1
0
mirror of https://github.com/vlang/v.git synced 2023-08-10 21:13:21 +03:00

strconv: atof_quick for tasks that need speed but not big accuracy

This commit is contained in:
penguindark 2019-12-19 01:37:53 +01:00 committed by Alexander Medvednikov
parent df2f98e276
commit 929e7c1193
2 changed files with 348 additions and 10 deletions

View File

@ -13,11 +13,12 @@ fn test_atof() {
// float64
src_num := [
f64(0.3),
-0.3 ,
-0.3,
0.004,
-0.004,
0.0 ,
-0.0
0.0,
-0.0,
31234567890123
]
// strings
@ -27,20 +28,32 @@ fn test_atof() {
'0.004',
'-0.004',
'0.0',
'-0.0'
'-0.0',
'31234567890123',
]
// check conversion1 string <=> string
// check conversion case 1 string <=> string
for c,x in src_num {
// slow atof
assert strconv.atof64(src_num_str[c]).strlong() == x.strlong()
// quick atof
mut s1 := (strconv.atof_quick(src_num_str[c]).str())
s1 = s1[..src_num_str[c].len]
mut s2 := (x.str())
s2 = s2[..src_num_str[c].len]
assert s1 == s2
// test C.atof
assert x.strsci(18) == f64(C.atof(src_num_str[c].str)).strsci(18)
}
// check conversion2 string <==> f64
// check conversion case 2 string <==> f64
// we don't test atof_quick beacuse we already know the rounding error
for c,x in src_num_str {
a:=strconv.atof64(x)
b:=src_num[c]
assert a.strlong() == b.strlong()
b := src_num[c].strlong()
a1 := strconv.atof64(x).strlong()
assert a1 == b
}
// special cases
@ -55,4 +68,4 @@ fn test_atof() {
f1=-0.0
assert *ptr == u64(0x8000000000000000)
}
}

325
vlib/strconv/atofq.v Normal file
View File

@ -0,0 +1,325 @@
/**********************************************************************
*
* atof util
*
* Copyright (c) 2019 Dario Deledda. All rights reserved.
* Use of this source code is governed by an MIT license
* that can be found in the LICENSE file.
*
* This file contains utilities for convert a string in a f64 variable in a very quick way
* IEEE 754 standard is used
*
* Know limitation:
* - round to 0 approximation
* - loos of precision with big exponents
*
*
**********************************************************************/
module strconv
// same used in atof, here only for references
//const(
// DOUBLE_PLUS_ZERO = u64(0x0000000000000000)
// DOUBLE_MINUS_ZERO = 0x8000000000000000
// DOUBLE_PLUS_INFINITY = 0x7FF0000000000000
// DOUBLE_MINUS_INFINITY = 0xFFF0000000000000
// atof_quick return a f64 number from a string in a quick way
