BF7D71432F3D6A9, 0x94B3A202EB1C3F39], // 1e-282
+ [0xDAF5CCD93FB0CC53, 0xB9E08A83A5E34F07], // 1e-281
+ [0xD1B3400F8F9CFF68, 0xE858AD248F5C22C9], // 1e-280
+ [0x23100809B9C21FA1, 0x91376C36D99995BE], // 1e-279
+ [0xABD40A0C2832A78A, 0xB58547448FFFFB2D], // 1e-278
+ [0x16C90C8F323F516C, 0xE2E69915B3FFF9F9], // 1e-277
+ [0xAE3DA7D97F6792E3, 0x8DD01FAD907FFC3B], // 1e-276
+ [0x99CD11CFDF41779C, 0xB1442798F49FFB4A], // 1e-275
+ [0x40405643D711D583, 0xDD95317F31C7FA1D], // 1e-274
+ [0x482835EA666B2572, 0x8A7D3EEF7F1CFC52], // 1e-273
+ [0xDA3243650005EECF, 0xAD1C8EAB5EE43B66], // 1e-272
+ [0x90BED43E40076A82, 0xD863B256369D4A40], // 1e-271
+ [0x5A7744A6E804A291, 0x873E4F75E2224E68], // 1e-270
+ [0x711515D0A205CB36, 0xA90DE3535AAAE202], // 1e-269
+ [0x0D5A5B44CA873E03, 0xD3515C2831559A83], // 1e-268
+ [0xE858790AFE9486C2, 0x8412D9991ED58091], // 1e-267
+ [0x626E974DBE39A872, 0xA5178FFF668AE0B6], // 1e-266
+ [0xFB0A3D212DC8128F, 0xCE5D73FF402D98E3], // 1e-265
+ [0x7CE66634BC9D0B99, 0x80FA687F881C7F8E], // 1e-264
+ [0x1C1FFFC1EBC44E80, 0xA139029F6A239F72], // 1e-263
+ [0xA327FFB266B56220, 0xC987434744AC874E], // 1e-262
+ [0x4BF1FF9F0062BAA8, 0xFBE9141915D7A922], // 1e-261
+ [0x6F773FC3603DB4A9, 0x9D71AC8FADA6C9B5], // 1e-260
+ [0xCB550FB4384D21D3, 0xC4CE17B399107C22], // 1e-259
+ [0x7E2A53A146606A48, 0xF6019DA07F549B2B], // 1e-258
+ [0x2EDA7444CBFC426D, 0x99C102844F94E0FB], // 1e-257
+ [0xFA911155FEFB5308, 0xC0314325637A1939], // 1e-256
+ [0x793555AB7EBA27CA, 0xF03D93EEBC589F88], // 1e-255
+ [0x4BC1558B2F3458DE, 0x96267C7535B763B5], // 1e-254
+ [0x9EB1AAEDFB016F16, 0xBBB01B9283253CA2], // 1e-253
+ [0x465E15A979C1CADC, 0xEA9C227723EE8BCB], // 1e-252
+ [0x0BFACD89EC191EC9, 0x92A1958A7675175F], // 1e-251
+ [0xCEF980EC671F667B, 0xB749FAED14125D36], // 1e-250
+ [0x82B7E12780E7401A, 0xE51C79A85916F484], // 1e-249
+ [0xD1B2ECB8B0908810, 0x8F31CC0937AE58D2], // 1e-248
+ [0x861FA7E6DCB4AA15, 0xB2FE3F0B8599EF07], // 1e-247
+ [0x67A791E093E1D49A, 0xDFBDCECE67006AC9], // 1e-246
+ [0xE0C8BB2C5C6D24E0, 0x8BD6A141006042BD], // 1e-245
+ [0x58FAE9F773886E18, 0xAECC49914078536D], // 1e-244
+ [0xAF39A475506A899E, 0xDA7F5BF590966848], // 1e-243
+ [0x6D8406C952429603, 0x888F99797A5E012D], // 1e-242
+ [0xC8E5087BA6D33B83, 0xAAB37FD7D8F58178], // 1e-241
+ [0xFB1E4A9A90880A64, 0xD5605FCDCF32E1D6], // 1e-240
+ [0x5CF2EEA09A55067F, 0x855C3BE0A17FCD26], // 1e-239
+ [0xF42FAA48C0EA481E, 0xA6B34AD8C9DFC06F], // 1e-238
+ [0xF13B94DAF124DA26, 0xD0601D8EFC57B08B], // 1e-237
+ [0x76C53D08D6B70858, 0x823C12795DB6CE57], // 1e-236
+ [0x54768C4B0C64CA6E, 0xA2CB1717B52481ED], // 1e-235
+ [0xA9942F5DCF7DFD09, 0xCB7DDCDDA26DA268], // 1e-234
+ [0xD3F93B35435D7C4C, 0xFE5D54150B090B02], // 1e-233
+ [0xC47BC5014A1A6DAF, 0x9EFA548D26E5A6E1], // 1e-232
+ [0x359AB6419CA1091B, 0xC6B8E9B0709F109A], // 1e-231
+ [0xC30163D203C94B62, 0xF867241C8CC6D4C0], // 1e-230
+ [0x79E0DE63425DCF1D, 0x9B407691D7FC44F8], // 1e-229
+ [0x985915FC12F542E4, 0xC21094364DFB5636], // 1e-228
+ [0x3E6F5B7B17B2939D, 0xF294B943E17A2BC4], // 1e-227
+ [0xA705992CEECF9C42, 0x979CF3CA6CEC5B5A], // 1e-226
+ [0x50C6FF782A838353, 0xBD8430BD08277231], // 1e-225
+ [0xA4F8BF5635246428, 0xECE53CEC4A314EBD], // 1e-224
+ [0x871B7795E136BE99, 0x940F4613AE5ED136], // 1e-223
+ [0x28E2557B59846E3F, 0xB913179899F68584], // 1e-222
+ [0x331AEADA2FE589CF, 0xE757DD7EC07426E5], // 1e-221
+ [0x3FF0D2C85DEF7621, 0x9096EA6F3848984F], // 1e-220
+ [0x0FED077A756B53A9, 0xB4BCA50B065ABE63], // 1e-219
+ [0xD3E8495912C62894, 0xE1EBCE4DC7F16DFB], // 1e-218
+ [0x64712DD7ABBBD95C, 0x8D3360F09CF6E4BD], // 1e-217
+ [0xBD8D794D96AACFB3, 0xB080392CC4349DEC], // 1e-216
+ [0xECF0D7A0FC5583A0, 0xDCA04777F541C567], // 1e-215
+ [0xF41686C49DB57244, 0x89E42CAAF9491B60], // 1e-214
+ [0x311C2875C522CED5, 0xAC5D37D5B79B6239], // 1e-213
