mirrors/Nim
1
0
Fork 0
mirror of https://github.com/nim-lang/Nim.git synced 2025-12-29 01:14:41 +00:00
Code Issues Packages Projects Releases Wiki Activity
Files
version-2-2
Nim/lib/std/private/dragonbox.nim
Jacek Sieka 2123969cc4 orc: fix overflow checking regression (#25089) 
Raising exceptions halfway through a memory allocation is undefined
behavior since exceptions themselves require multiple allocations and
the allocator functions are not reentrant.

It is of course also expensive performance-wise to introduce lots of
exception-raising code everywhere since it breaks many optimisations and
bloats the code.

Finally, performing pointer arithmetic with signed integers is incorrect
for example on on a 32-bit systems that allows up to 3gb of address
space for applications (large address extensions) and unnecessary
elsewhere - broadly, stuff inside the memory allocator is generated by
the compiler or controlled by the standard library meaning that
applications should not be forced to pay this price.

If we wanted to check for overflow, the right way would be in the
initial allocation location where both the size and count of objects is
known.

The code is updated to use the same arithmetic operator style as for
refc with unchecked operations rather than disabling overflow checking
wholesale in the allocator module - there are reasons for both, but
going with the existing flow seems like an easier place to start.

(cherry picked from commit 8b9972c8b6)
2025-09-17 09:04:16 +02:00

1317 lines
64 KiB
Nim
Raw Permalink Blame History

## Copyright 2020 Junekey Jeon
## Copyright 2020 Alexander Bolz
##
## Distributed under the Boost Software License, Version 1.0.
## (See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt)
## char* output_end = Dtoa(buffer, value);
##
## Converts the given double-precision number into decimal form and stores the result in the given
## buffer.
##
## The buffer must be large enough, i.e. >= DtoaMinBufferLength.
## The output format is similar to printf("%g").
## The output is _not_ null-terminted.
##
## The output is optimal, i.e. the output string
## 1. rounds back to the input number when read in (using round-to-nearest-even)
## 2. is as short as possible,
## 3. is as close to the input number as possible.
##
## Note:
## This function may temporarily write up to DtoaMinBufferLength characters into the buffer.
import std/private/digitsutils
when defined(nimPreviewSlimSystem):
import std/assertions
const
dtoaMinBufferLength*: cint = 64
## This file contains an implementation of Junekey Jeon's Dragonbox algorithm.
##
## It is a simplified version of the reference implementation found here:
## https://github.com/jk-jeon/dragonbox
##
## The reference implementation also works with single-precision floating-point numbers and
## has options to configure the rounding mode.
template dragonbox_Assert*(x: untyped): untyped =
assert(x)
# ==================================================================================================
#
# ==================================================================================================
type
ValueType* = float
BitsType* = uint64
type
Double* = object
bits*: BitsType
const ## = p (includes the hidden bit)
significandSize*: int32 = 53
const ## static constexpr int32_t MaxExponent = 1024 - 1 - (SignificandSize - 1);
## static constexpr int32_t MinExponent = std::numeric_limits<value_type>::min_exponent - 1 - (SignificandSize - 1);
exponentBias*: int32 = 1024 - 1 + (significandSize - 1)
const
maxIeeeExponent*: BitsType = BitsType(2 * 1024 - 1)
const ## = 2^(p-1)
hiddenBit*: BitsType = BitsType(1) shl (significandSize - 1)
const ## = 2^(p-1) - 1
significandMask*: BitsType = hiddenBit - 1
const
exponentMask*: BitsType = maxIeeeExponent shl (significandSize - 1)
const
signMask*: BitsType = not (not BitsType(0) shr 1)
proc constructDouble*(bits: BitsType): Double =
result = Double(bits: bits)
proc constructDouble*(value: ValueType): Double =
result = Double(bits: cast[typeof(result.bits)](value))
proc physicalSignificand*(this: Double): BitsType {.noSideEffect.} =
return this.bits and significandMask
proc physicalExponent*(this: Double): BitsType {.noSideEffect.} =
return (this.bits and exponentMask) shr (significandSize - 1)
proc isFinite*(this: Double): bool {.noSideEffect.} =
return (this.bits and exponentMask) != exponentMask
proc isInf*(this: Double): bool {.noSideEffect.} =
return (this.bits and exponentMask) == exponentMask and
(this.bits and significandMask) == 0
proc isNaN*(this: Double): bool {.noSideEffect.} =
return (this.bits and exponentMask) == exponentMask and
(this.bits and significandMask) != 0
proc isZero*(this: Double): bool {.noSideEffect.} =
return (this.bits and not signMask) == 0
proc signBit*(this: Double): int {.noSideEffect.} =
return ord((this.bits and signMask) != 0)
# ==================================================================================================
#
# ==================================================================================================
## namespace
## Returns floor(x / 2^n).
##
## Technically, right-shift of negative integers is implementation defined...
## Should easily be optimized into SAR (or equivalent) instruction.
proc floorDivPow2*(x: int32; n: int32): int32 {.inline.} =
return x shr n
proc floorLog2Pow10*(e: int32): int32 {.inline.} =
dragonbox_Assert(e >= -1233)
dragonbox_Assert(e <= 1233)
return floorDivPow2(e * 1741647, 19)
proc floorLog10Pow2*(e: int32): int32 {.inline.} =
dragonbox_Assert(e >= -1500)
dragonbox_Assert(e <= 1500)
return floorDivPow2(e * 1262611, 22)
proc floorLog10ThreeQuartersPow2*(e: int32): int32 {.inline.} =
dragonbox_Assert(e >= -1500)
dragonbox_Assert(e <= 1500)
return floorDivPow2(e * 1262611 - 524031, 22)
# ==================================================================================================
#
# ==================================================================================================
type
uint64x2* {.bycopy.} = object
hi*: uint64
lo*: uint64
proc computePow10*(k: int32): uint64x2 {.inline.} =
const
kMin: int32 = -292
const
kMax: int32 = 326
const
pow10: array[kMax - kMin + 1, uint64x2] = [
uint64x2(hi: 0xFF77B1FCBEBCDC4F'u, lo: 0x25E8E89C13BB0F7B'u),
uint64x2(hi: 0x9FAACF3DF73609B1'u, lo: 0x77B191618C54E9AD'u),
uint64x2(hi: 0xC795830D75038C1D'u, lo: 0xD59DF5B9EF6A2418'u),
uint64x2(hi: 0xF97AE3D0D2446F25'u, lo: 0x4B0573286B44AD1E'u),
uint64x2(hi: 0x9BECCE62836AC577'u, lo: 0x4EE367F9430AEC33'u),
uint64x2(hi: 0xC2E801FB244576D5'u, lo: 0x229C41F793CDA740'u),
uint64x2(hi: 0xF3A20279ED56D48A'u, lo: 0x6B43527578C11110'u),
uint64x2(hi: 0x9845418C345644D6'u, lo: 0x830A13896B78AAAA'u),
uint64x2(hi: 0xBE5691EF416BD60C'u, lo: 0x23CC986BC656D554'u),
uint64x2(hi: 0xEDEC366B11C6CB8F'u, lo: 0x2CBFBE86B7EC8AA9'u),
uint64x2(hi: 0x94B3A202EB1C3F39'u, lo: 0x7BF7D71432F3D6AA'u),
uint64x2(hi: 0xB9E08A83A5E34F07'u, lo: 0xDAF5CCD93FB0CC54'u),
uint64x2(hi: 0xE858AD248F5C22C9'u, lo: 0xD1B3400F8F9CFF69'u),
uint64x2(hi: 0x91376C36D99995BE'u, lo: 0x23100809B9C21FA2'u),
uint64x2(hi: 0xB58547448FFFFB2D'u, lo: 0xABD40A0C2832A78B'u),
uint64x2(hi: 0xE2E69915B3FFF9F9'u, lo: 0x16C90C8F323F516D'u),
uint64x2(hi: 0x8DD01FAD907FFC3B'u, lo: 0xAE3DA7D97F6792E4'u),
uint64x2(hi: 0xB1442798F49FFB4A'u, lo: 0x99CD11CFDF41779D'u),
uint64x2(hi: 0xDD95317F31C7FA1D'u, lo: 0x40405643D711D584'u),
uint64x2(hi: 0x8A7D3EEF7F1CFC52'u, lo: 0x482835EA666B2573'u),
uint64x2(hi: 0xAD1C8EAB5EE43B66'u, lo: 0xDA3243650005EED0'u),