pub fn atof_quick(s string) f64 {
mut f := f64(0.0) // result
mut sign := f64(1.0) // result sign
mut i :=0 // index
// skip white spaces
for i < s.len && s[i] == ` ` {
i++
}
//check sign
if i < s.len {
if s[i] == `-` {
sign = -1.0
i++
}else if s[i] == `+` {
i++
}
}
// infinite
if s[i] == `i` && i+2 < s.len && s[i+1] == `n` && s[i+2] == `f` {
mut d := *u64(&f)
if sign > 0.0 {
*d = DOUBLE_PLUS_INFINITY
}else{
*d = DOUBLE_MINUS_INFINITY
}
return f
}
// skip zeros
for i<s.len && s[i]==`0` {
i++
// we have a zero, manage it
if i >= s.len {
mut d := *u64(&f)
if sign > 0.0 {
*d = DOUBLE_PLUS_ZERO
}else{
*d = DOUBLE_MINUS_ZERO
}
return f
}
}
// integer part
for i < s.len && (s[i] >= `0` && s[i] <= `9`) {
f *= f64(10.0)
f += f64(s[i] - `0`)
i++
}
// decimal point
if i < s.len && s[i] == `.` {
i++
mut frac_mul := f64(0.1)
for i < s.len && (s[i] >= `0` && s[i] <= `9`) {
f += f64(s[i] - `0`) * frac_mul
frac_mul *= f64(0.1)
i++
}
}
// exponent management
if i < s.len && (s[i] == `e` || s[i] == `E`) {
i++
mut exp := 0
mut exp_sign := 1
// negative exponent
if i < s.len {
if s[i] == `-` {
exp_sign = -1
i++
}else if s[i] == `+` {
i++
}
}
// skip zeros
for i < s.len && s[i] == `0` {
i++
}
for i < s.len && (s[i] >= `0` && s[i] <= `9`) {
exp *= 10
exp += int(s[i] - `0`)
i++
}
if exp_sign == 1 {
if exp > pos_exp.len {
mut d := *u64(&f)
if sign > 0 {
*d = DOUBLE_PLUS_INFINITY
}else{
*d = DOUBLE_MINUS_INFINITY
}
return f
}
tmp_mul := f64(0.0)
mut ptr_d := *u64(&tmp_mul)
*ptr_d = pos_exp[exp]
//C.printf("exp: %d [0x%016llx] %f,",exp,pos_exp[exp],tmp_mul)
f = f * tmp_mul
} else {
if exp > neg_exp.len {
mut d := *u64(&f)
if (sign > 0) {
*d = DOUBLE_PLUS_ZERO
}else{
*d = DOUBLE_MINUS_ZERO
}
return f
}
tmp_mul := f64(0.0)
mut ptr_d := *u64(&tmp_mul)
*ptr_d = neg_exp[exp]
//C.printf("exp: %d [0x%016llx] %f,",exp,pos_exp[exp],tmp_mul)
f = f * tmp_mul
}
}
f = f * sign
return f
}
const(
// positive exp of 10 binary form
pos_exp = [
0x3ff0000000000000,
0x4024000000000000,0x4059000000000000,0x408f400000000000,0x40c3880000000000,
0x40f86a0000000000,0x412e848000000000,0x416312d000000000,0x4197d78400000000,
0x41cdcd6500000000,0x4202a05f20000000,0x42374876e8000000,0x426d1a94a2000000,
0x42a2309ce5400000,0x42d6bcc41e900000,0x430c6bf526340000,0x4341c37937e08000,
0x4376345785d8a000,0x43abc16d674ec800,0x43e158e460913d00,0x4415af1d78b58c40,
