Odin/core/strconv/fast_float.odin

package strconv

import "base:intrinsics"
import "core:math/bits"

_ :: bits // needed for STRCONV_FAST_FLOAT=false

/*
	Decimal to binary float conversion: a fast scanner for decimal floats
	and the Eisel-Lemire algorithm.

	Ported from ffc.h (https://github.com/kolemannix/ffc.h)
	Made available under the Boost Software License 1.0,
	see LICENSE at the bottom of the file.

	List of contributors:
		Daniel Lemire, João Paulo Magalhaes: Original fast_float implementation
		Koleman Nix:                         C port (ffc.h)
*/

/*
	References:
	- Daniel Lemire, "Number Parsing at a Gigabyte per Second",
	  Software: Practice and Experience 51 (8), 2021. https://arxiv.org/abs/2101.11408
	- Noble Mushtak, Daniel Lemire, "Fast Number Parsing Without Fallback",
	  Software: Practice and Experience 53 (7), 2023. https://arxiv.org/abs/2212.06644
*/

/*
	Disable with `-define:STRCONV_FAST_FLOAT=false` to drop the Eisel-Lemire step
	and its table.
*/
FAST_FLOAT :: #config(STRCONV_FAST_FLOAT, true)

_SMALLEST_POWER_OF_FIVE :: -342

/*
Computes the `T` closest to `w * 10^q`, rounding ties to even.

`w` must be the exact decimal significand. When the input had more digits than fit
in a `u64`, call this with both the truncated significand `w` and `w + 1`: if both
calls return the same bits, the result is correct. Otherwise, use a slow path.

**Inputs**
- T: `f32` or `f64`
- q: The decimal exponent
- w: The decimal significand

**Returns**
- The IEEE-754 bit pattern of the result, without the sign bit. An overflow gives the bit pattern of infinity.
*/
fast_float_compute_float :: proc "contextless" ($T: typeid, q: int, w: u64) -> u64 where T == f32 || T == f64 #no_bounds_check {
	when T == f64 {
		MANTISSA_EXPLICIT_BITS     :: 52
		MINIMUM_EXPONENT           :: -1023
		INFINITE_POWER             :: 0x7ff
		SMALLEST_POWER_OF_TEN      :: -342
		LARGEST_POWER_OF_TEN       :: 308
		MIN_EXPONENT_ROUND_TO_EVEN :: -4
		MAX_EXPONENT_ROUND_TO_EVEN :: 23
	} else {
		MANTISSA_EXPLICIT_BITS     :: 23
		MINIMUM_EXPONENT           :: -127
		INFINITE_POWER             :: 0xff
		SMALLEST_POWER_OF_TEN      :: -64
		LARGEST_POWER_OF_TEN       :: 38
		MIN_EXPONENT_ROUND_TO_EVEN :: -17
		MAX_EXPONENT_ROUND_TO_EVEN :: 10
	}

	// w <= max(u64) and q < SMALLEST_POWER_OF_TEN always rounds to zero.
	if w == 0 || q < SMALLEST_POWER_OF_TEN {
		return 0
	}
	if q > LARGEST_POWER_OF_TEN {
		return INFINITE_POWER << MANTISSA_EXPLICIT_BITS
	}

	// Set the most significant bit of w.
	lz := bits.count_leading_zeros(w)
	w := w
	w <<= lz

	// Compute a 128-bit approximation of w * 5^q. We need the product to be accurate
	// to MANTISSA_EXPLICIT_BITS+3 bits. If the lower bits of the high word are all ones,
	// the error in the first product could affect them, so we refine the result with
	// the lower half of the power of five.
	PRECISION_MASK :: max(u64) >> (MANTISSA_EXPLICIT_BITS + 3)
	pow5 := _POWER_OF_FIVE_128[q - _SMALLEST_POWER_OF_FIVE]
	high, low := bits.mul_u64(w, pow5[0])
	if high & PRECISION_MASK == PRECISION_MASK {
		second_high, _ := bits.mul_u64(w, pow5[1])
		low += second_high
		if second_high > low {
			high += 1
		}
	}
	// Mushtak & Lemire (2023) prove that this product is always accurate enough.

	upperbit := int(high >> 63)
	shift    := uint(upperbit + 64 - MANTISSA_EXPLICIT_BITS - 3)
	mantissa := high >> shift
	// ((152170 + 65536) * q) >> 16 is floor(q * log2(10)) for |q| < 1650.
	power2   := (((152170 + 65536) * q) >> 16) + 63 + upperbit - int(lz) - MINIMUM_EXPONENT

	if power2 <= 0 {
		// Subnormal result.
		if -power2 + 1 >= 64 {
			return 0
		}
		mantissa >>= uint(-power2 + 1)
		mantissa += mantissa & 1 // round up
		mantissa >>= 1
		// Rounding up can give the smallest normal number. Then the hidden bit
		// is set, and it is also the lowest bit of the exponent.
		return mantissa
	}

	// We usually round up. If the value is exactly halfway between two floats,
	// and the lower float is even, we must round down. An exact halfway value is
	// possible only for a small range of exponents.
	if low <= 1 && q >= MIN_EXPONENT_ROUND_TO_EVEN && q <= MAX_EXPONENT_ROUND_TO_EVEN && mantissa & 3 == 1 {
		if mantissa << shift == high {
			mantissa &~= 1
		}
	}
	mantissa += mantissa & 1 // round up
	mantissa >>= 1
	if mantissa >= 2 << MANTISSA_EXPLICIT_BITS {
		mantissa = 1 << MANTISSA_EXPLICIT_BITS
		power2 += 1
	}
	mantissa &~= 1 << MANTISSA_EXPLICIT_BITS
	if power2 >= INFINITE_POWER {
		return INFINITE_POWER << MANTISSA_EXPLICIT_BITS
	}
	return mantissa | u64(power2) << MANTISSA_EXPLICIT_BITS
}

@(private)
MAX_SIG_DIGITS :: 19 // 10^19 - 1 < 2^64

/*
Scans a decimal floating-point number at the start of `s`.
A fast scanner for the decimal float syntax: `[+-] digits [. digits] [(e|E) [+-] digits]`
It skips a `_` between digits

**Returns**
- mantissa, exp: The value is `mantissa * 10^exp`. If `trunc` is true, the scanner dropped the significant digits after the first 19. Then the exact value is in the range `[mantissa, mantissa + 1) * 10^exp`.
- neg: The number has a minus sign.
- nr: The number of bytes in the number.
- ok: `false` if `s` is not a number
*/
parse_number_string :: #force_inline proc "contextless" (s: string) -> (mantissa: u64, exp: int, neg, trunc: bool, nr: int, ok: bool) #no_bounds_check {
	n := len(s)
	if n == 0 {
		return
	}
	// Written without branches, because the sign of the input is often unpredictable.
	neg = s[0] == '-'
	i := int(neg || s[0] == '+')
	if i+2 < n && s[i] == '0' && lower(s[i+1]) == 'x' {
		return // a hex float
	}

	// Integer part
	int_start := i
	for i < n && s[i] - '0' <= 9 {
		mantissa = mantissa*10 + u64(s[i] - '0')
		i += 1
	}
	digits := i - int_start
	if i < n && s[i] == '_' {
		more: int = ---
		i, mantissa, more = parse_digits_with_separators(s, i, mantissa)
		digits += more
	}

	int_digits := digits
	digits_end := i

	// Fraction part
	if i < n && s[i] == '.' {
		i += 1
		frac_start := i
		i, mantissa = loop_parse_if_eight_digits(s, i, mantissa)
		for i < n && s[i] - '0' <= 9 {
			mantissa = mantissa*10 + u64(s[i] - '0')
			i += 1
		}
		frac_digits := i - frac_start
		if i < n && s[i] == '_' {
			more: int = ---
			i, mantissa, more = parse_digits_with_separators(s, i, mantissa)
			frac_digits += more
		}
		exp = -frac_digits
		digits += frac_digits
		digits_end = i
	}
	if digits == 0 {
		return
	}

	// Exponent part. The first byte after `e` and the sign must be a digit.
	if i < n && lower(s[i]) == 'e' {
		i += 1
		exp_neg := false
		if i < n && (s[i] == '+' || s[i] == '-') {
			exp_neg = s[i] == '-'
			i += 1
		}
		if i >= n || s[i] - '0' > 9 {
			return // not a valid exponent, so not a number
		}
		x := 0
		for i < n && s[i] - '0' <= 9 {
			if x < 100_000 { // larger exponents overflow or underflow anyway
				x = x*10 + int(s[i] - '0')
			}
			i += 1
		}
		if i < n && s[i] == '_' {
			i, x = parse_exponent_with_separators(s, i, x)
		}
		exp += -x if exp_neg else x
	}

	if digits > MAX_SIG_DIGITS {
		mantissa, exp, trunc = read_significant_digits(s, int_start, digits_end, int_digits, exp + (digits - int_digits))
	}

	if mantissa == 0 {
		exp = 0
	}
	nr, ok = i, true
	return
}


// Returns the new position, the mantissa and the number of digits
@(cold)
parse_digits_with_separators :: proc "contextless" (s: string, i: int, mantissa: u64) -> (int, u64, int) #no_bounds_check {
	i, mantissa := i, mantissa
	digits := 0
	for i < len(s) {
		if s[i] - '0' <= 9 {
			mantissa = mantissa*10 + u64(s[i] - '0')
			digits += 1
		} else if s[i] != '_' {
			break
		}
		i += 1
	}
	return i, mantissa, digits
}

@(cold)
parse_exponent_with_separators :: proc "contextless" (s: string, i: int, x: int) -> (int, int) #no_bounds_check {
	i, x := i, x
	for i < len(s) {
		if s[i] - '0' <= 9 {
			if x < 100_000 { // larger exponents overflow or underflow anyway
				x = x*10 + int(s[i] - '0')
			}
		} else if s[i] != '_' {
			break
		}
		i += 1
	}
	return i, x
}

/*
Reads the first 19 significant digits of a decimal number again. The scanner uses it only
if the number has more than 19 digits, because then the mantissa can overflow.