+ [0x7D633293366B828B, 0xD77485CB25823AC7], // 1e-212
+ [0xAE5DFF9C02033197, 0x86A8D39EF77164BC], // 1e-211
+ [0xD9F57F830283FDFC, 0xA8530886B54DBDEB], // 1e-210
+ [0xD072DF63C324FD7B, 0xD267CAA862A12D66], // 1e-209
+ [0x4247CB9E59F71E6D, 0x8380DEA93DA4BC60], // 1e-208
+ [0x52D9BE85F074E608, 0xA46116538D0DEB78], // 1e-207
+ [0x67902E276C921F8B, 0xCD795BE870516656], // 1e-206
+ [0x00BA1CD8A3DB53B6, 0x806BD9714632DFF6], // 1e-205
+ [0x80E8A40ECCD228A4, 0xA086CFCD97BF97F3], // 1e-204
+ [0x6122CD128006B2CD, 0xC8A883C0FDAF7DF0], // 1e-203
+ [0x796B805720085F81, 0xFAD2A4B13D1B5D6C], // 1e-202
+ [0xCBE3303674053BB0, 0x9CC3A6EEC6311A63], // 1e-201
+ [0xBEDBFC4411068A9C, 0xC3F490AA77BD60FC], // 1e-200
+ [0xEE92FB5515482D44, 0xF4F1B4D515ACB93B], // 1e-199
+ [0x751BDD152D4D1C4A, 0x991711052D8BF3C5], // 1e-198
+ [0xD262D45A78A0635D, 0xBF5CD54678EEF0B6], // 1e-197
+ [0x86FB897116C87C34, 0xEF340A98172AACE4], // 1e-196
+ [0xD45D35E6AE3D4DA0, 0x9580869F0E7AAC0E], // 1e-195
+ [0x8974836059CCA109, 0xBAE0A846D2195712], // 1e-194
+ [0x2BD1A438703FC94B, 0xE998D258869FACD7], // 1e-193
+ [0x7B6306A34627DDCF, 0x91FF83775423CC06], // 1e-192
+ [0x1A3BC84C17B1D542, 0xB67F6455292CBF08], // 1e-191
+ [0x20CABA5F1D9E4A93, 0xE41F3D6A7377EECA], // 1e-190
+ [0x547EB47B7282EE9C, 0x8E938662882AF53E], // 1e-189
+ [0xE99E619A4F23AA43, 0xB23867FB2A35B28D], // 1e-188
+ [0x6405FA00E2EC94D4, 0xDEC681F9F4C31F31], // 1e-187
+ [0xDE83BC408DD3DD04, 0x8B3C113C38F9F37E], // 1e-186
+ [0x9624AB50B148D445, 0xAE0B158B4738705E], // 1e-185
+ [0x3BADD624DD9B0957, 0xD98DDAEE19068C76], // 1e-184
+ [0xE54CA5D70A80E5D6, 0x87F8A8D4CFA417C9], // 1e-183
+ [0x5E9FCF4CCD211F4C, 0xA9F6D30A038D1DBC], // 1e-182
+ [0x7647C3200069671F, 0xD47487CC8470652B], // 1e-181
+ [0x29ECD9F40041E073, 0x84C8D4DFD2C63F3B], // 1e-180
+ [0xF468107100525890, 0xA5FB0A17C777CF09], // 1e-179
+ [0x7182148D4066EEB4, 0xCF79CC9DB955C2CC], // 1e-178
+ [0xC6F14CD848405530, 0x81AC1FE293D599BF], // 1e-177
+ [0xB8ADA00E5A506A7C, 0xA21727DB38CB002F], // 1e-176
+ [0xA6D90811F0E4851C, 0xCA9CF1D206FDC03B], // 1e-175
+ [0x908F4A166D1DA663, 0xFD442E4688BD304A], // 1e-174
+ [0x9A598E4E043287FE, 0x9E4A9CEC15763E2E], // 1e-173
+ [0x40EFF1E1853F29FD, 0xC5DD44271AD3CDBA], // 1e-172
+ [0xD12BEE59E68EF47C, 0xF7549530E188C128], // 1e-171
+ [0x82BB74F8301958CE, 0x9A94DD3E8CF578B9], // 1e-170
+ [0xE36A52363C1FAF01, 0xC13A148E3032D6E7], // 1e-169
+ [0xDC44E6C3CB279AC1, 0xF18899B1BC3F8CA1], // 1e-168
+ [0x29AB103A5EF8C0B9, 0x96F5600F15A7B7E5], // 1e-167
+ [0x7415D448F6B6F0E7, 0xBCB2B812DB11A5DE], // 1e-166
+ [0x111B495B3464AD21, 0xEBDF661791D60F56], // 1e-165
+ [0xCAB10DD900BEEC34, 0x936B9FCEBB25C995], // 1e-164
+ [0x3D5D514F40EEA742, 0xB84687C269EF3BFB], // 1e-163
+ [0x0CB4A5A3112A5112, 0xE65829B3046B0AFA], // 1e-162
+ [0x47F0E785EABA72AB, 0x8FF71A0FE2C2E6DC], // 1e-161
+ [0x59ED216765690F56, 0xB3F4E093DB73A093], // 1e-160
+ [0x306869C13EC3532C, 0xE0F218B8D25088B8], // 1e-159
+ [0x1E414218C73A13FB, 0x8C974F7383725573], // 1e-158
+ [0xE5D1929EF90898FA, 0xAFBD2350644EEACF], // 1e-157
+ [0xDF45F746B74ABF39, 0xDBAC6C247D62A583], // 1e-156
+ [0x6B8BBA8C328EB783, 0x894BC396CE5DA772], // 1e-155
+ [0x066EA92F3F326564, 0xAB9EB47C81F5114F], // 1e-154
+ [0xC80A537B0EFEFEBD, 0xD686619BA27255A2], // 1e-153
+ [0xBD06742CE95F5F36, 0x8613FD0145877585], // 1e-152
+ [0x2C48113823B73704, 0xA798FC4196E952E7], // 1e-151
+ [0xF75A15862CA504C5, 0xD17F3B51FCA3A7A0], // 1e-150
+ [0x9A984D73DBE722FB, 0x82EF85133DE648C4], // 1e-149
+ [0xC13E60D0D2E0EBBA, 0xA3AB66580D5FDAF5], // 1e-148
+ [0x318DF905079926A8, 0xCC963FEE10B7D1B3], // 1e-147
+ [0xFDF17746497F7052, 0xFFBBCFE994E5C61F], // 1e-146
+ [0xFEB6EA8BEDEFA633, 0x9FD561F1FD0F9BD3], // 1e-145
+ [0xFE64A52EE96B8FC0, 0xC7CABA6E7C5382C8], // 1e-144
+ [0x3DFDCE7AA3C673B0, 0xF9BD690A1B68637B], // 1e-143
+ [0x06BEA10CA65C084E, 0x9C1661A651213E2D], // 1e-142