0x444b1ae4d6e2ef50,0x4480f0cf064dd592,0x44b52d02c7e14af6,0x44ea784379d99db4,
0x45208b2a2c280291,0x4554adf4b7320335,0x4589d971e4fe8402,0x45c027e72f1f1281,
0x45f431e0fae6d721,0x46293e5939a08cea,0x465f8def8808b024,0x4693b8b5b5056e17,
0x46c8a6e32246c99c,0x46fed09bead87c03,0x4733426172c74d82,0x476812f9cf7920e3,
0x479e17b84357691b,0x47d2ced32a16a1b1,0x48078287f49c4a1d,0x483d6329f1c35ca5,
0x48725dfa371a19e7,0x48a6f578c4e0a061,0x48dcb2d6f618c879,0x4911efc659cf7d4c,
0x49466bb7f0435c9e,0x497c06a5ec5433c6,0x49b18427b3b4a05c,0x49e5e531a0a1c873,
0x4a1b5e7e08ca3a8f,0x4a511b0ec57e649a,0x4a8561d276ddfdc0,0x4ababa4714957d30,
0x4af0b46c6cdd6e3e,0x4b24e1878814c9ce,0x4b5a19e96a19fc41,0x4b905031e2503da9,
0x4bc4643e5ae44d13,0x4bf97d4df19d6057,0x4c2fdca16e04b86d,0x4c63e9e4e4c2f344,
0x4c98e45e1df3b015,0x4ccf1d75a5709c1b,0x4d03726987666191,0x4d384f03e93ff9f5,
0x4d6e62c4e38ff872,0x4da2fdbb0e39fb47,0x4dd7bd29d1c87a19,0x4e0dac74463a989f,
0x4e428bc8abe49f64,0x4e772ebad6ddc73d,0x4eacfa698c95390c,0x4ee21c81f7dd43a7,
0x4f16a3a275d49491,0x4f4c4c8b1349b9b5,0x4f81afd6ec0e1411,0x4fb61bcca7119916,
0x4feba2bfd0d5ff5b,0x502145b7e285bf99,0x50559725db272f7f,0x508afcef51f0fb5f,
0x50c0de1593369d1b,0x50f5159af8044462,0x512a5b01b605557b,0x516078e111c3556d,
0x5194971956342ac8,0x51c9bcdfabc1357a,0x5200160bcb58c16c,0x52341b8ebe2ef1c7,
0x526922726dbaae39,0x529f6b0f092959c7,0x52d3a2e965b9d81d,0x53088ba3bf284e24,
0x533eae8caef261ad,0x53732d17ed577d0c,0x53a7f85de8ad5c4f,0x53ddf67562d8b363,
0x5412ba095dc7701e,0x5447688bb5394c25,0x547d42aea2879f2e,0x54b249ad2594c37d,
0x54e6dc186ef9f45c,0x551c931e8ab87173,0x5551dbf316b346e8,0x558652efdc6018a2,
0x55bbe7abd3781eca,0x55f170cb642b133f,0x5625ccfe3d35d80e,0x565b403dcc834e12,
0x569108269fd210cb,0x56c54a3047c694fe,0x56fa9cbc59b83a3d,0x5730a1f5b8132466,
0x5764ca732617ed80,0x5799fd0fef9de8e0,0x57d03e29f5c2b18c,0x58044db473335def,
0x583961219000356b,0x586fb969f40042c5,0x58a3d3e2388029bb,0x58d8c8dac6a0342a,
0x590efb1178484135,0x59435ceaeb2d28c1,0x59783425a5f872f1,0x59ae412f0f768fad,
0x59e2e8bd69aa19cc,0x5a17a2ecc414a03f,0x5a4d8ba7f519c84f,0x5a827748f9301d32,
0x5ab7151b377c247e,0x5aecda62055b2d9e,0x5b22087d4358fc82,0x5b568a9c942f3ba3,
0x5b8c2d43b93b0a8c,0x5bc19c4a53c4e697,0x5bf6035ce8b6203d,0x5c2b843422e3a84d,
0x5c6132a095ce4930,0x5c957f48bb41db7c,0x5ccadf1aea12525b,0x5d00cb70d24b7379,
0x5d34fe4d06de5057,0x5d6a3de04895e46d,0x5da066ac2d5daec4,0x5dd4805738b51a75,
