@@ -63,22 +63,32 @@ pub fn formatFloat(buf: []u8, v_: anytype, options: FormatOptions) FormatError![
comptime std.debug.assert(@typeInfo(T) == .Float);
const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
const DT = if (@bitSizeOf(T) <= 64) u64 else u128;
const tables = switch (DT) {
u64 => if (@import("builtin").mode == .ReleaseSmall) &Backend64_TablesSmall else &Backend64_TablesFull,
u128 => &Backend128_Tables,
else => unreachable,
};
const has_explicit_leading_bit = std.math.floatMantissaBits(T) - std.math.floatFractionalBits(T) != 0;
const d = binaryToDecimal(@as(I, @bitCast(v)), std.math.floatMantissaBits(T), std.math.floatExponentBits(T), has_explicit_leading_bit);
const d = binaryToDecimal(DT, @as(I, @bitCast(v)), std.math.floatMantissaBits(T), std.math.floatExponentBits(T), has_explicit_leading_bit, tables);
return switch (options.mode) {
.scientific => formatScientific(buf, d, options.precision),
.decimal => formatDecimal(buf, d, options.precision),
.scientific => formatScientific(DT, buf, d, options.precision),
.decimal => formatDecimal(DT, buf, d, options.precision),
};
}
pub const FloatDecimal128 = struct {
mantissa: u128,
exponent: i32,
sign: bool,
};
pub fn FloatDecimal(comptime T: type) type {
comptime std.debug.assert(T == u64 or T == u128);
return struct {
mantissa: T,
exponent: i32,
sign: bool,
};
}
fn copySpecialStr(buf: []u8, f: FloatDecimal128) []const u8 {
fn copySpecialStr(buf: []u8, f: anytype) []const u8 {
if (f.sign) {
buf[0] = '-';
}
@@ -124,7 +134,7 @@ const RoundMode = enum {
scientific,
};
fn round(f: FloatDecimal128, mode: RoundMode, precision: usize) FloatDecimal128 {
fn round(comptime T: type, f: FloatDecimal(T), mode: RoundMode, precision: usize) FloatDecimal(T) {
var round_digit: usize = 0;
var output = f.mantissa;
var exp = f.exponent;
@@ -174,7 +184,7 @@ fn round(f: FloatDecimal128, mode: RoundMode, precision: usize) FloatDecimal128
};
}
/// Write a FloatDecimal128 to a buffer in scientific form.
/// Write a FloatDecimal to a buffer in scientific form.
///
/// The buffer provided must be greater than `min_buffer_size` in length. If no precision is
/// specified, this function will never return an error. If a precision is specified, up to
@@ -182,7 +192,7 @@ fn round(f: FloatDecimal128, mode: RoundMode, precision: usize) FloatDecimal128
/// will not fit.
///
/// It is recommended to bound decimal formatting with an exact precision.
pub fn formatScientific(buf: []u8, f_: FloatDecimal128, precision: ?usize) FormatError![]const u8 {
pub fn formatScientific(comptime T: type, buf: []u8, f_: FloatDecimal(T), precision: ?usize) FormatError![]const u8 {
std.debug.assert(buf.len >= min_buffer_size);
var f = f_;
@@ -191,7 +201,7 @@ pub fn formatScientific(buf: []u8, f_: FloatDecimal128, precision: ?usize) Forma
}
if (precision) |prec| {
f = round(f, .scientific, prec);
f = round(T, f, .scientific, prec);
}
var output = f.mantissa;
@@ -248,12 +258,12 @@ pub fn formatScientific(buf: []u8, f_: FloatDecimal128, precision: ?usize) Forma
return buf[0..index];
}
/// Write a FloatDecimal128 to a buffer in decimal form.
/// Write a FloatDecimal to a buffer in decimal form.
///
/// The buffer provided must be greater than `min_buffer_size` bytes in length. If no precision is
/// specified, this may still return an error. If precision is specified, `2 + precision` bytes will
/// always be written.
pub fn formatDecimal(buf: []u8, f_: FloatDecimal128, precision: ?usize) FormatError![]const u8 {
pub fn formatDecimal(comptime T: type, buf: []u8, f_: FloatDecimal(T), precision: ?usize) FormatError![]const u8 {
std.debug.assert(buf.len >= min_buffer_size);
var f = f_;
@@ -262,7 +272,7 @@ pub fn formatDecimal(buf: []u8, f_: FloatDecimal128, precision: ?usize) FormatEr
}
if (precision) |prec| {
f = round(f, .decimal, prec);
f = round(T, f, .decimal, prec);
}
var output = f.mantissa;
@@ -348,11 +358,15 @@ fn cast_i32(v: anytype) i32 {
}
/// Convert a binary float representation to decimal.
pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explicit_leading_bit: bool) FloatDecimal128 {
pub fn binaryToDecimal(comptime T: type, bits: T, mantissa_bits: std.math.Log2Int(T), exponent_bits: u5, explicit_leading_bit: bool, comptime tables: anytype) FloatDecimal(T) {
if (T != tables.T) {
@compileError("table type does not match backend type: " ++ @typeName(tables.T) ++ " != " ++ @typeName(T));
}
const bias = (@as(u32, 1) << (exponent_bits - 1)) - 1;
const ieee_sign = ((bits >> (mantissa_bits + exponent_bits)) & 1) != 0;
const ieee_mantissa = bits & ((@as(u128, 1) << mantissa_bits) - 1);
const ieee_exponent: u32 = @intCast((bits >> mantissa_bits) & ((@as(u128, 1) << exponent_bits) - 1));
const ieee_mantissa = bits & ((@as(T, 1) << mantissa_bits) - 1);
const ieee_exponent: u32 = @intCast((bits >> mantissa_bits) & ((@as(T, 1) << exponent_bits) - 1));
if (ieee_exponent == 0 and ieee_mantissa == 0) {
return .{
@@ -363,14 +377,14 @@ pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explici
}
if (ieee_exponent == ((@as(u32, 1) << exponent_bits) - 1)) {
return .{
.mantissa = if (explicit_leading_bit) ieee_mantissa & ((@as(u128, 1) << (mantissa_bits - 1)) - 1) else ieee_mantissa,
.exponent = 0x7fffffff,
.mantissa = if (explicit_leading_bit) ieee_mantissa & ((@as(T, 1) << (mantissa_bits - 1)) - 1) else ieee_mantissa,
.exponent = special_exponent,
.sign = ieee_sign,
};
}
var e2: i32 = undefined;
var m2: u128 = undefined;
var m2: T = undefined;
if (explicit_leading_bit) {
if (ieee_exponent == 0) {
e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
@@ -384,7 +398,7 @@ pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explici
m2 = ieee_mantissa;
} else {
e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
m2 = (@as(u128, 1) << mantissa_bits) | ieee_mantissa;
m2 = (@as(T, 1) << mantissa_bits) | ieee_mantissa;
}
}
const even = (m2 & 1) == 0;
@@ -392,29 +406,29 @@ pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explici
// Step 2: Determine the interval of legal decimal representations.