**Inputs**
- s, i: The input, and the position of the first digit before the `.`.
- end: The position after the last digit.
- int_digits: The number of digits before the `.`.
- e: The exponent after the `e`, or 0.

**Returns**
- mantissa, exp: The value is `mantissa * 10^exp`, without the digits that were not read again.
- trunc: `true` if the procedure did not read all the digits again.
*/
@(cold)
read_significant_digits :: proc "contextless" (s: string, i, end, int_digits, e: int) -> (mantissa: u64, exp: int, trunc: bool) #no_bounds_check {
	i := i
	exp = e
	int_left := int_digits
	nd := 0
	for i < end && nd < MAX_SIG_DIGITS {
		c := s[i]
		i += 1
		if c - '0' > 9 {
			continue // a `_` or the `.`
		}
		if int_left > 0 {
			int_left -= 1
		} else {
			exp -= 1
		}
		if mantissa == 0 && c == '0' {
			continue
		}
		mantissa = mantissa*10 + u64(c - '0')
		nd += 1
	}
	exp += int_left
	return mantissa, exp, i < end
}

// Loads 8 bytes starting at `s[i]` in little-endian order
read8_to_u64 :: #force_inline proc "contextless" (s: string, i: int) -> u64 {
	return u64(intrinsics.unaligned_load((^u64le)(&raw_data(s)[i])))
}

read4_to_u32 :: #force_inline proc "contextless" (s: string, i: int) -> u32 {
	return u32(intrinsics.unaligned_load((^u32le)(&raw_data(s)[i])))
}

// Reports if all 8 bytes of `v` are ASCII digits
is_made_of_eight_digits_fast :: #force_inline proc "contextless" (v: u64) -> bool {
	return ((v + 0x4646_4646_4646_4646) | (v - 0x3030_3030_3030_3030)) & 0x8080_8080_8080_8080 == 0
}

is_made_of_four_digits_fast :: #force_inline proc "contextless" (v: u32) -> bool {
	return ((v + 0x4646_4646) | (v - 0x3030_3030)) & 0x8080_8080 == 0
}

// Returns the new position and mantissa
loop_parse_if_eight_digits :: #force_inline proc "contextless" (s: string, i: int, m: u64) -> (int, u64) #no_bounds_check {
	i, m := i, m
	for i+8 <= len(s) {
		v := read8_to_u64(s, i)
		if !is_made_of_eight_digits_fast(v) {
			break
		}
		m = m*100_000_000 + parse_eight_digits_unrolled(v)
		i += 8
	}
	if i+4 <= len(s) {
		v := read4_to_u32(s, i)
		if is_made_of_four_digits_fast(v) {
			m = m*10_000 + parse_four_digits_unrolled(v)
			i += 4
		}
	}
	return i, m
}

// Converts 8 ASCII digits (the first digit in the lowest byte) to their value
parse_eight_digits_unrolled :: #force_inline proc "contextless" (chars: u64) -> u64 {
	MASK :: 0x0000_00ff_0000_00ff
	MUL1 :: 0x000f_4240_0000_0064 // 100 + (1000000 << 32)
	MUL2 :: 0x0000_2710_0000_0001 // 1 + (10000 << 32)
	v := chars - 0x3030_3030_3030_3030
	v = v*10 + v>>8
	return u64(u32(((v & MASK)*MUL1 + ((v>>16) & MASK)*MUL2) >> 32))
}

parse_four_digits_unrolled :: #force_inline proc "contextless" (chars: u32) -> u64 {
	v := chars - 0x3030_3030
	v = v*10 + v>>8
	return u64(((v & 0x00ff_00ff) * 0x0064_0001) >> 16)
}