0x5e09a06d06e26112,0x5e400444244d7cab,0x5e7405552d60dbd6,0x5ea906aa78b912cc,
0x5edf485516e7577f,0x5f138d352e5096af,0x5f48708279e4bc5b,0x5f7e8ca3185deb72,
0x5fb317e5ef3ab327,0x5fe7dddf6b095ff1,0x601dd55745cbb7ed,0x6052a5568b9f52f4,
0x60874eac2e8727b1,0x60bd22573a28f19d,0x60f2357684599702,0x6126c2d4256ffcc3,
0x615c73892ecbfbf4,0x6191c835bd3f7d78,0x61c63a432c8f5cd6,0x61fbc8d3f7b3340c,
0x62315d847ad00087,0x6265b4e5998400a9,0x629b221effe500d4,0x62d0f5535fef2084,
0x630532a837eae8a5,0x633a7f5245e5a2cf,0x63708f936baf85c1,0x63a4b378469b6732,
0x63d9e056584240fe,0x64102c35f729689f,0x6444374374f3c2c6,0x647945145230b378,
0x64af965966bce056,0x64e3bdf7e0360c36,0x6518ad75d8438f43,0x654ed8d34e547314,
0x6583478410f4c7ec,0x65b819651531f9e8,0x65ee1fbe5a7e7861,0x6622d3d6f88f0b3d,
0x665788ccb6b2ce0c,0x668d6affe45f818f,0x66c262dfeebbb0f9,0x66f6fb97ea6a9d38,
0x672cba7de5054486,0x6761f48eaf234ad4,0x679671b25aec1d89,0x67cc0e1ef1a724eb,
0x680188d357087713,0x6835eb082cca94d7,0x686b65ca37fd3a0d,0x68a11f9e62fe4448,
0x68d56785fbbdd55a,0x690ac1677aad4ab1,0x6940b8e0acac4eaf,0x6974e718d7d7625a,
0x69aa20df0dcd3af1,0x69e0548b68a044d6,0x6a1469ae42c8560c,0x6a498419d37a6b8f,
0x6a7fe52048590673,0x6ab3ef342d37a408,0x6ae8eb0138858d0a,0x6b1f25c186a6f04c,
0x6b537798f4285630,0x6b88557f31326bbb,0x6bbe6adefd7f06aa,0x6bf302cb5e6f642a,
0x6c27c37e360b3d35,0x6c5db45dc38e0c82,0x6c9290ba9a38c7d1,0x6cc734e940c6f9c6,
0x6cfd022390f8b837,0x6d3221563a9b7323,0x6d66a9abc9424feb,0x6d9c5416bb92e3e6,
0x6dd1b48e353bce70,0x6e0621b1c28ac20c,0x6e3baa1e332d728f,0x6e714a52dffc6799,
0x6ea59ce797fb817f,0x6edb04217dfa61df,0x6f10e294eebc7d2c,0x6f451b3a2a6b9c76,
0x6f7a6208b5068394,0x6fb07d457124123d,0x6fe49c96cd6d16cc,0x7019c3bc80c85c7f,
0x70501a55d07d39cf,0x708420eb449c8843,0x70b9292615c3aa54,0x70ef736f9b3494e9,
0x7123a825c100dd11,0x7158922f31411456,0x718eb6bafd91596b,0x71c33234de7ad7e3,
0x71f7fec216198ddc,0x722dfe729b9ff153,0x7262bf07a143f6d4,0x72976ec98994f489,
0x72cd4a7bebfa31ab,0x73024e8d737c5f0b,0x7336e230d05b76cd,0x736c9abd04725481,
0x73a1e0b622c774d0,0x73d658e3ab795204,0x740bef1c9657a686,0x74417571ddf6c814,
0x7475d2ce55747a18,0x74ab4781ead1989e,0x74e10cb132c2ff63,0x75154fdd7f73bf3c,
0x754aa3d4df50af0b,0x7580a6650b926d67,0x75b4cffe4e7708c0,0x75ea03fde214caf1,
0x7620427ead4cfed6,0x7654531e58a03e8c,0x768967e5eec84e2f,0x76bfc1df6a7a61bb,
0x76f3d92ba28c7d15,0x7728cf768b2f9c5a,0x775f03542dfb8370,0x779362149cbd3226,