const mv = 4 * m2;
const mm_shift: u1 = @intFromBool((ieee_mantissa != if (explicit_leading_bit) (@as(u128, 1) << (mantissa_bits - 1)) else 0) or (ieee_exponent == 0));
const mm_shift: u1 = @intFromBool((ieee_mantissa != if (explicit_leading_bit) (@as(T, 1) << (mantissa_bits - 1)) else 0) or (ieee_exponent == 0));
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
var vr: u128 = undefined;
var vp: u128 = undefined;
var vm: u128 = undefined;
var vr: T = undefined;
var vp: T = undefined;
var vm: T = undefined;
var e10: i32 = undefined;
var vm_is_trailing_zeros = false;
var vr_is_trailing_zeros = false;
if (e2 >= 0) {
const q: u32 = log10Pow2(@intCast(e2)) - @intFromBool(e2 > 3);
e10 = cast_i32(q);
const k: i32 = @intCast(FLOAT_128_POW5_INV_BITCOUNT + pow5Bits(q) - 1);
const k: i32 = @intCast(tables.POW5_INV_BITCOUNT + pow5Bits(q) - 1);
const i: u32 = @intCast(-e2 + cast_i32(q) + k);
const pow5 = computeInvPow5(q);
vr = mulShift(4 * m2, &pow5, i);
vp = mulShift(4 * m2 + 2, &pow5, i);
vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, i);
const pow5 = tables.computeInvPow5(q);
vr = tables.mulShift(4 * m2, &pow5, i);
vp = tables.mulShift(4 * m2 + 2, &pow5, i);
vm = tables.mulShift(4 * m2 - 1 - mm_shift, &pow5, i);
if (q <= 55) {
if (q <= tables.bound1) {
if (mv % 5 == 0) {
vr_is_trailing_zeros = multipleOfPowerOf5(mv, q -% 1);
vr_is_trailing_zeros = multipleOfPowerOf5(mv, if (tables.adjust_q) q -% 1 else q);
} else if (accept_bounds) {
vm_is_trailing_zeros = multipleOfPowerOf5(mv - 1 - mm_shift, q);
} else {
@@ -425,13 +439,13 @@ pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explici
const q: u32 = log10Pow5(@intCast(-e2)) - @intFromBool(-e2 > 1);
e10 = cast_i32(q) + e2;
const i: i32 = -e2 - cast_i32(q);
const k: i32 = cast_i32(pow5Bits(@intCast(i))) - FLOAT_128_POW5_BITCOUNT;
const k: i32 = cast_i32(pow5Bits(@intCast(i))) - tables.POW5_BITCOUNT;
const j: u32 = @intCast(cast_i32(q) - k);
const pow5 = computePow5(@intCast(i));
vr = mulShift(4 * m2, &pow5, j);
vp = mulShift(4 * m2 + 2, &pow5, j);
vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, j);
const pow5 = tables.computePow5(@intCast(i));
vr = tables.mulShift(4 * m2, &pow5, j);
vp = tables.mulShift(4 * m2 + 2, &pow5, j);
vm = tables.mulShift(4 * m2 - 1 - mm_shift, &pow5, j);
if (q <= 1) {
vr_is_trailing_zeros = true;
@@ -440,8 +454,8 @@ pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explici
} else {
vp -= 1;
}
} else if (q < 127) {
vr_is_trailing_zeros = multipleOfPowerOf2(mv, q - 1);
} else if (q < tables.bound2) {
vr_is_trailing_zeros = multipleOfPowerOf2(mv, if (tables.adjust_q) q - 1 else q);
}
}
@@ -481,15 +495,40 @@ pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explici
};
}
fn decimalLength(v: u128) u32 {
const LARGEST_POW10 = (@as(u128, 5421010862427522170) << 64) | 687399551400673280;
var p10 = LARGEST_POW10;
var i: u32 = 39;
while (i > 0) : (i -= 1) {
if (v >= p10) return i;
p10 /= 10;
fn decimalLength(v: anytype) u32 {
switch (@TypeOf(v)) {
u32, u64 => {
std.debug.assert(v < 100000000000000000);
if (v >= 10000000000000000) return 17;
if (v >= 1000000000000000) return 16;
if (v >= 100000000000000) return 15;
if (v >= 10000000000000) return 14;
if (v >= 1000000000000) return 13;
if (v >= 100000000000) return 12;
if (v >= 10000000000) return 11;
if (v >= 1000000000) return 10;
if (v >= 100000000) return 9;
if (v >= 10000000) return 8;
if (v >= 1000000) return 7;
if (v >= 100000) return 6;
if (v >= 10000) return 5;
if (v >= 1000) return 4;
if (v >= 100) return 3;
if (v >= 10) return 2;
return 1;
},
u128 => {
const LARGEST_POW10 = (@as(u128, 5421010862427522170) << 64) | 687399551400673280;
var p10 = LARGEST_POW10;
var i: u32 = 39;
while (i > 0) : (i -= 1) {
if (v >= p10) return i;
p10 /= 10;
}
return 1;
},
else => unreachable,
}
return 1;
}
// floor(log_10(2^e))
@@ -510,7 +549,7 @@ fn pow5Bits(e: u32) u32 {
return @intCast(((@as(u64, @intCast(e)) * 163391164108059) >> 46) + 1);
}
fn pow5Factor(value_: u128) u32 {
fn pow5Factor(value_: anytype) u32 {
var count: u32 = 0;
var value = value_;
while (value > 0) : ({
@@ -522,49 +561,19 @@ fn pow5Factor(value_: u128) u32 {
return 0;
}
fn multipleOfPowerOf5(value: u128, p: u32) bool {
fn multipleOfPowerOf5(value: anytype, p: u32) bool {
const T = @TypeOf(value);
std.debug.assert(@typeInfo(T) == .Int);
return pow5Factor(value) >= p;
}
fn multipleOfPowerOf2(value: u128, p: u32) bool {
return (value & ((@as(u128, 1) << @as(u7, @intCast(p))) - 1)) == 0;
fn multipleOfPowerOf2(value: anytype, p: u32) bool {
const T = @TypeOf(value);
std.debug.assert(@typeInfo(T) == .Int);
return (value & ((@as(T, 1) << @as(std.math.Log2Int(T), @intCast(p))) - 1)) == 0;
}
fn computeInvPow5(i: u32) [4]u64 {
const base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
const base2 = base * POW5_TABLE_SIZE;
const mul = &GENERIC_POW5_INV_SPLIT[base]; // 1 / 5^base2
if (i == base2) {
return .{ mul[0] + 1, mul[1], mul[2], mul[3] };
} else {
const offset = base2 - i;
const m = &GENERIC_POW5_TABLE[offset]; // 5^offset
const delta = pow5Bits(base2) - pow5Bits(i);
const shift: u6 = @intCast(2 * (i % 32));
const corr: u32 = @intCast(((POW5_INV_ERRORS[i / 32] >> shift) & 3) + 1);
return mul_128_256_shift(m, mul, delta, corr);
}
}
fn computePow5(i: u32) [4]u64 {
const base = i / POW5_TABLE_SIZE;
const base2 = base * POW5_TABLE_SIZE;
const mul = &GENERIC_POW5_SPLIT[base];
if (i == base2) {
return mul.*;
} else {
const offset = i - base2;
const m = &GENERIC_POW5_TABLE[offset];
const delta = pow5Bits(i) - pow5Bits(base2);
const shift: u6 = @intCast(2 * (i % 32));
const corr: u32 = @intCast((POW5_ERRORS[i / 32] >> shift) & 3);
return mul_128_256_shift(m, mul, delta, corr);
}
}
fn mulShift(m: u128, mul: *const [4]u64, j: u32) u128 {
fn mulShift128(m: u128, mul: *const [4]u64, j: u32) u128 {
std.debug.assert(j > 128);
const a: [2]u64 = .{ @truncate(m), @truncate(m >> 64) };
const r = mul_128_256_shift(&a, mul, j, 0);
@@ -620,15 +629,560 @@ fn mul_128_256_shift(a: *const [2]u64, b: *const [4]u64, shift: u32, corr: u32)
return .{ @truncate(r0), @truncate(r0 >> 64), @truncate(r1), @truncate(r1 >> 64) };
}
pub const Backend128_Tables = struct {
const T = u128;
const mulShift = mulShift128;
const POW5_INV_BITCOUNT = FLOAT128_POW5_INV_BITCOUNT;
const POW5_BITCOUNT = FLOAT128_POW5_BITCOUNT;
const bound1 = 55;
const bound2 = 127;
const adjust_q = true;
fn computePow5(i: u32) [4]u64 {
const base = i / FLOAT128_POW5_TABLE_SIZE;
const base2 = base * FLOAT128_POW5_TABLE_SIZE;
const mul = &FLOAT128_POW5_SPLIT[base];
if (i == base2) {
return mul.*;