+ [0x486E494FCFF30A62, 0xC31BFA0FE5698DB8], // 1e-141
+ [0x5A89DBA3C3EFCCFA, 0xF3E2F893DEC3F126], // 1e-140
+ [0xF89629465A75E01C, 0x986DDB5C6B3A76B7], // 1e-139
+ [0xF6BBB397F1135823, 0xBE89523386091465], // 1e-138
+ [0x746AA07DED582E2C, 0xEE2BA6C0678B597F], // 1e-137
+ [0xA8C2A44EB4571CDC, 0x94DB483840B717EF], // 1e-136
+ [0x92F34D62616CE413, 0xBA121A4650E4DDEB], // 1e-135
+ [0x77B020BAF9C81D17, 0xE896A0D7E51E1566], // 1e-134
+ [0x0ACE1474DC1D122E, 0x915E2486EF32CD60], // 1e-133
+ [0x0D819992132456BA, 0xB5B5ADA8AAFF80B8], // 1e-132
+ [0x10E1FFF697ED6C69, 0xE3231912D5BF60E6], // 1e-131
+ [0xCA8D3FFA1EF463C1, 0x8DF5EFABC5979C8F], // 1e-130
+ [0xBD308FF8A6B17CB2, 0xB1736B96B6FD83B3], // 1e-129
+ [0xAC7CB3F6D05DDBDE, 0xDDD0467C64BCE4A0], // 1e-128
+ [0x6BCDF07A423AA96B, 0x8AA22C0DBEF60EE4], // 1e-127
+ [0x86C16C98D2C953C6, 0xAD4AB7112EB3929D], // 1e-126
+ [0xE871C7BF077BA8B7, 0xD89D64D57A607744], // 1e-125
+ [0x11471CD764AD4972, 0x87625F056C7C4A8B], // 1e-124
+ [0xD598E40D3DD89BCF, 0xA93AF6C6C79B5D2D], // 1e-123
+ [0x4AFF1D108D4EC2C3, 0xD389B47879823479], // 1e-122
+ [0xCEDF722A585139BA, 0x843610CB4BF160CB], // 1e-121
+ [0xC2974EB4EE658828, 0xA54394FE1EEDB8FE], // 1e-120
+ [0x733D226229FEEA32, 0xCE947A3DA6A9273E], // 1e-119
+ [0x0806357D5A3F525F, 0x811CCC668829B887], // 1e-118
+ [0xCA07C2DCB0CF26F7, 0xA163FF802A3426A8], // 1e-117
+ [0xFC89B393DD02F0B5, 0xC9BCFF6034C13052], // 1e-116
+ [0xBBAC2078D443ACE2, 0xFC2C3F3841F17C67], // 1e-115
+ [0xD54B944B84AA4C0D, 0x9D9BA7832936EDC0], // 1e-114
+ [0x0A9E795E65D4DF11, 0xC5029163F384A931], // 1e-113
+ [0x4D4617B5FF4A16D5, 0xF64335BCF065D37D], // 1e-112
+ [0x504BCED1BF8E4E45, 0x99EA0196163FA42E], // 1e-111
+ [0xE45EC2862F71E1D6, 0xC06481FB9BCF8D39], // 1e-110
+ [0x5D767327BB4E5A4C, 0xF07DA27A82C37088], // 1e-109
+ [0x3A6A07F8D510F86F, 0x964E858C91BA2655], // 1e-108
+ [0x890489F70A55368B, 0xBBE226EFB628AFEA], // 1e-107
+ [0x2B45AC74CCEA842E, 0xEADAB0ABA3B2DBE5], // 1e-106
+ [0x3B0B8BC90012929D, 0x92C8AE6B464FC96F], // 1e-105
+ [0x09CE6EBB40173744, 0xB77ADA0617E3BBCB], // 1e-104
+ [0xCC420A6A101D0515, 0xE55990879DDCAABD], // 1e-103
+ [0x9FA946824A12232D, 0x8F57FA54C2A9EAB6], // 1e-102
+ [0x47939822DC96ABF9, 0xB32DF8E9F3546564], // 1e-101
+ [0x59787E2B93BC56F7, 0xDFF9772470297EBD], // 1e-100
+ [0x57EB4EDB3C55B65A, 0x8BFBEA76C619EF36], // 1e-99
+ [0xEDE622920B6B23F1, 0xAEFAE51477A06B03], // 1e-98
+ [0xE95FAB368E45ECED, 0xDAB99E59958885C4], // 1e-97
+ [0x11DBCB0218EBB414, 0x88B402F7FD75539B], // 1e-96
+ [0xD652BDC29F26A119, 0xAAE103B5FCD2A881], // 1e-95
+ [0x4BE76D3346F0495F, 0xD59944A37C0752A2], // 1e-94
+ [0x6F70A4400C562DDB, 0x857FCAE62D8493A5], // 1e-93
+ [0xCB4CCD500F6BB952, 0xA6DFBD9FB8E5B88E], // 1e-92
+ [0x7E2000A41346A7A7, 0xD097AD07A71F26B2], // 1e-91
+ [0x8ED400668C0C28C8, 0x825ECC24C873782F], // 1e-90
+ [0x728900802F0F32FA, 0xA2F67F2DFA90563B], // 1e-89
+ [0x4F2B40A03AD2FFB9, 0xCBB41EF979346BCA], // 1e-88
+ [0xE2F610C84987BFA8, 0xFEA126B7D78186BC], // 1e-87
+ [0x0DD9CA7D2DF4D7C9, 0x9F24B832E6B0F436], // 1e-86
+ [0x91503D1C79720DBB, 0xC6EDE63FA05D3143], // 1e-85
+ [0x75A44C6397CE912A, 0xF8A95FCF88747D94], // 1e-84
+ [0xC986AFBE3EE11ABA, 0x9B69DBE1B548CE7C], // 1e-83
+ [0xFBE85BADCE996168, 0xC24452DA229B021B], // 1e-82
+ [0xFAE27299423FB9C3, 0xF2D56790AB41C2A2], // 1e-81
+ [0xDCCD879FC967D41A, 0x97C560BA6B0919A5], // 1e-80
+ [0x5400E987BBC1C920, 0xBDB6B8E905CB600F], // 1e-79
+ [0x290123E9AAB23B68, 0xED246723473E3813], // 1e-78
+ [0xF9A0B6720AAF6521, 0x9436C0760C86E30B], // 1e-77
+ [0xF808E40E8D5B3E69, 0xB94470938FA89BCE], // 1e-76
+ [0xB60B1D1230B20E04, 0xE7958CB87392C2C2], // 1e-75
+ [0xB1C6F22B5E6F48C2, 0x90BD77F3483BB9B9], // 1e-74
+ [0x1E38AEB6360B1AF3, 0xB4ECD5F01A4AA828], // 1e-73
+ [0x25C6DA63C38DE1B0, 0xE2280B6C20DD5232], // 1e-72