0x77c83a99c3ec7eb0,0x77fe494034e79e5c,0x7832edc82110c2f9,0x7867a93a2954f3b8,
0x789d9388b3aa30a5,0x78d27c35704a5e67,0x79071b42cc5cf601,0x793ce2137f743382,
0x79720d4c2fa8a031,0x79a6909f3b92c83d,0x79dc34c70a777a4d,0x7a11a0fc668aac70,
0x7a46093b802d578c,0x7a7b8b8a6038ad6f,0x7ab137367c236c65,0x7ae585041b2c477f,
0x7b1ae64521f7595e,0x7b50cfeb353a97db,0x7b8503e602893dd2,0x7bba44df832b8d46,
0x7bf06b0bb1fb384c,0x7c2485ce9e7a065f,0x7c59a742461887f6,0x7c9008896bcf54fa,
0x7cc40aabc6c32a38,0x7cf90d56b873f4c7,0x7d2f50ac6690f1f8,0x7d63926bc01a973b,
0x7d987706b0213d0a,0x7dce94c85c298c4c,0x7e031cfd3999f7b0,0x7e37e43c8800759c,
0x7e6ddd4baa009303,0x7ea2aa4f4a405be2,0x7ed754e31cd072da,0x7f0d2a1be4048f90,
0x7f423a516e82d9ba,0x7f76c8e5ca239029,0x7fac7b1f3cac7433,0x7fe1ccf385ebc8a0
]
// negative exp of 10 binary form
neg_exp = [
0x3ff0000000000000,
0x3fb999999999999a,0x3f847ae147ae147b,0x3f50624dd2f1a9fc,0x3f1a36e2eb1c432d,
0x3ee4f8b588e368f1,0x3eb0c6f7a0b5ed8d,0x3e7ad7f29abcaf48,0x3e45798ee2308c3a,
0x3e112e0be826d695,0x3ddb7cdfd9d7bdbb,0x3da5fd7fe1796495,0x3d719799812dea11,
0x3d3c25c268497682,0x3d06849b86a12b9b,0x3cd203af9ee75616,0x3c9cd2b297d889bc,
0x3c670ef54646d497,0x3c32725dd1d243ac,0x3bfd83c94fb6d2ac,0x3bc79ca10c924223,
0x3b92e3b40a0e9b4f,0x3b5e392010175ee6,0x3b282db34012b251,0x3af357c299a88ea7,
0x3abef2d0f5da7dd9,0x3a88c240c4aecb14,0x3a53ce9a36f23c10,0x3a1fb0f6be506019,
0x39e95a5efea6b347,0x39b4484bfeebc2a0,0x398039d665896880,0x3949f623d5a8a733,
0x3914c4e977ba1f5c,0x38e09d8792fb4c49,0x38aa95a5b7f87a0f,0x38754484932d2e72,
0x3841039d428a8b8f,0x380b38fb9daa78e4,0x37d5c72fb1552d83,0x37a16c262777579c,
0x376be03d0bf225c7,0x37364cfda3281e39,0x3701d7314f534b61,0x36cc8b8218854567,
0x3696d601ad376ab9,0x366244ce242c5561,0x362d3ae36d13bbce,0x35f7624f8a762fd8,
0x35c2b50c6ec4f313,0x358dee7a4ad4b81f,0x3557f1fb6f10934c,0x352327fc58da0f70,
0x34eea6608e29b24d,0x34b8851a0b548ea4,0x34839dae6f76d883,0x344f62b0b257c0d2,
0x34191bc08eac9a41,0x33e41633a556e1ce,0x33b011c2eaabe7d8,0x3379b604aaaca626,
0x3344919d5556eb52,0x3310747ddddf22a8,0x32da53fc9631d10d,0x32a50ffd44f4a73d,
0x3270d9976a5d5297,0x323af5bf109550f2,0x32059165a6ddda5b,0x31d1411e1f17e1e3,
0x319b9b6364f30304,0x316615e91d8f359d,0x3131ab20e472914a,0x30fc45016d841baa,
0x30c69d9abe034955,0x309217aefe690777,0x305cf2b1970e7258,0x3027288e1271f513,