uint64x2(hi: 0xD863B256369D4A40'u, lo: 0x90BED43E40076A83'u),
uint64x2(hi: 0x873E4F75E2224E68'u, lo: 0x5A7744A6E804A292'u),
uint64x2(hi: 0xA90DE3535AAAE202'u, lo: 0x711515D0A205CB37'u),
uint64x2(hi: 0xD3515C2831559A83'u, lo: 0x0D5A5B44CA873E04'u),
uint64x2(hi: 0x8412D9991ED58091'u, lo: 0xE858790AFE9486C3'u),
uint64x2(hi: 0xA5178FFF668AE0B6'u, lo: 0x626E974DBE39A873'u),
uint64x2(hi: 0xCE5D73FF402D98E3'u, lo: 0xFB0A3D212DC81290'u),
uint64x2(hi: 0x80FA687F881C7F8E'u, lo: 0x7CE66634BC9D0B9A'u),
uint64x2(hi: 0xA139029F6A239F72'u, lo: 0x1C1FFFC1EBC44E81'u),
uint64x2(hi: 0xC987434744AC874E'u, lo: 0xA327FFB266B56221'u),
uint64x2(hi: 0xFBE9141915D7A922'u, lo: 0x4BF1FF9F0062BAA9'u),
uint64x2(hi: 0x9D71AC8FADA6C9B5'u, lo: 0x6F773FC3603DB4AA'u),
uint64x2(hi: 0xC4CE17B399107C22'u, lo: 0xCB550FB4384D21D4'u),
uint64x2(hi: 0xF6019DA07F549B2B'u, lo: 0x7E2A53A146606A49'u),
uint64x2(hi: 0x99C102844F94E0FB'u, lo: 0x2EDA7444CBFC426E'u),
uint64x2(hi: 0xC0314325637A1939'u, lo: 0xFA911155FEFB5309'u),
uint64x2(hi: 0xF03D93EEBC589F88'u, lo: 0x793555AB7EBA27CB'u),
uint64x2(hi: 0x96267C7535B763B5'u, lo: 0x4BC1558B2F3458DF'u),
uint64x2(hi: 0xBBB01B9283253CA2'u, lo: 0x9EB1AAEDFB016F17'u),
uint64x2(hi: 0xEA9C227723EE8BCB'u, lo: 0x465E15A979C1CADD'u),
uint64x2(hi: 0x92A1958A7675175F'u, lo: 0x0BFACD89EC191ECA'u),
uint64x2(hi: 0xB749FAED14125D36'u, lo: 0xCEF980EC671F667C'u),
uint64x2(hi: 0xE51C79A85916F484'u, lo: 0x82B7E12780E7401B'u),
uint64x2(hi: 0x8F31CC0937AE58D2'u, lo: 0xD1B2ECB8B0908811'u),
uint64x2(hi: 0xB2FE3F0B8599EF07'u, lo: 0x861FA7E6DCB4AA16'u),
uint64x2(hi: 0xDFBDCECE67006AC9'u, lo: 0x67A791E093E1D49B'u),
uint64x2(hi: 0x8BD6A141006042BD'u, lo: 0xE0C8BB2C5C6D24E1'u),
uint64x2(hi: 0xAECC49914078536D'u, lo: 0x58FAE9F773886E19'u),
uint64x2(hi: 0xDA7F5BF590966848'u, lo: 0xAF39A475506A899F'u),
uint64x2(hi: 0x888F99797A5E012D'u, lo: 0x6D8406C952429604'u),
uint64x2(hi: 0xAAB37FD7D8F58178'u, lo: 0xC8E5087BA6D33B84'u),
uint64x2(hi: 0xD5605FCDCF32E1D6'u, lo: 0xFB1E4A9A90880A65'u),
uint64x2(hi: 0x855C3BE0A17FCD26'u, lo: 0x5CF2EEA09A550680'u),
uint64x2(hi: 0xA6B34AD8C9DFC06F'u, lo: 0xF42FAA48C0EA481F'u),
uint64x2(hi: 0xD0601D8EFC57B08B'u, lo: 0xF13B94DAF124DA27'u),
uint64x2(hi: 0x823C12795DB6CE57'u, lo: 0x76C53D08D6B70859'u),
uint64x2(hi: 0xA2CB1717B52481ED'u, lo: 0x54768C4B0C64CA6F'u),
uint64x2(hi: 0xCB7DDCDDA26DA268'u, lo: 0xA9942F5DCF7DFD0A'u),
uint64x2(hi: 0xFE5D54150B090B02'u, lo: 0xD3F93B35435D7C4D'u),
uint64x2(hi: 0x9EFA548D26E5A6E1'u, lo: 0xC47BC5014A1A6DB0'u),
uint64x2(hi: 0xC6B8E9B0709F109A'u, lo: 0x359AB6419CA1091C'u),
uint64x2(hi: 0xF867241C8CC6D4C0'u, lo: 0xC30163D203C94B63'u),
uint64x2(hi: 0x9B407691D7FC44F8'u, lo: 0x79E0DE63425DCF1E'u),
uint64x2(hi: 0xC21094364DFB5636'u, lo: 0x985915FC12F542E5'u),
uint64x2(hi: 0xF294B943E17A2BC4'u, lo: 0x3E6F5B7B17B2939E'u),
uint64x2(hi: 0x979CF3CA6CEC5B5A'u, lo: 0xA705992CEECF9C43'u),
uint64x2(hi: 0xBD8430BD08277231'u, lo: 0x50C6FF782A838354'u),
uint64x2(hi: 0xECE53CEC4A314EBD'u, lo: 0xA4F8BF5635246429'u),
uint64x2(hi: 0x940F4613AE5ED136'u, lo: 0x871B7795E136BE9A'u),
uint64x2(hi: 0xB913179899F68584'u, lo: 0x28E2557B59846E40'u),
uint64x2(hi: 0xE757DD7EC07426E5'u, lo: 0x331AEADA2FE589D0'u),
uint64x2(hi: 0x9096EA6F3848984F'u, lo: 0x3FF0D2C85DEF7622'u),
uint64x2(hi: 0xB4BCA50B065ABE63'u, lo: 0x0FED077A756B53AA'u),
uint64x2(hi: 0xE1EBCE4DC7F16DFB'u, lo: 0xD3E8495912C62895'u),
uint64x2(hi: 0x8D3360F09CF6E4BD'u, lo: 0x64712DD7ABBBD95D'u),
uint64x2(hi: 0xB080392CC4349DEC'u, lo: 0xBD8D794D96AACFB4'u),
uint64x2(hi: 0xDCA04777F541C567'u, lo: 0xECF0D7A0FC5583A1'u),
uint64x2(hi: 0x89E42CAAF9491B60'u, lo: 0xF41686C49DB57245'u),
uint64x2(hi: 0xAC5D37D5B79B6239'u, lo: 0x311C2875C522CED6'u),
uint64x2(hi: 0xD77485CB25823AC7'u, lo: 0x7D633293366B828C'u),
uint64x2(hi: 0x86A8D39EF77164BC'u, lo: 0xAE5DFF9C02033198'u),
uint64x2(hi: 0xA8530886B54DBDEB'u, lo: 0xD9F57F830283FDFD'u),
uint64x2(hi: 0xD267CAA862A12D66'u, lo: 0xD072DF63C324FD7C'u),
uint64x2(hi: 0x8380DEA93DA4BC60'u, lo: 0x4247CB9E59F71E6E'u),
uint64x2(hi: 0xA46116538D0DEB78'u, lo: 0x52D9BE85F074E609'u),
uint64x2(hi: 0xCD795BE870516656'u, lo: 0x67902E276C921F8C'u),
uint64x2(hi: 0x806BD9714632DFF6'u, lo: 0x00BA1CD8A3DB53B7'u),
uint64x2(hi: 0xA086CFCD97BF97F3'u, lo: 0x80E8A40ECCD228A5'u),
uint64x2(hi: 0xC8A883C0FDAF7DF0'u, lo: 0x6122CD128006B2CE'u),
uint64x2(hi: 0xFAD2A4B13D1B5D6C'u, lo: 0x796B805720085F82'u),
uint64x2(hi: 0x9CC3A6EEC6311A63'u, lo: 0xCBE3303674053BB1'u),
uint64x2(hi: 0xC3F490AA77BD60FC'u, lo: 0xBEDBFC4411068A9D'u),
uint64x2(hi: 0xF4F1B4D515ACB93B'u, lo: 0xEE92FB5515482D45'u),
uint64x2(hi: 0x991711052D8BF3C5'u, lo: 0x751BDD152D4D1C4B'u),
uint64x2(hi: 0xBF5CD54678EEF0B6'u, lo: 0xD262D45A78A0635E'u),
uint64x2(hi: 0xEF340A98172AACE4'u, lo: 0x86FB897116C87C35'u),
uint64x2(hi: 0x9580869F0E7AAC0E'u, lo: 0xD45D35E6AE3D4DA1'u),
uint64x2(hi: 0xBAE0A846D2195712'u, lo: 0x8974836059CCA10A'u),
uint64x2(hi: 0xE998D258869FACD7'u, lo: 0x2BD1A438703FC94C'u),
uint64x2(hi: 0x91FF83775423CC06'u, lo: 0x7B6306A34627DDD0'u),
uint64x2(hi: 0xB67F6455292CBF08'u, lo: 0x1A3BC84C17B1D543'u),
uint64x2(hi: 0xE41F3D6A7377EECA'u, lo: 0x20CABA5F1D9E4A94'u),
uint64x2(hi: 0x8E938662882AF53E'u, lo: 0x547EB47B7282EE9D'u),
uint64x2(hi: 0xB23867FB2A35B28D'u, lo: 0xE99E619A4F23AA44'u),
uint64x2(hi: 0xDEC681F9F4C31F31'u, lo: 0x6405FA00E2EC94D5'u),
uint64x2(hi: 0x8B3C113C38F9F37E'u, lo: 0xDE83BC408DD3DD05'u),
uint64x2(hi: 0xAE0B158B4738705E'u, lo: 0x9624AB50B148D446'u),
uint64x2(hi: 0xD98DDAEE19068C76'u, lo: 0x3BADD624DD9B0958'u),
uint64x2(hi: 0x87F8A8D4CFA417C9'u, lo: 0xE54CA5D70A80E5D7'u),
uint64x2(hi: 0xA9F6D30A038D1DBC'u, lo: 0x5E9FCF4CCD211F4D'u),
uint64x2(hi: 0xD47487CC8470652B'u, lo: 0x7647C32000696720'u),
uint64x2(hi: 0x84C8D4DFD2C63F3B'u, lo: 0x29ECD9F40041E074'u),
uint64x2(hi: 0xA5FB0A17C777CF09'u, lo: 0xF468107100525891'u),
uint64x2(hi: 0xCF79CC9DB955C2CC'u, lo: 0x7182148D4066EEB5'u),
uint64x2(hi: 0x81AC1FE293D599BF'u, lo: 0xC6F14CD848405531'u),
uint64x2(hi: 0xA21727DB38CB002F'u, lo: 0xB8ADA00E5A506A7D'u),
uint64x2(hi: 0xCA9CF1D206FDC03B'u, lo: 0xA6D90811F0E4851D'u),
uint64x2(hi: 0xFD442E4688BD304A'u, lo: 0x908F4A166D1DA664'u),
uint64x2(hi: 0x9E4A9CEC15763E2E'u, lo: 0x9A598E4E043287FF'u),
uint64x2(hi: 0xC5DD44271AD3CDBA'u, lo: 0x40EFF1E1853F29FE'u),
uint64x2(hi: 0xF7549530E188C128'u, lo: 0xD12BEE59E68EF47D'u),
uint64x2(hi: 0x9A94DD3E8CF578B9'u, lo: 0x82BB74F8301958CF'u),
uint64x2(hi: 0xC13A148E3032D6E7'u, lo: 0xE36A52363C1FAF02'u),
uint64x2(hi: 0xF18899B1BC3F8CA1'u, lo: 0xDC44E6C3CB279AC2'u),
uint64x2(hi: 0x96F5600F15A7B7E5'u, lo: 0x29AB103A5EF8C0BA'u),
uint64x2(hi: 0xBCB2B812DB11A5DE'u, lo: 0x7415D448F6B6F0E8'u),
uint64x2(hi: 0xEBDF661791D60F56'u, lo: 0x111B495B3464AD22'u),
uint64x2(hi: 0x936B9FCEBB25C995'u, lo: 0xCAB10DD900BEEC35'u),
uint64x2(hi: 0xB84687C269EF3BFB'u, lo: 0x3D5D514F40EEA743'u),
uint64x2(hi: 0xE65829B3046B0AFA'u, lo: 0x0CB4A5A3112A5113'u),
uint64x2(hi: 0x8FF71A0FE2C2E6DC'u, lo: 0x47F0E785EABA72AC'u),
uint64x2(hi: 0xB3F4E093DB73A093'u, lo: 0x59ED216765690F57'u),
uint64x2(hi: 0xE0F218B8D25088B8'u, lo: 0x306869C13EC3532D'u),
uint64x2(hi: 0x8C974F7383725573'u, lo: 0x1E414218C73A13FC'u),
uint64x2(hi: 0xAFBD2350644EEACF'u, lo: 0xE5D1929EF90898FB'u),
uint64x2(hi: 0xDBAC6C247D62A583'u, lo: 0xDF45F746B74ABF3A'u),
uint64x2(hi: 0x894BC396CE5DA772'u, lo: 0x6B8BBA8C328EB784'u),
uint64x2(hi: 0xAB9EB47C81F5114F'u, lo: 0x066EA92F3F326565'u),
uint64x2(hi: 0xD686619BA27255A2'u, lo: 0xC80A537B0EFEFEBE'u),
uint64x2(hi: 0x8613FD0145877585'u, lo: 0xBD06742CE95F5F37'u),