// 128-bit truncated mantissas of 5^-342 to 5^308, with the most significant
// bit set. Generated by fast_float script/table_generation.py.
@(rodata)
_POWER_OF_FIVE_128 := [651][2]u64{
	{0xeef453d6923bd65a, 0x113faa2906a13b3f}, // 5^-342
	{0x9558b4661b6565f8, 0x4ac7ca59a424c507}, // 5^-341
	{0xbaaee17fa23ebf76, 0x5d79bcf00d2df649}, // 5^-340
	{0xe95a99df8ace6f53, 0xf4d82c2c107973dc}, // 5^-339
	{0x91d8a02bb6c10594, 0x79071b9b8a4be869}, // 5^-338
	{0xb64ec836a47146f9, 0x9748e2826cdee284}, // 5^-337
	{0xe3e27a444d8d98b7, 0xfd1b1b2308169b25}, // 5^-336
	{0x8e6d8c6ab0787f72, 0xfe30f0f5e50e20f7}, // 5^-335
	{0xb208ef855c969f4f, 0xbdbd2d335e51a935}, // 5^-334
	{0xde8b2b66b3bc4723, 0xad2c788035e61382}, // 5^-333
	{0x8b16fb203055ac76, 0x4c3bcb5021afcc31}, // 5^-332
	{0xaddcb9e83c6b1793, 0xdf4abe242a1bbf3d}, // 5^-331
	{0xd953e8624b85dd78, 0xd71d6dad34a2af0d}, // 5^-330
	{0x87d4713d6f33aa6b, 0x8672648c40e5ad68}, // 5^-329
	{0xa9c98d8ccb009506, 0x680efdaf511f18c2}, // 5^-328
	{0xd43bf0effdc0ba48, 0x0212bd1b2566def2}, // 5^-327
	{0x84a57695fe98746d, 0x014bb630f7604b57}, // 5^-326
	{0xa5ced43b7e3e9188, 0x419ea3bd35385e2d}, // 5^-325
	{0xcf42894a5dce35ea, 0x52064cac828675b9}, // 5^-324
	{0x818995ce7aa0e1b2, 0x7343efebd1940993}, // 5^-323
	{0xa1ebfb4219491a1f, 0x1014ebe6c5f90bf8}, // 5^-322
	{0xca66fa129f9b60a6, 0xd41a26e077774ef6}, // 5^-321
	{0xfd00b897478238d0, 0x8920b098955522b4}, // 5^-320
	{0x9e20735e8cb16382, 0x55b46e5f5d5535b0}, // 5^-319
	{0xc5a890362fddbc62, 0xeb2189f734aa831d}, // 5^-318
	{0xf712b443bbd52b7b, 0xa5e9ec7501d523e4}, // 5^-317
	{0x9a6bb0aa55653b2d, 0x47b233c92125366e}, // 5^-316
	{0xc1069cd4eabe89f8, 0x999ec0bb696e840a}, // 5^-315
	{0xf148440a256e2c76, 0xc00670ea43ca250d}, // 5^-314
	{0x96cd2a865764dbca, 0x380406926a5e5728}, // 5^-313
	{0xbc807527ed3e12bc, 0xc605083704f5ecf2}, // 5^-312
	{0xeba09271e88d976b, 0xf7864a44c633682e}, // 5^-311
	{0x93445b8731587ea3, 0x7ab3ee6afbe0211d}, // 5^-310
	{0xb8157268fdae9e4c, 0x5960ea05bad82964}, // 5^-309
	{0xe61acf033d1a45df, 0x6fb92487298e33bd}, // 5^-308
	{0x8fd0c16206306bab, 0xa5d3b6d479f8e056}, // 5^-307
	{0xb3c4f1ba87bc8696, 0x8f48a4899877186c}, // 5^-306
	{0xe0b62e2929aba83c, 0x331acdabfe94de87}, // 5^-305
	{0x8c71dcd9ba0b4925, 0x9ff0c08b7f1d0b14}, // 5^-304
	{0xaf8e5410288e1b6f, 0x07ecf0ae5ee44dd9}, // 5^-303
	{0xdb71e91432b1a24a, 0xc9e82cd9f69d6150}, // 5^-302
	{0x892731ac9faf056e, 0xbe311c083a225cd2}, // 5^-301
	{0xab70fe17c79ac6ca, 0x6dbd630a48aaf406}, // 5^-300
	{0xd64d3d9db981787d, 0x092cbbccdad5b108}, // 5^-299
	{0x85f0468293f0eb4e, 0x25bbf56008c58ea5}, // 5^-298
	{0xa76c582338ed2621, 0xaf2af2b80af6f24e}, // 5^-297
	{0xd1476e2c07286faa, 0x1af5af660db4aee1}, // 5^-296
	{0x82cca4db847945ca, 0x50d98d9fc890ed4d}, // 5^-295
	{0xa37fce126597973c, 0xe50ff107bab528a0}, // 5^-294
	{0xcc5fc196fefd7d0c, 0x1e53ed49a96272c8}, // 5^-293
	{0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7a}, // 5^-292
	{0x9faacf3df73609b1, 0x77b191618c54e9ac}, // 5^-291
	{0xc795830d75038c1d, 0xd59df5b9ef6a2417}, // 5^-290
	{0xf97ae3d0d2446f25, 0x4b0573286b44ad1d}, // 5^-289
	{0x9becce62836ac577, 0x4ee367f9430aec32}, // 5^-288
	{0xc2e801fb244576d5, 0x229c41f793cda73f}, // 5^-287
	{0xf3a20279ed56d48a, 0x6b43527578c1110f}, // 5^-286
	{0x9845418c345644d6, 0x830a13896b78aaa9}, // 5^-285
	{0xbe5691ef416bd60c, 0x23cc986bc656d553}, // 5^-284
	{0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa8}, // 5^-283
	{0x94b3a202eb1c3f39, 0x7bf7d71432f3d6a9}, // 5^-282
	{0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc53}, // 5^-281
	{0xe858ad248f5c22c9, 0xd1b3400f8f9cff68}, // 5^-280
	{0x91376c36d99995be, 0x23100809b9c21fa1}, // 5^-279
	{0xb58547448ffffb2d, 0xabd40a0c2832a78a}, // 5^-278
	{0xe2e69915b3fff9f9, 0x16c90c8f323f516c}, // 5^-277
	{0x8dd01fad907ffc3b, 0xae3da7d97f6792e3}, // 5^-276
	{0xb1442798f49ffb4a, 0x99cd11cfdf41779c}, // 5^-275
	{0xdd95317f31c7fa1d, 0x40405643d711d583}, // 5^-274
	{0x8a7d3eef7f1cfc52, 0x482835ea666b2572}, // 5^-273
	{0xad1c8eab5ee43b66, 0xda3243650005eecf}, // 5^-272
	{0xd863b256369d4a40, 0x90bed43e40076a82}, // 5^-271
	{0x873e4f75e2224e68, 0x5a7744a6e804a291}, // 5^-270
	{0xa90de3535aaae202, 0x711515d0a205cb36}, // 5^-269
	{0xd3515c2831559a83, 0x0d5a5b44ca873e03}, // 5^-268
	{0x8412d9991ed58091, 0xe858790afe9486c2}, // 5^-267
	{0xa5178fff668ae0b6, 0x626e974dbe39a872}, // 5^-266
	{0xce5d73ff402d98e3, 0xfb0a3d212dc8128f}, // 5^-265
	{0x80fa687f881c7f8e, 0x7ce66634bc9d0b99}, // 5^-264
	{0xa139029f6a239f72, 0x1c1fffc1ebc44e80}, // 5^-263
	{0xc987434744ac874e, 0xa327ffb266b56220}, // 5^-262
	{0xfbe9141915d7a922, 0x4bf1ff9f0062baa8}, // 5^-261
	{0x9d71ac8fada6c9b5, 0x6f773fc3603db4a9}, // 5^-260
	{0xc4ce17b399107c22, 0xcb550fb4384d21d3}, // 5^-259
	{0xf6019da07f549b2b, 0x7e2a53a146606a48}, // 5^-258
	{0x99c102844f94e0fb, 0x2eda7444cbfc426d}, // 5^-257
	{0xc0314325637a1939, 0xfa911155fefb5308}, // 5^-256
	{0xf03d93eebc589f88, 0x793555ab7eba27ca}, // 5^-255
	{0x96267c7535b763b5, 0x4bc1558b2f3458de}, // 5^-254
	{0xbbb01b9283253ca2, 0x9eb1aaedfb016f16}, // 5^-253
	{0xea9c227723ee8bcb, 0x465e15a979c1cadc}, // 5^-252
	{0x92a1958a7675175f, 0x0bfacd89ec191ec9}, // 5^-251
	{0xb749faed14125d36, 0xcef980ec671f667b}, // 5^-250
	{0xe51c79a85916f484, 0x82b7e12780e7401a}, // 5^-249
	{0x8f31cc0937ae58d2, 0xd1b2ecb8b0908810}, // 5^-248
	{0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa15}, // 5^-247
	{0xdfbdcece67006ac9, 0x67a791e093e1d49a}, // 5^-246
	{0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e0}, // 5^-245
	{0xaecc49914078536d, 0x58fae9f773886e18}, // 5^-244
	{0xda7f5bf590966848, 0xaf39a475506a899e}, // 5^-243
	{0x888f99797a5e012d, 0x6d8406c952429603}, // 5^-242
	{0xaab37fd7d8f58178, 0xc8e5087ba6d33b83}, // 5^-241
	{0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a64}, // 5^-240
	{0x855c3be0a17fcd26, 0x5cf2eea09a55067f}, // 5^-239
	{0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481e}, // 5^-238
	{0xd0601d8efc57b08b, 0xf13b94daf124da26}, // 5^-237
	{0x823c12795db6ce57, 0x76c53d08d6b70858}, // 5^-236