} else {
const offset = i - base2;
const m = &FLOAT128_POW5_TABLE[offset];
const delta = pow5Bits(i) - pow5Bits(base2);
const shift: u6 = @intCast(2 * (i % 32));
const corr: u32 = @intCast((FLOAT128_POW5_ERRORS[i / 32] >> shift) & 3);
return mul_128_256_shift(m, mul, delta, corr);
}
}
fn computeInvPow5(i: u32) [4]u64 {
const base = (i + FLOAT128_POW5_TABLE_SIZE - 1) / FLOAT128_POW5_TABLE_SIZE;
const base2 = base * FLOAT128_POW5_TABLE_SIZE;
const mul = &FLOAT128_POW5_INV_SPLIT[base]; // 1 / 5^base2
if (i == base2) {
return .{ mul[0] + 1, mul[1], mul[2], mul[3] };
} else {
const offset = base2 - i;
const m = &FLOAT128_POW5_TABLE[offset]; // 5^offset
const delta = pow5Bits(base2) - pow5Bits(i);
const shift: u6 = @intCast(2 * (i % 32));
const corr: u32 = @intCast(((FLOAT128_POW5_INV_ERRORS[i / 32] >> shift) & 3) + 1);
return mul_128_256_shift(m, mul, delta, corr);
}
}
};
fn mulShift64(m: u64, mul: *const [2]u64, j: u32) u64 {
std.debug.assert(j > 64);
const b0 = @as(u128, m) * mul[0];
const b2 = @as(u128, m) * mul[1];
if (j < 128) {
const shift: u6 = @intCast(j - 64);
return @intCast(((b0 >> 64) + b2) >> shift);
} else {
return 0;
}
}
pub const Backend64_TablesFull = struct {
const T = u64;
const mulShift = mulShift64;
const POW5_INV_BITCOUNT = FLOAT64_POW5_INV_BITCOUNT;
const POW5_BITCOUNT = FLOAT64_POW5_BITCOUNT;
const bound1 = 21;
const bound2 = 63;
const adjust_q = false;
fn computePow5(i: u32) [2]u64 {
return FLOAT64_POW5_SPLIT[i];
}
fn computeInvPow5(i: u32) [2]u64 {
return FLOAT64_POW5_INV_SPLIT[i];
}
};
pub const Backend64_TablesSmall = struct {
const T = u64;
const mulShift = mulShift64;
const POW5_INV_BITCOUNT = FLOAT64_POW5_INV_BITCOUNT;
const POW5_BITCOUNT = FLOAT64_POW5_BITCOUNT;
const bound1 = 21;
const bound2 = 63;
const adjust_q = false;
fn computePow5(i: u32) [2]u64 {
const base = i / FLOAT64_POW5_TABLE_SIZE;
const base2 = base * FLOAT64_POW5_TABLE_SIZE;
const mul = &FLOAT64_POW5_SPLIT2[base];
if (i == base2) {
return .{ mul[0], mul[1] };
} else {
const offset = i - base2;
const m = FLOAT64_POW5_TABLE[offset];
const b0 = @as(u128, m) * mul[0];
const b2 = @as(u128, m) * mul[1];
const delta: u7 = @intCast(pow5Bits(i) - pow5Bits(base2));
const shift: u5 = @intCast((i % 16) << 1);
const shifted_sum = ((b0 >> delta) + (b2 << (64 - delta))) + 1 + ((FLOAT64_POW5_OFFSETS[i / 16] >> shift) & 3);
return .{ @truncate(shifted_sum), @truncate(shifted_sum >> 64) };
}
}
fn computeInvPow5(i: u32) [2]u64 {
const base = (i + FLOAT64_POW5_TABLE_SIZE - 1) / FLOAT64_POW5_TABLE_SIZE;
const base2 = base * FLOAT64_POW5_TABLE_SIZE;
const mul = &FLOAT64_POW5_INV_SPLIT2[base]; // 1 / 5^base2
if (i == base2) {
return .{ mul[0], mul[1] };
} else {
const offset = base2 - i;
const m = FLOAT64_POW5_TABLE[offset]; // 5^offset
const b0 = @as(u128, m) * (mul[0] - 1);
const b2 = @as(u128, m) * mul[1]; // 1/5^base2 * 5^offset = 1/5^(base2-offset) = 1/5^i
const delta: u7 = @intCast(pow5Bits(base2) - pow5Bits(i));
const shift: u5 = @intCast((i % 16) << 1);
const shifted_sum = ((b0 >> delta) + (b2 << (64 - delta))) + 1 + ((FLOAT64_POW5_INV_OFFSETS[i / 16] >> shift) & 3);
return .{ @truncate(shifted_sum), @truncate(shifted_sum >> 64) };
}
}
};
const FLOAT64_POW5_INV_BITCOUNT = 125;
const FLOAT64_POW5_BITCOUNT = 125;
// zig fmt: off
//
// 4.5KiB of tables.
// f64 small tables: 816 bytes
const FLOAT_128_POW5_INV_BITCOUNT = 249;
const FLOAT_128_POW5_BITCOUNT = 249;
const POW5_TABLE_SIZE = 56;
const FLOAT64_POW5_TABLE_SIZE: comptime_int = FLOAT64_POW5_TABLE.len;
const GENERIC_POW5_TABLE: [POW5_TABLE_SIZE][2]u64 = .{
const FLOAT64_POW5_TABLE: [26]u64 = .{
1, 5,
25, 125,
625, 3125,
15625, 78125,
390625, 1953125,
9765625, 48828125,
244140625, 1220703125,
6103515625, 30517578125,
152587890625, 762939453125,
3814697265625, 19073486328125,
95367431640625, 476837158203125,
2384185791015625, 11920928955078125,
59604644775390625, 298023223876953125,
};
const FLOAT64_POW5_SPLIT2: [13][2]u64 = .{
.{ 0, 1152921504606846976 },
.{ 0, 1490116119384765625 },
.{ 1032610780636961552, 1925929944387235853 },
.{ 7910200175544436838, 1244603055572228341 },
.{ 16941905809032713930, 1608611746708759036 },
.{ 13024893955298202172, 2079081953128979843 },
.{ 6607496772837067824, 1343575221513417750 },
.{ 17332926989895652603, 1736530273035216783 },
.{ 13037379183483547984, 2244412773384604712 },
.{ 1605989338741628675, 1450417759929778918 },
.{ 9630225068416591280, 1874621017369538693 },
.{ 665883850346957067, 1211445438634777304 },
.{ 14931890668723713708, 1565756531257009982 }
};
const FLOAT64_POW5_OFFSETS: [21]u32 = .{
0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x40000000, 0x59695995, 0x55545555, 0x56555515,
0x41150504, 0x40555410, 0x44555145, 0x44504540,
0x45555550, 0x40004000, 0x96440440, 0x55565565,
0x54454045, 0x40154151, 0x55559155, 0x51405555,
0x00000105,
};
const FLOAT64_POW5_INV_SPLIT2: [15][2]u64 = .{
.{ 1, 2305843009213693952 },
.{ 5955668970331000884, 1784059615882449851 },
.{ 8982663654677661702, 1380349269358112757 },
.{ 7286864317269821294, 2135987035920910082 },
.{ 7005857020398200553, 1652639921975621497 },
.{ 17965325103354776697, 1278668206209430417 },
.{ 8928596168509315048, 1978643211784836272 },
.{ 10075671573058298858, 1530901034580419511 },
.{ 597001226353042382, 1184477304306571148 },
.{ 1527430471115325346, 1832889850782397517 },
.{ 12533209867169019542, 1418129833677084982 },
.{ 5577825024675947042, 2194449627517475473 },
.{ 11006974540203867551, 1697873161311732311 },
.{ 10313493231639821582, 1313665730009899186 },
.{ 12701016819766672773, 2032799256770390445 }
};
const FLOAT64_POW5_INV_OFFSETS: [19]u32 = .{
0x54544554, 0x04055545, 0x10041000, 0x00400414,
0x40010000, 0x41155555, 0x00000454, 0x00010044,
0x40000000, 0x44000041, 0x50454450, 0x55550054,
0x51655554, 0x40004000, 0x01000001, 0x00010500,
0x51515411, 0x05555554, 0x00000000,
};
// zig fmt: off
// f64 full tables: 10688 bytes
const FLOAT64_POW5_SPLIT: [326][2]u64 = .{
.{ 0, 1152921504606846976 }, .{ 0, 1441151880758558720 },
.{ 0, 1801439850948198400 }, .{ 0, 2251799813685248000 },
.{ 0, 1407374883553280000 }, .{ 0, 1759218604441600000 },
.{ 0, 2199023255552000000 }, .{ 0, 1374389534720000000 },
.{ 0, 1717986918400000000 }, .{ 0, 2147483648000000000 },
.{ 0, 1342177280000000000 }, .{ 0, 1677721600000000000 },
.{ 0, 2097152000000000000 }, .{ 0, 1310720000000000000 },
.{ 0, 1638400000000000000 }, .{ 0, 2048000000000000000 },
.{ 0, 1280000000000000000 }, .{ 0, 1600000000000000000 },
.{ 0, 2000000000000000000 }, .{ 0, 1250000000000000000 },
.{ 0, 1562500000000000000 }, .{ 0, 1953125000000000000 },