uint64x2(hi: 0xA798FC4196E952E7'u, lo: 0x2C48113823B73705'u),
uint64x2(hi: 0xD17F3B51FCA3A7A0'u, lo: 0xF75A15862CA504C6'u),
uint64x2(hi: 0x82EF85133DE648C4'u, lo: 0x9A984D73DBE722FC'u),
uint64x2(hi: 0xA3AB66580D5FDAF5'u, lo: 0xC13E60D0D2E0EBBB'u),
uint64x2(hi: 0xCC963FEE10B7D1B3'u, lo: 0x318DF905079926A9'u),
uint64x2(hi: 0xFFBBCFE994E5C61F'u, lo: 0xFDF17746497F7053'u),
uint64x2(hi: 0x9FD561F1FD0F9BD3'u, lo: 0xFEB6EA8BEDEFA634'u),
uint64x2(hi: 0xC7CABA6E7C5382C8'u, lo: 0xFE64A52EE96B8FC1'u),
uint64x2(hi: 0xF9BD690A1B68637B'u, lo: 0x3DFDCE7AA3C673B1'u),
uint64x2(hi: 0x9C1661A651213E2D'u, lo: 0x06BEA10CA65C084F'u),
uint64x2(hi: 0xC31BFA0FE5698DB8'u, lo: 0x486E494FCFF30A63'u),
uint64x2(hi: 0xF3E2F893DEC3F126'u, lo: 0x5A89DBA3C3EFCCFB'u),
uint64x2(hi: 0x986DDB5C6B3A76B7'u, lo: 0xF89629465A75E01D'u),
uint64x2(hi: 0xBE89523386091465'u, lo: 0xF6BBB397F1135824'u),
uint64x2(hi: 0xEE2BA6C0678B597F'u, lo: 0x746AA07DED582E2D'u),
uint64x2(hi: 0x94DB483840B717EF'u, lo: 0xA8C2A44EB4571CDD'u),
uint64x2(hi: 0xBA121A4650E4DDEB'u, lo: 0x92F34D62616CE414'u),
uint64x2(hi: 0xE896A0D7E51E1566'u, lo: 0x77B020BAF9C81D18'u),
uint64x2(hi: 0x915E2486EF32CD60'u, lo: 0x0ACE1474DC1D122F'u),
uint64x2(hi: 0xB5B5ADA8AAFF80B8'u, lo: 0x0D819992132456BB'u),
uint64x2(hi: 0xE3231912D5BF60E6'u, lo: 0x10E1FFF697ED6C6A'u),
uint64x2(hi: 0x8DF5EFABC5979C8F'u, lo: 0xCA8D3FFA1EF463C2'u),
uint64x2(hi: 0xB1736B96B6FD83B3'u, lo: 0xBD308FF8A6B17CB3'u),
uint64x2(hi: 0xDDD0467C64BCE4A0'u, lo: 0xAC7CB3F6D05DDBDF'u),
uint64x2(hi: 0x8AA22C0DBEF60EE4'u, lo: 0x6BCDF07A423AA96C'u),
uint64x2(hi: 0xAD4AB7112EB3929D'u, lo: 0x86C16C98D2C953C7'u),
uint64x2(hi: 0xD89D64D57A607744'u, lo: 0xE871C7BF077BA8B8'u),
uint64x2(hi: 0x87625F056C7C4A8B'u, lo: 0x11471CD764AD4973'u),
uint64x2(hi: 0xA93AF6C6C79B5D2D'u, lo: 0xD598E40D3DD89BD0'u),
uint64x2(hi: 0xD389B47879823479'u, lo: 0x4AFF1D108D4EC2C4'u),
uint64x2(hi: 0x843610CB4BF160CB'u, lo: 0xCEDF722A585139BB'u),
uint64x2(hi: 0xA54394FE1EEDB8FE'u, lo: 0xC2974EB4EE658829'u),
uint64x2(hi: 0xCE947A3DA6A9273E'u, lo: 0x733D226229FEEA33'u),
uint64x2(hi: 0x811CCC668829B887'u, lo: 0x0806357D5A3F5260'u),
uint64x2(hi: 0xA163FF802A3426A8'u, lo: 0xCA07C2DCB0CF26F8'u),
uint64x2(hi: 0xC9BCFF6034C13052'u, lo: 0xFC89B393DD02F0B6'u),
uint64x2(hi: 0xFC2C3F3841F17C67'u, lo: 0xBBAC2078D443ACE3'u),
uint64x2(hi: 0x9D9BA7832936EDC0'u, lo: 0xD54B944B84AA4C0E'u),
uint64x2(hi: 0xC5029163F384A931'u, lo: 0x0A9E795E65D4DF12'u),
uint64x2(hi: 0xF64335BCF065D37D'u, lo: 0x4D4617B5FF4A16D6'u),
uint64x2(hi: 0x99EA0196163FA42E'u, lo: 0x504BCED1BF8E4E46'u),
uint64x2(hi: 0xC06481FB9BCF8D39'u, lo: 0xE45EC2862F71E1D7'u),
uint64x2(hi: 0xF07DA27A82C37088'u, lo: 0x5D767327BB4E5A4D'u),
uint64x2(hi: 0x964E858C91BA2655'u, lo: 0x3A6A07F8D510F870'u),
uint64x2(hi: 0xBBE226EFB628AFEA'u, lo: 0x890489F70A55368C'u),
uint64x2(hi: 0xEADAB0ABA3B2DBE5'u, lo: 0x2B45AC74CCEA842F'u),
uint64x2(hi: 0x92C8AE6B464FC96F'u, lo: 0x3B0B8BC90012929E'u),
uint64x2(hi: 0xB77ADA0617E3BBCB'u, lo: 0x09CE6EBB40173745'u),
uint64x2(hi: 0xE55990879DDCAABD'u, lo: 0xCC420A6A101D0516'u),
uint64x2(hi: 0x8F57FA54C2A9EAB6'u, lo: 0x9FA946824A12232E'u),
uint64x2(hi: 0xB32DF8E9F3546564'u, lo: 0x47939822DC96ABFA'u),
uint64x2(hi: 0xDFF9772470297EBD'u, lo: 0x59787E2B93BC56F8'u),
uint64x2(hi: 0x8BFBEA76C619EF36'u, lo: 0x57EB4EDB3C55B65B'u),
uint64x2(hi: 0xAEFAE51477A06B03'u, lo: 0xEDE622920B6B23F2'u),
uint64x2(hi: 0xDAB99E59958885C4'u, lo: 0xE95FAB368E45ECEE'u),
uint64x2(hi: 0x88B402F7FD75539B'u, lo: 0x11DBCB0218EBB415'u),
uint64x2(hi: 0xAAE103B5FCD2A881'u, lo: 0xD652BDC29F26A11A'u),
uint64x2(hi: 0xD59944A37C0752A2'u, lo: 0x4BE76D3346F04960'u),
uint64x2(hi: 0x857FCAE62D8493A5'u, lo: 0x6F70A4400C562DDC'u),
uint64x2(hi: 0xA6DFBD9FB8E5B88E'u, lo: 0xCB4CCD500F6BB953'u),
uint64x2(hi: 0xD097AD07A71F26B2'u, lo: 0x7E2000A41346A7A8'u),
uint64x2(hi: 0x825ECC24C873782F'u, lo: 0x8ED400668C0C28C9'u),
uint64x2(hi: 0xA2F67F2DFA90563B'u, lo: 0x728900802F0F32FB'u),
uint64x2(hi: 0xCBB41EF979346BCA'u, lo: 0x4F2B40A03AD2FFBA'u),
uint64x2(hi: 0xFEA126B7D78186BC'u, lo: 0xE2F610C84987BFA9'u),
uint64x2(hi: 0x9F24B832E6B0F436'u, lo: 0x0DD9CA7D2DF4D7CA'u),
uint64x2(hi: 0xC6EDE63FA05D3143'u, lo: 0x91503D1C79720DBC'u),
uint64x2(hi: 0xF8A95FCF88747D94'u, lo: 0x75A44C6397CE912B'u),
uint64x2(hi: 0x9B69DBE1B548CE7C'u, lo: 0xC986AFBE3EE11ABB'u),
uint64x2(hi: 0xC24452DA229B021B'u, lo: 0xFBE85BADCE996169'u),
uint64x2(hi: 0xF2D56790AB41C2A2'u, lo: 0xFAE27299423FB9C4'u),
uint64x2(hi: 0x97C560BA6B0919A5'u, lo: 0xDCCD879FC967D41B'u),
uint64x2(hi: 0xBDB6B8E905CB600F'u, lo: 0x5400E987BBC1C921'u),
uint64x2(hi: 0xED246723473E3813'u, lo: 0x290123E9AAB23B69'u),
uint64x2(hi: 0x9436C0760C86E30B'u, lo: 0xF9A0B6720AAF6522'u),
uint64x2(hi: 0xB94470938FA89BCE'u, lo: 0xF808E40E8D5B3E6A'u),
uint64x2(hi: 0xE7958CB87392C2C2'u, lo: 0xB60B1D1230B20E05'u),
uint64x2(hi: 0x90BD77F3483BB9B9'u, lo: 0xB1C6F22B5E6F48C3'u),
uint64x2(hi: 0xB4ECD5F01A4AA828'u, lo: 0x1E38AEB6360B1AF4'u),
uint64x2(hi: 0xE2280B6C20DD5232'u, lo: 0x25C6DA63C38DE1B1'u),
uint64x2(hi: 0x8D590723948A535F'u, lo: 0x579C487E5A38AD0F'u),
uint64x2(hi: 0xB0AF48EC79ACE837'u, lo: 0x2D835A9DF0C6D852'u),
uint64x2(hi: 0xDCDB1B2798182244'u, lo: 0xF8E431456CF88E66'u),
uint64x2(hi: 0x8A08F0F8BF0F156B'u, lo: 0x1B8E9ECB641B5900'u),
uint64x2(hi: 0xAC8B2D36EED2DAC5'u, lo: 0xE272467E3D222F40'u),
uint64x2(hi: 0xD7ADF884AA879177'u, lo: 0x5B0ED81DCC6ABB10'u),
uint64x2(hi: 0x86CCBB52EA94BAEA'u, lo: 0x98E947129FC2B4EA'u),
uint64x2(hi: 0xA87FEA27A539E9A5'u, lo: 0x3F2398D747B36225'u),
uint64x2(hi: 0xD29FE4B18E88640E'u, lo: 0x8EEC7F0D19A03AAE'u),
uint64x2(hi: 0x83A3EEEEF9153E89'u, lo: 0x1953CF68300424AD'u),
uint64x2(hi: 0xA48CEAAAB75A8E2B'u, lo: 0x5FA8C3423C052DD8'u),
uint64x2(hi: 0xCDB02555653131B6'u, lo: 0x3792F412CB06794E'u),
uint64x2(hi: 0x808E17555F3EBF11'u, lo: 0xE2BBD88BBEE40BD1'u),
uint64x2(hi: 0xA0B19D2AB70E6ED6'u, lo: 0x5B6ACEAEAE9D0EC5'u),
uint64x2(hi: 0xC8DE047564D20A8B'u, lo: 0xF245825A5A445276'u),
uint64x2(hi: 0xFB158592BE068D2E'u, lo: 0xEED6E2F0F0D56713'u),
uint64x2(hi: 0x9CED737BB6C4183D'u, lo: 0x55464DD69685606C'u),
uint64x2(hi: 0xC428D05AA4751E4C'u, lo: 0xAA97E14C3C26B887'u),
uint64x2(hi: 0xF53304714D9265DF'u, lo: 0xD53DD99F4B3066A9'u),
uint64x2(hi: 0x993FE2C6D07B7FAB'u, lo: 0xE546A8038EFE402A'u),
uint64x2(hi: 0xBF8FDB78849A5F96'u, lo: 0xDE98520472BDD034'u),
uint64x2(hi: 0xEF73D256A5C0F77C'u, lo: 0x963E66858F6D4441'u),
uint64x2(hi: 0x95A8637627989AAD'u, lo: 0xDDE7001379A44AA9'u),
uint64x2(hi: 0xBB127C53B17EC159'u, lo: 0x5560C018580D5D53'u),
uint64x2(hi: 0xE9D71B689DDE71AF'u, lo: 0xAAB8F01E6E10B4A7'u),
uint64x2(hi: 0x9226712162AB070D'u, lo: 0xCAB3961304CA70E9'u),
uint64x2(hi: 0xB6B00D69BB55C8D1'u, lo: 0x3D607B97C5FD0D23'u),
uint64x2(hi: 0xE45C10C42A2B3B05'u, lo: 0x8CB89A7DB77C506B'u),
uint64x2(hi: 0x8EB98A7A9A5B04E3'u, lo: 0x77F3608E92ADB243'u),
uint64x2(hi: 0xB267ED1940F1C61C'u, lo: 0x55F038B237591ED4'u),
uint64x2(hi: 0xDF01E85F912E37A3'u, lo: 0x6B6C46DEC52F6689'u),
uint64x2(hi: 0x8B61313BBABCE2C6'u, lo: 0x2323AC4B3B3DA016'u),
uint64x2(hi: 0xAE397D8AA96C1B77'u, lo: 0xABEC975E0A0D081B'u),
uint64x2(hi: 0xD9C7DCED53C72255'u, lo: 0x96E7BD358C904A22'u),
uint64x2(hi: 0x881CEA14545C7575'u, lo: 0x7E50D64177DA2E55'u),
uint64x2(hi: 0xAA242499697392D2'u, lo: 0xDDE50BD1D5D0B9EA'u),
uint64x2(hi: 0xD4AD2DBFC3D07787'u, lo: 0x955E4EC64B44E865'u),
uint64x2(hi: 0x84EC3C97DA624AB4'u, lo: 0xBD5AF13BEF0B113F'u),
uint64x2(hi: 0xA6274BBDD0FADD61'u, lo: 0xECB1AD8AEACDD58F'u),
uint64x2(hi: 0xCFB11EAD453994BA'u, lo: 0x67DE18EDA5814AF3'u),