+ [0x579C487E5A38AD0E, 0x8D590723948A535F], // 1e-71
+ [0x2D835A9DF0C6D851, 0xB0AF48EC79ACE837], // 1e-70
+ [0xF8E431456CF88E65, 0xDCDB1B2798182244], // 1e-69
+ [0x1B8E9ECB641B58FF, 0x8A08F0F8BF0F156B], // 1e-68
+ [0xE272467E3D222F3F, 0xAC8B2D36EED2DAC5], // 1e-67
+ [0x5B0ED81DCC6ABB0F, 0xD7ADF884AA879177], // 1e-66
+ [0x98E947129FC2B4E9, 0x86CCBB52EA94BAEA], // 1e-65
+ [0x3F2398D747B36224, 0xA87FEA27A539E9A5], // 1e-64
+ [0x8EEC7F0D19A03AAD, 0xD29FE4B18E88640E], // 1e-63
+ [0x1953CF68300424AC, 0x83A3EEEEF9153E89], // 1e-62
+ [0x5FA8C3423C052DD7, 0xA48CEAAAB75A8E2B], // 1e-61
+ [0x3792F412CB06794D, 0xCDB02555653131B6], // 1e-60
+ [0xE2BBD88BBEE40BD0, 0x808E17555F3EBF11], // 1e-59
+ [0x5B6ACEAEAE9D0EC4, 0xA0B19D2AB70E6ED6], // 1e-58
+ [0xF245825A5A445275, 0xC8DE047564D20A8B], // 1e-57
+ [0xEED6E2F0F0D56712, 0xFB158592BE068D2E], // 1e-56
+ [0x55464DD69685606B, 0x9CED737BB6C4183D], // 1e-55
+ [0xAA97E14C3C26B886, 0xC428D05AA4751E4C], // 1e-54
+ [0xD53DD99F4B3066A8, 0xF53304714D9265DF], // 1e-53
+ [0xE546A8038EFE4029, 0x993FE2C6D07B7FAB], // 1e-52
+ [0xDE98520472BDD033, 0xBF8FDB78849A5F96], // 1e-51
+ [0x963E66858F6D4440, 0xEF73D256A5C0F77C], // 1e-50
+ [0xDDE7001379A44AA8, 0x95A8637627989AAD], // 1e-49
+ [0x5560C018580D5D52, 0xBB127C53B17EC159], // 1e-48
+ [0xAAB8F01E6E10B4A6, 0xE9D71B689DDE71AF], // 1e-47
+ [0xCAB3961304CA70E8, 0x9226712162AB070D], // 1e-46
+ [0x3D607B97C5FD0D22, 0xB6B00D69BB55C8D1], // 1e-45
+ [0x8CB89A7DB77C506A, 0xE45C10C42A2B3B05], // 1e-44
+ [0x77F3608E92ADB242, 0x8EB98A7A9A5B04E3], // 1e-43
+ [0x55F038B237591ED3, 0xB267ED1940F1C61C], // 1e-42
+ [0x6B6C46DEC52F6688, 0xDF01E85F912E37A3], // 1e-41
+ [0x2323AC4B3B3DA015, 0x8B61313BBABCE2C6], // 1e-40
+ [0xABEC975E0A0D081A, 0xAE397D8AA96C1B77], // 1e-39
+ [0x96E7BD358C904A21, 0xD9C7DCED53C72255], // 1e-38
+ [0x7E50D64177DA2E54, 0x881CEA14545C7575], // 1e-37
+ [0xDDE50BD1D5D0B9E9, 0xAA242499697392D2], // 1e-36
+ [0x955E4EC64B44E864, 0xD4AD2DBFC3D07787], // 1e-35
+ [0xBD5AF13BEF0B113E, 0x84EC3C97DA624AB4], // 1e-34
+ [0xECB1AD8AEACDD58E, 0xA6274BBDD0FADD61], // 1e-33
+ [0x67DE18EDA5814AF2, 0xCFB11EAD453994BA], // 1e-32
+ [0x80EACF948770CED7, 0x81CEB32C4B43FCF4], // 1e-31
+ [0xA1258379A94D028D, 0xA2425FF75E14FC31], // 1e-30
+ [0x096EE45813A04330, 0xCAD2F7F5359A3B3E], // 1e-29
+ [0x8BCA9D6E188853FC, 0xFD87B5F28300CA0D], // 1e-28
+ [0x775EA264CF55347D, 0x9E74D1B791E07E48], // 1e-27
+ [0x95364AFE032A819D, 0xC612062576589DDA], // 1e-26
+ [0x3A83DDBD83F52204, 0xF79687AED3EEC551], // 1e-25
+ [0xC4926A9672793542, 0x9ABE14CD44753B52], // 1e-24
+ [0x75B7053C0F178293, 0xC16D9A0095928A27], // 1e-23
+ [0x5324C68B12DD6338, 0xF1C90080BAF72CB1], // 1e-22
+ [0xD3F6FC16EBCA5E03, 0x971DA05074DA7BEE], // 1e-21
+ [0x88F4BB1CA6BCF584, 0xBCE5086492111AEA], // 1e-20
+ [0x2B31E9E3D06C32E5, 0xEC1E4A7DB69561A5], // 1e-19
+ [0x3AFF322E62439FCF, 0x9392EE8E921D5D07], // 1e-18
+ [0x09BEFEB9FAD487C2, 0xB877AA3236A4B449], // 1e-17
+ [0x4C2EBE687989A9B3, 0xE69594BEC44DE15B], // 1e-16
+ [0x0F9D37014BF60A10, 0x901D7CF73AB0ACD9], // 1e-15
+ [0x538484C19EF38C94, 0xB424DC35095CD80F], // 1e-14
+ [0x2865A5F206B06FB9, 0xE12E13424BB40E13], // 1e-13
+ [0xF93F87B7442E45D3, 0x8CBCCC096F5088CB], // 1e-12
+ [0xF78F69A51539D748, 0xAFEBFF0BCB24AAFE], // 1e-11
+ [0xB573440E5A884D1B, 0xDBE6FECEBDEDD5BE], // 1e-10
+ [0x31680A88F8953030, 0x89705F4136B4A597], // 1e-9
+ [0xFDC20D2B36BA7C3D, 0xABCC77118461CEFC], // 1e-8
+ [0x3D32907604691B4C, 0xD6BF94D5E57A42BC], // 1e-7
+ [0xA63F9A49C2C1B10F, 0x8637BD05AF6C69B5], // 1e-6
+ [0x0FCF80DC33721D53, 0xA7C5AC471B478423], // 1e-5
+ [0xD3C36113404EA4A8, 0xD1B71758E219652B], // 1e-4
+ [0x645A1CAC083126E9, 0x83126E978D4FDF3B], // 1e-3
+ [0x3D70A3D70A3D70A3, 0xA3D70A3D70A3D70A], // 1e-2
+ [0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC], // 1e-1
+ [0x0000000000000000, 0x8000000000000000], // 1e0