.{ 0, 1220703125000000000 }, .{ 0, 1525878906250000000 },
.{ 0, 1907348632812500000 }, .{ 0, 1192092895507812500 },
.{ 0, 1490116119384765625 }, .{ 4611686018427387904, 1862645149230957031 },
.{ 9799832789158199296, 1164153218269348144 }, .{ 12249790986447749120, 1455191522836685180 },
.{ 15312238733059686400, 1818989403545856475 }, .{ 14528612397897220096, 2273736754432320594 },
.{ 13692068767113150464, 1421085471520200371 }, .{ 12503399940464050176, 1776356839400250464 },
.{ 15629249925580062720, 2220446049250313080 }, .{ 9768281203487539200, 1387778780781445675 },
.{ 7598665485932036096, 1734723475976807094 }, .{ 274959820560269312, 2168404344971008868 },
.{ 9395221924704944128, 1355252715606880542 }, .{ 2520655369026404352, 1694065894508600678 },
.{ 12374191248137781248, 2117582368135750847 }, .{ 14651398557727195136, 1323488980084844279 },
.{ 13702562178731606016, 1654361225106055349 }, .{ 3293144668132343808, 2067951531382569187 },
.{ 18199116482078572544, 1292469707114105741 }, .{ 8913837547316051968, 1615587133892632177 },
.{ 15753982952572452864, 2019483917365790221 }, .{ 12152082354571476992, 1262177448353618888 },
.{ 15190102943214346240, 1577721810442023610 }, .{ 9764256642163156992, 1972152263052529513 },
.{ 17631875447420442880, 1232595164407830945 }, .{ 8204786253993389888, 1540743955509788682 },
.{ 1032610780636961552, 1925929944387235853 }, .{ 2951224747111794922, 1203706215242022408 },
.{ 3689030933889743652, 1504632769052528010 }, .{ 13834660704216955373, 1880790961315660012 },
.{ 17870034976990372916, 1175494350822287507 }, .{ 17725857702810578241, 1469367938527859384 },
.{ 3710578054803671186, 1836709923159824231 }, .{ 26536550077201078, 2295887403949780289 },
.{ 11545800389866720434, 1434929627468612680 }, .{ 14432250487333400542, 1793662034335765850 },
.{ 8816941072311974870, 2242077542919707313 }, .{ 17039803216263454053, 1401298464324817070 },
.{ 12076381983474541759, 1751623080406021338 }, .{ 5872105442488401391, 2189528850507526673 },
.{ 15199280947623720629, 1368455531567204170 }, .{ 9775729147674874978, 1710569414459005213 },
.{ 16831347453020981627, 2138211768073756516 }, .{ 1296220121283337709, 1336382355046097823 },
.{ 15455333206886335848, 1670477943807622278 }, .{ 10095794471753144002, 2088097429759527848 },
.{ 6309871544845715001, 1305060893599704905 }, .{ 12499025449484531656, 1631326116999631131 },
.{ 11012095793428276666, 2039157646249538914 }, .{ 11494245889320060820, 1274473528905961821 },
.{ 532749306367912313, 1593091911132452277 }, .{ 5277622651387278295, 1991364888915565346 },
.{ 7910200175544436838, 1244603055572228341 }, .{ 14499436237857933952, 1555753819465285426 },
.{ 8900923260467641632, 1944692274331606783 }, .{ 12480606065433357876, 1215432671457254239 },
.{ 10989071563364309441, 1519290839321567799 }, .{ 9124653435777998898, 1899113549151959749 },
.{ 8008751406574943263, 1186945968219974843 }, .{ 5399253239791291175, 1483682460274968554 },
.{ 15972438586593889776, 1854603075343710692 }, .{ 759402079766405302, 1159126922089819183 },
.{ 14784310654990170340, 1448908652612273978 }, .{ 9257016281882937117, 1811135815765342473 },
.{ 16182956370781059300, 2263919769706678091 }, .{ 7808504722524468110, 1414949856066673807 },
.{ 5148944884728197234, 1768687320083342259 }, .{ 1824495087482858639, 2210859150104177824 },
.{ 1140309429676786649, 1381786968815111140 }, .{ 1425386787095983311, 1727233711018888925 },
.{ 6393419502297367043, 2159042138773611156 }, .{ 13219259225790630210, 1349401336733506972 },
.{ 16524074032238287762, 1686751670916883715 }, .{ 16043406521870471799, 2108439588646104644 },
.{ 803757039314269066, 1317774742903815403 }, .{ 14839754354425000045, 1647218428629769253 },
.{ 4714634887749086344, 2059023035787211567 }, .{ 9864175832484260821, 1286889397367007229 },
.{ 16941905809032713930, 1608611746708759036 }, .{ 2730638187581340797, 2010764683385948796 },
.{ 10930020904093113806, 1256727927116217997 }, .{ 18274212148543780162, 1570909908895272496 },
.{ 4396021111970173586, 1963637386119090621 }, .{ 5053356204195052443, 1227273366324431638 },
.{ 15540067292098591362, 1534091707905539547 }, .{ 14813398096695851299, 1917614634881924434 },
.{ 13870059828862294966, 1198509146801202771 }, .{ 12725888767650480803, 1498136433501503464 },
.{ 15907360959563101004, 1872670541876879330 }, .{ 14553786618154326031, 1170419088673049581 },
.{ 4357175217410743827, 1463023860841311977 }, .{ 10058155040190817688, 1828779826051639971 },
.{ 7961007781811134206, 2285974782564549964 }, .{ 14199001900486734687, 1428734239102843727 },
.{ 13137066357181030455, 1785917798878554659 }, .{ 11809646928048900164, 2232397248598193324 },
.{ 16604401366885338411, 1395248280373870827 }, .{ 16143815690179285109, 1744060350467338534 },
.{ 10956397575869330579, 2180075438084173168 }, .{ 6847748484918331612, 1362547148802608230 },
.{ 17783057643002690323, 1703183936003260287 }, .{ 17617136035325974999, 2128979920004075359 },
.{ 17928239049719816230, 1330612450002547099 }, .{ 17798612793722382384, 1663265562503183874 },
.{ 13024893955298202172, 2079081953128979843 }, .{ 5834715712847682405, 1299426220705612402 },
.{ 16516766677914378815, 1624282775882015502 }, .{ 11422586310538197711, 2030353469852519378 },
.{ 11750802462513761473, 1268970918657824611 }, .{ 10076817059714813937, 1586213648322280764 },
.{ 12596021324643517422, 1982767060402850955 }, .{ 5566670318688504437, 1239229412751781847 },
.{ 2346651879933242642, 1549036765939727309 }, .{ 7545000868343941206, 1936295957424659136 },
.{ 4715625542714963254, 1210184973390411960 }, .{ 5894531928393704067, 1512731216738014950 },
.{ 16591536947346905892, 1890914020922518687 }, .{ 17287239619732898039, 1181821263076574179 },
.{ 16997363506238734644, 1477276578845717724 }, .{ 2799960309088866689, 1846595723557147156 },
.{ 10973347230035317489, 1154122327223216972 }, .{ 13716684037544146861, 1442652909029021215 },
.{ 12534169028502795672, 1803316136286276519 }, .{ 11056025267201106687, 2254145170357845649 },
.{ 18439230838069161439, 1408840731473653530 }, .{ 13825666510731675991, 1761050914342066913 },
.{ 3447025083132431277, 2201313642927583642 }, .{ 6766076695385157452, 1375821026829739776 },
.{ 8457595869231446815, 1719776283537174720 }, .{ 10571994836539308519, 2149720354421468400 },
.{ 6607496772837067824, 1343575221513417750 }, .{ 17482743002901110588, 1679469026891772187 },
.{ 17241742735199000331, 2099336283614715234 }, .{ 15387775227926763111, 1312085177259197021 },
.{ 5399660979626290177, 1640106471573996277 }, .{ 11361262242960250625, 2050133089467495346 },