uint64x2(hi: 0x81CEB32C4B43FCF4'u, lo: 0x80EACF948770CED8'u),
uint64x2(hi: 0xA2425FF75E14FC31'u, lo: 0xA1258379A94D028E'u),
uint64x2(hi: 0xCAD2F7F5359A3B3E'u, lo: 0x096EE45813A04331'u),
uint64x2(hi: 0xFD87B5F28300CA0D'u, lo: 0x8BCA9D6E188853FD'u),
uint64x2(hi: 0x9E74D1B791E07E48'u, lo: 0x775EA264CF55347E'u),
uint64x2(hi: 0xC612062576589DDA'u, lo: 0x95364AFE032A819E'u),
uint64x2(hi: 0xF79687AED3EEC551'u, lo: 0x3A83DDBD83F52205'u),
uint64x2(hi: 0x9ABE14CD44753B52'u, lo: 0xC4926A9672793543'u),
uint64x2(hi: 0xC16D9A0095928A27'u, lo: 0x75B7053C0F178294'u),
uint64x2(hi: 0xF1C90080BAF72CB1'u, lo: 0x5324C68B12DD6339'u),
uint64x2(hi: 0x971DA05074DA7BEE'u, lo: 0xD3F6FC16EBCA5E04'u),
uint64x2(hi: 0xBCE5086492111AEA'u, lo: 0x88F4BB1CA6BCF585'u),
uint64x2(hi: 0xEC1E4A7DB69561A5'u, lo: 0x2B31E9E3D06C32E6'u),
uint64x2(hi: 0x9392EE8E921D5D07'u, lo: 0x3AFF322E62439FD0'u),
uint64x2(hi: 0xB877AA3236A4B449'u, lo: 0x09BEFEB9FAD487C3'u),
uint64x2(hi: 0xE69594BEC44DE15B'u, lo: 0x4C2EBE687989A9B4'u),
uint64x2(hi: 0x901D7CF73AB0ACD9'u, lo: 0x0F9D37014BF60A11'u),
uint64x2(hi: 0xB424DC35095CD80F'u, lo: 0x538484C19EF38C95'u),
uint64x2(hi: 0xE12E13424BB40E13'u, lo: 0x2865A5F206B06FBA'u),
uint64x2(hi: 0x8CBCCC096F5088CB'u, lo: 0xF93F87B7442E45D4'u),
uint64x2(hi: 0xAFEBFF0BCB24AAFE'u, lo: 0xF78F69A51539D749'u),
uint64x2(hi: 0xDBE6FECEBDEDD5BE'u, lo: 0xB573440E5A884D1C'u),
uint64x2(hi: 0x89705F4136B4A597'u, lo: 0x31680A88F8953031'u),
uint64x2(hi: 0xABCC77118461CEFC'u, lo: 0xFDC20D2B36BA7C3E'u),
uint64x2(hi: 0xD6BF94D5E57A42BC'u, lo: 0x3D32907604691B4D'u),
uint64x2(hi: 0x8637BD05AF6C69B5'u, lo: 0xA63F9A49C2C1B110'u),
uint64x2(hi: 0xA7C5AC471B478423'u, lo: 0x0FCF80DC33721D54'u),
uint64x2(hi: 0xD1B71758E219652B'u, lo: 0xD3C36113404EA4A9'u),
uint64x2(hi: 0x83126E978D4FDF3B'u, lo: 0x645A1CAC083126EA'u),
uint64x2(hi: 0xA3D70A3D70A3D70A'u, lo: 0x3D70A3D70A3D70A4'u),
uint64x2(hi: 0xCCCCCCCCCCCCCCCC'u, lo: 0xCCCCCCCCCCCCCCCD'u),
uint64x2(hi: 0x8000000000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xA000000000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xC800000000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xFA00000000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x9C40000000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xC350000000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xF424000000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x9896800000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xBEBC200000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xEE6B280000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x9502F90000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xBA43B74000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xE8D4A51000000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x9184E72A00000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xB5E620F480000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xE35FA931A0000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x8E1BC9BF04000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xB1A2BC2EC5000000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xDE0B6B3A76400000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x8AC7230489E80000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xAD78EBC5AC620000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xD8D726B7177A8000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x878678326EAC9000'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xA968163F0A57B400'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xD3C21BCECCEDA100'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x84595161401484A0'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xA56FA5B99019A5C8'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0xCECB8F27F4200F3A'u, lo: 0x0000000000000000'u),
uint64x2(hi: 0x813F3978F8940984'u, lo: 0x4000000000000000'u),
uint64x2(hi: 0xA18F07D736B90BE5'u, lo: 0x5000000000000000'u),
uint64x2(hi: 0xC9F2C9CD04674EDE'u, lo: 0xA400000000000000'u),
uint64x2(hi: 0xFC6F7C4045812296'u, lo: 0x4D00000000000000'u),
uint64x2(hi: 0x9DC5ADA82B70B59D'u, lo: 0xF020000000000000'u),
uint64x2(hi: 0xC5371912364CE305'u, lo: 0x6C28000000000000'u),
uint64x2(hi: 0xF684DF56C3E01BC6'u, lo: 0xC732000000000000'u),
uint64x2(hi: 0x9A130B963A6C115C'u, lo: 0x3C7F400000000000'u),
uint64x2(hi: 0xC097CE7BC90715B3'u, lo: 0x4B9F100000000000'u),
uint64x2(hi: 0xF0BDC21ABB48DB20'u, lo: 0x1E86D40000000000'u),
uint64x2(hi: 0x96769950B50D88F4'u, lo: 0x1314448000000000'u),
uint64x2(hi: 0xBC143FA4E250EB31'u, lo: 0x17D955A000000000'u),
uint64x2(hi: 0xEB194F8E1AE525FD'u, lo: 0x5DCFAB0800000000'u),
uint64x2(hi: 0x92EFD1B8D0CF37BE'u, lo: 0x5AA1CAE500000000'u),
uint64x2(hi: 0xB7ABC627050305AD'u, lo: 0xF14A3D9E40000000'u),
uint64x2(hi: 0xE596B7B0C643C719'u, lo: 0x6D9CCD05D0000000'u),
uint64x2(hi: 0x8F7E32CE7BEA5C6F'u, lo: 0xE4820023A2000000'u),
uint64x2(hi: 0xB35DBF821AE4F38B'u, lo: 0xDDA2802C8A800000'u),
uint64x2(hi: 0xE0352F62A19E306E'u, lo: 0xD50B2037AD200000'u),
uint64x2(hi: 0x8C213D9DA502DE45'u, lo: 0x4526F422CC340000'u),
uint64x2(hi: 0xAF298D050E4395D6'u, lo: 0x9670B12B7F410000'u),
uint64x2(hi: 0xDAF3F04651D47B4C'u, lo: 0x3C0CDD765F114000'u),
uint64x2(hi: 0x88D8762BF324CD0F'u, lo: 0xA5880A69FB6AC800'u),
uint64x2(hi: 0xAB0E93B6EFEE0053'u, lo: 0x8EEA0D047A457A00'u),
uint64x2(hi: 0xD5D238A4ABE98068'u, lo: 0x72A4904598D6D880'u),
uint64x2(hi: 0x85A36366EB71F041'u, lo: 0x47A6DA2B7F864750'u),
uint64x2(hi: 0xA70C3C40A64E6C51'u, lo: 0x999090B65F67D924'u),
uint64x2(hi: 0xD0CF4B50CFE20765'u, lo: 0xFFF4B4E3F741CF6D'u),
uint64x2(hi: 0x82818F1281ED449F'u, lo: 0xBFF8F10E7A8921A4'u),
uint64x2(hi: 0xA321F2D7226895C7'u, lo: 0xAFF72D52192B6A0D'u),
uint64x2(hi: 0xCBEA6F8CEB02BB39'u, lo: 0x9BF4F8A69F764490'u),
uint64x2(hi: 0xFEE50B7025C36A08'u, lo: 0x02F236D04753D5B4'u),
uint64x2(hi: 0x9F4F2726179A2245'u, lo: 0x01D762422C946590'u),
uint64x2(hi: 0xC722F0EF9D80AAD6'u, lo: 0x424D3AD2B7B97EF5'u),
uint64x2(hi: 0xF8EBAD2B84E0D58B'u, lo: 0xD2E0898765A7DEB2'u),
uint64x2(hi: 0x9B934C3B330C8577'u, lo: 0x63CC55F49F88EB2F'u),
uint64x2(hi: 0xC2781F49FFCFA6D5'u, lo: 0x3CBF6B71C76B25FB'u),
uint64x2(hi: 0xF316271C7FC3908A'u, lo: 0x8BEF464E3945EF7A'u),
uint64x2(hi: 0x97EDD871CFDA3A56'u, lo: 0x97758BF0E3CBB5AC'u),
uint64x2(hi: 0xBDE94E8E43D0C8EC'u, lo: 0x3D52EEED1CBEA317'u),
uint64x2(hi: 0xED63A231D4C4FB27'u, lo: 0x4CA7AAA863EE4BDD'u),
uint64x2(hi: 0x945E455F24FB1CF8'u, lo: 0x8FE8CAA93E74EF6A'u),
uint64x2(hi: 0xB975D6B6EE39E436'u, lo: 0xB3E2FD538E122B44'u),
uint64x2(hi: 0xE7D34C64A9C85D44'u, lo: 0x60DBBCA87196B616'u),
uint64x2(hi: 0x90E40FBEEA1D3A4A'u, lo: 0xBC8955E946FE31CD'u),
uint64x2(hi: 0xB51D13AEA4A488DD'u, lo: 0x6BABAB6398BDBE41'u),
uint64x2(hi: 0xE264589A4DCDAB14'u, lo: 0xC696963C7EED2DD1'u),
uint64x2(hi: 0x8D7EB76070A08AEC'u, lo: 0xFC1E1DE5CF543CA2'u),
uint64x2(hi: 0xB0DE65388CC8ADA8'u, lo: 0x3B25A55F43294BCB'u),
uint64x2(hi: 0xDD15FE86AFFAD912'u, lo: 0x49EF0EB713F39EBE'u),
uint64x2(hi: 0x8A2DBF142DFCC7AB'u, lo: 0x6E3569326C784337'u),
uint64x2(hi: 0xACB92ED9397BF996'u, lo: 0x49C2C37F07965404'u),
uint64x2(hi: 0xD7E77A8F87DAF7FB'u, lo: 0xDC33745EC97BE906'u),
uint64x2(hi: 0x86F0AC99B4E8DAFD'u, lo: 0x69A028BB3DED71A3'u),
uint64x2(hi: 0xA8ACD7C0222311BC'u, lo: 0xC40832EA0D68CE0C'u),
uint64x2(hi: 0xD2D80DB02AABD62B'u, lo: 0xF50A3FA490C30190'u),
uint64x2(hi: 0x83C7088E1AAB65DB'u, lo: 0x792667C6DA79E0FA'u),
uint64x2(hi: 0xA4B8CAB1A1563F52'u, lo: 0x577001B891185938'u),
uint64x2(hi: 0xCDE6FD5E09ABCF26'u, lo: 0xED4C0226B55E6F86'u),