	{0xa2cb1717b52481ed, 0x54768c4b0c64ca6e}, // 5^-235
	{0xcb7ddcdda26da268, 0xa9942f5dcf7dfd09}, // 5^-234
	{0xfe5d54150b090b02, 0xd3f93b35435d7c4c}, // 5^-233
	{0x9efa548d26e5a6e1, 0xc47bc5014a1a6daf}, // 5^-232
	{0xc6b8e9b0709f109a, 0x359ab6419ca1091b}, // 5^-231
	{0xf867241c8cc6d4c0, 0xc30163d203c94b62}, // 5^-230
	{0x9b407691d7fc44f8, 0x79e0de63425dcf1d}, // 5^-229
	{0xc21094364dfb5636, 0x985915fc12f542e4}, // 5^-228
	{0xf294b943e17a2bc4, 0x3e6f5b7b17b2939d}, // 5^-227
	{0x979cf3ca6cec5b5a, 0xa705992ceecf9c42}, // 5^-226
	{0xbd8430bd08277231, 0x50c6ff782a838353}, // 5^-225
	{0xece53cec4a314ebd, 0xa4f8bf5635246428}, // 5^-224
	{0x940f4613ae5ed136, 0x871b7795e136be99}, // 5^-223
	{0xb913179899f68584, 0x28e2557b59846e3f}, // 5^-222
	{0xe757dd7ec07426e5, 0x331aeada2fe589cf}, // 5^-221
	{0x9096ea6f3848984f, 0x3ff0d2c85def7621}, // 5^-220
	{0xb4bca50b065abe63, 0x0fed077a756b53a9}, // 5^-219
	{0xe1ebce4dc7f16dfb, 0xd3e8495912c62894}, // 5^-218
	{0x8d3360f09cf6e4bd, 0x64712dd7abbbd95c}, // 5^-217
	{0xb080392cc4349dec, 0xbd8d794d96aacfb3}, // 5^-216
	{0xdca04777f541c567, 0xecf0d7a0fc5583a0}, // 5^-215
	{0x89e42caaf9491b60, 0xf41686c49db57244}, // 5^-214
	{0xac5d37d5b79b6239, 0x311c2875c522ced5}, // 5^-213
	{0xd77485cb25823ac7, 0x7d633293366b828b}, // 5^-212
	{0x86a8d39ef77164bc, 0xae5dff9c02033197}, // 5^-211
	{0xa8530886b54dbdeb, 0xd9f57f830283fdfc}, // 5^-210
	{0xd267caa862a12d66, 0xd072df63c324fd7b}, // 5^-209
	{0x8380dea93da4bc60, 0x4247cb9e59f71e6d}, // 5^-208
	{0xa46116538d0deb78, 0x52d9be85f074e608}, // 5^-207
	{0xcd795be870516656, 0x67902e276c921f8b}, // 5^-206
	{0x806bd9714632dff6, 0x00ba1cd8a3db53b6}, // 5^-205
	{0xa086cfcd97bf97f3, 0x80e8a40eccd228a4}, // 5^-204
	{0xc8a883c0fdaf7df0, 0x6122cd128006b2cd}, // 5^-203
	{0xfad2a4b13d1b5d6c, 0x796b805720085f81}, // 5^-202
	{0x9cc3a6eec6311a63, 0xcbe3303674053bb0}, // 5^-201
	{0xc3f490aa77bd60fc, 0xbedbfc4411068a9c}, // 5^-200
	{0xf4f1b4d515acb93b, 0xee92fb5515482d44}, // 5^-199
	{0x991711052d8bf3c5, 0x751bdd152d4d1c4a}, // 5^-198
	{0xbf5cd54678eef0b6, 0xd262d45a78a0635d}, // 5^-197
	{0xef340a98172aace4, 0x86fb897116c87c34}, // 5^-196
	{0x9580869f0e7aac0e, 0xd45d35e6ae3d4da0}, // 5^-195
	{0xbae0a846d2195712, 0x8974836059cca109}, // 5^-194
	{0xe998d258869facd7, 0x2bd1a438703fc94b}, // 5^-193
	{0x91ff83775423cc06, 0x7b6306a34627ddcf}, // 5^-192
	{0xb67f6455292cbf08, 0x1a3bc84c17b1d542}, // 5^-191
	{0xe41f3d6a7377eeca, 0x20caba5f1d9e4a93}, // 5^-190
	{0x8e938662882af53e, 0x547eb47b7282ee9c}, // 5^-189
	{0xb23867fb2a35b28d, 0xe99e619a4f23aa43}, // 5^-188
	{0xdec681f9f4c31f31, 0x6405fa00e2ec94d4}, // 5^-187
	{0x8b3c113c38f9f37e, 0xde83bc408dd3dd04}, // 5^-186
	{0xae0b158b4738705e, 0x9624ab50b148d445}, // 5^-185
	{0xd98ddaee19068c76, 0x3badd624dd9b0957}, // 5^-184
	{0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d6}, // 5^-183
	{0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4c}, // 5^-182
	{0xd47487cc8470652b, 0x7647c3200069671f}, // 5^-181
	{0x84c8d4dfd2c63f3b, 0x29ecd9f40041e073}, // 5^-180
	{0xa5fb0a17c777cf09, 0xf468107100525890}, // 5^-179
	{0xcf79cc9db955c2cc, 0x7182148d4066eeb4}, // 5^-178
	{0x81ac1fe293d599bf, 0xc6f14cd848405530}, // 5^-177
	{0xa21727db38cb002f, 0xb8ada00e5a506a7c}, // 5^-176
	{0xca9cf1d206fdc03b, 0xa6d90811f0e4851c}, // 5^-175
	{0xfd442e4688bd304a, 0x908f4a166d1da663}, // 5^-174
	{0x9e4a9cec15763e2e, 0x9a598e4e043287fe}, // 5^-173
	{0xc5dd44271ad3cdba, 0x40eff1e1853f29fd}, // 5^-172
	{0xf7549530e188c128, 0xd12bee59e68ef47c}, // 5^-171
	{0x9a94dd3e8cf578b9, 0x82bb74f8301958ce}, // 5^-170
	{0xc13a148e3032d6e7, 0xe36a52363c1faf01}, // 5^-169
	{0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac1}, // 5^-168
	{0x96f5600f15a7b7e5, 0x29ab103a5ef8c0b9}, // 5^-167
	{0xbcb2b812db11a5de, 0x7415d448f6b6f0e7}, // 5^-166
	{0xebdf661791d60f56, 0x111b495b3464ad21}, // 5^-165
	{0x936b9fcebb25c995, 0xcab10dd900beec34}, // 5^-164
	{0xb84687c269ef3bfb, 0x3d5d514f40eea742}, // 5^-163
	{0xe65829b3046b0afa, 0x0cb4a5a3112a5112}, // 5^-162
	{0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ab}, // 5^-161
	{0xb3f4e093db73a093, 0x59ed216765690f56}, // 5^-160
	{0xe0f218b8d25088b8, 0x306869c13ec3532c}, // 5^-159
	{0x8c974f7383725573, 0x1e414218c73a13fb}, // 5^-158
	{0xafbd2350644eeacf, 0xe5d1929ef90898fa}, // 5^-157
	{0xdbac6c247d62a583, 0xdf45f746b74abf39}, // 5^-156
	{0x894bc396ce5da772, 0x6b8bba8c328eb783}, // 5^-155
	{0xab9eb47c81f5114f, 0x066ea92f3f326564}, // 5^-154
	{0xd686619ba27255a2, 0xc80a537b0efefebd}, // 5^-153
	{0x8613fd0145877585, 0xbd06742ce95f5f36}, // 5^-152
	{0xa798fc4196e952e7, 0x2c48113823b73704}, // 5^-151
	{0xd17f3b51fca3a7a0, 0xf75a15862ca504c5}, // 5^-150
	{0x82ef85133de648c4, 0x9a984d73dbe722fb}, // 5^-149
	{0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebba}, // 5^-148
	{0xcc963fee10b7d1b3, 0x318df905079926a8}, // 5^-147
	{0xffbbcfe994e5c61f, 0xfdf17746497f7052}, // 5^-146
	{0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa633}, // 5^-145
	{0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc0}, // 5^-144
	{0xf9bd690a1b68637b, 0x3dfdce7aa3c673b0}, // 5^-143
	{0x9c1661a651213e2d, 0x06bea10ca65c084e}, // 5^-142
	{0xc31bfa0fe5698db8, 0x486e494fcff30a62}, // 5^-141
	{0xf3e2f893dec3f126, 0x5a89dba3c3efccfa}, // 5^-140
	{0x986ddb5c6b3a76b7, 0xf89629465a75e01c}, // 5^-139
	{0xbe89523386091465, 0xf6bbb397f1135823}, // 5^-138
	{0xee2ba6c0678b597f, 0x746aa07ded582e2c}, // 5^-137
	{0x94db483840b717ef, 0xa8c2a44eb4571cdc}, // 5^-136
	{0xba121a4650e4ddeb, 0x92f34d62616ce413}, // 5^-135
	{0xe896a0d7e51e1566, 0x77b020baf9c81d17}, // 5^-134
	{0x915e2486ef32cd60, 0x0ace1474dc1d122e}, // 5^-133
	{0xb5b5ada8aaff80b8, 0x0d819992132456ba}, // 5^-132
	{0xe3231912d5bf60e6, 0x10e1fff697ed6c69}, // 5^-131
	{0x8df5efabc5979c8f, 0xca8d3ffa1ef463c1}, // 5^-130
	{0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb2}, // 5^-129
	{0xddd0467c64bce4a0, 0xac7cb3f6d05ddbde}, // 5^-128
	{0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96b}, // 5^-127
	{0xad4ab7112eb3929d, 0x86c16c98d2c953c6}, // 5^-126