+ [0x0000000000000000, 0xA000000000000000], // 1e1
+ [0x0000000000000000, 0xC800000000000000], // 1e2
+ [0x0000000000000000, 0xFA00000000000000], // 1e3
+ [0x0000000000000000, 0x9C40000000000000], // 1e4
+ [0x0000000000000000, 0xC350000000000000], // 1e5
+ [0x0000000000000000, 0xF424000000000000], // 1e6
+ [0x0000000000000000, 0x9896800000000000], // 1e7
+ [0x0000000000000000, 0xBEBC200000000000], // 1e8
+ [0x0000000000000000, 0xEE6B280000000000], // 1e9
+ [0x0000000000000000, 0x9502F90000000000], // 1e10
+ [0x0000000000000000, 0xBA43B74000000000], // 1e11
+ [0x0000000000000000, 0xE8D4A51000000000], // 1e12
+ [0x0000000000000000, 0x9184E72A00000000], // 1e13
+ [0x0000000000000000, 0xB5E620F480000000], // 1e14
+ [0x0000000000000000, 0xE35FA931A0000000], // 1e15
+ [0x0000000000000000, 0x8E1BC9BF04000000], // 1e16
+ [0x0000000000000000, 0xB1A2BC2EC5000000], // 1e17
+ [0x0000000000000000, 0xDE0B6B3A76400000], // 1e18
+ [0x0000000000000000, 0x8AC7230489E80000], // 1e19
+ [0x0000000000000000, 0xAD78EBC5AC620000], // 1e20
+ [0x0000000000000000, 0xD8D726B7177A8000], // 1e21
+ [0x0000000000000000, 0x878678326EAC9000], // 1e22
+ [0x0000000000000000, 0xA968163F0A57B400], // 1e23
+ [0x0000000000000000, 0xD3C21BCECCEDA100], // 1e24
+ [0x0000000000000000, 0x84595161401484A0], // 1e25
+ [0x0000000000000000, 0xA56FA5B99019A5C8], // 1e26
+ [0x0000000000000000, 0xCECB8F27F4200F3A], // 1e27
+ [0x4000000000000000, 0x813F3978F8940984], // 1e28
+ [0x5000000000000000, 0xA18F07D736B90BE5], // 1e29
+ [0xA400000000000000, 0xC9F2C9CD04674EDE], // 1e30
+ [0x4D00000000000000, 0xFC6F7C4045812296], // 1e31
+ [0xF020000000000000, 0x9DC5ADA82B70B59D], // 1e32
+ [0x6C28000000000000, 0xC5371912364CE305], // 1e33
+ [0xC732000000000000, 0xF684DF56C3E01BC6], // 1e34
+ [0x3C7F400000000000, 0x9A130B963A6C115C], // 1e35
+ [0x4B9F100000000000, 0xC097CE7BC90715B3], // 1e36
+ [0x1E86D40000000000, 0xF0BDC21ABB48DB20], // 1e37
+ [0x1314448000000000, 0x96769950B50D88F4], // 1e38
+ [0x17D955A000000000, 0xBC143FA4E250EB31], // 1e39
+ [0x5DCFAB0800000000, 0xEB194F8E1AE525FD], // 1e40
+ [0x5AA1CAE500000000, 0x92EFD1B8D0CF37BE], // 1e41
+ [0xF14A3D9E40000000, 0xB7ABC627050305AD], // 1e42
+ [0x6D9CCD05D0000000, 0xE596B7B0C643C719], // 1e43
+ [0xE4820023A2000000, 0x8F7E32CE7BEA5C6F], // 1e44
+ [0xDDA2802C8A800000, 0xB35DBF821AE4F38B], // 1e45
+ [0xD50B2037AD200000, 0xE0352F62A19E306E], // 1e46
+ [0x4526F422CC340000, 0x8C213D9DA502DE45], // 1e47
+ [0x9670B12B7F410000, 0xAF298D050E4395D6], // 1e48
+ [0x3C0CDD765F114000, 0xDAF3F04651D47B4C], // 1e49
+ [0xA5880A69FB6AC800, 0x88D8762BF324CD0F], // 1e50
+ [0x8EEA0D047A457A00, 0xAB0E93B6EFEE0053], // 1e51
+ [0x72A4904598D6D880, 0xD5D238A4ABE98068], // 1e52
+ [0x47A6DA2B7F864750, 0x85A36366EB71F041], // 1e53
+ [0x999090B65F67D924, 0xA70C3C40A64E6C51], // 1e54
+ [0xFFF4B4E3F741CF6D, 0xD0CF4B50CFE20765], // 1e55
+ [0xBFF8F10E7A8921A4, 0x82818F1281ED449F], // 1e56
+ [0xAFF72D52192B6A0D, 0xA321F2D7226895C7], // 1e57
+ [0x9BF4F8A69F764490, 0xCBEA6F8CEB02BB39], // 1e58
+ [0x02F236D04753D5B4, 0xFEE50B7025C36A08], // 1e59
+ [0x01D762422C946590, 0x9F4F2726179A2245], // 1e60
+ [0x424D3AD2B7B97EF5, 0xC722F0EF9D80AAD6], // 1e61
+ [0xD2E0898765A7DEB2, 0xF8EBAD2B84E0D58B], // 1e62
+ [0x63CC55F49F88EB2F, 0x9B934C3B330C8577], // 1e63
+ [0x3CBF6B71C76B25FB, 0xC2781F49FFCFA6D5], // 1e64
+ [0x8BEF464E3945EF7A, 0xF316271C7FC3908A], // 1e65
+ [0x97758BF0E3CBB5AC, 0x97EDD871CFDA3A56], // 1e66
+ [0x3D52EEED1CBEA317, 0xBDE94E8E43D0C8EC], // 1e67
+ [0x4CA7AAA863EE4BDD, 0xED63A231D4C4FB27], // 1e68
+ [0x8FE8CAA93E74EF6A, 0x945E455F24FB1CF8], // 1e69
+ [0xB3E2FD538E122B44, 0xB975D6B6EE39E436], // 1e70
+ [0x60DBBCA87196B616, 0xE7D34C64A9C85D44], // 1e71
+ [0xBC8955E946FE31CD, 0x90E40FBEEA1D3A4A], // 1e72
+ [0x6BABAB6398BDBE41, 0xB51D13AEA4A488DD], // 1e73