uint64x2(hi: 0x80B05E5AC60B6178'u, lo: 0x544F8158315B05B4'u),
uint64x2(hi: 0xA0DC75F1778E39D6'u, lo: 0x696361AE3DB1C721'u),
uint64x2(hi: 0xC913936DD571C84C'u, lo: 0x03BC3A19CD1E38E9'u),
uint64x2(hi: 0xFB5878494ACE3A5F'u, lo: 0x04AB48A04065C723'u),
uint64x2(hi: 0x9D174B2DCEC0E47B'u, lo: 0x62EB0D64283F9C76'u),
uint64x2(hi: 0xC45D1DF942711D9A'u, lo: 0x3BA5D0BD324F8394'u),
uint64x2(hi: 0xF5746577930D6500'u, lo: 0xCA8F44EC7EE36479'u),
uint64x2(hi: 0x9968BF6ABBE85F20'u, lo: 0x7E998B13CF4E1ECB'u),
uint64x2(hi: 0xBFC2EF456AE276E8'u, lo: 0x9E3FEDD8C321A67E'u),
uint64x2(hi: 0xEFB3AB16C59B14A2'u, lo: 0xC5CFE94EF3EA101E'u),
uint64x2(hi: 0x95D04AEE3B80ECE5'u, lo: 0xBBA1F1D158724A12'u),
uint64x2(hi: 0xBB445DA9CA61281F'u, lo: 0x2A8A6E45AE8EDC97'u),
uint64x2(hi: 0xEA1575143CF97226'u, lo: 0xF52D09D71A3293BD'u),
uint64x2(hi: 0x924D692CA61BE758'u, lo: 0x593C2626705F9C56'u),
uint64x2(hi: 0xB6E0C377CFA2E12E'u, lo: 0x6F8B2FB00C77836C'u),
uint64x2(hi: 0xE498F455C38B997A'u, lo: 0x0B6DFB9C0F956447'u),
uint64x2(hi: 0x8EDF98B59A373FEC'u, lo: 0x4724BD4189BD5EAC'u),
uint64x2(hi: 0xB2977EE300C50FE7'u, lo: 0x58EDEC91EC2CB657'u),
uint64x2(hi: 0xDF3D5E9BC0F653E1'u, lo: 0x2F2967B66737E3ED'u),
uint64x2(hi: 0x8B865B215899F46C'u, lo: 0xBD79E0D20082EE74'u),
uint64x2(hi: 0xAE67F1E9AEC07187'u, lo: 0xECD8590680A3AA11'u),
uint64x2(hi: 0xDA01EE641A708DE9'u, lo: 0xE80E6F4820CC9495'u),
uint64x2(hi: 0x884134FE908658B2'u, lo: 0x3109058D147FDCDD'u),
uint64x2(hi: 0xAA51823E34A7EEDE'u, lo: 0xBD4B46F0599FD415'u),
uint64x2(hi: 0xD4E5E2CDC1D1EA96'u, lo: 0x6C9E18AC7007C91A'u),
uint64x2(hi: 0x850FADC09923329E'u, lo: 0x03E2CF6BC604DDB0'u),
uint64x2(hi: 0xA6539930BF6BFF45'u, lo: 0x84DB8346B786151C'u),
uint64x2(hi: 0xCFE87F7CEF46FF16'u, lo: 0xE612641865679A63'u),
uint64x2(hi: 0x81F14FAE158C5F6E'u, lo: 0x4FCB7E8F3F60C07E'u),
uint64x2(hi: 0xA26DA3999AEF7749'u, lo: 0xE3BE5E330F38F09D'u),
uint64x2(hi: 0xCB090C8001AB551C'u, lo: 0x5CADF5BFD3072CC5'u),
uint64x2(hi: 0xFDCB4FA002162A63'u, lo: 0x73D9732FC7C8F7F6'u),
uint64x2(hi: 0x9E9F11C4014DDA7E'u, lo: 0x2867E7FDDCDD9AFA'u),
uint64x2(hi: 0xC646D63501A1511D'u, lo: 0xB281E1FD541501B8'u),
uint64x2(hi: 0xF7D88BC24209A565'u, lo: 0x1F225A7CA91A4226'u),
uint64x2(hi: 0x9AE757596946075F'u, lo: 0x3375788DE9B06958'u),
uint64x2(hi: 0xC1A12D2FC3978937'u, lo: 0x0052D6B1641C83AE'u),
uint64x2(hi: 0xF209787BB47D6B84'u, lo: 0xC0678C5DBD23A49A'u),
uint64x2(hi: 0x9745EB4D50CE6332'u, lo: 0xF840B7BA963646E0'u),
uint64x2(hi: 0xBD176620A501FBFF'u, lo: 0xB650E5A93BC3D898'u),
uint64x2(hi: 0xEC5D3FA8CE427AFF'u, lo: 0xA3E51F138AB4CEBE'u),
uint64x2(hi: 0x93BA47C980E98CDF'u, lo: 0xC66F336C36B10137'u),
uint64x2(hi: 0xB8A8D9BBE123F017'u, lo: 0xB80B0047445D4184'u),
uint64x2(hi: 0xE6D3102AD96CEC1D'u, lo: 0xA60DC059157491E5'u),
uint64x2(hi: 0x9043EA1AC7E41392'u, lo: 0x87C89837AD68DB2F'u),
uint64x2(hi: 0xB454E4A179DD1877'u, lo: 0x29BABE4598C311FB'u),
uint64x2(hi: 0xE16A1DC9D8545E94'u, lo: 0xF4296DD6FEF3D67A'u),
uint64x2(hi: 0x8CE2529E2734BB1D'u, lo: 0x1899E4A65F58660C'u),
uint64x2(hi: 0xB01AE745B101E9E4'u, lo: 0x5EC05DCFF72E7F8F'u),
uint64x2(hi: 0xDC21A1171D42645D'u, lo: 0x76707543F4FA1F73'u),
uint64x2(hi: 0x899504AE72497EBA'u, lo: 0x6A06494A791C53A8'u),
uint64x2(hi: 0xABFA45DA0EDBDE69'u, lo: 0x0487DB9D17636892'u),
uint64x2(hi: 0xD6F8D7509292D603'u, lo: 0x45A9D2845D3C42B6'u),
uint64x2(hi: 0x865B86925B9BC5C2'u, lo: 0x0B8A2392BA45A9B2'u),
uint64x2(hi: 0xA7F26836F282B732'u, lo: 0x8E6CAC7768D7141E'u),
uint64x2(hi: 0xD1EF0244AF2364FF'u, lo: 0x3207D795430CD926'u),
uint64x2(hi: 0x8335616AED761F1F'u, lo: 0x7F44E6BD49E807B8'u),
uint64x2(hi: 0xA402B9C5A8D3A6E7'u, lo: 0x5F16206C9C6209A6'u),
uint64x2(hi: 0xCD036837130890A1'u, lo: 0x36DBA887C37A8C0F'u),
uint64x2(hi: 0x802221226BE55A64'u, lo: 0xC2494954DA2C9789'u),
uint64x2(hi: 0xA02AA96B06DEB0FD'u, lo: 0xF2DB9BAA10B7BD6C'u),
uint64x2(hi: 0xC83553C5C8965D3D'u, lo: 0x6F92829494E5ACC7'u),
uint64x2(hi: 0xFA42A8B73ABBF48C'u, lo: 0xCB772339BA1F17F9'u),
uint64x2(hi: 0x9C69A97284B578D7'u, lo: 0xFF2A760414536EFB'u),
uint64x2(hi: 0xC38413CF25E2D70D'u, lo: 0xFEF5138519684ABA'u),
uint64x2(hi: 0xF46518C2EF5B8CD1'u, lo: 0x7EB258665FC25D69'u),
uint64x2(hi: 0x98BF2F79D5993802'u, lo: 0xEF2F773FFBD97A61'u),
uint64x2(hi: 0xBEEEFB584AFF8603'u, lo: 0xAAFB550FFACFD8FA'u),
uint64x2(hi: 0xEEAABA2E5DBF6784'u, lo: 0x95BA2A53F983CF38'u),
uint64x2(hi: 0x952AB45CFA97A0B2'u, lo: 0xDD945A747BF26183'u),
uint64x2(hi: 0xBA756174393D88DF'u, lo: 0x94F971119AEEF9E4'u),
uint64x2(hi: 0xE912B9D1478CEB17'u, lo: 0x7A37CD5601AAB85D'u),
uint64x2(hi: 0x91ABB422CCB812EE'u, lo: 0xAC62E055C10AB33A'u),
uint64x2(hi: 0xB616A12B7FE617AA'u, lo: 0x577B986B314D6009'u),
uint64x2(hi: 0xE39C49765FDF9D94'u, lo: 0xED5A7E85FDA0B80B'u),
uint64x2(hi: 0x8E41ADE9FBEBC27D'u, lo: 0x14588F13BE847307'u),
uint64x2(hi: 0xB1D219647AE6B31C'u, lo: 0x596EB2D8AE258FC8'u),
uint64x2(hi: 0xDE469FBD99A05FE3'u, lo: 0x6FCA5F8ED9AEF3BB'u),
uint64x2(hi: 0x8AEC23D680043BEE'u, lo: 0x25DE7BB9480D5854'u),
uint64x2(hi: 0xADA72CCC20054AE9'u, lo: 0xAF561AA79A10AE6A'u),
uint64x2(hi: 0xD910F7FF28069DA4'u, lo: 0x1B2BA1518094DA04'u),
uint64x2(hi: 0x87AA9AFF79042286'u, lo: 0x90FB44D2F05D0842'u),
uint64x2(hi: 0xA99541BF57452B28'u, lo: 0x353A1607AC744A53'u),
uint64x2(hi: 0xD3FA922F2D1675F2'u, lo: 0x42889B8997915CE8'u),
uint64x2(hi: 0x847C9B5D7C2E09B7'u, lo: 0x69956135FEBADA11'u),
uint64x2(hi: 0xA59BC234DB398C25'u, lo: 0x43FAB9837E699095'u),
uint64x2(hi: 0xCF02B2C21207EF2E'u, lo: 0x94F967E45E03F4BB'u),
uint64x2(hi: 0x8161AFB94B44F57D'u, lo: 0x1D1BE0EEBAC278F5'u),
uint64x2(hi: 0xA1BA1BA79E1632DC'u, lo: 0x6462D92A69731732'u),
uint64x2(hi: 0xCA28A291859BBF93'u, lo: 0x7D7B8F7503CFDCFE'u),
uint64x2(hi: 0xFCB2CB35E702AF78'u, lo: 0x5CDA735244C3D43E'u),
uint64x2(hi: 0x9DEFBF01B061ADAB'u, lo: 0x3A0888136AFA64A7'u),
uint64x2(hi: 0xC56BAEC21C7A1916'u, lo: 0x088AAA1845B8FDD0'u),
uint64x2(hi: 0xF6C69A72A3989F5B'u, lo: 0x8AAD549E57273D45'u),
uint64x2(hi: 0x9A3C2087A63F6399'u, lo: 0x36AC54E2F678864B'u),
uint64x2(hi: 0xC0CB28A98FCF3C7F'u, lo: 0x84576A1BB416A7DD'u),
uint64x2(hi: 0xF0FDF2D3F3C30B9F'u, lo: 0x656D44A2A11C51D5'u),
uint64x2(hi: 0x969EB7C47859E743'u, lo: 0x9F644AE5A4B1B325'u),
uint64x2(hi: 0xBC4665B596706114'u, lo: 0x873D5D9F0DDE1FEE'u),
uint64x2(hi: 0xEB57FF22FC0C7959'u, lo: 0xA90CB506D155A7EA'u),
uint64x2(hi: 0x9316FF75DD87CBD8'u, lo: 0x09A7F12442D588F2'u),
uint64x2(hi: 0xB7DCBF5354E9BECE'u, lo: 0x0C11ED6D538AEB2F'u),
uint64x2(hi: 0xE5D3EF282A242E81'u, lo: 0x8F1668C8A86DA5FA'u),
uint64x2(hi: 0x8FA475791A569D10'u, lo: 0xF96E017D694487BC'u),
uint64x2(hi: 0xB38D92D760EC4455'u, lo: 0x37C981DCC395A9AC'u),
uint64x2(hi: 0xE070F78D3927556A'u, lo: 0x85BBE253F47B1417'u),
uint64x2(hi: 0x8C469AB843B89562'u, lo: 0x93956D7478CCEC8E'u),
uint64x2(hi: 0xAF58416654A6BABB'u, lo: 0x387AC8D1970027B2'u),
uint64x2(hi: 0xDB2E51BFE9D0696A'u, lo: 0x06997B05FCC0319E'u),
uint64x2(hi: 0x88FCF317F22241E2'u, lo: 0x441FECE3BDF81F03'u),
uint64x2(hi: 0xAB3C2FDDEEAAD25A'u, lo: 0xD527E81CAD7626C3'u),
uint64x2(hi: 0xD60B3BD56A5586F1'u, lo: 0x8A71E223D8D3B074'u),
uint64x2(hi: 0x85C7056562757456'u, lo: 0xF6872D5667844E49'u),
uint64x2(hi: 0xA738C6BEBB12D16C'u, lo: 0xB428F8AC016561DB'u),
uint64x2(hi: 0xD106F86E69D785C7'u, lo: 0xE13336D701BEBA52'u),
uint64x2(hi: 0x82A45B450226B39C'u, lo: 0xECC0024661173473'u),
uint64x2(hi: 0xA34D721642B06084'u, lo: 0x27F002D7F95D0190'u),
uint64x2(hi: 0xCC20CE9BD35C78A5'u, lo: 0x31EC038DF7B441F4'u),
uint64x2(hi: 0xFF290242C83396CE'u, lo: 0x7E67047175A15271'u),
uint64x2(hi: 0x9F79A169BD203E41'u, lo: 0x0F0062C6E984D386'u),
uint64x2(hi: 0xC75809C42C684DD1'u, lo: 0x52C07B78A3E60868'u),