	{0xd89d64d57a607744, 0xe871c7bf077ba8b7}, // 5^-125
	{0x87625f056c7c4a8b, 0x11471cd764ad4972}, // 5^-124
	{0xa93af6c6c79b5d2d, 0xd598e40d3dd89bcf}, // 5^-123
	{0xd389b47879823479, 0x4aff1d108d4ec2c3}, // 5^-122
	{0x843610cb4bf160cb, 0xcedf722a585139ba}, // 5^-121
	{0xa54394fe1eedb8fe, 0xc2974eb4ee658828}, // 5^-120
	{0xce947a3da6a9273e, 0x733d226229feea32}, // 5^-119
	{0x811ccc668829b887, 0x0806357d5a3f525f}, // 5^-118
	{0xa163ff802a3426a8, 0xca07c2dcb0cf26f7}, // 5^-117
	{0xc9bcff6034c13052, 0xfc89b393dd02f0b5}, // 5^-116
	{0xfc2c3f3841f17c67, 0xbbac2078d443ace2}, // 5^-115
	{0x9d9ba7832936edc0, 0xd54b944b84aa4c0d}, // 5^-114
	{0xc5029163f384a931, 0x0a9e795e65d4df11}, // 5^-113
	{0xf64335bcf065d37d, 0x4d4617b5ff4a16d5}, // 5^-112
	{0x99ea0196163fa42e, 0x504bced1bf8e4e45}, // 5^-111
	{0xc06481fb9bcf8d39, 0xe45ec2862f71e1d6}, // 5^-110
	{0xf07da27a82c37088, 0x5d767327bb4e5a4c}, // 5^-109
	{0x964e858c91ba2655, 0x3a6a07f8d510f86f}, // 5^-108
	{0xbbe226efb628afea, 0x890489f70a55368b}, // 5^-107
	{0xeadab0aba3b2dbe5, 0x2b45ac74ccea842e}, // 5^-106
	{0x92c8ae6b464fc96f, 0x3b0b8bc90012929d}, // 5^-105
	{0xb77ada0617e3bbcb, 0x09ce6ebb40173744}, // 5^-104
	{0xe55990879ddcaabd, 0xcc420a6a101d0515}, // 5^-103
	{0x8f57fa54c2a9eab6, 0x9fa946824a12232d}, // 5^-102
	{0xb32df8e9f3546564, 0x47939822dc96abf9}, // 5^-101
	{0xdff9772470297ebd, 0x59787e2b93bc56f7}, // 5^-100
	{0x8bfbea76c619ef36, 0x57eb4edb3c55b65a}, // 5^-99
	{0xaefae51477a06b03, 0xede622920b6b23f1}, // 5^-98
	{0xdab99e59958885c4, 0xe95fab368e45eced}, // 5^-97
	{0x88b402f7fd75539b, 0x11dbcb0218ebb414}, // 5^-96
	{0xaae103b5fcd2a881, 0xd652bdc29f26a119}, // 5^-95
	{0xd59944a37c0752a2, 0x4be76d3346f0495f}, // 5^-94
	{0x857fcae62d8493a5, 0x6f70a4400c562ddb}, // 5^-93
	{0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb952}, // 5^-92
	{0xd097ad07a71f26b2, 0x7e2000a41346a7a7}, // 5^-91
	{0x825ecc24c873782f, 0x8ed400668c0c28c8}, // 5^-90
	{0xa2f67f2dfa90563b, 0x728900802f0f32fa}, // 5^-89
	{0xcbb41ef979346bca, 0x4f2b40a03ad2ffb9}, // 5^-88
	{0xfea126b7d78186bc, 0xe2f610c84987bfa8}, // 5^-87
	{0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7c9}, // 5^-86
	{0xc6ede63fa05d3143, 0x91503d1c79720dbb}, // 5^-85
	{0xf8a95fcf88747d94, 0x75a44c6397ce912a}, // 5^-84
	{0x9b69dbe1b548ce7c, 0xc986afbe3ee11aba}, // 5^-83
	{0xc24452da229b021b, 0xfbe85badce996168}, // 5^-82
	{0xf2d56790ab41c2a2, 0xfae27299423fb9c3}, // 5^-81
	{0x97c560ba6b0919a5, 0xdccd879fc967d41a}, // 5^-80
	{0xbdb6b8e905cb600f, 0x5400e987bbc1c920}, // 5^-79
	{0xed246723473e3813, 0x290123e9aab23b68}, // 5^-78
	{0x9436c0760c86e30b, 0xf9a0b6720aaf6521}, // 5^-77
	{0xb94470938fa89bce, 0xf808e40e8d5b3e69}, // 5^-76
	{0xe7958cb87392c2c2, 0xb60b1d1230b20e04}, // 5^-75
	{0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c2}, // 5^-74
	{0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af3}, // 5^-73
	{0xe2280b6c20dd5232, 0x25c6da63c38de1b0}, // 5^-72
	{0x8d590723948a535f, 0x579c487e5a38ad0e}, // 5^-71
	{0xb0af48ec79ace837, 0x2d835a9df0c6d851}, // 5^-70
	{0xdcdb1b2798182244, 0xf8e431456cf88e65}, // 5^-69
	{0x8a08f0f8bf0f156b, 0x1b8e9ecb641b58ff}, // 5^-68
	{0xac8b2d36eed2dac5, 0xe272467e3d222f3f}, // 5^-67
	{0xd7adf884aa879177, 0x5b0ed81dcc6abb0f}, // 5^-66
	{0x86ccbb52ea94baea, 0x98e947129fc2b4e9}, // 5^-65
	{0xa87fea27a539e9a5, 0x3f2398d747b36224}, // 5^-64
	{0xd29fe4b18e88640e, 0x8eec7f0d19a03aad}, // 5^-63
	{0x83a3eeeef9153e89, 0x1953cf68300424ac}, // 5^-62
	{0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd7}, // 5^-61
	{0xcdb02555653131b6, 0x3792f412cb06794d}, // 5^-60
	{0x808e17555f3ebf11, 0xe2bbd88bbee40bd0}, // 5^-59
	{0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec4}, // 5^-58
	{0xc8de047564d20a8b, 0xf245825a5a445275}, // 5^-57
	{0xfb158592be068d2e, 0xeed6e2f0f0d56712}, // 5^-56
	{0x9ced737bb6c4183d, 0x55464dd69685606b}, // 5^-55
	{0xc428d05aa4751e4c, 0xaa97e14c3c26b886}, // 5^-54
	{0xf53304714d9265df, 0xd53dd99f4b3066a8}, // 5^-53
	{0x993fe2c6d07b7fab, 0xe546a8038efe4029}, // 5^-52
	{0xbf8fdb78849a5f96, 0xde98520472bdd033}, // 5^-51
	{0xef73d256a5c0f77c, 0x963e66858f6d4440}, // 5^-50
	{0x95a8637627989aad, 0xdde7001379a44aa8}, // 5^-49
	{0xbb127c53b17ec159, 0x5560c018580d5d52}, // 5^-48
	{0xe9d71b689dde71af, 0xaab8f01e6e10b4a6}, // 5^-47
	{0x9226712162ab070d, 0xcab3961304ca70e8}, // 5^-46
	{0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d22}, // 5^-45
	{0xe45c10c42a2b3b05, 0x8cb89a7db77c506a}, // 5^-44
	{0x8eb98a7a9a5b04e3, 0x77f3608e92adb242}, // 5^-43
	{0xb267ed1940f1c61c, 0x55f038b237591ed3}, // 5^-42
	{0xdf01e85f912e37a3, 0x6b6c46dec52f6688}, // 5^-41
	{0x8b61313bbabce2c6, 0x2323ac4b3b3da015}, // 5^-40
	{0xae397d8aa96c1b77, 0xabec975e0a0d081a}, // 5^-39
	{0xd9c7dced53c72255, 0x96e7bd358c904a21}, // 5^-38
	{0x881cea14545c7575, 0x7e50d64177da2e54}, // 5^-37
	{0xaa242499697392d2, 0xdde50bd1d5d0b9e9}, // 5^-36
	{0xd4ad2dbfc3d07787, 0x955e4ec64b44e864}, // 5^-35
	{0x84ec3c97da624ab4, 0xbd5af13bef0b113e}, // 5^-34
	{0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58e}, // 5^-33
	{0xcfb11ead453994ba, 0x67de18eda5814af2}, // 5^-32
	{0x81ceb32c4b43fcf4, 0x80eacf948770ced7}, // 5^-31
	{0xa2425ff75e14fc31, 0xa1258379a94d028d}, // 5^-30
	{0xcad2f7f5359a3b3e, 0x096ee45813a04330}, // 5^-29
	{0xfd87b5f28300ca0d, 0x8bca9d6e188853fc}, // 5^-28
	{0x9e74d1b791e07e48, 0x775ea264cf55347e}, // 5^-27
	{0xc612062576589dda, 0x95364afe032a819e}, // 5^-26
	{0xf79687aed3eec551, 0x3a83ddbd83f52205}, // 5^-25
	{0x9abe14cd44753b52, 0xc4926a9672793543}, // 5^-24
	{0xc16d9a0095928a27, 0x75b7053c0f178294}, // 5^-23
	{0xf1c90080baf72cb1, 0x5324c68b12dd6339}, // 5^-22
	{0x971da05074da7bee, 0xd3f6fc16ebca5e04}, // 5^-21
	{0xbce5086492111aea, 0x88f4bb1ca6bcf585}, // 5^-20
	{0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6}, // 5^-19
	{0x9392ee8e921d5d07, 0x3aff322e62439fd0}, // 5^-18
	{0xb877aa3236a4b449, 0x09befeb9fad487c3}, // 5^-17
	{0xe69594bec44de15b, 0x4c2ebe687989a9b4}, // 5^-16
	{0x901d7cf73ab0acd9, 0x0f9d37014bf60a11}, // 5^-15
	{0xb424dc35095cd80f, 0x538484c19ef38c95}, // 5^-14