+ [0xC696963C7EED2DD1, 0xE264589A4DCDAB14], // 1e74
+ [0xFC1E1DE5CF543CA2, 0x8D7EB76070A08AEC], // 1e75
+ [0x3B25A55F43294BCB, 0xB0DE65388CC8ADA8], // 1e76
+ [0x49EF0EB713F39EBE, 0xDD15FE86AFFAD912], // 1e77
+ [0x6E3569326C784337, 0x8A2DBF142DFCC7AB], // 1e78
+ [0x49C2C37F07965404, 0xACB92ED9397BF996], // 1e79
+ [0xDC33745EC97BE906, 0xD7E77A8F87DAF7FB], // 1e80
+ [0x69A028BB3DED71A3, 0x86F0AC99B4E8DAFD], // 1e81
+ [0xC40832EA0D68CE0C, 0xA8ACD7C0222311BC], // 1e82
+ [0xF50A3FA490C30190, 0xD2D80DB02AABD62B], // 1e83
+ [0x792667C6DA79E0FA, 0x83C7088E1AAB65DB], // 1e84
+ [0x577001B891185938, 0xA4B8CAB1A1563F52], // 1e85
+ [0xED4C0226B55E6F86, 0xCDE6FD5E09ABCF26], // 1e86
+ [0x544F8158315B05B4, 0x80B05E5AC60B6178], // 1e87
+ [0x696361AE3DB1C721, 0xA0DC75F1778E39D6], // 1e88
+ [0x03BC3A19CD1E38E9, 0xC913936DD571C84C], // 1e89
+ [0x04AB48A04065C723, 0xFB5878494ACE3A5F], // 1e90
+ [0x62EB0D64283F9C76, 0x9D174B2DCEC0E47B], // 1e91
+ [0x3BA5D0BD324F8394, 0xC45D1DF942711D9A], // 1e92
+ [0xCA8F44EC7EE36479, 0xF5746577930D6500], // 1e93
+ [0x7E998B13CF4E1ECB, 0x9968BF6ABBE85F20], // 1e94
+ [0x9E3FEDD8C321A67E, 0xBFC2EF456AE276E8], // 1e95
+ [0xC5CFE94EF3EA101E, 0xEFB3AB16C59B14A2], // 1e96
+ [0xBBA1F1D158724A12, 0x95D04AEE3B80ECE5], // 1e97
+ [0x2A8A6E45AE8EDC97, 0xBB445DA9CA61281F], // 1e98
+ [0xF52D09D71A3293BD, 0xEA1575143CF97226], // 1e99
+ [0x593C2626705F9C56, 0x924D692CA61BE758], // 1e100
+ [0x6F8B2FB00C77836C, 0xB6E0C377CFA2E12E], // 1e101
+ [0x0B6DFB9C0F956447, 0xE498F455C38B997A], // 1e102
+ [0x4724BD4189BD5EAC, 0x8EDF98B59A373FEC], // 1e103
+ [0x58EDEC91EC2CB657, 0xB2977EE300C50FE7], // 1e104
+ [0x2F2967B66737E3ED, 0xDF3D5E9BC0F653E1], // 1e105
+ [0xBD79E0D20082EE74, 0x8B865B215899F46C], // 1e106
+ [0xECD8590680A3AA11, 0xAE67F1E9AEC07187], // 1e107
+ [0xE80E6F4820CC9495, 0xDA01EE641A708DE9], // 1e108
+ [0x3109058D147FDCDD, 0x884134FE908658B2], // 1e109
+ [0xBD4B46F0599FD415, 0xAA51823E34A7EEDE], // 1e110
+ [0x6C9E18AC7007C91A, 0xD4E5E2CDC1D1EA96], // 1e111
+ [0x03E2CF6BC604DDB0, 0x850FADC09923329E], // 1e112
+ [0x84DB8346B786151C, 0xA6539930BF6BFF45], // 1e113
+ [0xE612641865679A63, 0xCFE87F7CEF46FF16], // 1e114
+ [0x4FCB7E8F3F60C07E, 0x81F14FAE158C5F6E], // 1e115
+ [0xE3BE5E330F38F09D, 0xA26DA3999AEF7749], // 1e116
+ [0x5CADF5BFD3072CC5, 0xCB090C8001AB551C], // 1e117
+ [0x73D9732FC7C8F7F6, 0xFDCB4FA002162A63], // 1e118
+ [0x2867E7FDDCDD9AFA, 0x9E9F11C4014DDA7E], // 1e119
+ [0xB281E1FD541501B8, 0xC646D63501A1511D], // 1e120
+ [0x1F225A7CA91A4226, 0xF7D88BC24209A565], // 1e121
+ [0x3375788DE9B06958, 0x9AE757596946075F], // 1e122
+ [0x0052D6B1641C83AE, 0xC1A12D2FC3978937], // 1e123
+ [0xC0678C5DBD23A49A, 0xF209787BB47D6B84], // 1e124
+ [0xF840B7BA963646E0, 0x9745EB4D50CE6332], // 1e125
+ [0xB650E5A93BC3D898, 0xBD176620A501FBFF], // 1e126
+ [0xA3E51F138AB4CEBE, 0xEC5D3FA8CE427AFF], // 1e127
+ [0xC66F336C36B10137, 0x93BA47C980E98CDF], // 1e128
+ [0xB80B0047445D4184, 0xB8A8D9BBE123F017], // 1e129
+ [0xA60DC059157491E5, 0xE6D3102AD96CEC1D], // 1e130
+ [0x87C89837AD68DB2F, 0x9043EA1AC7E41392], // 1e131
+ [0x29BABE4598C311FB, 0xB454E4A179DD1877], // 1e132
+ [0xF4296DD6FEF3D67A, 0xE16A1DC9D8545E94], // 1e133
+ [0x1899E4A65F58660C, 0x8CE2529E2734BB1D], // 1e134
+ [0x5EC05DCFF72E7F8F, 0xB01AE745B101E9E4], // 1e135
+ [0x76707543F4FA1F73, 0xDC21A1171D42645D], // 1e136
+ [0x6A06494A791C53A8, 0x899504AE72497EBA], // 1e137
+ [0x0487DB9D17636892, 0xABFA45DA0EDBDE69], // 1e138
+ [0x45A9D2845D3C42B6, 0xD6F8D7509292D603], // 1e139
+ [0x0B8A2392BA45A9B2, 0x865B86925B9BC5C2], // 1e140
+ [0x8E6CAC7768D7141E, 0xA7F26836F282B732], // 1e141
+ [0x3207D795430CD926, 0xD1EF0244AF2364FF], // 1e142
+ [0x7F44E6BD49E807B8, 0x8335616AED761F1F], // 1e143
+ [0x5F16206C9C6209A6, 0xA402B9C5A8D3A6E7], // 1e144
+ [0x36DBA887C37A8C0F, 0xCD036837130890A1], // 1e145
