Commit 31791ae15bfa8590cb235ce9d7c87a97d5136eef | zig

author	Marc Tiehuis <marc@tiehu.is> 2024-03-21 13:57:57+13:00
committer	Veikka Tuominen <git@vexu.eu> 2024-03-21 17:10:41+02:00
log	31791ae15bfa8590cb235ce9d7c87a97d5136eef
tree	bf981a8a7b4afbb4edc63e9d44fcac20fd555d3b
parent	afdc41cfd61db23f545d9239b61695e2ae991713

rename ryu128 -> format_float

Symmetry with parse_float and to hide the implementation from the user.
Additionally, we expose the entire namespace and provide some aliases so
everything is available to a user.

Closes #19366

4 files changed, 1150 insertions(+), 1147 deletions(-)

CMakeLists.txt
lib
- std
  - fmt.zig
  - fmt
    format_float.zig
    ryu128.zig

CMakeLists.txt+1-1

...	...	@@ -235,7 +235,7 @@ set(ZIG_STAGE2_SOURCES
235	235	"${CMAKE_SOURCE_DIR}/lib/std/elf.zig"
236	236	"${CMAKE_SOURCE_DIR}/lib/std/fifo.zig"
237	237	"${CMAKE_SOURCE_DIR}/lib/std/fmt.zig"
238		"${CMAKE_SOURCE_DIR}/lib/std/fmt/ryu128.zig"
	238	"${CMAKE_SOURCE_DIR}/lib/std/fmt/format_float.zig"
239	239	"${CMAKE_SOURCE_DIR}/lib/std/fmt/parse_float.zig"
240	240	"${CMAKE_SOURCE_DIR}/lib/std/fs.zig"
241	241	"${CMAKE_SOURCE_DIR}/lib/std/fs/AtomicFile.zig"

lib/std/fmt.zig+10-7

...	...	@@ -9,7 +9,6 @@ const assert = std.debug.assert;
9	9	const mem = std.mem;
10	10	const unicode = std.unicode;
11	11	const meta = std.meta;
12		const ryu128 = @import("fmt/ryu128.zig");
13	12	const lossyCast = std.math.lossyCast;
14	13	const expectFmt = std.testing.expectFmt;
15	14
...	...	@@ -757,21 +756,25 @@ pub fn formatIntValue(
757	756	return formatInt(int_value, base, case, options, writer);
758	757	}
759	758
	759	pub const format_float = @import("fmt/format_float.zig");
	760	pub const formatFloat = format_float.formatFloat;
	761	pub const FormatFloatError = format_float.FormatError;
	762
760	763	fn formatFloatValue(
761	764	value: anytype,
762	765	comptime fmt: []const u8,
763	766	options: FormatOptions,
764	767	writer: anytype,
765	768	) !void {
766		var buf: [ryu128.bufferSize(.decimal, f64)]u8 = undefined;
	769	var buf: [format_float.bufferSize(.decimal, f64)]u8 = undefined;
767	770
768	771	if (fmt.len == 0 or comptime std.mem.eql(u8, fmt, "e")) {
769		const s = ryu128.format(&buf, value, .{ .mode = .scientific, .precision = options.precision }) catch \|err\| switch (err) {
	772	const s = formatFloat(&buf, value, .{ .mode = .scientific, .precision = options.precision }) catch \|err\| switch (err) {
770	773	error.BufferTooSmall => "(float)",
771	774	};
772	775	return formatBuf(s, options, writer);
773	776	} else if (comptime std.mem.eql(u8, fmt, "d")) {
774		const s = ryu128.format(&buf, value, .{ .mode = .decimal, .precision = options.precision }) catch \|err\| switch (err) {
	777	const s = formatFloat(&buf, value, .{ .mode = .decimal, .precision = options.precision }) catch \|err\| switch (err) {
775	778	error.BufferTooSmall => "(float)",
776	779	};
777	780	return formatBuf(s, options, writer);
...	...	@@ -787,7 +790,7 @@ fn formatFloatValue(
787	790	}
788	791
789	792	test {
790		_ = &ryu128;
	793	_ = &format_float;
791	794	}
792	795
793	796	pub const Case = enum { lower, upper };
...	...	@@ -890,7 +893,7 @@ fn formatSizeImpl(comptime base: comptime_int) type {
890	893	return formatBuf("0B", options, writer);
891	894	}
892	895	// The worst case in terms of space needed is 32 bytes + 3 for the suffix.
893		var buf: [ryu128.min_buffer_size + 3]u8 = undefined;
	896	var buf: [format_float.min_buffer_size + 3]u8 = undefined;
894	897
895	898	const mags_si = " kMGTPEZY";
896	899	const mags_iec = " KMGTPEZY";
...	...	@@ -908,7 +911,7 @@ fn formatSizeImpl(comptime base: comptime_int) type {
908	911	else => unreachable,
909	912	};
910	913
911		const s = ryu128.format(&buf, new_value, .{ .mode = .decimal, .precision = options.precision }) catch \|err\| switch (err) {
	914	const s = formatFloat(&buf, new_value, .{ .mode = .decimal, .precision = options.precision }) catch \|err\| switch (err) {
912	915	error.BufferTooSmall => unreachable,
913	916	};
914	917