	{0xe12e13424bb40e13, 0x2865a5f206b06fba}, // 5^-13
	{0x8cbccc096f5088cb, 0xf93f87b7442e45d4}, // 5^-12
	{0xafebff0bcb24aafe, 0xf78f69a51539d749}, // 5^-11
	{0xdbe6fecebdedd5be, 0xb573440e5a884d1c}, // 5^-10
	{0x89705f4136b4a597, 0x31680a88f8953031}, // 5^-9
	{0xabcc77118461cefc, 0xfdc20d2b36ba7c3e}, // 5^-8
	{0xd6bf94d5e57a42bc, 0x3d32907604691b4d}, // 5^-7
	{0x8637bd05af6c69b5, 0xa63f9a49c2c1b110}, // 5^-6
	{0xa7c5ac471b478423, 0x0fcf80dc33721d54}, // 5^-5
	{0xd1b71758e219652b, 0xd3c36113404ea4a9}, // 5^-4
	{0x83126e978d4fdf3b, 0x645a1cac083126ea}, // 5^-3
	{0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4}, // 5^-2
	{0xcccccccccccccccc, 0xcccccccccccccccd}, // 5^-1
	{0x8000000000000000, 0x0000000000000000}, // 5^0
	{0xa000000000000000, 0x0000000000000000}, // 5^1
	{0xc800000000000000, 0x0000000000000000}, // 5^2
	{0xfa00000000000000, 0x0000000000000000}, // 5^3
	{0x9c40000000000000, 0x0000000000000000}, // 5^4
	{0xc350000000000000, 0x0000000000000000}, // 5^5
	{0xf424000000000000, 0x0000000000000000}, // 5^6
	{0x9896800000000000, 0x0000000000000000}, // 5^7
	{0xbebc200000000000, 0x0000000000000000}, // 5^8
	{0xee6b280000000000, 0x0000000000000000}, // 5^9
	{0x9502f90000000000, 0x0000000000000000}, // 5^10
	{0xba43b74000000000, 0x0000000000000000}, // 5^11
	{0xe8d4a51000000000, 0x0000000000000000}, // 5^12
	{0x9184e72a00000000, 0x0000000000000000}, // 5^13
	{0xb5e620f480000000, 0x0000000000000000}, // 5^14
	{0xe35fa931a0000000, 0x0000000000000000}, // 5^15
	{0x8e1bc9bf04000000, 0x0000000000000000}, // 5^16
	{0xb1a2bc2ec5000000, 0x0000000000000000}, // 5^17
	{0xde0b6b3a76400000, 0x0000000000000000}, // 5^18
	{0x8ac7230489e80000, 0x0000000000000000}, // 5^19
	{0xad78ebc5ac620000, 0x0000000000000000}, // 5^20
	{0xd8d726b7177a8000, 0x0000000000000000}, // 5^21
	{0x878678326eac9000, 0x0000000000000000}, // 5^22
	{0xa968163f0a57b400, 0x0000000000000000}, // 5^23
	{0xd3c21bcecceda100, 0x0000000000000000}, // 5^24
	{0x84595161401484a0, 0x0000000000000000}, // 5^25
	{0xa56fa5b99019a5c8, 0x0000000000000000}, // 5^26
	{0xcecb8f27f4200f3a, 0x0000000000000000}, // 5^27
	{0x813f3978f8940984, 0x4000000000000000}, // 5^28
	{0xa18f07d736b90be5, 0x5000000000000000}, // 5^29
	{0xc9f2c9cd04674ede, 0xa400000000000000}, // 5^30
	{0xfc6f7c4045812296, 0x4d00000000000000}, // 5^31
	{0x9dc5ada82b70b59d, 0xf020000000000000}, // 5^32
	{0xc5371912364ce305, 0x6c28000000000000}, // 5^33
	{0xf684df56c3e01bc6, 0xc732000000000000}, // 5^34
	{0x9a130b963a6c115c, 0x3c7f400000000000}, // 5^35
	{0xc097ce7bc90715b3, 0x4b9f100000000000}, // 5^36
	{0xf0bdc21abb48db20, 0x1e86d40000000000}, // 5^37
	{0x96769950b50d88f4, 0x1314448000000000}, // 5^38
	{0xbc143fa4e250eb31, 0x17d955a000000000}, // 5^39
	{0xeb194f8e1ae525fd, 0x5dcfab0800000000}, // 5^40
	{0x92efd1b8d0cf37be, 0x5aa1cae500000000}, // 5^41
	{0xb7abc627050305ad, 0xf14a3d9e40000000}, // 5^42
	{0xe596b7b0c643c719, 0x6d9ccd05d0000000}, // 5^43
	{0x8f7e32ce7bea5c6f, 0xe4820023a2000000}, // 5^44
	{0xb35dbf821ae4f38b, 0xdda2802c8a800000}, // 5^45
	{0xe0352f62a19e306e, 0xd50b2037ad200000}, // 5^46
	{0x8c213d9da502de45, 0x4526f422cc340000}, // 5^47
	{0xaf298d050e4395d6, 0x9670b12b7f410000}, // 5^48
	{0xdaf3f04651d47b4c, 0x3c0cdd765f114000}, // 5^49
	{0x88d8762bf324cd0f, 0xa5880a69fb6ac800}, // 5^50
	{0xab0e93b6efee0053, 0x8eea0d047a457a00}, // 5^51
	{0xd5d238a4abe98068, 0x72a4904598d6d880}, // 5^52
	{0x85a36366eb71f041, 0x47a6da2b7f864750}, // 5^53
	{0xa70c3c40a64e6c51, 0x999090b65f67d924}, // 5^54
	{0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d}, // 5^55
	{0x82818f1281ed449f, 0xbff8f10e7a8921a4}, // 5^56
	{0xa321f2d7226895c7, 0xaff72d52192b6a0d}, // 5^57
	{0xcbea6f8ceb02bb39, 0x9bf4f8a69f764490}, // 5^58
	{0xfee50b7025c36a08, 0x02f236d04753d5b4}, // 5^59
	{0x9f4f2726179a2245, 0x01d762422c946590}, // 5^60
	{0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef5}, // 5^61
	{0xf8ebad2b84e0d58b, 0xd2e0898765a7deb2}, // 5^62
	{0x9b934c3b330c8577, 0x63cc55f49f88eb2f}, // 5^63
	{0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fb}, // 5^64
	{0xf316271c7fc3908a, 0x8bef464e3945ef7a}, // 5^65
	{0x97edd871cfda3a56, 0x97758bf0e3cbb5ac}, // 5^66
	{0xbde94e8e43d0c8ec, 0x3d52eeed1cbea317}, // 5^67
	{0xed63a231d4c4fb27, 0x4ca7aaa863ee4bdd}, // 5^68
	{0x945e455f24fb1cf8, 0x8fe8caa93e74ef6a}, // 5^69
	{0xb975d6b6ee39e436, 0xb3e2fd538e122b44}, // 5^70
	{0xe7d34c64a9c85d44, 0x60dbbca87196b616}, // 5^71
	{0x90e40fbeea1d3a4a, 0xbc8955e946fe31cd}, // 5^72
	{0xb51d13aea4a488dd, 0x6babab6398bdbe41}, // 5^73
	{0xe264589a4dcdab14, 0xc696963c7eed2dd1}, // 5^74
	{0x8d7eb76070a08aec, 0xfc1e1de5cf543ca2}, // 5^75
	{0xb0de65388cc8ada8, 0x3b25a55f43294bcb}, // 5^76
	{0xdd15fe86affad912, 0x49ef0eb713f39ebe}, // 5^77
	{0x8a2dbf142dfcc7ab, 0x6e3569326c784337}, // 5^78
	{0xacb92ed9397bf996, 0x49c2c37f07965404}, // 5^79
	{0xd7e77a8f87daf7fb, 0xdc33745ec97be906}, // 5^80
	{0x86f0ac99b4e8dafd, 0x69a028bb3ded71a3}, // 5^81
	{0xa8acd7c0222311bc, 0xc40832ea0d68ce0c}, // 5^82
	{0xd2d80db02aabd62b, 0xf50a3fa490c30190}, // 5^83
	{0x83c7088e1aab65db, 0x792667c6da79e0fa}, // 5^84
	{0xa4b8cab1a1563f52, 0x577001b891185938}, // 5^85
	{0xcde6fd5e09abcf26, 0xed4c0226b55e6f86}, // 5^86
	{0x80b05e5ac60b6178, 0x544f8158315b05b4}, // 5^87
	{0xa0dc75f1778e39d6, 0x696361ae3db1c721}, // 5^88
	{0xc913936dd571c84c, 0x03bc3a19cd1e38e9}, // 5^89
	{0xfb5878494ace3a5f, 0x04ab48a04065c723}, // 5^90
	{0x9d174b2dcec0e47b, 0x62eb0d64283f9c76}, // 5^91
	{0xc45d1df942711d9a, 0x3ba5d0bd324f8394}, // 5^92
	{0xf5746577930d6500, 0xca8f44ec7ee36479}, // 5^93
	{0x9968bf6abbe85f20, 0x7e998b13cf4e1ecb}, // 5^94
	{0xbfc2ef456ae276e8, 0x9e3fedd8c321a67e}, // 5^95
	{0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101e}, // 5^96
	{0x95d04aee3b80ece5, 0xbba1f1d158724a12}, // 5^97
	{0xbb445da9ca61281f, 0x2a8a6e45ae8edc97}, // 5^98
	{0xea1575143cf97226, 0xf52d09d71a3293bd}, // 5^99
	{0x924d692ca61be758, 0x593c2626705f9c56}, // 5^100
	{0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836c}, // 5^101
	{0xe498f455c38b997a, 0x0b6dfb9c0f956447}, // 5^102