+ [0xC2494954DA2C9789, 0x802221226BE55A64], // 1e146
+ [0xF2DB9BAA10B7BD6C, 0xA02AA96B06DEB0FD], // 1e147
+ [0x6F92829494E5ACC7, 0xC83553C5C8965D3D], // 1e148
+ [0xCB772339BA1F17F9, 0xFA42A8B73ABBF48C], // 1e149
+ [0xFF2A760414536EFB, 0x9C69A97284B578D7], // 1e150
+ [0xFEF5138519684ABA, 0xC38413CF25E2D70D], // 1e151
+ [0x7EB258665FC25D69, 0xF46518C2EF5B8CD1], // 1e152
+ [0xEF2F773FFBD97A61, 0x98BF2F79D5993802], // 1e153
+ [0xAAFB550FFACFD8FA, 0xBEEEFB584AFF8603], // 1e154
+ [0x95BA2A53F983CF38, 0xEEAABA2E5DBF6784], // 1e155
+ [0xDD945A747BF26183, 0x952AB45CFA97A0B2], // 1e156
+ [0x94F971119AEEF9E4, 0xBA756174393D88DF], // 1e157
+ [0x7A37CD5601AAB85D, 0xE912B9D1478CEB17], // 1e158
+ [0xAC62E055C10AB33A, 0x91ABB422CCB812EE], // 1e159
+ [0x577B986B314D6009, 0xB616A12B7FE617AA], // 1e160
+ [0xED5A7E85FDA0B80B, 0xE39C49765FDF9D94], // 1e161
+ [0x14588F13BE847307, 0x8E41ADE9FBEBC27D], // 1e162
+ [0x596EB2D8AE258FC8, 0xB1D219647AE6B31C], // 1e163
+ [0x6FCA5F8ED9AEF3BB, 0xDE469FBD99A05FE3], // 1e164
+ [0x25DE7BB9480D5854, 0x8AEC23D680043BEE], // 1e165
+ [0xAF561AA79A10AE6A, 0xADA72CCC20054AE9], // 1e166
+ [0x1B2BA1518094DA04, 0xD910F7FF28069DA4], // 1e167
+ [0x90FB44D2F05D0842, 0x87AA9AFF79042286], // 1e168
+ [0x353A1607AC744A53, 0xA99541BF57452B28], // 1e169
+ [0x42889B8997915CE8, 0xD3FA922F2D1675F2], // 1e170
+ [0x69956135FEBADA11, 0x847C9B5D7C2E09B7], // 1e171
+ [0x43FAB9837E699095, 0xA59BC234DB398C25], // 1e172
+ [0x94F967E45E03F4BB, 0xCF02B2C21207EF2E], // 1e173
+ [0x1D1BE0EEBAC278F5, 0x8161AFB94B44F57D], // 1e174
+ [0x6462D92A69731732, 0xA1BA1BA79E1632DC], // 1e175
+ [0x7D7B8F7503CFDCFE, 0xCA28A291859BBF93], // 1e176
+ [0x5CDA735244C3D43E, 0xFCB2CB35E702AF78], // 1e177
+ [0x3A0888136AFA64A7, 0x9DEFBF01B061ADAB], // 1e178
+ [0x088AAA1845B8FDD0, 0xC56BAEC21C7A1916], // 1e179
+ [0x8AAD549E57273D45, 0xF6C69A72A3989F5B], // 1e180
+ [0x36AC54E2F678864B, 0x9A3C2087A63F6399], // 1e181
+ [0x84576A1BB416A7DD, 0xC0CB28A98FCF3C7F], // 1e182
+ [0x656D44A2A11C51D5, 0xF0FDF2D3F3C30B9F], // 1e183
+ [0x9F644AE5A4B1B325, 0x969EB7C47859E743], // 1e184
+ [0x873D5D9F0DDE1FEE, 0xBC4665B596706114], // 1e185
+ [0xA90CB506D155A7EA, 0xEB57FF22FC0C7959], // 1e186
+ [0x09A7F12442D588F2, 0x9316FF75DD87CBD8], // 1e187
+ [0x0C11ED6D538AEB2F, 0xB7DCBF5354E9BECE], // 1e188
+ [0x8F1668C8A86DA5FA, 0xE5D3EF282A242E81], // 1e189
+ [0xF96E017D694487BC, 0x8FA475791A569D10], // 1e190
+ [0x37C981DCC395A9AC, 0xB38D92D760EC4455], // 1e191
+ [0x85BBE253F47B1417, 0xE070F78D3927556A], // 1e192
+ [0x93956D7478CCEC8E, 0x8C469AB843B89562], // 1e193
+ [0x387AC8D1970027B2, 0xAF58416654A6BABB], // 1e194
+ [0x06997B05FCC0319E, 0xDB2E51BFE9D0696A], // 1e195
+ [0x441FECE3BDF81F03, 0x88FCF317F22241E2], // 1e196
+ [0xD527E81CAD7626C3, 0xAB3C2FDDEEAAD25A], // 1e197
+ [0x8A71E223D8D3B074, 0xD60B3BD56A5586F1], // 1e198
+ [0xF6872D5667844E49, 0x85C7056562757456], // 1e199
+ [0xB428F8AC016561DB, 0xA738C6BEBB12D16C], // 1e200
+ [0xE13336D701BEBA52, 0xD106F86E69D785C7], // 1e201
+ [0xECC0024661173473, 0x82A45B450226B39C], // 1e202
+ [0x27F002D7F95D0190, 0xA34D721642B06084], // 1e203
+ [0x31EC038DF7B441F4, 0xCC20CE9BD35C78A5], // 1e204
+ [0x7E67047175A15271, 0xFF290242C83396CE], // 1e205
+ [0x0F0062C6E984D386, 0x9F79A169BD203E41], // 1e206
+ [0x52C07B78A3E60868, 0xC75809C42C684DD1], // 1e207
+ [0xA7709A56CCDF8A82, 0xF92E0C3537826145], // 1e208
+ [0x88A66076400BB691, 0x9BBCC7A142B17CCB], // 1e209
+ [0x6ACFF893D00EA435, 0xC2ABF989935DDBFE], // 1e210
+ [0x0583F6B8C4124D43, 0xF356F7EBF83552FE], // 1e211
+ [0xC3727A337A8B704A, 0x98165AF37B2153DE], // 1e212
+ [0x744F18C0592E4C5C, 0xBE1BF1B059E9A8D6], // 1e213
+ [0x1162DEF06F79DF73, 0xEDA2EE1C7064130C], // 1e214
+ [0x8ADDCB5645AC2BA8, 0x9485D4D1C63E8BE7], // 1e215
+ [0x6D953E2BD7173692, 0xB9A74A0637CE2EE1], // 1e216
+ [0xC8FA8DB6CCDD0437, 0xE8111C87C5C1BA99], // 1e217