lib/std/fmt/format_float.zig created+1139

...	...	@@ -0,0 +1,1139 @@
	1	//! This file implements the ryu floating point conversion algorithm:
	2	//! https://dl.acm.org/doi/pdf/10.1145/3360595
	3
	4	const std = @import("std");
	5	const expectFmt = std.testing.expectFmt;
	6
	7	const special_exponent = 0x7fffffff;
	8
	9	/// Any buffer used for `format` must be at least this large. This is asserted. A runtime check will
	10	/// additionally be performed if more bytes are required.
	11	pub const min_buffer_size = 53;
	12
	13	/// Returns the minimum buffer size needed to print every float of a specific type and format.
	14	pub fn bufferSize(comptime mode: Format, comptime T: type) comptime_int {
	15	comptime std.debug.assert(@typeInfo(T) == .Float);
	16	return switch (mode) {
	17	.scientific => 53,
	18	// Based on minimum subnormal values.
	19	.decimal => switch (@bitSizeOf(T)) {
	20	16 => @max(15, min_buffer_size),
	21	32 => 55,
	22	64 => 347,
	23	80 => 4996,
	24	128 => 5011,
	25	else => unreachable,
	26	},
	27	};
	28	}
	29
	30	pub const FormatError = error{
	31	BufferTooSmall,
	32	};
	33
	34	pub const Format = enum {
	35	scientific,
	36	decimal,
	37	};
	38
	39	pub const FormatOptions = struct {
	40	mode: Format = .scientific,
	41	precision: ?usize = null,
	42	};
	43
	44	/// Format a floating-point value and write it to buffer. Returns a slice to the buffer containing
	45	/// the string representation.
	46	///
	47	/// Full precision is the default. Any full precision float can be reparsed with std.fmt.parseFloat
	48	/// unambiguously.
	49	///
	50	/// Scientific mode is recommended generally as the output is more compact and any type can be
	51	/// written in full precision using a buffer of only `min_buffer_size`.
	52	///
	53	/// When printing full precision decimals, use `bufferSize` to get the required space. It is
	54	/// recommended to bound decimal output with a fixed precision to reduce the required buffer size.
	55	pub fn formatFloat(buf: []u8, v_: anytype, options: FormatOptions) FormatError![]const u8 {
	56	const v = switch (@TypeOf(v_)) {
	57	// comptime_float internally is a f128; this preserves precision.
	58	comptime_float => @as(f128, v_),
	59	else => v_,
	60	};
	61
	62	const T = @TypeOf(v);
	63	comptime std.debug.assert(@typeInfo(T) == .Float);
	64	const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
	65
	66	const has_explicit_leading_bit = std.math.floatMantissaBits(T) - std.math.floatFractionalBits(T) != 0;
	67	const d = binaryToDecimal(@as(I, @bitCast(v)), std.math.floatMantissaBits(T), std.math.floatExponentBits(T), has_explicit_leading_bit);
	68
	69	return switch (options.mode) {
	70	.scientific => formatScientific(buf, d, options.precision),
	71	.decimal => formatDecimal(buf, d, options.precision),
	72	};
	73	}
	74
	75	pub const FloatDecimal128 = struct {
	76	mantissa: u128,
	77	exponent: i32,
	78	sign: bool,
	79	};
	80
	81	fn copySpecialStr(buf: []u8, f: FloatDecimal128) []const u8 {
	82	if (f.sign) {
	83	buf[0] = '-';
	84	}
	85	const offset: usize = @intFromBool(f.sign);
	86	if (f.mantissa != 0) {
	87	@memcpy(buf[offset..][0..3], "nan");