.{ 11712474920277544544, 1281333180917184591 }, .{ 10028907631919542777, 1601666476146480739 },
.{ 7924448521472040567, 2002083095183100924 }, .{ 14176152362774801162, 1251301934489438077 },
.{ 3885132398186337741, 1564127418111797597 }, .{ 9468101516160310080, 1955159272639746996 },
.{ 15140935484454969608, 1221974545399841872 }, .{ 479425281859160394, 1527468181749802341 },
.{ 5210967620751338397, 1909335227187252926 }, .{ 17091912818251750210, 1193334516992033078 },
.{ 12141518985959911954, 1491668146240041348 }, .{ 15176898732449889943, 1864585182800051685 },
.{ 11791404716994875166, 1165365739250032303 }, .{ 10127569877816206054, 1456707174062540379 },
.{ 8047776328842869663, 1820883967578175474 }, .{ 836348374198811271, 2276104959472719343 },
.{ 7440246761515338900, 1422565599670449589 }, .{ 13911994470321561530, 1778206999588061986 },
.{ 8166621051047176104, 2222758749485077483 }, .{ 2798295147690791113, 1389224218428173427 },
.{ 17332926989895652603, 1736530273035216783 }, .{ 17054472718942177850, 2170662841294020979 },
.{ 8353202440125167204, 1356664275808763112 }, .{ 10441503050156459005, 1695830344760953890 },
.{ 3828506775840797949, 2119787930951192363 }, .{ 86973725686804766, 1324867456844495227 },
.{ 13943775212390669669, 1656084321055619033 }, .{ 3594660960206173375, 2070105401319523792 },
.{ 2246663100128858359, 1293815875824702370 }, .{ 12031700912015848757, 1617269844780877962 },
.{ 5816254103165035138, 2021587305976097453 }, .{ 5941001823691840913, 1263492066235060908 },
.{ 7426252279614801142, 1579365082793826135 }, .{ 4671129331091113523, 1974206353492282669 },
.{ 5225298841145639904, 1233878970932676668 }, .{ 6531623551432049880, 1542348713665845835 },
.{ 3552843420862674446, 1927935892082307294 }, .{ 16055585193321335241, 1204959932551442058 },
.{ 10846109454796893243, 1506199915689302573 }, .{ 18169322836923504458, 1882749894611628216 },
.{ 11355826773077190286, 1176718684132267635 }, .{ 9583097447919099954, 1470898355165334544 },
.{ 11978871809898874942, 1838622943956668180 }, .{ 14973589762373593678, 2298278679945835225 },
.{ 2440964573842414192, 1436424174966147016 }, .{ 3051205717303017741, 1795530218707683770 },
.{ 13037379183483547984, 2244412773384604712 }, .{ 8148361989677217490, 1402757983365377945 },
.{ 14797138505523909766, 1753447479206722431 }, .{ 13884737113477499304, 2191809349008403039 },
.{ 15595489723564518921, 1369880843130251899 }, .{ 14882676136028260747, 1712351053912814874 },
.{ 9379973133180550126, 2140438817391018593 }, .{ 17391698254306313589, 1337774260869386620 },
.{ 3292878744173340370, 1672217826086733276 }, .{ 4116098430216675462, 2090272282608416595 },
.{ 266718509671728212, 1306420176630260372 }, .{ 333398137089660265, 1633025220787825465 },
.{ 5028433689789463235, 2041281525984781831 }, .{ 10060300083759496378, 1275800953740488644 },
.{ 12575375104699370472, 1594751192175610805 }, .{ 1884160825592049379, 1993438990219513507 },
.{ 17318501580490888525, 1245899368887195941 }, .{ 7813068920331446945, 1557374211108994927 },
.{ 5154650131986920777, 1946717763886243659 }, .{ 915813323278131534, 1216698602428902287 },
.{ 14979824709379828129, 1520873253036127858 }, .{ 9501408849870009354, 1901091566295159823 },
.{ 12855909558809837702, 1188182228934474889 }, .{ 2234828893230133415, 1485227786168093612 },
.{ 2793536116537666769, 1856534732710117015 }, .{ 8663489100477123587, 1160334207943823134 },
.{ 1605989338741628675, 1450417759929778918 }, .{ 11230858710281811652, 1813022199912223647 },
.{ 9426887369424876662, 2266277749890279559 }, .{ 12809333633531629769, 1416423593681424724 },
.{ 16011667041914537212, 1770529492101780905 }, .{ 6179525747111007803, 2213161865127226132 },
.{ 13085575628799155685, 1383226165704516332 }, .{ 16356969535998944606, 1729032707130645415 },
.{ 15834525901571292854, 2161290883913306769 }, .{ 2979049660840976177, 1350806802445816731 },
.{ 17558870131333383934, 1688508503057270913 }, .{ 8113529608884566205, 2110635628821588642 },
.{ 9682642023980241782, 1319147268013492901 }, .{ 16714988548402690132, 1648934085016866126 },
.{ 11670363648648586857, 2061167606271082658 }, .{ 11905663298832754689, 1288229753919426661 },
.{ 1047021068258779650, 1610287192399283327 }, .{ 15143834390605638274, 2012858990499104158 },
.{ 4853210475701136017, 1258036869061940099 }, .{ 1454827076199032118, 1572546086327425124 },
.{ 1818533845248790147, 1965682607909281405 }, .{ 3442426662494187794, 1228551629943300878 },
.{ 13526405364972510550, 1535689537429126097 }, .{ 3072948650933474476, 1919611921786407622 },
.{ 15755650962115585259, 1199757451116504763 }, .{ 15082877684217093670, 1499696813895630954 },
.{ 9630225068416591280, 1874621017369538693 }, .{ 8324733676974063502, 1171638135855961683 },
.{ 5794231077790191473, 1464547669819952104 }, .{ 7242788847237739342, 1830684587274940130 },
.{ 18276858095901949986, 2288355734093675162 }, .{ 16034722328366106645, 1430222333808546976 },
.{ 1596658836748081690, 1787777917260683721 }, .{ 6607509564362490017, 2234722396575854651 },
.{ 1823850468512862308, 1396701497859909157 }, .{ 6891499104068465790, 1745876872324886446 },
.{ 17837745916940358045, 2182346090406108057 }, .{ 4231062170446641922, 1363966306503817536 },
.{ 5288827713058302403, 1704957883129771920 }, .{ 6611034641322878003, 2131197353912214900 },
.{ 13355268687681574560, 1331998346195134312 }, .{ 16694085859601968200, 1664997932743917890 },
.{ 11644235287647684442, 2081247415929897363 }, .{ 4971804045566108824, 1300779634956185852 },
.{ 6214755056957636030, 1625974543695232315 }, .{ 3156757802769657134, 2032468179619040394 },
.{ 6584659645158423613, 1270292612261900246 }, .{ 17454196593302805324, 1587865765327375307 },
.{ 17206059723201118751, 1984832206659219134 }, .{ 6142101308573311315, 1240520129162011959 },
.{ 3065940617289251240, 1550650161452514949 }, .{ 8444111790038951954, 1938312701815643686 },
.{ 665883850346957067, 1211445438634777304 }, .{ 832354812933696334, 1514306798293471630 },
.{ 10263815553021896226, 1892883497866839537 }, .{ 17944099766707154901, 1183052186166774710 },
.{ 13206752671529167818, 1478815232708468388 }, .{ 16508440839411459773, 1848519040885585485 },
.{ 12623618533845856310, 1155324400553490928 }, .{ 15779523167307320387, 1444155500691863660 },
.{ 1277659885424598868, 1805194375864829576 }, .{ 1597074856780748586, 2256492969831036970 },
.{ 5609857803915355770, 1410308106144398106 }, .{ 16235694291748970521, 1762885132680497632 },
.{ 1847873790976661535, 2203606415850622041 }, .{ 12684136165428883219, 1377254009906638775 },