+ [0x1D9C9892400A22A2, 0x910AB1D4DB9914A0], // 1e218
+ [0x2503BEB6D00CAB4B, 0xB54D5E4A127F59C8], // 1e219
+ [0x2E44AE64840FD61D, 0xE2A0B5DC971F303A], // 1e220
+ [0x5CEAECFED289E5D2, 0x8DA471A9DE737E24], // 1e221
+ [0x7425A83E872C5F47, 0xB10D8E1456105DAD], // 1e222
+ [0xD12F124E28F77719, 0xDD50F1996B947518], // 1e223
+ [0x82BD6B70D99AAA6F, 0x8A5296FFE33CC92F], // 1e224
+ [0x636CC64D1001550B, 0xACE73CBFDC0BFB7B], // 1e225
+ [0x3C47F7E05401AA4E, 0xD8210BEFD30EFA5A], // 1e226
+ [0x65ACFAEC34810A71, 0x8714A775E3E95C78], // 1e227
+ [0x7F1839A741A14D0D, 0xA8D9D1535CE3B396], // 1e228
+ [0x1EDE48111209A050, 0xD31045A8341CA07C], // 1e229
+ [0x934AED0AAB460432, 0x83EA2B892091E44D], // 1e230
+ [0xF81DA84D5617853F, 0xA4E4B66B68B65D60], // 1e231
+ [0x36251260AB9D668E, 0xCE1DE40642E3F4B9], // 1e232
+ [0xC1D72B7C6B426019, 0x80D2AE83E9CE78F3], // 1e233
+ [0xB24CF65B8612F81F, 0xA1075A24E4421730], // 1e234
+ [0xDEE033F26797B627, 0xC94930AE1D529CFC], // 1e235
+ [0x169840EF017DA3B1, 0xFB9B7CD9A4A7443C], // 1e236
+ [0x8E1F289560EE864E, 0x9D412E0806E88AA5], // 1e237
+ [0xF1A6F2BAB92A27E2, 0xC491798A08A2AD4E], // 1e238
+ [0xAE10AF696774B1DB, 0xF5B5D7EC8ACB58A2], // 1e239
+ [0xACCA6DA1E0A8EF29, 0x9991A6F3D6BF1765], // 1e240
+ [0x17FD090A58D32AF3, 0xBFF610B0CC6EDD3F], // 1e241
+ [0xDDFC4B4CEF07F5B0, 0xEFF394DCFF8A948E], // 1e242
+ [0x4ABDAF101564F98E, 0x95F83D0A1FB69CD9], // 1e243
+ [0x9D6D1AD41ABE37F1, 0xBB764C4CA7A4440F], // 1e244
+ [0x84C86189216DC5ED, 0xEA53DF5FD18D5513], // 1e245
+ [0x32FD3CF5B4E49BB4, 0x92746B9BE2F8552C], // 1e246
+ [0x3FBC8C33221DC2A1, 0xB7118682DBB66A77], // 1e247
+ [0x0FABAF3FEAA5334A, 0xE4D5E82392A40515], // 1e248
+ [0x29CB4D87F2A7400E, 0x8F05B1163BA6832D], // 1e249
+ [0x743E20E9EF511012, 0xB2C71D5BCA9023F8], // 1e250
+ [0x914DA9246B255416, 0xDF78E4B2BD342CF6], // 1e251
+ [0x1AD089B6C2F7548E, 0x8BAB8EEFB6409C1A], // 1e252
+ [0xA184AC2473B529B1, 0xAE9672ABA3D0C320], // 1e253
+ [0xC9E5D72D90A2741E, 0xDA3C0F568CC4F3E8], // 1e254
+ [0x7E2FA67C7A658892, 0x8865899617FB1871], // 1e255
+ [0xDDBB901B98FEEAB7, 0xAA7EEBFB9DF9DE8D], // 1e256
+ [0x552A74227F3EA565, 0xD51EA6FA85785631], // 1e257
+ [0xD53A88958F87275F, 0x8533285C936B35DE], // 1e258
+ [0x8A892ABAF368F137, 0xA67FF273B8460356], // 1e259
+ [0x2D2B7569B0432D85, 0xD01FEF10A657842C], // 1e260
+ [0x9C3B29620E29FC73, 0x8213F56A67F6B29B], // 1e261
+ [0x8349F3BA91B47B8F, 0xA298F2C501F45F42], // 1e262
+ [0x241C70A936219A73, 0xCB3F2F7642717713], // 1e263
+ [0xED238CD383AA0110, 0xFE0EFB53D30DD4D7], // 1e264
+ [0xF4363804324A40AA, 0x9EC95D1463E8A506], // 1e265
+ [0xB143C6053EDCD0D5, 0xC67BB4597CE2CE48], // 1e266
+ [0xDD94B7868E94050A, 0xF81AA16FDC1B81DA], // 1e267
+ [0xCA7CF2B4191C8326, 0x9B10A4E5E9913128], // 1e268
+ [0xFD1C2F611F63A3F0, 0xC1D4CE1F63F57D72], // 1e269
+ [0xBC633B39673C8CEC, 0xF24A01A73CF2DCCF], // 1e270
+ [0xD5BE0503E085D813, 0x976E41088617CA01], // 1e271
+ [0x4B2D8644D8A74E18, 0xBD49D14AA79DBC82], // 1e272
+ [0xDDF8E7D60ED1219E, 0xEC9C459D51852BA2], // 1e273
+ [0xCABB90E5C942B503, 0x93E1AB8252F33B45], // 1e274
+ [0x3D6A751F3B936243, 0xB8DA1662E7B00A17], // 1e275
+ [0x0CC512670A783AD4, 0xE7109BFBA19C0C9D], // 1e276
+ [0x27FB2B80668B24C5, 0x906A617D450187E2], // 1e277
+ [0xB1F9F660802DEDF6, 0xB484F9DC9641E9DA], // 1e278
+ [0x5E7873F8A0396973, 0xE1A63853BBD26451], // 1e279
+ [0xDB0B487B6423E1E8, 0x8D07E33455637EB2], // 1e280
+ [0x91CE1A9A3D2CDA62, 0xB049DC016ABC5E5F], // 1e281
+ [0x7641A140CC7810FB, 0xDC5C5301C56B75F7], // 1e282
+ [0xA9E904C87FCB0A9D, 0x89B9B3E11B6329BA], // 1e283
+ [0x546345FA9FBDCD44, 0xAC2820D9623BF429], // 1e284
+ [0xA97C177947AD4095, 0xD732290FBACAF133], // 1e285
+ [0x49ED8EABCCCC485D, 0x867F59A9D4BED6C0], // 1e286
+ [0x5C68F256BFFF5A74, 0xA81F301449EE8C70], // 1e287
+ [0x73832EEC6FFF3111, 0xD226FC195C6A2F8C], // 1e288
+];
+