uint64x2(hi: 0xF92E0C3537826145'u, lo: 0xA7709A56CCDF8A82'u),
uint64x2(hi: 0x9BBCC7A142B17CCB'u, lo: 0x88A66076400BB691'u),
uint64x2(hi: 0xC2ABF989935DDBFE'u, lo: 0x6ACFF893D00EA435'u),
uint64x2(hi: 0xF356F7EBF83552FE'u, lo: 0x0583F6B8C4124D43'u),
uint64x2(hi: 0x98165AF37B2153DE'u, lo: 0xC3727A337A8B704A'u),
uint64x2(hi: 0xBE1BF1B059E9A8D6'u, lo: 0x744F18C0592E4C5C'u),
uint64x2(hi: 0xEDA2EE1C7064130C'u, lo: 0x1162DEF06F79DF73'u),
uint64x2(hi: 0x9485D4D1C63E8BE7'u, lo: 0x8ADDCB5645AC2BA8'u),
uint64x2(hi: 0xB9A74A0637CE2EE1'u, lo: 0x6D953E2BD7173692'u),
uint64x2(hi: 0xE8111C87C5C1BA99'u, lo: 0xC8FA8DB6CCDD0437'u),
uint64x2(hi: 0x910AB1D4DB9914A0'u, lo: 0x1D9C9892400A22A2'u),
uint64x2(hi: 0xB54D5E4A127F59C8'u, lo: 0x2503BEB6D00CAB4B'u),
uint64x2(hi: 0xE2A0B5DC971F303A'u, lo: 0x2E44AE64840FD61D'u),
uint64x2(hi: 0x8DA471A9DE737E24'u, lo: 0x5CEAECFED289E5D2'u),
uint64x2(hi: 0xB10D8E1456105DAD'u, lo: 0x7425A83E872C5F47'u),
uint64x2(hi: 0xDD50F1996B947518'u, lo: 0xD12F124E28F77719'u),
uint64x2(hi: 0x8A5296FFE33CC92F'u, lo: 0x82BD6B70D99AAA6F'u),
uint64x2(hi: 0xACE73CBFDC0BFB7B'u, lo: 0x636CC64D1001550B'u),
uint64x2(hi: 0xD8210BEFD30EFA5A'u, lo: 0x3C47F7E05401AA4E'u),
uint64x2(hi: 0x8714A775E3E95C78'u, lo: 0x65ACFAEC34810A71'u),
uint64x2(hi: 0xA8D9D1535CE3B396'u, lo: 0x7F1839A741A14D0D'u),
uint64x2(hi: 0xD31045A8341CA07C'u, lo: 0x1EDE48111209A050'u),
uint64x2(hi: 0x83EA2B892091E44D'u, lo: 0x934AED0AAB460432'u),
uint64x2(hi: 0xA4E4B66B68B65D60'u, lo: 0xF81DA84D5617853F'u),
uint64x2(hi: 0xCE1DE40642E3F4B9'u, lo: 0x36251260AB9D668E'u),
uint64x2(hi: 0x80D2AE83E9CE78F3'u, lo: 0xC1D72B7C6B426019'u),
uint64x2(hi: 0xA1075A24E4421730'u, lo: 0xB24CF65B8612F81F'u),
uint64x2(hi: 0xC94930AE1D529CFC'u, lo: 0xDEE033F26797B627'u),
uint64x2(hi: 0xFB9B7CD9A4A7443C'u, lo: 0x169840EF017DA3B1'u),
uint64x2(hi: 0x9D412E0806E88AA5'u, lo: 0x8E1F289560EE864E'u),
uint64x2(hi: 0xC491798A08A2AD4E'u, lo: 0xF1A6F2BAB92A27E2'u),
uint64x2(hi: 0xF5B5D7EC8ACB58A2'u, lo: 0xAE10AF696774B1DB'u),
uint64x2(hi: 0x9991A6F3D6BF1765'u, lo: 0xACCA6DA1E0A8EF29'u),
uint64x2(hi: 0xBFF610B0CC6EDD3F'u, lo: 0x17FD090A58D32AF3'u),
uint64x2(hi: 0xEFF394DCFF8A948E'u, lo: 0xDDFC4B4CEF07F5B0'u),
uint64x2(hi: 0x95F83D0A1FB69CD9'u, lo: 0x4ABDAF101564F98E'u),
uint64x2(hi: 0xBB764C4CA7A4440F'u, lo: 0x9D6D1AD41ABE37F1'u),
uint64x2(hi: 0xEA53DF5FD18D5513'u, lo: 0x84C86189216DC5ED'u),
uint64x2(hi: 0x92746B9BE2F8552C'u, lo: 0x32FD3CF5B4E49BB4'u),
uint64x2(hi: 0xB7118682DBB66A77'u, lo: 0x3FBC8C33221DC2A1'u),
uint64x2(hi: 0xE4D5E82392A40515'u, lo: 0x0FABAF3FEAA5334A'u),
uint64x2(hi: 0x8F05B1163BA6832D'u, lo: 0x29CB4D87F2A7400E'u),
uint64x2(hi: 0xB2C71D5BCA9023F8'u, lo: 0x743E20E9EF511012'u),
uint64x2(hi: 0xDF78E4B2BD342CF6'u, lo: 0x914DA9246B255416'u),
uint64x2(hi: 0x8BAB8EEFB6409C1A'u, lo: 0x1AD089B6C2F7548E'u),
uint64x2(hi: 0xAE9672ABA3D0C320'u, lo: 0xA184AC2473B529B1'u),
uint64x2(hi: 0xDA3C0F568CC4F3E8'u, lo: 0xC9E5D72D90A2741E'u),
uint64x2(hi: 0x8865899617FB1871'u, lo: 0x7E2FA67C7A658892'u),
uint64x2(hi: 0xAA7EEBFB9DF9DE8D'u, lo: 0xDDBB901B98FEEAB7'u),
uint64x2(hi: 0xD51EA6FA85785631'u, lo: 0x552A74227F3EA565'u),
uint64x2(hi: 0x8533285C936B35DE'u, lo: 0xD53A88958F87275F'u),
uint64x2(hi: 0xA67FF273B8460356'u, lo: 0x8A892ABAF368F137'u),
uint64x2(hi: 0xD01FEF10A657842C'u, lo: 0x2D2B7569B0432D85'u),
uint64x2(hi: 0x8213F56A67F6B29B'u, lo: 0x9C3B29620E29FC73'u),
uint64x2(hi: 0xA298F2C501F45F42'u, lo: 0x8349F3BA91B47B8F'u),
uint64x2(hi: 0xCB3F2F7642717713'u, lo: 0x241C70A936219A73'u),
uint64x2(hi: 0xFE0EFB53D30DD4D7'u, lo: 0xED238CD383AA0110'u),
uint64x2(hi: 0x9EC95D1463E8A506'u, lo: 0xF4363804324A40AA'u),
uint64x2(hi: 0xC67BB4597CE2CE48'u, lo: 0xB143C6053EDCD0D5'u),
uint64x2(hi: 0xF81AA16FDC1B81DA'u, lo: 0xDD94B7868E94050A'u),
uint64x2(hi: 0x9B10A4E5E9913128'u, lo: 0xCA7CF2B4191C8326'u),
uint64x2(hi: 0xC1D4CE1F63F57D72'u, lo: 0xFD1C2F611F63A3F0'u),
uint64x2(hi: 0xF24A01A73CF2DCCF'u, lo: 0xBC633B39673C8CEC'u),
uint64x2(hi: 0x976E41088617CA01'u, lo: 0xD5BE0503E085D813'u),
uint64x2(hi: 0xBD49D14AA79DBC82'u, lo: 0x4B2D8644D8A74E18'u),
uint64x2(hi: 0xEC9C459D51852BA2'u, lo: 0xDDF8E7D60ED1219E'u),
uint64x2(hi: 0x93E1AB8252F33B45'u, lo: 0xCABB90E5C942B503'u),
uint64x2(hi: 0xB8DA1662E7B00A17'u, lo: 0x3D6A751F3B936243'u),
uint64x2(hi: 0xE7109BFBA19C0C9D'u, lo: 0x0CC512670A783AD4'u),
uint64x2(hi: 0x906A617D450187E2'u, lo: 0x27FB2B80668B24C5'u),
uint64x2(hi: 0xB484F9DC9641E9DA'u, lo: 0xB1F9F660802DEDF6'u),
uint64x2(hi: 0xE1A63853BBD26451'u, lo: 0x5E7873F8A0396973'u),
uint64x2(hi: 0x8D07E33455637EB2'u, lo: 0xDB0B487B6423E1E8'u),
uint64x2(hi: 0xB049DC016ABC5E5F'u, lo: 0x91CE1A9A3D2CDA62'u),
uint64x2(hi: 0xDC5C5301C56B75F7'u, lo: 0x7641A140CC7810FB'u),
uint64x2(hi: 0x89B9B3E11B6329BA'u, lo: 0xA9E904C87FCB0A9D'u),
uint64x2(hi: 0xAC2820D9623BF429'u, lo: 0x546345FA9FBDCD44'u),
uint64x2(hi: 0xD732290FBACAF133'u, lo: 0xA97C177947AD4095'u),
uint64x2(hi: 0x867F59A9D4BED6C0'u, lo: 0x49ED8EABCCCC485D'u),
uint64x2(hi: 0xA81F301449EE8C70'u, lo: 0x5C68F256BFFF5A74'u),
uint64x2(hi: 0xD226FC195C6A2F8C'u, lo: 0x73832EEC6FFF3111'u),
uint64x2(hi: 0x83585D8FD9C25DB7'u, lo: 0xC831FD53C5FF7EAB'u),
uint64x2(hi: 0xA42E74F3D032F525'u, lo: 0xBA3E7CA8B77F5E55'u),
uint64x2(hi: 0xCD3A1230C43FB26F'u, lo: 0x28CE1BD2E55F35EB'u),
uint64x2(hi: 0x80444B5E7AA7CF85'u, lo: 0x7980D163CF5B81B3'u),
uint64x2(hi: 0xA0555E361951C366'u, lo: 0xD7E105BCC332621F'u),
uint64x2(hi: 0xC86AB5C39FA63440'u, lo: 0x8DD9472BF3FEFAA7'u),
uint64x2(hi: 0xFA856334878FC150'u, lo: 0xB14F98F6F0FEB951'u),
uint64x2(hi: 0x9C935E00D4B9D8D2'u, lo: 0x6ED1BF9A569F33D3'u),
uint64x2(hi: 0xC3B8358109E84F07'u, lo: 0x0A862F80EC4700C8'u),
uint64x2(hi: 0xF4A642E14C6262C8'u, lo: 0xCD27BB612758C0FA'u),
uint64x2(hi: 0x98E7E9CCCFBD7DBD'u, lo: 0x8038D51CB897789C'u),
uint64x2(hi: 0xBF21E44003ACDD2C'u, lo: 0xE0470A63E6BD56C3'u),
uint64x2(hi: 0xEEEA5D5004981478'u, lo: 0x1858CCFCE06CAC74'u),
uint64x2(hi: 0x95527A5202DF0CCB'u, lo: 0x0F37801E0C43EBC8'u),
uint64x2(hi: 0xBAA718E68396CFFD'u, lo: 0xD30560258F54E6BA'u),
uint64x2(hi: 0xE950DF20247C83FD'u, lo: 0x47C6B82EF32A2069'u),
uint64x2(hi: 0x91D28B7416CDD27E'u, lo: 0x4CDC331D57FA5441'u),
uint64x2(hi: 0xB6472E511C81471D'u, lo: 0xE0133FE4ADF8E952'u),
uint64x2(hi: 0xE3D8F9E563A198E5'u, lo: 0x58180FDDD97723A6'u),
uint64x2(hi: 0x8E679C2F5E44FF8F'u, lo: 0x570F09EAA7EA7648'u),
uint64x2(hi: 0xB201833B35D63F73'u, lo: 0x2CD2CC6551E513DA'u),
uint64x2(hi: 0xDE81E40A034BCF4F'u, lo: 0xF8077F7EA65E58D1'u),
uint64x2(hi: 0x8B112E86420F6191'u, lo: 0xFB04AFAF27FAF782'u),
uint64x2(hi: 0xADD57A27D29339F6'u, lo: 0x79C5DB9AF1F9B563'u),
uint64x2(hi: 0xD94AD8B1C7380874'u, lo: 0x18375281AE7822BC'u),
uint64x2(hi: 0x87CEC76F1C830548'u, lo: 0x8F2293910D0B15B5'u),
uint64x2(hi: 0xA9C2794AE3A3C69A'u, lo: 0xB2EB3875504DDB22'u),
uint64x2(hi: 0xD433179D9C8CB841'u, lo: 0x5FA60692A46151EB'u),
uint64x2(hi: 0x849FEEC281D7F328'u, lo: 0xDBC7C41BA6BCD333'u),
uint64x2(hi: 0xA5C7EA73224DEFF3'u, lo: 0x12B9B522906C0800'u),
uint64x2(hi: 0xCF39E50FEAE16BEF'u, lo: 0xD768226B34870A00'u),
uint64x2(hi: 0x81842F29F2CCE375'u, lo: 0xE6A1158300D46640'u),
uint64x2(hi: 0xA1E53AF46F801C53'u, lo: 0x60495AE3C1097FD0'u),
uint64x2(hi: 0xCA5E89B18B602368'u, lo: 0x385BB19CB14BDFC4'u),
uint64x2(hi: 0xFCF62C1DEE382C42'u, lo: 0x46729E03DD9ED7B5'u),
uint64x2(hi: 0x9E19DB92B4E31BA9'u, lo: 0x6C07A2C26A8346D1'u),
uint64x2(hi: 0xC5A05277621BE293'u, lo: 0xC7098B7305241885'u),
uint64x2(hi: 0xF70867153AA2DB38'u, lo: 0xB8CBEE4FC66D1EA7'u)]
dragonbox_Assert(k >= kMin)
dragonbox_Assert(k <= kMax)
return pow10[k - kMin]