.{ 11243484188358716120, 1721567512383298469 }, .{ 219297180166231438, 2151959390479123087 },
.{ 7054589765244976505, 1344974619049451929 }, .{ 13429923224983608535, 1681218273811814911 },
.{ 12175718012802122765, 2101522842264768639 }, .{ 14527352785642408584, 1313451776415480399 },
.{ 13547504963625622826, 1641814720519350499 }, .{ 12322695186104640628, 2052268400649188124 },
.{ 16925056528170176201, 1282667750405742577 }, .{ 7321262604930556539, 1603334688007178222 },
.{ 18374950293017971482, 2004168360008972777 }, .{ 4566814905495150320, 1252605225005607986 },
.{ 14931890668723713708, 1565756531257009982 }, .{ 9441491299049866327, 1957195664071262478 },
.{ 1289246043478778550, 1223247290044539049 }, .{ 6223243572775861092, 1529059112555673811 },
.{ 3167368447542438461, 1911323890694592264 }, .{ 1979605279714024038, 1194577431684120165 },
.{ 7086192618069917952, 1493221789605150206 }, .{ 18081112809442173248, 1866527237006437757 },
.{ 13606538515115052232, 1166579523129023598 }, .{ 7784801107039039482, 1458224403911279498 },
.{ 507629346944023544, 1822780504889099373 }, .{ 5246222702107417334, 2278475631111374216 },
.{ 3278889188817135834, 1424047269444608885 }, .{ 8710297504448807696, 1780059086805761106 }
};
const FLOAT64_POW5_INV_SPLIT: [342][2]u64 = .{
.{ 1, 2305843009213693952 }, .{ 11068046444225730970, 1844674407370955161 },
.{ 5165088340638674453, 1475739525896764129 }, .{ 7821419487252849886, 1180591620717411303 },
.{ 8824922364862649494, 1888946593147858085 }, .{ 7059937891890119595, 1511157274518286468 },
.{ 13026647942995916322, 1208925819614629174 }, .{ 9774590264567735146, 1934281311383406679 },
.{ 11509021026396098440, 1547425049106725343 }, .{ 16585914450600699399, 1237940039285380274 },
.{ 15469416676735388068, 1980704062856608439 }, .{ 16064882156130220778, 1584563250285286751 },
.{ 9162556910162266299, 1267650600228229401 }, .{ 7281393426775805432, 2028240960365167042 },
.{ 16893161185646375315, 1622592768292133633 }, .{ 2446482504291369283, 1298074214633706907 },
.{ 7603720821608101175, 2076918743413931051 }, .{ 2393627842544570617, 1661534994731144841 },
.{ 16672297533003297786, 1329227995784915872 }, .{ 11918280793837635165, 2126764793255865396 },
.{ 5845275820328197809, 1701411834604692317 }, .{ 15744267100488289217, 1361129467683753853 },
.{ 3054734472329800808, 2177807148294006166 }, .{ 17201182836831481939, 1742245718635204932 },
.{ 6382248639981364905, 1393796574908163946 }, .{ 2832900194486363201, 2230074519853062314 },
.{ 5955668970331000884, 1784059615882449851 }, .{ 1075186361522890384, 1427247692705959881 },
.{ 12788344622662355584, 2283596308329535809 }, .{ 13920024512871794791, 1826877046663628647 },
.{ 3757321980813615186, 1461501637330902918 }, .{ 10384555214134712795, 1169201309864722334 },
.{ 5547241898389809503, 1870722095783555735 }, .{ 4437793518711847602, 1496577676626844588 },
.{ 10928932444453298728, 1197262141301475670 }, .{ 17486291911125277965, 1915619426082361072 },
.{ 6610335899416401726, 1532495540865888858 }, .{ 12666966349016942027, 1225996432692711086 },
.{ 12888448528943286597, 1961594292308337738 }, .{ 17689456452638449924, 1569275433846670190 },
.{ 14151565162110759939, 1255420347077336152 }, .{ 7885109000409574610, 2008672555323737844 },
.{ 9997436015069570011, 1606938044258990275 }, .{ 7997948812055656009, 1285550435407192220 },
.{ 12796718099289049614, 2056880696651507552 }, .{ 2858676849947419045, 1645504557321206042 },
.{ 13354987924183666206, 1316403645856964833 }, .{ 17678631863951955605, 2106245833371143733 },
.{ 3074859046935833515, 1684996666696914987 }, .{ 13527933681774397782, 1347997333357531989 },
.{ 10576647446613305481, 2156795733372051183 }, .{ 15840015586774465031, 1725436586697640946 },
.{ 8982663654677661702, 1380349269358112757 }, .{ 18061610662226169046, 2208558830972980411 },
.{ 10759939715039024913, 1766847064778384329 }, .{ 12297300586773130254, 1413477651822707463 },
.{ 15986332124095098083, 2261564242916331941 }, .{ 9099716884534168143, 1809251394333065553 },
.{ 14658471137111155161, 1447401115466452442 }, .{ 4348079280205103483, 1157920892373161954 },
.{ 14335624477811986218, 1852673427797059126 }, .{ 7779150767507678651, 1482138742237647301 },
.{ 2533971799264232598, 1185710993790117841 }, .{ 15122401323048503126, 1897137590064188545 },
.{ 12097921058438802501, 1517710072051350836 }, .{ 5988988032009131678, 1214168057641080669 },
.{ 16961078480698431330, 1942668892225729070 }, .{ 13568862784558745064, 1554135113780583256 },
.{ 7165741412905085728, 1243308091024466605 }, .{ 11465186260648137165, 1989292945639146568 },
.{ 16550846638002330379, 1591434356511317254 }, .{ 16930026125143774626, 1273147485209053803 },
.{ 4951948911778577463, 2037035976334486086 }, .{ 272210314680951647, 1629628781067588869 },
.{ 3907117066486671641, 1303703024854071095 }, .{ 6251387306378674625, 2085924839766513752 },
.{ 16069156289328670670, 1668739871813211001 }, .{ 9165976216721026213, 1334991897450568801 },
.{ 7286864317269821294, 2135987035920910082 }, .{ 16897537898041588005, 1708789628736728065 },
.{ 13518030318433270404, 1367031702989382452 }, .{ 6871453250525591353, 2187250724783011924 },
.{ 9186511415162383406, 1749800579826409539 }, .{ 11038557946871817048, 1399840463861127631 },
.{ 10282995085511086630, 2239744742177804210 }, .{ 8226396068408869304, 1791795793742243368 },
.{ 13959814484210916090, 1433436634993794694 }, .{ 11267656730511734774, 2293498615990071511 },
.{ 5324776569667477496, 1834798892792057209 }, .{ 7949170070475892320, 1467839114233645767 },
.{ 17427382500606444826, 1174271291386916613 }, .{ 5747719112518849781, 1878834066219066582 },
.{ 15666221734240810795, 1503067252975253265 }, .{ 12532977387392648636, 1202453802380202612 },
.{ 5295368560860596524, 1923926083808324180 }, .{ 4236294848688477220, 1539140867046659344 },
.{ 7078384693692692099, 1231312693637327475 }, .{ 11325415509908307358, 1970100309819723960 },
.{ 9060332407926645887, 1576080247855779168 }, .{ 14626963555825137356, 1260864198284623334 },
.{ 12335095245094488799, 2017382717255397335 }, .{ 9868076196075591040, 1613906173804317868 },
.{ 15273158586344293478, 1291124939043454294 }, .{ 13369007293925138595, 2065799902469526871 },
.{ 7005857020398200553, 1652639921975621497 }, .{ 16672732060544291412, 1322111937580497197 },
.{ 11918976037903224966, 2115379100128795516 }, .{ 5845832015580669650, 1692303280103036413 },
.{ 12055363241948356366, 1353842624082429130 }, .{ 841837113407818570, 2166148198531886609 },