	88	return buf[0 .. 3 + offset];
	89	}
	90	@memcpy(buf[offset..][0..3], "inf");
	91	return buf[0 .. 3 + offset];
	92	}
	93
	94	fn writeDecimal(buf: []u8, value: anytype, count: usize) void {
	95	var i: usize = 0;
	96
	97	while (i + 2 < count) : (i += 2) {
	98	const c: u8 = @intCast(value.* % 100);
	99	value.* /= 100;
	100	const d = std.fmt.digits2(c);
	101	buf[count - i - 1] = d[1];
	102	buf[count - i - 2] = d[0];
	103	}
	104
	105	while (i < count) : (i += 1) {
	106	const c: u8 = @intCast(value.* % 10);
	107	value.* /= 10;
	108	buf[count - i - 1] = '0' + c;
	109	}
	110	}
	111
	112	fn isPowerOf10(n_: u128) bool {
	113	var n = n_;
	114	while (n != 0) : (n /= 10) {
	115	if (n % 10 != 0) return false;
	116	}
	117	return true;
	118	}
	119
	120	const RoundMode = enum {
	121	/// 1234.56 = precision 2
	122	decimal,
	123	/// 1.23456e3 = precision 5
	124	scientific,
	125	};
	126
	127	fn round(f: FloatDecimal128, mode: RoundMode, precision: usize) FloatDecimal128 {
	128	var round_digit: usize = 0;
	129	var output = f.mantissa;
	130	var exp = f.exponent;
	131	const olength = decimalLength(output);
	132
	133	switch (mode) {
	134	.decimal => {
	135	if (f.exponent > 0) {
	136	round_digit = (olength - 1) + precision + @as(usize, @intCast(f.exponent));
	137	} else {
	138	const min_exp_required = @as(usize, @intCast(-f.exponent));
	139	if (precision + olength > min_exp_required) {
	140	round_digit = precision + olength - min_exp_required;
	141	}
	142	}
	143	},
	144	.scientific => {
	145	round_digit = 1 + precision;
	146	},
	147	}
	148
	149	if (round_digit < olength) {
	150	var nlength = olength;
	151	for (round_digit + 1..olength) \|_\| {
	152	output /= 10;
	153	exp += 1;
	154	nlength -= 1;
	155	}
	156
	157	if (output % 10 >= 5) {
	158	output /= 10;
	159	output += 1;
	160	exp += 1;
	161
	162	// e.g. 9999 -> 10000
	163	if (isPowerOf10(output)) {
	164	output /= 10;
	165	exp += 1;
	166	}
	167	}
	168	}
	169
	170	return .{
	171	.mantissa = output,
	172	.exponent = exp,
	173	.sign = f.sign,
	174	};
	175	}
	176
	177	/// Write a FloatDecimal128 to a buffer in scientific form.
	178	///
	179	/// The buffer provided must be greater than `min_buffer_size` in length. If no precision is
	180	/// specified, this function will never return an error. If a precision is specified, up to
	181	/// `8 + precision` bytes will be written to the buffer. An error will be returned if the content
	182	/// will not fit.
	183	///
	184	/// It is recommended to bound decimal formatting with an exact precision.
	185	pub fn formatScientific(buf: []u8, f_: FloatDecimal128, precision: ?usize) FormatError![]const u8 {
	186	std.debug.assert(buf.len >= min_buffer_size);
	187	var f = f_;
	188
	189	if (f.exponent == special_exponent) {
	190	return copySpecialStr(buf, f);
	191	}
	192
	193	if (precision) \|prec\| {
	194	f = round(f, .scientific, prec);
	195	}
	196
	197	var output = f.mantissa;
	198	const olength = decimalLength(output);
	199
	200	if (precision) \|prec\| {
	201	// fixed bound: sign(1) + leading_digit(1) + point(1) + exp_sign(1) + exp_max(4)
	202	const req_bytes = 8 + prec;