0x2ff286d80ec190dc,0x2fbda48ce468e7c7,0x2f87b6d71d20b96c,0x2f52f8ac174d6123,
0x2f1e5aacf2156838,0x2ee8488a5b445360,0x2eb36d3b7c36a91a,0x2e7f152bf9f10e90,
0x2e48ddbcc7f40ba6,0x2e13e497065cd61f,0x2ddfd424d6faf031,0x2da97683df2f268d,
0x2d745ecfe5bf520b,0x2d404bd984990e6f,0x2d0a12f5a0f4e3e5,0x2cd4dbf7b3f71cb7,
0x2ca0aff95cc5b092,0x2c6ab328946f80ea,0x2c355c2076bf9a55,0x2c0116805effaeaa,
0x2bcb5733cb32b111,0x2b95df5ca28ef40d,0x2b617f7d4ed8c33e,0x2b2bff2ee48e0530,
0x2af665bf1d3e6a8d,0x2ac1eaff4a98553d,0x2a8cab3210f3bb95,0x2a56ef5b40c2fc77,
0x2a225915cd68c9f9,0x29ed5b561574765b,0x29b77c44ddf6c516,0x2982c9d0b1923745,
0x294e0fb44f50586e,0x29180c903f7379f2,0x28e33d4032c2c7f5,0x28aec866b79e0cba,
0x2878a0522c7e7095,0x2843b374f06526de,0x280f8587e7083e30,0x27d9379fec069826,
0x27a42c7ff0054685,0x277023998cd10537,0x2739d28f47b4d525,0x2704a8729fc3ddb7,
0x26d086c219697e2c,0x269a71368f0f3047,0x2665275ed8d8f36c,0x2630ec4be0ad8f89,
0x25fb13ac9aaf4c0f,0x25c5a956e225d672,0x2591544581b7dec2,0x255bba08cf8c979d,
0x25262e6d72d6dfb0,0x24f1bebdf578b2f4,0x24bc6463225ab7ec,0x2486b6b5b5155ff0,
0x24522bc490dde65a,0x241d12d41afca3c3,0x23e7424348ca1c9c,0x23b29b69070816e3,
0x237dc574d80cf16b,0x2347d12a4670c123,0x23130dbb6b8d674f,0x22de7c5f127bd87e,
0x22a8637f41fcad32,0x227382cc34ca2428,0x223f37ad21436d0c,0x2208f9574dcf8a70,
0x21d3faac3e3fa1f3,0x219ff779fd329cb9,0x216992c7fdc216fa,0x2134756ccb01abfb,
0x21005df0a267bcc9,0x20ca2fe76a3f9475,0x2094f31f8832dd2a,0x2060c27fa028b0ef,
0x202ad0cc33744e4b,0x1ff573d68f903ea2,0x1fc1297872d9cbb5,0x1f8b758d848fac55,
0x1f55f7a46a0c89dd,0x1f2192e9ee706e4b,0x1eec1e43171a4a11,0x1eb67e9c127b6e74,
0x1e81fee341fc585d,0x1e4ccb0536608d61,0x1e1708d0f84d3de7,0x1de26d73f9d764b9,
0x1dad7becc2f23ac2,0x1d779657025b6235,0x1d42deac01e2b4f7,0x1d0e3113363787f2,
0x1cd8274291c6065b,0x1ca3529ba7d19eaf,0x1c6eea92a61c3118,0x1c38bba884e35a7a,
0x1c03c9539d82aec8,0x1bcfa885c8d117a6,0x1b99539e3a40dfb8,0x1b6442e4fb671960,
0x1b303583fc527ab3,0x1af9ef3993b72ab8,0x1ac4bf6142f8eefa,0x1a90991a9bfa58c8,
0x1a5a8e90f9908e0d,0x1a253eda614071a4,0x19f0ff151a99f483,0x19bb31bb5dc320d2,
0x1985c162b168e70e,0x1951678227871f3e,0x191bd8d03f3e9864,0x18e6470cff6546b6,
0x18b1d270cc51055f,0x187c83e7ad4e6efe,0x1846cfec8aa52598,0x18123ff06eea847a,
0x17dd331a4b10d3f6,0x17a75c1508da432b,0x1772b010d3e1cf56,0x173de6815302e556,
0x1707eb9aa8cf1dde,0x16d322e220a5b17e,0x169e9e369aa2b597,0x16687e92154ef7ac,