.{ 4362818505468165179, 1732918558825509287 }, .{ 14558301248600263113, 1386334847060407429 },
.{ 12225235553534690011, 2218135755296651887 }, .{ 2401490813343931363, 1774508604237321510 },
.{ 1921192650675145090, 1419606883389857208 }, .{ 17831303500047873437, 2271371013423771532 },
.{ 6886345170554478103, 1817096810739017226 }, .{ 1819727321701672159, 1453677448591213781 },
.{ 16213177116328979020, 1162941958872971024 }, .{ 14873036941900635463, 1860707134196753639 },
.{ 15587778368262418694, 1488565707357402911 }, .{ 8780873879868024632, 1190852565885922329 },
.{ 2981351763563108441, 1905364105417475727 }, .{ 13453127855076217722, 1524291284333980581 },
.{ 7073153469319063855, 1219433027467184465 }, .{ 11317045550910502167, 1951092843947495144 },
.{ 12742985255470312057, 1560874275157996115 }, .{ 10194388204376249646, 1248699420126396892 },
.{ 1553625868034358140, 1997919072202235028 }, .{ 8621598323911307159, 1598335257761788022 },
.{ 17965325103354776697, 1278668206209430417 }, .{ 13987124906400001422, 2045869129935088668 },
.{ 121653480894270168, 1636695303948070935 }, .{ 97322784715416134, 1309356243158456748 },
.{ 14913111714512307107, 2094969989053530796 }, .{ 8241140556867935363, 1675975991242824637 },
.{ 17660958889720079260, 1340780792994259709 }, .{ 17189487779326395846, 2145249268790815535 },
.{ 13751590223461116677, 1716199415032652428 }, .{ 18379969808252713988, 1372959532026121942 },
.{ 14650556434236701088, 2196735251241795108 }, .{ 652398703163629901, 1757388200993436087 },
.{ 11589965406756634890, 1405910560794748869 }, .{ 7475898206584884855, 2249456897271598191 },
.{ 2291369750525997561, 1799565517817278553 }, .{ 9211793429904618695, 1439652414253822842 },
.{ 18428218302589300235, 2303443862806116547 }, .{ 7363877012587619542, 1842755090244893238 },
.{ 13269799239553916280, 1474204072195914590 }, .{ 10615839391643133024, 1179363257756731672 },
.{ 2227947767661371545, 1886981212410770676 }, .{ 16539753473096738529, 1509584969928616540 },
.{ 13231802778477390823, 1207667975942893232 }, .{ 6413489186596184024, 1932268761508629172 },
.{ 16198837793502678189, 1545815009206903337 }, .{ 5580372605318321905, 1236652007365522670 },
.{ 8928596168509315048, 1978643211784836272 }, .{ 18210923379033183008, 1582914569427869017 },
.{ 7190041073742725760, 1266331655542295214 }, .{ 436019273762630246, 2026130648867672343 },
.{ 7727513048493924843, 1620904519094137874 }, .{ 9871359253537050198, 1296723615275310299 },
.{ 4726128361433549347, 2074757784440496479 }, .{ 7470251503888749801, 1659806227552397183 },
.{ 13354898832594820487, 1327844982041917746 }, .{ 13989140502667892133, 2124551971267068394 },
.{ 14880661216876224029, 1699641577013654715 }, .{ 11904528973500979224, 1359713261610923772 },
.{ 4289851098633925465, 2175541218577478036 }, .{ 18189276137874781665, 1740432974861982428 },
.{ 3483374466074094362, 1392346379889585943 }, .{ 1884050330976640656, 2227754207823337509 },
.{ 5196589079523222848, 1782203366258670007 }, .{ 15225317707844309248, 1425762693006936005 },
.{ 5913764258841343181, 2281220308811097609 }, .{ 8420360221814984868, 1824976247048878087 },
.{ 17804334621677718864, 1459980997639102469 }, .{ 17932816512084085415, 1167984798111281975 },
.{ 10245762345624985047, 1868775676978051161 }, .{ 4507261061758077715, 1495020541582440929 },
.{ 7295157664148372495, 1196016433265952743 }, .{ 7982903447895485668, 1913626293225524389 },
.{ 10075671573058298858, 1530901034580419511 }, .{ 4371188443704728763, 1224720827664335609 },
.{ 14372599139411386667, 1959553324262936974 }, .{ 15187428126271019657, 1567642659410349579 },
.{ 15839291315758726049, 1254114127528279663 }, .{ 3206773216762499739, 2006582604045247462 },
.{ 13633465017635730761, 1605266083236197969 }, .{ 14596120828850494932, 1284212866588958375 },
.{ 4907049252451240275, 2054740586542333401 }, .{ 236290587219081897, 1643792469233866721 },
.{ 14946427728742906810, 1315033975387093376 }, .{ 16535586736504830250, 2104054360619349402 },
.{ 5849771759720043554, 1683243488495479522 }, .{ 15747863852001765813, 1346594790796383617 },
.{ 10439186904235184007, 2154551665274213788 }, .{ 15730047152871967852, 1723641332219371030 },
.{ 12584037722297574282, 1378913065775496824 }, .{ 9066413911450387881, 2206260905240794919 },
.{ 10942479943902220628, 1765008724192635935 }, .{ 8753983955121776503, 1412006979354108748 },
.{ 10317025513452932081, 2259211166966573997 }, .{ 874922781278525018, 1807368933573259198 },
.{ 8078635854506640661, 1445895146858607358 }, .{ 13841606313089133175, 1156716117486885886 },
.{ 14767872471458792434, 1850745787979017418 }, .{ 746251532941302978, 1480596630383213935 },
.{ 597001226353042382, 1184477304306571148 }, .{ 15712597221132509104, 1895163686890513836 },
.{ 8880728962164096960, 1516130949512411069 }, .{ 10793931984473187891, 1212904759609928855 },
.{ 17270291175157100626, 1940647615375886168 }, .{ 2748186495899949531, 1552518092300708935 },
.{ 2198549196719959625, 1242014473840567148 }, .{ 18275073973719576693, 1987223158144907436 },
.{ 10930710364233751031, 1589778526515925949 }, .{ 12433917106128911148, 1271822821212740759 },
.{ 8826220925580526867, 2034916513940385215 }, .{ 7060976740464421494, 1627933211152308172 },
.{ 16716827836597268165, 1302346568921846537 }, .{ 11989529279587987770, 2083754510274954460 },
.{ 9591623423670390216, 1667003608219963568 }, .{ 15051996368420132820, 1333602886575970854 },
.{ 13015147745246481542, 2133764618521553367 }, .{ 3033420566713364587, 1707011694817242694 },
.{ 6116085268112601993, 1365609355853794155 }, .{ 9785736428980163188, 2184974969366070648 },
.{ 15207286772667951197, 1747979975492856518 }, .{ 1097782973908629988, 1398383980394285215 },
.{ 1756452758253807981, 2237414368630856344 }, .{ 5094511021344956708, 1789931494904685075 },
.{ 4075608817075965366, 1431945195923748060 }, .{ 6520974107321544586, 2291112313477996896 },
.{ 1527430471115325346, 1832889850782397517 }, .{ 12289990821117991246, 1466311880625918013 },
.{ 17210690286378213644, 1173049504500734410 }, .{ 9090360384495590213, 1876879207201175057 },
.{ 18340334751822203140, 1501503365760940045 }, .{ 14672267801457762512, 1201202692608752036 },
.{ 16096930852848599373, 1921924308174003258 }, .{ 1809498238053148529, 1537539446539202607 },
.{ 12515645034668249793, 1230031557231362085 }, .{ 1578287981759648052, 1968050491570179337 },
.{ 12330676829633449412, 1574440393256143469 }, .{ 13553890278448669853, 1259552314604914775 },
.{ 3239480371808320148, 2015283703367863641 }, .{ 17348979556414297411, 1612226962694290912 },