	203	if (buf.len < req_bytes) {
	204	return error.BufferTooSmall;
	205	}
	206	}
	207
	208	// Step 5: Print the scientific representation
	209	var index: usize = 0;
	210	if (f.sign) {
	211	buf[index] = '-';
	212	index += 1;
	213	}
	214
	215	// 1.12345
	216	writeDecimal(buf[index + 2 ..], &output, olength - 1);
	217	buf[index] = '0' + @as(u8, @intCast(output % 10));
	218	buf[index + 1] = '.';
	219	index += 2;
	220	const dp_index = index;
	221	if (olength > 1) index += olength - 1 else index -= 1;
	222
	223	if (precision) \|prec\| {
	224	index += @intFromBool(olength == 1);
	225	if (prec > olength - 1) {
	226	const len = prec - (olength - 1);
	227	@memset(buf[index..][0..len], '0');
	228	index += len;
	229	} else {
	230	index = dp_index + prec - @intFromBool(prec == 0);
	231	}
	232	}
	233
	234	// e100
	235	buf[index] = 'e';
	236	index += 1;
	237	var exp = f.exponent + @as(i32, @intCast(olength)) - 1;
	238	if (exp < 0) {
	239	buf[index] = '-';
	240	index += 1;
	241	exp = -exp;
	242	}
	243	var uexp: u32 = @intCast(exp);
	244	const elength = decimalLength(uexp);
	245	writeDecimal(buf[index..], &uexp, elength);
	246	index += elength;
	247
	248	return buf[0..index];
	249	}
	250
	251	/// Write a FloatDecimal128 to a buffer in decimal form.
	252	///
	253	/// The buffer provided must be greater than `min_buffer_size` bytes in length. If no precision is
	254	/// specified, this may still return an error. If precision is specified, `2 + precision` bytes will
	255	/// always be written.
	256	pub fn formatDecimal(buf: []u8, f_: FloatDecimal128, precision: ?usize) FormatError![]const u8 {
	257	std.debug.assert(buf.len >= min_buffer_size);
	258	var f = f_;
	259
	260	if (f.exponent == special_exponent) {
	261	return copySpecialStr(buf, f);
	262	}
	263
	264	if (precision) \|prec\| {
	265	f = round(f, .decimal, prec);
	266	}
	267
	268	var output = f.mantissa;
	269	const olength = decimalLength(output);
	270
	271	// fixed bound: leading_digit(1) + point(1)
	272	const req_bytes = if (f.exponent >= 0)
	273	2 + @abs(f.exponent) + olength + (precision orelse 0)
	274	else
	275	2 + @max(@abs(f.exponent) + olength, precision orelse 0);
	276	if (buf.len < req_bytes) {
	277	return error.BufferTooSmall;
	278	}
	279
	280	// Step 5: Print the decimal representation
	281	var index: usize = 0;
	282	if (f.sign) {
	283	buf[index] = '-';
	284	index += 1;
	285	}
	286
	287	const dp_offset = f.exponent + cast_i32(olength);
	288	if (dp_offset <= 0) {
	289	// 0.000001234
	290	buf[index] = '0';
	291	buf[index + 1] = '.';
	292	index += 2;
	293	const dp_index = index;
	294
	295	const dp_poffset: u32 = @intCast(-dp_offset);
	296	@memset(buf[index..][0..dp_poffset], '0');
	297	index += dp_poffset;
	298	writeDecimal(buf[index..], &output, olength);
	299	index += olength;
	300
	301	if (precision) \|prec\| {
	302	const dp_written = index - dp_index;
	303	if (prec > dp_written) {
	304	@memset(buf[index..][0 .. prec - dp_written], '0');
	305	}
	306	index = dp_index + prec - @intFromBool(prec == 0);
	307	}
	308	} else {
	309	// 123456000
	310	const dp_uoffset: usize = @intCast(dp_offset);
	311	if (dp_uoffset >= olength) {