## Returns whether value is divisible by 2^e2
proc multipleOfPow2*(value: uint64; e2: int32): bool {.inline.} =
dragonbox_Assert(e2 >= 0)
return e2 < 64 and (value and ((uint64(1) shl e2) - 1)) == 0
## Returns whether value is divisible by 5^e5
proc multipleOfPow5*(value: uint64; e5: int32): bool {.inline.} =
type
MulCmp {.bycopy.} = object
mul: uint64
cmp: uint64
const
mod5 = [MulCmp(mul: 0x0000000000000001'u, cmp: 0xFFFFFFFFFFFFFFFF'u),
MulCmp(mul: 0xCCCCCCCCCCCCCCCD'u, cmp: 0x3333333333333333'u),
MulCmp(mul: 0x8F5C28F5C28F5C29'u, cmp: 0x0A3D70A3D70A3D70'u),
MulCmp(mul: 0x1CAC083126E978D5'u, cmp: 0x020C49BA5E353F7C'u),
MulCmp(mul: 0xD288CE703AFB7E91'u, cmp: 0x0068DB8BAC710CB2'u),
MulCmp(mul: 0x5D4E8FB00BCBE61D'u, cmp: 0x0014F8B588E368F0'u),
MulCmp(mul: 0x790FB65668C26139'u, cmp: 0x000431BDE82D7B63'u),
MulCmp(mul: 0xE5032477AE8D46A5'u, cmp: 0x0000D6BF94D5E57A'u),
MulCmp(mul: 0xC767074B22E90E21'u, cmp: 0x00002AF31DC46118'u),
MulCmp(mul: 0x8E47CE423A2E9C6D'u, cmp: 0x0000089705F4136B'u),
MulCmp(mul: 0x4FA7F60D3ED61F49'u, cmp: 0x000001B7CDFD9D7B'u),
MulCmp(mul: 0x0FEE64690C913975'u, cmp: 0x00000057F5FF85E5'u),
MulCmp(mul: 0x3662E0E1CF503EB1'u, cmp: 0x000000119799812D'u),
MulCmp(mul: 0xA47A2CF9F6433FBD'u, cmp: 0x0000000384B84D09'u),
MulCmp(mul: 0x54186F653140A659'u, cmp: 0x00000000B424DC35'u),
MulCmp(mul: 0x7738164770402145'u, cmp: 0x0000000024075F3D'u),
MulCmp(mul: 0xE4A4D1417CD9A041'u, cmp: 0x000000000734ACA5'u),
MulCmp(mul: 0xC75429D9E5C5200D'u, cmp: 0x000000000170EF54'u),
MulCmp(mul: 0xC1773B91FAC10669'u, cmp: 0x000000000049C977'u),
MulCmp(mul: 0x26B172506559CE15'u, cmp: 0x00000000000EC1E4'u),
MulCmp(mul: 0xD489E3A9ADDEC2D1'u, cmp: 0x000000000002F394'u),
MulCmp(mul: 0x90E860BB892C8D5D'u, cmp: 0x000000000000971D'u),
MulCmp(mul: 0x502E79BF1B6F4F79'u, cmp: 0x0000000000001E39'u),
MulCmp(mul: 0xDCD618596BE30FE5'u, cmp: 0x000000000000060B'u),
MulCmp(mul: 0x2C2AD1AB7BFA3661'u, cmp: 0x0000000000000135'u)]
dragonbox_Assert(e5 >= 0)
dragonbox_Assert(e5 <= 24)
let m5: MulCmp = mod5[e5]
return value * m5.mul <= m5.cmp
type
FloatingDecimal64* {.bycopy.} = object
significand*: uint64
exponent*: int32
proc toDecimal64AsymmetricInterval*(e2: int32): FloatingDecimal64 {.inline.} =
## NB:
## accept_lower_endpoint = true
## accept_upper_endpoint = true
const
P: int32 = significandSize
## Compute k and beta
let minusK: int32 = floorLog10ThreeQuartersPow2(e2)
let betaMinus1: int32 = e2 + floorLog2Pow10(-minusK)
## Compute xi and zi
let pow10: uint64x2 = computePow10(-minusK)
let lowerEndpoint: uint64 = (pow10.hi - (pow10.hi shr (P + 1))) shr
(64 - P - betaMinus1)
let upperEndpoint: uint64 = (pow10.hi + (pow10.hi shr (P + 0))) shr
(64 - P - betaMinus1)
## If we don't accept the left endpoint (but we do!) or
## if the left endpoint is not an integer, increase it
let lowerEndpointIsInteger: bool = (2 <= e2 and e2 <= 3)
let xi: uint64 = lowerEndpoint + uint64(not lowerEndpointIsInteger)
let zi: uint64 = upperEndpoint
## Try bigger divisor
var q: uint64 = zi div 10
if q * 10 >= xi:
return FloatingDecimal64(significand: q, exponent: minusK + 1)
q = ((pow10.hi shr (64 - (P + 1) - betaMinus1)) + 1) div 2
## When tie occurs, choose one of them according to the rule
if e2 == -77:
dec(q, ord(q mod 2 != 0))
## Round to even.
else:
inc(q, ord(q < xi))
return FloatingDecimal64(significand: q, exponent: minusK)
proc computeDelta*(pow10: uint64x2; betaMinus1: int32): uint32 {.inline.} =
dragonbox_Assert(betaMinus1 >= 0)
dragonbox_Assert(betaMinus1 <= 63)
return cast[uint32](pow10.hi shr (64 - 1 - betaMinus1))
when defined(sizeof_Int128):
proc mul128*(x: uint64; y: uint64): uint64x2 {.inline.} =
## 1 mulx
type
uint128T = uint128
let p: uint128T = uint128T(x) * y
let hi: uint64 = cast[uint64](p shr 64)
let lo: uint64 = cast[uint64](p)
return (hi, lo)
elif defined(vcc) and defined(cpu64):
proc umul128(x, y: uint64, z: ptr uint64): uint64 {.importc: "_umul128", header: "<intrin.h>".}
proc mul128*(x: uint64; y: uint64): uint64x2 {.inline.} =
var hi: uint64 = 0
var lo: uint64 = umul128(x, y, addr(hi))
return uint64x2(hi: hi, lo: lo)
else:
proc lo32*(x: uint64): uint32 {.inline.} =
return cast[uint32](x)
proc hi32*(x: uint64): uint32 {.inline.} =
return cast[uint32](x shr 32)
proc mul128*(a: uint64; b: uint64): uint64x2 {.inline.} =
let b00: uint64 = uint64(lo32(a)) * lo32(b)
let b01: uint64 = uint64(lo32(a)) * hi32(b)
let b10: uint64 = uint64(hi32(a)) * lo32(b)
let b11: uint64 = uint64(hi32(a)) * hi32(b)
let mid1: uint64 = b10 + hi32(b00)
let mid2: uint64 = b01 + lo32(mid1)
let hi: uint64 = b11 + hi32(mid1) + hi32(mid2)
let lo: uint64 = lo32(b00) or uint64(lo32(mid2)) shl 32
return uint64x2(hi: hi, lo: lo)
## Returns (x * y) / 2^128
proc mulShift*(x: uint64; y: uint64x2): uint64 {.inline.} =
## 2 mulx
var p1: uint64x2 = mul128(x, y.hi)
var p0: uint64x2 = mul128(x, y.lo)
p1.lo += p0.hi
inc(p1.hi, ord(p1.lo < p0.hi))
return p1.hi
proc mulParity*(twoF: uint64; pow10: uint64x2; betaMinus1: int32): bool {.inline.} =
## 1 mulx, 1 mul
dragonbox_Assert(betaMinus1 >= 1)
dragonbox_Assert(betaMinus1 <= 63)
let p01: uint64 = twoF * pow10.hi
let p10: uint64 = mul128(twoF, pow10.lo).hi
let mid: uint64 = p01 + p10
return (mid and (uint64(1) shl (64 - betaMinus1))) != 0
proc isIntegralEndpoint*(twoF: uint64; e2: int32; minusK: int32): bool {.inline.} =
if e2 < -2:
return false
if e2 <= 9:
return true
if e2 <= 86:
return multipleOfPow5(twoF, minusK)
return false
proc isIntegralMidpoint*(twoF: uint64; e2: int32; minusK: int32): bool {.inline.} =
if e2 < -4:
return multipleOfPow2(twoF, minusK - e2 + 1)
if e2 <= 9:
return true
if e2 <= 86:
return multipleOfPow5(twoF, minusK)
return false
proc toDecimal64*(ieeeSignificand: uint64; ieeeExponent: uint64): FloatingDecimal64 {.
inline.} =
const
kappa: int32 = 2
const
bigDivisor: uint32 = 1000
## 10^(kappa + 1)
const
smallDivisor: uint32 = 100
## 10^(kappa)
##
## Step 1:
## integer promotion & Schubfach multiplier calculation.
##
var m2: uint64
var e2: int32
if ieeeExponent != 0:
m2 = hiddenBit or ieeeSignificand
e2 = cast[int32](ieeeExponent) - exponentBias
if 0 <= -e2 and -e2 < significandSize and multipleOfPow2(m2, -e2):
## Small integer.
return FloatingDecimal64(significand: m2 shr -e2, exponent: 0)
if ieeeSignificand == 0 and ieeeExponent > 1:
## Shorter interval case; proceed like Schubfach.
return toDecimal64AsymmetricInterval(e2)
else:
## Subnormal case; interval is always regular.
m2 = ieeeSignificand
e2 = 1 - exponentBias
let isEven: bool = (m2 mod 2 == 0)
let acceptLower: bool = isEven
let acceptUpper: bool = isEven
## Compute k and beta.
let minusK: int32 = floorLog10Pow2(e2) - kappa
let betaMinus1: int32 = e2 + floorLog2Pow10(-minusK)
dragonbox_Assert(betaMinus1 >= 6)
dragonbox_Assert(betaMinus1 <= 9)
let pow10: uint64x2 = computePow10(-minusK)
## Compute delta
## 10^kappa <= delta < 10^(kappa + 1)
## 100 <= delta < 1000
let delta: uint32 = computeDelta(pow10, betaMinus1)
dragonbox_Assert(delta >= smallDivisor)
dragonbox_Assert(delta < bigDivisor)
let twoFl: uint64 = 2 * m2 - 1
let twoFc: uint64 = 2 * m2
let twoFr: uint64 = 2 * m2 + 1
## (54 bits)
## Compute zi
## (54 + 9 = 63 bits)
let zi: uint64 = mulShift(twoFr shl betaMinus1, pow10)
## 2 mulx
##
## Step 2:
## Try larger divisor.
##
var q: uint64 = zi div bigDivisor
## uint64_t q = Mul128(zi, 0x83126E978D4FDF3Cu).hi >> 9; // 1 mulx
var r: uint32 = cast[uint32](zi) - bigDivisor * cast[uint32](q)
## r = zi % BigDivisor
## 0 <= r < 1000
if r < delta: ## likely ~50% ?!