0x16339874ddd8c623,0x15ff5a549627a36c,0x15c91510781fb5f0,0x159410d9f9b2f7f3,
0x15600d7b2e28c65c,0x1529af2b7d0e0a2d,0x14f48c22ca71a1bd,0x14c0701bd527b498,
0x148a4cf9550c5426,0x14550a6110d6a9b8,0x1420d51a73deee2d,0x13eaee90b964b047,
0x13b58ba6fab6f36c,0x13813c85955f2923,0x134b9408eefea839,0x1316100725988694,
0x12e1a66c1e139edd,0x12ac3d79c9b8fe2e,0x12769794a160cb58,0x124212dd4de70913,
0x120ceafbafd80e85,0x11d72262f3133ed1,0x11a281e8c275cbda,0x116d9ca79d89462a,
0x1137b08617a104ee,0x1102f39e794d9d8b,0x10ce5297287c2f45,0x1098421286c9bf6b,
0x1063680ed23aff89,0x102f0ce4839198db,0x0ff8d71d360e13e2,0x0fc3df4a91a4dcb5,
0x0f8fcbaa82a16121,0x0f596fbb9bb44db4,0x0f245962e2f6a490,0x0ef047824f2bb6da,
0x0eba0c03b1df8af6,0x0e84d6695b193bf8,0x0e50ab877c142ffa,0x0e1aac0bf9b9e65c,
0x0de5566ffafb1eb0,0x0db111f32f2f4bc0,0x0d7b4feb7eb212cd,0x0d45d98932280f0a,
0x0d117ad428200c08,0x0cdbf7b9d9cce00d,0x0ca65fc7e170b33e,0x0c71e6398126f5cb,
0x0c3ca38f350b22df,0x0c06e93f5da2824c,0x0bd25432b14ecea3,0x0b9d53844ee47dd1,
0x0b677603725064a8,0x0b32c4cf8ea6b6ec,0x0afe07b27dd78b14,0x0ac8062864ac6f43,
0x0a9338205089f29c,0x0a5ec033b40fea93,0x0a2899c2f6732210,0x09f3ae3591f5b4d9,
0x09bf7d228322baf5,0x098930e868e89591,0x0954272053ed4474,0x09201f4d0ff10390,
0x08e9cbae7fe805b3,0x08b4a2f1ffecd15c,0x0880825b3323dab0,0x084a6a2b85062ab3,
0x081521bc6a6b555c,0x07e0e7c9eebc444a,0x07ab0c764ac6d3a9,0x0775a391d56bdc87,
0x07414fa7ddefe3a0,0x070bb2a62fe638ff,0x06d62884f31e93ff,0x06a1ba03f5b21000,
0x066c5cd322b67fff,0x0636b0a8e891ffff,0x060226ed86db3333,0x05cd0b15a491eb84,
0x05973c115074bc6a,0x05629674405d6388,0x052dbd86cd6238d9,0x04f7cad23de82d7b,
0x04c308a831868ac9,0x048e74404f3daadb,0x04585d003f6488af,0x04237d99cc506d59,
0x03ef2f5c7a1a488e,0x03b8f2b061aea072,0x0383f559e7bee6c1,0x034feef63f97d79c,
0x03198bf832dfdfb0,0x02e46ff9c24cb2f3,0x02b059949b708f29,0x027a28edc580e50e,
0x0244ed8b04671da5,0x0210be08d0527e1d,0x01dac9a7b3b7302f,0x01a56e1fc2f8f359,
0x017124e63593f5e1,0x013b6e3d22865634,0x0105f1ca820511c3,0x00d18e3b9b374169,
0x009c16c5c5253575,0x0066789e3750f791,0x0031fa182c40c60d,0x000730d67819e8d2,
0x0000b8157268fdaf,0x000012688b70e62b,0x000001d74124e3d1,0x0000002f201d49fb,
0x00000004b6695433,0x0000000078a42205,0x000000000c1069cd,0x000000000134d761,
0x00000000001ee257,0x00000000000316a2,0x0000000000004f10,0x00000000000007e8,
0x00000000000000ca,0x0000000000000014,0x0000000000000002
]
)