	{0x8edf98b59a373fec, 0x4724bd4189bd5eac}, // 5^103
	{0xb2977ee300c50fe7, 0x58edec91ec2cb657}, // 5^104
	{0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ed}, // 5^105
	{0x8b865b215899f46c, 0xbd79e0d20082ee74}, // 5^106
	{0xae67f1e9aec07187, 0xecd8590680a3aa11}, // 5^107
	{0xda01ee641a708de9, 0xe80e6f4820cc9495}, // 5^108
	{0x884134fe908658b2, 0x3109058d147fdcdd}, // 5^109
	{0xaa51823e34a7eede, 0xbd4b46f0599fd415}, // 5^110
	{0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91a}, // 5^111
	{0x850fadc09923329e, 0x03e2cf6bc604ddb0}, // 5^112
	{0xa6539930bf6bff45, 0x84db8346b786151c}, // 5^113
	{0xcfe87f7cef46ff16, 0xe612641865679a63}, // 5^114
	{0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07e}, // 5^115
	{0xa26da3999aef7749, 0xe3be5e330f38f09d}, // 5^116
	{0xcb090c8001ab551c, 0x5cadf5bfd3072cc5}, // 5^117
	{0xfdcb4fa002162a63, 0x73d9732fc7c8f7f6}, // 5^118
	{0x9e9f11c4014dda7e, 0x2867e7fddcdd9afa}, // 5^119
	{0xc646d63501a1511d, 0xb281e1fd541501b8}, // 5^120
	{0xf7d88bc24209a565, 0x1f225a7ca91a4226}, // 5^121
	{0x9ae757596946075f, 0x3375788de9b06958}, // 5^122
	{0xc1a12d2fc3978937, 0x0052d6b1641c83ae}, // 5^123
	{0xf209787bb47d6b84, 0xc0678c5dbd23a49a}, // 5^124
	{0x9745eb4d50ce6332, 0xf840b7ba963646e0}, // 5^125
	{0xbd176620a501fbff, 0xb650e5a93bc3d898}, // 5^126
	{0xec5d3fa8ce427aff, 0xa3e51f138ab4cebe}, // 5^127
	{0x93ba47c980e98cdf, 0xc66f336c36b10137}, // 5^128
	{0xb8a8d9bbe123f017, 0xb80b0047445d4184}, // 5^129
	{0xe6d3102ad96cec1d, 0xa60dc059157491e5}, // 5^130
	{0x9043ea1ac7e41392, 0x87c89837ad68db2f}, // 5^131
	{0xb454e4a179dd1877, 0x29babe4598c311fb}, // 5^132
	{0xe16a1dc9d8545e94, 0xf4296dd6fef3d67a}, // 5^133
	{0x8ce2529e2734bb1d, 0x1899e4a65f58660c}, // 5^134
	{0xb01ae745b101e9e4, 0x5ec05dcff72e7f8f}, // 5^135
	{0xdc21a1171d42645d, 0x76707543f4fa1f73}, // 5^136
	{0x899504ae72497eba, 0x6a06494a791c53a8}, // 5^137
	{0xabfa45da0edbde69, 0x0487db9d17636892}, // 5^138
	{0xd6f8d7509292d603, 0x45a9d2845d3c42b6}, // 5^139
	{0x865b86925b9bc5c2, 0x0b8a2392ba45a9b2}, // 5^140
	{0xa7f26836f282b732, 0x8e6cac7768d7141e}, // 5^141
	{0xd1ef0244af2364ff, 0x3207d795430cd926}, // 5^142
	{0x8335616aed761f1f, 0x7f44e6bd49e807b8}, // 5^143
	{0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a6}, // 5^144
	{0xcd036837130890a1, 0x36dba887c37a8c0f}, // 5^145
	{0x802221226be55a64, 0xc2494954da2c9789}, // 5^146
	{0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6c}, // 5^147
	{0xc83553c5c8965d3d, 0x6f92829494e5acc7}, // 5^148
	{0xfa42a8b73abbf48c, 0xcb772339ba1f17f9}, // 5^149
	{0x9c69a97284b578d7, 0xff2a760414536efb}, // 5^150
	{0xc38413cf25e2d70d, 0xfef5138519684aba}, // 5^151
	{0xf46518c2ef5b8cd1, 0x7eb258665fc25d69}, // 5^152
	{0x98bf2f79d5993802, 0xef2f773ffbd97a61}, // 5^153
	{0xbeeefb584aff8603, 0xaafb550ffacfd8fa}, // 5^154
	{0xeeaaba2e5dbf6784, 0x95ba2a53f983cf38}, // 5^155
	{0x952ab45cfa97a0b2, 0xdd945a747bf26183}, // 5^156
	{0xba756174393d88df, 0x94f971119aeef9e4}, // 5^157
	{0xe912b9d1478ceb17, 0x7a37cd5601aab85d}, // 5^158
	{0x91abb422ccb812ee, 0xac62e055c10ab33a}, // 5^159
	{0xb616a12b7fe617aa, 0x577b986b314d6009}, // 5^160
	{0xe39c49765fdf9d94, 0xed5a7e85fda0b80b}, // 5^161
	{0x8e41ade9fbebc27d, 0x14588f13be847307}, // 5^162
	{0xb1d219647ae6b31c, 0x596eb2d8ae258fc8}, // 5^163
	{0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bb}, // 5^164
	{0x8aec23d680043bee, 0x25de7bb9480d5854}, // 5^165
	{0xada72ccc20054ae9, 0xaf561aa79a10ae6a}, // 5^166
	{0xd910f7ff28069da4, 0x1b2ba1518094da04}, // 5^167
	{0x87aa9aff79042286, 0x90fb44d2f05d0842}, // 5^168
	{0xa99541bf57452b28, 0x353a1607ac744a53}, // 5^169
	{0xd3fa922f2d1675f2, 0x42889b8997915ce8}, // 5^170
	{0x847c9b5d7c2e09b7, 0x69956135febada11}, // 5^171
	{0xa59bc234db398c25, 0x43fab9837e699095}, // 5^172
	{0xcf02b2c21207ef2e, 0x94f967e45e03f4bb}, // 5^173
	{0x8161afb94b44f57d, 0x1d1be0eebac278f5}, // 5^174
	{0xa1ba1ba79e1632dc, 0x6462d92a69731732}, // 5^175
	{0xca28a291859bbf93, 0x7d7b8f7503cfdcfe}, // 5^176
	{0xfcb2cb35e702af78, 0x5cda735244c3d43e}, // 5^177
	{0x9defbf01b061adab, 0x3a0888136afa64a7}, // 5^178
	{0xc56baec21c7a1916, 0x088aaa1845b8fdd0}, // 5^179
	{0xf6c69a72a3989f5b, 0x8aad549e57273d45}, // 5^180
	{0x9a3c2087a63f6399, 0x36ac54e2f678864b}, // 5^181
	{0xc0cb28a98fcf3c7f, 0x84576a1bb416a7dd}, // 5^182
	{0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d5}, // 5^183
	{0x969eb7c47859e743, 0x9f644ae5a4b1b325}, // 5^184
	{0xbc4665b596706114, 0x873d5d9f0dde1fee}, // 5^185
	{0xeb57ff22fc0c7959, 0xa90cb506d155a7ea}, // 5^186
	{0x9316ff75dd87cbd8, 0x09a7f12442d588f2}, // 5^187
	{0xb7dcbf5354e9bece, 0x0c11ed6d538aeb2f}, // 5^188
	{0xe5d3ef282a242e81, 0x8f1668c8a86da5fa}, // 5^189
	{0x8fa475791a569d10, 0xf96e017d694487bc}, // 5^190
	{0xb38d92d760ec4455, 0x37c981dcc395a9ac}, // 5^191
	{0xe070f78d3927556a, 0x85bbe253f47b1417}, // 5^192
	{0x8c469ab843b89562, 0x93956d7478ccec8e}, // 5^193
	{0xaf58416654a6babb, 0x387ac8d1970027b2}, // 5^194
	{0xdb2e51bfe9d0696a, 0x06997b05fcc0319e}, // 5^195
	{0x88fcf317f22241e2, 0x441fece3bdf81f03}, // 5^196
	{0xab3c2fddeeaad25a, 0xd527e81cad7626c3}, // 5^197
	{0xd60b3bd56a5586f1, 0x8a71e223d8d3b074}, // 5^198
	{0x85c7056562757456, 0xf6872d5667844e49}, // 5^199
	{0xa738c6bebb12d16c, 0xb428f8ac016561db}, // 5^200
	{0xd106f86e69d785c7, 0xe13336d701beba52}, // 5^201
	{0x82a45b450226b39c, 0xecc0024661173473}, // 5^202
	{0xa34d721642b06084, 0x27f002d7f95d0190}, // 5^203
	{0xcc20ce9bd35c78a5, 0x31ec038df7b441f4}, // 5^204
	{0xff290242c83396ce, 0x7e67047175a15271}, // 5^205
	{0x9f79a169bd203e41, 0x0f0062c6e984d386}, // 5^206
	{0xc75809c42c684dd1, 0x52c07b78a3e60868}, // 5^207
	{0xf92e0c3537826145, 0xa7709a56ccdf8a82}, // 5^208
	{0x9bbcc7a142b17ccb, 0x88a66076400bb691}, // 5^209
	{0xc2abf989935ddbfe, 0x6acff893d00ea435}, // 5^210
	{0xf356f7ebf83552fe, 0x0583f6b8c4124d43}, // 5^211
	{0x98165af37b2153de, 0xc3727a337a8b704a}, // 5^212
	{0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5c}, // 5^213
	{0xeda2ee1c7064130c, 0x1162def06f79df73}, // 5^214