	312	writeDecimal(buf[index..], &output, olength);
	313	index += olength;
	314	@memset(buf[index..][0 .. dp_uoffset - olength], '0');
	315	index += dp_uoffset - olength;
	316
	317	if (precision) \|prec\| {
	318	if (prec != 0) {
	319	buf[index] = '.';
	320	index += 1;
	321	@memset(buf[index..][0..prec], '0');
	322	index += prec;
	323	}
	324	}
	325	} else {
	326	// 12345.6789
	327	writeDecimal(buf[index + dp_uoffset + 1 ..], &output, olength - dp_uoffset);
	328	buf[index + dp_uoffset] = '.';
	329	const dp_index = index + dp_uoffset + 1;
	330	writeDecimal(buf[index..], &output, dp_uoffset);
	331	index += olength + 1;
	332
	333	if (precision) \|prec\| {
	334	const dp_written = olength - dp_uoffset;
	335	if (prec > dp_written) {
	336	@memset(buf[index..][0 .. prec - dp_written], '0');
	337	}
	338	index = dp_index + prec - @intFromBool(prec == 0);
	339	}
	340	}
	341	}
	342
	343	return buf[0..index];
	344	}
	345
	346	fn cast_i32(v: anytype) i32 {
	347	return @intCast(v);
	348	}
	349
	350	/// Convert a binary float representation to decimal.
	351	pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explicit_leading_bit: bool) FloatDecimal128 {
	352	const bias = (@as(u32, 1) << (exponent_bits - 1)) - 1;
	353	const ieee_sign = ((bits >> (mantissa_bits + exponent_bits)) & 1) != 0;
	354	const ieee_mantissa = bits & ((@as(u128, 1) << mantissa_bits) - 1);
	355	const ieee_exponent: u32 = @intCast((bits >> mantissa_bits) & ((@as(u128, 1) << exponent_bits) - 1));
	356
	357	if (ieee_exponent == 0 and ieee_mantissa == 0) {
	358	return .{
	359	.mantissa = 0,
	360	.exponent = 0,
	361	.sign = ieee_sign,
	362	};
	363	}
	364	if (ieee_exponent == ((@as(u32, 1) << exponent_bits) - 1)) {
	365	return .{
	366	.mantissa = if (explicit_leading_bit) ieee_mantissa & ((@as(u128, 1) << (mantissa_bits - 1)) - 1) else ieee_mantissa,
	367	.exponent = 0x7fffffff,
	368	.sign = ieee_sign,
	369	};
	370	}
	371
	372	var e2: i32 = undefined;
	373	var m2: u128 = undefined;
	374	if (explicit_leading_bit) {
	375	if (ieee_exponent == 0) {
	376	e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
	377	} else {
	378	e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
	379	}
	380	m2 = ieee_mantissa;
	381	} else {
	382	if (ieee_exponent == 0) {
	383	e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
	384	m2 = ieee_mantissa;
	385	} else {
	386	e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
	387	m2 = (@as(u128, 1) << mantissa_bits) \| ieee_mantissa;
	388	}
	389	}
	390	const even = (m2 & 1) == 0;
	391	const accept_bounds = even;
	392
	393	// Step 2: Determine the interval of legal decimal representations.
	394	const mv = 4 * m2;
	395	const mm_shift: u1 = @intFromBool((ieee_mantissa != if (explicit_leading_bit) (@as(u128, 1) << (mantissa_bits - 1)) else 0) or (ieee_exponent == 0));
	396
	397	// Step 3: Convert to a decimal power base using 128-bit arithmetic.
	398	var vr: u128 = undefined;
	399	var vp: u128 = undefined;
	400	var vm: u128 = undefined;
	401	var e10: i32 = undefined;
	402	var vm_is_trailing_zeros = false;
	403	var vr_is_trailing_zeros = false;
	404	if (e2 >= 0) {