## (r > deltai)
## Exclude the right endpoint if necessary
if r != 0 or acceptUpper or not isIntegralEndpoint(twoFr, e2, minusK):
return FloatingDecimal64(significand: q, exponent: minusK + kappa + 1)
dragonbox_Assert(q != 0)
dec(q)
r = bigDivisor
elif r == delta: ## unlikely
## Compare fractional parts.
## Check conditions in the order different from the paper
## to take advantage of short-circuiting
if (acceptLower and isIntegralEndpoint(twoFl, e2, minusK)) or
mulParity(twoFl, pow10, betaMinus1):
return FloatingDecimal64(significand: q, exponent: minusK + kappa + 1)
else:
discard
##
## Step 3:
## Find the significand with the smaller divisor
##
q = q * 10
## 1 hmul
## 0 <= r <= 1000
let dist: uint32 = r - (delta div 2) + (smallDivisor div 2)
let distQ: uint32 = dist div 100
## 1 mul
## const uint32_t dist_r = dist % 100;
q += distQ
## if /*likely*/ (dist_r == 0)
if dist == distQ * 100:
## const bool approx_y_parity = ((dist ^ (SmallDivisor / 2)) & 1) != 0;
let approxYParity: bool = (dist and 1) != 0
## Check z^(f) >= epsilon^(f)
## We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1,
## where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f)
## Since there are only 2 possibilities, we only need to care about the
## parity. Also, zi and r should have the same parity since the divisor
## is an even number
if mulParity(twoFc, pow10, betaMinus1) != approxYParity:
dec(q)
elif q mod 2 != 0 and isIntegralMidpoint(twoFc, e2, minusK):
dec(q)
return FloatingDecimal64(significand: q, exponent: minusK + kappa)
# ==================================================================================================
# ToChars
# ==================================================================================================
proc utoa8DigitsSkipTrailingZeros*(buf: var openArray[char]; pos: int; digits: uint32): int {.inline.} =
dragonbox_Assert(digits >= 1)
dragonbox_Assert(digits <= 99999999'u32)
let q: uint32 = digits div 10000
let r: uint32 = digits mod 10000
let qH: uint32 = q div 100
let qL: uint32 = q mod 100
utoa2Digits(buf, pos, qH)
utoa2Digits(buf, pos + 2, qL)
if r == 0:
return trailingZeros2Digits(if qL == 0: qH else: qL) + (if qL == 0: 6 else: 4)
else:
let rH: uint32 = r div 100
let rL: uint32 = r mod 100
utoa2Digits(buf, pos + 4, rH)
utoa2Digits(buf, pos + 6, rL)
return trailingZeros2Digits(if rL == 0: rH else: rL) + (if rL == 0: 2 else: 0)
proc printDecimalDigitsBackwards*(buf: var openArray[char]; pos: int; output64: uint64): int {.inline.} =
var pos = pos
var output64 = output64
var tz = 0
## number of trailing zeros removed.
var nd = 0
## number of decimal digits processed.
## At most 17 digits remaining
if output64 >= 100000000'u64:
let q: uint64 = output64 div 100000000'u64
let r: uint32 = cast[uint32](output64 mod 100000000'u64)
output64 = q
dec(pos, 8)
if r != 0:
tz = utoa8DigitsSkipTrailingZeros(buf, pos, r)
dragonbox_Assert(tz >= 0)
dragonbox_Assert(tz <= 7)
else:
tz = 8
nd = 8
dragonbox_Assert(output64 <= high(uint32))
var output = cast[uint32](output64)
if output >= 10000:
let q: uint32 = output div 10000
let r: uint32 = output mod 10000
output = q
dec(pos, 4)
if r != 0:
let rH: uint32 = r div 100
let rL: uint32 = r mod 100
utoa2Digits(buf, pos, rH)
utoa2Digits(buf, pos + 2, rL)
if tz == nd:
inc(tz, trailingZeros2Digits(if rL == 0: rH else: rL) +
(if rL == 0: 2 else: 0))
else:
if tz == nd:
inc(tz, 4)
else:
for i in 0..3: buf[pos+i] = '0'
## (actually not required...)
inc(nd, 4)
if output >= 100:
let q: uint32 = output div 100
let r: uint32 = output mod 100
output = q
dec(pos, 2)
utoa2Digits(buf, pos, r)
if tz == nd:
inc(tz, trailingZeros2Digits(r))
inc(nd, 2)
if output >= 100:
let q2: uint32 = output div 100
let r2: uint32 = output mod 100
output = q2
dec(pos, 2)
utoa2Digits(buf, pos, r2)
if tz == nd:
inc(tz, trailingZeros2Digits(r2))
inc(nd, 2)
dragonbox_Assert(output >= 1)
dragonbox_Assert(output <= 99)
if output >= 10:
let q: uint32 = output
dec(pos, 2)
utoa2Digits(buf, pos, q)
if tz == nd:
inc(tz, trailingZeros2Digits(q))
else:
let q: uint32 = output
dragonbox_Assert(q >= 1)
dragonbox_Assert(q <= 9)
dec(pos)
buf[pos] = chr(ord('0') + q)
return tz
proc decimalLength*(v: uint64): int {.inline.} =
dragonbox_Assert(v >= 1)
dragonbox_Assert(v <= 99999999999999999'u64)
if cast[uint32](v shr 32) != 0:
if v >= 10000000000000000'u64:
return 17
if v >= 1000000000000000'u64:
return 16
if v >= 100000000000000'u64:
return 15
if v >= 10000000000000'u64:
return 14
if v >= 1000000000000'u64:
return 13
if v >= 100000000000'u64:
return 12
if v >= 10000000000'u64:
return 11
return 10
let v32: uint32 = cast[uint32](v)
if v32 >= 1000000000'u32:
return 10
if v32 >= 100000000'u32:
return 9
if v32 >= 10000000'u32:
return 8
if v32 >= 1000000'u32:
return 7
if v32 >= 100000'u32:
return 6
if v32 >= 10000'u32:
return 5
if v32 >= 1000'u32:
return 4
if v32 >= 100'u32:
return 3
if v32 >= 10'u32:
return 2
return 1
proc formatDigits*[T: Ordinal](buffer: var openArray[char]; pos: T; digits: uint64; decimalExponent: int;
forceTrailingDotZero = false): int {.inline.} =
const
minFixedDecimalPoint = -6
const
maxFixedDecimalPoint = 17
var pos:int = pos.int
assert(minFixedDecimalPoint <= -1, "internal error")
assert(maxFixedDecimalPoint >= 17, "internal error")
dragonbox_Assert(digits >= 1)
dragonbox_Assert(digits <= 99999999999999999'u64)
dragonbox_Assert(decimalExponent >= -999)
dragonbox_Assert(decimalExponent <= 999)
var numDigits = decimalLength(digits)
let decimalPoint = numDigits + decimalExponent
let useFixed: bool = minFixedDecimalPoint <= decimalPoint and
decimalPoint <= maxFixedDecimalPoint
## Prepare the buffer.
for i in 0..<32: buffer[pos+i] = '0'
assert(minFixedDecimalPoint >= -30, "internal error")
assert(maxFixedDecimalPoint <= 32, "internal error")
var decimalDigitsPosition: int
if useFixed:
if decimalPoint <= 0:
## 0.[000]digits
decimalDigitsPosition = 2 - decimalPoint
else:
## dig.its
## digits[000]
decimalDigitsPosition = 0
else:
## dE+123 or d.igitsE+123
decimalDigitsPosition = 1
var digitsEnd = pos + int(decimalDigitsPosition + numDigits)
let tz = printDecimalDigitsBackwards(buffer, digitsEnd, digits)
dec(digitsEnd, tz)
dec(numDigits, tz)
## decimal_exponent += tz; // => decimal_point unchanged.
if useFixed:
if decimalPoint <= 0:
## 0.[000]digits
buffer[pos+1] = '.'
pos = digitsEnd
elif decimalPoint < numDigits:
## dig.its
when true: #defined(vcc) and not defined(clang):
## VC does not inline the memmove call below. (Even if compiled with /arch:AVX2.)
## However, memcpy will be inlined.
var tmp = default(array[16, char])
for i in 0..<16: tmp[i] = buffer[i+pos+decimalPoint]
for i in 0..<16: buffer[i+pos+decimalPoint+1] = tmp[i]
else:
memmove(buffer +! (decimalPoint + 1), buffer +! decimalPoint, 16)
buffer[pos+decimalPoint] = '.'
pos = digitsEnd + 1
else:
## digits[000]
inc(pos, decimalPoint)
if forceTrailingDotZero:
buffer[pos] = '.'
buffer[pos+1] = '0'
inc(pos, 2)
else:
## Copy the first digit one place to the left.
buffer[pos] = buffer[pos+1]
if numDigits == 1:
## dE+123
inc(pos)
else:
## d.igitsE+123
buffer[pos+1] = '.'
pos = digitsEnd
let scientificExponent: int = decimalPoint - 1
## SF_ASSERT(scientific_exponent != 0);
buffer[pos] = 'e'
buffer[pos+1] = if scientificExponent < 0: '-' else: '+'
inc(pos, 2)
let k: uint32 = cast[uint32](if scientificExponent < 0: -scientificExponent else: scientificExponent)
if k < 10:
buffer[pos] = chr(ord('0') + k)
inc(pos)
elif k < 100:
utoa2Digits(buffer, pos, k)
inc(pos, 2)
else:
let q: uint32 = k div 100
let r: uint32 = k mod 100
buffer[pos] = chr(ord('0') + q)
inc(pos)
utoa2Digits(buffer, pos, r)
inc(pos, 2)
return pos
proc toChars*(buffer: var openArray[char]; v: float; forceTrailingDotZero = false): int {.
inline.} =
var pos = 0
let significand: uint64 = physicalSignificand(constructDouble(v))
let exponent: uint64 = physicalExponent(constructDouble(v))
if exponent != maxIeeeExponent:
## Finite
buffer[pos] = '-'
inc(pos, signBit(constructDouble(v)))
if exponent != 0 or significand != 0:
## != 0
let dec = toDecimal64(significand, exponent)
return formatDigits(buffer, pos, dec.significand, dec.exponent.int,
forceTrailingDotZero)
else:
buffer[pos] = '0'
buffer[pos+1] = '.'
buffer[pos+2] = '0'
buffer[pos+3] = ' '
inc(pos, if forceTrailingDotZero: 3 else: 1)
return pos
if significand == 0:
buffer[pos] = '-'
inc(pos, signBit(constructDouble(v)))
buffer[pos] = 'i'
buffer[pos+1] = 'n'
buffer[pos+2] = 'f'
buffer[pos+3] = ' '
return pos + 3
else:
buffer[pos] = 'n'
buffer[pos+1] = 'a'
buffer[pos+2] = 'n'
buffer[pos+3] = ' '
return pos + 3
when false:
proc toString*(value: float): string =
var buffer: array[dtoaMinBufferLength, char]
let last = toChars(addr buffer, value)
let L = cast[int](last) - cast[int](addr(buffer))
result = newString(L)
copyMem(addr result[0], addr buffer[0], L)
Reference in New Issue View Git Blame Copy Permalink