	{0x9485d4d1c63e8be7, 0x8addcb5645ac2ba8}, // 5^215
	{0xb9a74a0637ce2ee1, 0x6d953e2bd7173692}, // 5^216
	{0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0437}, // 5^217
	{0x910ab1d4db9914a0, 0x1d9c9892400a22a2}, // 5^218
	{0xb54d5e4a127f59c8, 0x2503beb6d00cab4b}, // 5^219
	{0xe2a0b5dc971f303a, 0x2e44ae64840fd61d}, // 5^220
	{0x8da471a9de737e24, 0x5ceaecfed289e5d2}, // 5^221
	{0xb10d8e1456105dad, 0x7425a83e872c5f47}, // 5^222
	{0xdd50f1996b947518, 0xd12f124e28f77719}, // 5^223
	{0x8a5296ffe33cc92f, 0x82bd6b70d99aaa6f}, // 5^224
	{0xace73cbfdc0bfb7b, 0x636cc64d1001550b}, // 5^225
	{0xd8210befd30efa5a, 0x3c47f7e05401aa4e}, // 5^226
	{0x8714a775e3e95c78, 0x65acfaec34810a71}, // 5^227
	{0xa8d9d1535ce3b396, 0x7f1839a741a14d0d}, // 5^228
	{0xd31045a8341ca07c, 0x1ede48111209a050}, // 5^229
	{0x83ea2b892091e44d, 0x934aed0aab460432}, // 5^230
	{0xa4e4b66b68b65d60, 0xf81da84d5617853f}, // 5^231
	{0xce1de40642e3f4b9, 0x36251260ab9d668e}, // 5^232
	{0x80d2ae83e9ce78f3, 0xc1d72b7c6b426019}, // 5^233
	{0xa1075a24e4421730, 0xb24cf65b8612f81f}, // 5^234
	{0xc94930ae1d529cfc, 0xdee033f26797b627}, // 5^235
	{0xfb9b7cd9a4a7443c, 0x169840ef017da3b1}, // 5^236
	{0x9d412e0806e88aa5, 0x8e1f289560ee864e}, // 5^237
	{0xc491798a08a2ad4e, 0xf1a6f2bab92a27e2}, // 5^238
	{0xf5b5d7ec8acb58a2, 0xae10af696774b1db}, // 5^239
	{0x9991a6f3d6bf1765, 0xacca6da1e0a8ef29}, // 5^240
	{0xbff610b0cc6edd3f, 0x17fd090a58d32af3}, // 5^241
	{0xeff394dcff8a948e, 0xddfc4b4cef07f5b0}, // 5^242
	{0x95f83d0a1fb69cd9, 0x4abdaf101564f98e}, // 5^243
	{0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f1}, // 5^244
	{0xea53df5fd18d5513, 0x84c86189216dc5ed}, // 5^245
	{0x92746b9be2f8552c, 0x32fd3cf5b4e49bb4}, // 5^246
	{0xb7118682dbb66a77, 0x3fbc8c33221dc2a1}, // 5^247
	{0xe4d5e82392a40515, 0x0fabaf3feaa5334a}, // 5^248
	{0x8f05b1163ba6832d, 0x29cb4d87f2a7400e}, // 5^249
	{0xb2c71d5bca9023f8, 0x743e20e9ef511012}, // 5^250
	{0xdf78e4b2bd342cf6, 0x914da9246b255416}, // 5^251
	{0x8bab8eefb6409c1a, 0x1ad089b6c2f7548e}, // 5^252
	{0xae9672aba3d0c320, 0xa184ac2473b529b1}, // 5^253
	{0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741e}, // 5^254
	{0x8865899617fb1871, 0x7e2fa67c7a658892}, // 5^255
	{0xaa7eebfb9df9de8d, 0xddbb901b98feeab7}, // 5^256
	{0xd51ea6fa85785631, 0x552a74227f3ea565}, // 5^257
	{0x8533285c936b35de, 0xd53a88958f87275f}, // 5^258
	{0xa67ff273b8460356, 0x8a892abaf368f137}, // 5^259
	{0xd01fef10a657842c, 0x2d2b7569b0432d85}, // 5^260
	{0x8213f56a67f6b29b, 0x9c3b29620e29fc73}, // 5^261
	{0xa298f2c501f45f42, 0x8349f3ba91b47b8f}, // 5^262
	{0xcb3f2f7642717713, 0x241c70a936219a73}, // 5^263
	{0xfe0efb53d30dd4d7, 0xed238cd383aa0110}, // 5^264
	{0x9ec95d1463e8a506, 0xf4363804324a40aa}, // 5^265
	{0xc67bb4597ce2ce48, 0xb143c6053edcd0d5}, // 5^266
	{0xf81aa16fdc1b81da, 0xdd94b7868e94050a}, // 5^267
	{0x9b10a4e5e9913128, 0xca7cf2b4191c8326}, // 5^268
	{0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f0}, // 5^269
	{0xf24a01a73cf2dccf, 0xbc633b39673c8cec}, // 5^270
	{0x976e41088617ca01, 0xd5be0503e085d813}, // 5^271
	{0xbd49d14aa79dbc82, 0x4b2d8644d8a74e18}, // 5^272
	{0xec9c459d51852ba2, 0xddf8e7d60ed1219e}, // 5^273
	{0x93e1ab8252f33b45, 0xcabb90e5c942b503}, // 5^274
	{0xb8da1662e7b00a17, 0x3d6a751f3b936243}, // 5^275
	{0xe7109bfba19c0c9d, 0x0cc512670a783ad4}, // 5^276
	{0x906a617d450187e2, 0x27fb2b80668b24c5}, // 5^277
	{0xb484f9dc9641e9da, 0xb1f9f660802dedf6}, // 5^278
	{0xe1a63853bbd26451, 0x5e7873f8a0396973}, // 5^279
	{0x8d07e33455637eb2, 0xdb0b487b6423e1e8}, // 5^280
	{0xb049dc016abc5e5f, 0x91ce1a9a3d2cda62}, // 5^281
	{0xdc5c5301c56b75f7, 0x7641a140cc7810fb}, // 5^282
	{0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9d}, // 5^283
	{0xac2820d9623bf429, 0x546345fa9fbdcd44}, // 5^284
	{0xd732290fbacaf133, 0xa97c177947ad4095}, // 5^285
	{0x867f59a9d4bed6c0, 0x49ed8eabcccc485d}, // 5^286
	{0xa81f301449ee8c70, 0x5c68f256bfff5a74}, // 5^287
	{0xd226fc195c6a2f8c, 0x73832eec6fff3111}, // 5^288
	{0x83585d8fd9c25db7, 0xc831fd53c5ff7eab}, // 5^289
	{0xa42e74f3d032f525, 0xba3e7ca8b77f5e55}, // 5^290
	{0xcd3a1230c43fb26f, 0x28ce1bd2e55f35eb}, // 5^291
	{0x80444b5e7aa7cf85, 0x7980d163cf5b81b3}, // 5^292
	{0xa0555e361951c366, 0xd7e105bcc332621f}, // 5^293
	{0xc86ab5c39fa63440, 0x8dd9472bf3fefaa7}, // 5^294
	{0xfa856334878fc150, 0xb14f98f6f0feb951}, // 5^295
	{0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d3}, // 5^296
	{0xc3b8358109e84f07, 0x0a862f80ec4700c8}, // 5^297
	{0xf4a642e14c6262c8, 0xcd27bb612758c0fa}, // 5^298
	{0x98e7e9cccfbd7dbd, 0x8038d51cb897789c}, // 5^299
	{0xbf21e44003acdd2c, 0xe0470a63e6bd56c3}, // 5^300
	{0xeeea5d5004981478, 0x1858ccfce06cac74}, // 5^301
	{0x95527a5202df0ccb, 0x0f37801e0c43ebc8}, // 5^302
	{0xbaa718e68396cffd, 0xd30560258f54e6ba}, // 5^303
	{0xe950df20247c83fd, 0x47c6b82ef32a2069}, // 5^304
	{0x91d28b7416cdd27e, 0x4cdc331d57fa5441}, // 5^305
	{0xb6472e511c81471d, 0xe0133fe4adf8e952}, // 5^306
	{0xe3d8f9e563a198e5, 0x58180fddd97723a6}, // 5^307
	{0x8e679c2f5e44ff8f, 0x570f09eaa7ea7648}, // 5^308
}

/*
Ported from ffc.h and fast_float.

  ffc.h:      https://github.com/kolemannix/ffc.h
  fast_float: https://github.com/fastfloat/fast_float

Copyright (c) 2021 The fast_float authors

Boost Software License - Version 1.0 - August 17th, 2003

Permission is hereby granted, free of charge, to any person or organization
obtaining a copy of the software and accompanying documentation covered by
this license (the "Software") to use, reproduce, display, distribute,
execute, and transmit the Software, and to prepare derivative works of the
Software, and to permit third-parties to whom the Software is furnished to
do so, all subject to the following:

The copyright notices in the Software and this entire statement, including
the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
all derivative works of the Software, unless such copies or derivative
works are solely in the form of machine-executable object code generated by
a source language processor.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.
*/