.{ 6500486015647617283, 1289781570155432730 }, .{ 10400777625036187652, 2063650512248692368 },
.{ 15699319729512770768, 1650920409798953894 }, .{ 16248804598352126938, 1320736327839163115 },
.{ 7551343283653851484, 2113178124542660985 }, .{ 6041074626923081187, 1690542499634128788 },
.{ 12211557331022285596, 1352433999707303030 }, .{ 1091747655926105338, 2163894399531684849 },
.{ 4562746939482794594, 1731115519625347879 }, .{ 7339546366328145998, 1384892415700278303 },
.{ 8053925371383123274, 2215827865120445285 }, .{ 6443140297106498619, 1772662292096356228 },
.{ 12533209867169019542, 1418129833677084982 }, .{ 5295740528502789974, 2269007733883335972 },
.{ 15304638867027962949, 1815206187106668777 }, .{ 4865013464138549713, 1452164949685335022 },
.{ 14960057215536570740, 1161731959748268017 }, .{ 9178696285890871890, 1858771135597228828 },
.{ 14721654658196518159, 1487016908477783062 }, .{ 4398626097073393881, 1189613526782226450 },
.{ 7037801755317430209, 1903381642851562320 }, .{ 5630241404253944167, 1522705314281249856 },
.{ 814844308661245011, 1218164251424999885 }, .{ 1303750893857992017, 1949062802279999816 },
.{ 15800395974054034906, 1559250241823999852 }, .{ 5261619149759407279, 1247400193459199882 },
.{ 12107939454356961969, 1995840309534719811 }, .{ 5997002748743659252, 1596672247627775849 },
.{ 8486951013736837725, 1277337798102220679 }, .{ 2511075177753209390, 2043740476963553087 },
.{ 13076906586428298482, 1634992381570842469 }, .{ 14150874083884549109, 1307993905256673975 },
.{ 4194654460505726958, 2092790248410678361 }, .{ 18113118827372222859, 1674232198728542688 },
.{ 3422448617672047318, 1339385758982834151 }, .{ 16543964232501006678, 2143017214372534641 },
.{ 9545822571258895019, 1714413771498027713 }, .{ 15015355686490936662, 1371531017198422170 },
.{ 5577825024675947042, 2194449627517475473 }, .{ 11840957649224578280, 1755559702013980378 },
.{ 16851463748863483271, 1404447761611184302 }, .{ 12204946739213931940, 2247116418577894884 },
.{ 13453306206113055875, 1797693134862315907 }, .{ 3383947335406624054, 1438154507889852726 },
.{ 16482362180876329456, 2301047212623764361 }, .{ 9496540929959153242, 1840837770099011489 },
.{ 11286581558709232917, 1472670216079209191 }, .{ 5339916432225476010, 1178136172863367353 },
.{ 4854517476818851293, 1885017876581387765 }, .{ 3883613981455081034, 1508014301265110212 },
.{ 14174937629389795797, 1206411441012088169 }, .{ 11611853762797942306, 1930258305619341071 },
.{ 5600134195496443521, 1544206644495472857 }, .{ 15548153800622885787, 1235365315596378285 },
.{ 6430302007287065643, 1976584504954205257 }, .{ 16212288050055383484, 1581267603963364205 },
.{ 12969830440044306787, 1265014083170691364 }, .{ 9683682259845159889, 2024022533073106183 },
.{ 15125643437359948558, 1619218026458484946 }, .{ 8411165935146048523, 1295374421166787957 },
.{ 17147214310975587960, 2072599073866860731 }, .{ 10028422634038560045, 1658079259093488585 },
.{ 8022738107230848036, 1326463407274790868 }, .{ 9147032156827446534, 2122341451639665389 },
.{ 11006974540203867551, 1697873161311732311 }, .{ 5116230817421183718, 1358298529049385849 },
.{ 15564666937357714594, 2173277646479017358 }, .{ 1383687105660440706, 1738622117183213887 },
.{ 12174996128754083534, 1390897693746571109 }, .{ 8411947361780802685, 2225436309994513775 },
.{ 6729557889424642148, 1780349047995611020 }, .{ 5383646311539713719, 1424279238396488816 },
.{ 1235136468979721303, 2278846781434382106 }, .{ 15745504434151418335, 1823077425147505684 },
.{ 16285752362063044992, 1458461940118004547 }, .{ 5649904260166615347, 1166769552094403638 },
.{ 5350498001524674232, 1866831283351045821 }, .{ 591049586477829062, 1493465026680836657 },
.{ 11540886113407994219, 1194772021344669325 }, .{ 18673707743239135, 1911635234151470921 },
.{ 14772334225162232601, 1529308187321176736 }, .{ 8128518565387875758, 1223446549856941389 },
.{ 1937583260394870242, 1957514479771106223 }, .{ 8928764237799716840, 1566011583816884978 },
.{ 14521709019723594119, 1252809267053507982 }, .{ 8477339172590109297, 2004494827285612772 },
.{ 17849917782297818407, 1603595861828490217 }, .{ 6901236596354434079, 1282876689462792174 },
.{ 18420676183650915173, 2052602703140467478 }, .{ 3668494502695001169, 1642082162512373983 },
.{ 10313493231639821582, 1313665730009899186 }, .{ 9122891541139893884, 2101865168015838698 },
.{ 14677010862395735754, 1681492134412670958 }, .{ 673562245690857633, 1345193707530136767 }
};
// zig fmt: off
//
// f128 small tables: 9072 bytes
const FLOAT128_POW5_INV_BITCOUNT = 249;
const FLOAT128_POW5_BITCOUNT = 249;
const FLOAT128_POW5_TABLE_SIZE: comptime_int = FLOAT128_POW5_TABLE.len;
const FLOAT128_POW5_TABLE: [56][2]u64 = .{
.{ 1, 0 },
.{ 5, 0 },
.{ 25, 0 },
@@ -687,7 +1241,7 @@ const GENERIC_POW5_TABLE: [POW5_TABLE_SIZE][2]u64 = .{
.{ 18443565265187884909, 15046327690525280101 },
};
const GENERIC_POW5_SPLIT: [89][4]u64 = .{
const FLOAT128_POW5_SPLIT: [89][4]u64 = .{
.{ 0, 0, 0, 72057594037927936 },
.{ 0, 5206161169240293376, 4575641699882439235, 73468396926392969 },
.{ 3360510775605221349, 6983200512169538081, 4325643253124434363, 74906821675075173 },
@@ -781,7 +1335,7 @@ const GENERIC_POW5_SPLIT: [89][4]u64 = .{
// Unfortunately, the results are sometimes off by one or two. We use an additional
// lookup table to store those cases and adjust the result.
const POW5_ERRORS: [156]u64 = .{
const FLOAT128_POW5_ERRORS: [156]u64 = .{
0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9555596400000000,
0x65a6569525565555, 0x4415551445449655, 0x5105015504144541, 0x65a69969a6965964,
0x5054955969959656, 0x5105154515554145, 0x4055511051591555, 0x5500514455550115,
@@ -823,7 +1377,7 @@ const POW5_ERRORS: [156]u64 = .{
0x5044044040000000, 0x1045040440010500, 0x0000400000040000, 0x0000000000000000,
};
const GENERIC_POW5_INV_SPLIT: [89][4]u64 = .{
const FLOAT128_POW5_INV_SPLIT: [89][4]u64 = .{
.{ 0, 0, 0, 144115188075855872 },
.{ 1573859546583440065, 2691002611772552616, 6763753280790178510, 141347765182270746 },
.{ 12960290449513840412, 12345512957918226762, 18057899791198622765, 138633484706040742 },
@@ -915,7 +1469,7 @@ const GENERIC_POW5_INV_SPLIT: [89][4]u64 = .{
.{ 7184427196661305643, 14332510582433188173, 14230167953789677901, 104649889046128358 },
};
const POW5_INV_ERRORS: [154]u64 = .{
const FLOAT128_POW5_INV_ERRORS: [154]u64 = .{
0x1144155514145504, 0x0000541555401141, 0x0000000000000000, 0x0154454000000000,
0x4114105515544440, 0x0001001111500415, 0x4041411410011000, 0x5550114515155014,
0x1404100041554551, 0x0515000450404410, 0x5054544401140004, 0x5155501005555105,