	405	const q: u32 = log10Pow2(@intCast(e2)) - @intFromBool(e2 > 3);
	406	e10 = cast_i32(q);
	407	const k: i32 = @intCast(FLOAT_128_POW5_INV_BITCOUNT + pow5Bits(q) - 1);
	408	const i: u32 = @intCast(-e2 + cast_i32(q) + k);
	409
	410	const pow5 = computeInvPow5(q);
	411	vr = mulShift(4 * m2, &pow5, i);
	412	vp = mulShift(4 * m2 + 2, &pow5, i);
	413	vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, i);
	414
	415	if (q <= 55) {
	416	if (mv % 5 == 0) {
	417	vr_is_trailing_zeros = multipleOfPowerOf5(mv, q -% 1);
	418	} else if (accept_bounds) {
	419	vm_is_trailing_zeros = multipleOfPowerOf5(mv - 1 - mm_shift, q);
	420	} else {
	421	vp -= @intFromBool(multipleOfPowerOf5(mv + 2, q));
	422	}
	423	}
	424	} else {
	425	const q: u32 = log10Pow5(@intCast(-e2)) - @intFromBool(-e2 > 1);
	426	e10 = cast_i32(q) + e2;
	427	const i: i32 = -e2 - cast_i32(q);
	428	const k: i32 = cast_i32(pow5Bits(@intCast(i))) - FLOAT_128_POW5_BITCOUNT;
	429	const j: u32 = @intCast(cast_i32(q) - k);
	430
	431	const pow5 = computePow5(@intCast(i));
	432	vr = mulShift(4 * m2, &pow5, j);
	433	vp = mulShift(4 * m2 + 2, &pow5, j);
	434	vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, j);
	435
	436	if (q <= 1) {
	437	vr_is_trailing_zeros = true;
	438	if (accept_bounds) {
	439	vm_is_trailing_zeros = mm_shift == 1;
	440	} else {
	441	vp -= 1;
	442	}
	443	} else if (q < 127) {
	444	vr_is_trailing_zeros = multipleOfPowerOf2(mv, q - 1);
	445	}
	446	}
	447
	448	// Step 4: Find the shortest decimal representation in the interval of legal representations.
	449	var removed: u32 = 0;
	450	var last_removed_digit: u8 = 0;
	451
	452	while (vp / 10 > vm / 10) {
	453	vm_is_trailing_zeros = vm_is_trailing_zeros and vm % 10 == 0;
	454	vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
	455	last_removed_digit = @intCast(vr % 10);
	456	vr /= 10;
	457	vp /= 10;
	458	vm /= 10;
	459	removed += 1;
	460	}
	461
	462	if (vm_is_trailing_zeros) {
	463	while (vm % 10 == 0) {
	464	vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
	465	last_removed_digit = @intCast(vr % 10);
	466	vr /= 10;
	467	vp /= 10;
	468	vm /= 10;
	469	removed += 1;
	470	}
	471	}
	472
	473	if (vr_is_trailing_zeros and (last_removed_digit == 5) and (vr % 2 == 0)) {
	474	last_removed_digit = 4;
	475	}
	476
	477	return .{
	478	.mantissa = vr + @intFromBool((vr == vm and (!accept_bounds or !vm_is_trailing_zeros)) or last_removed_digit >= 5),
	479	.exponent = e10 + cast_i32(removed),
	480	.sign = ieee_sign,
	481	};
	482	}
	483
	484	fn decimalLength(v: u128) u32 {
	485	const LARGEST_POW10 = (@as(u128, 5421010862427522170) << 64) \| 687399551400673280;
	486	var p10 = LARGEST_POW10;
	487	var i: u32 = 39;
	488	while (i > 0) : (i -= 1) {
	489	if (v >= p10) return i;
	490	p10 /= 10;
	491	}
	492	return 1;
	493	}
	494
	495	// floor(log_10(2^e))
	496	fn log10Pow2(e: u32) u32 {
	497	std.debug.assert(e <= 1 << 15);
	498	return @intCast((@as(u64, @intCast(e)) * 169464822037455) >> 49);
	499	}
	500
	501	// floor(log_10(5^e))
	502	fn log10Pow5(e: u32) u32 {
	503	std.debug.assert(e <= 1 << 15);
	504	return @intCast((@as(u64, @intCast(e)) * 196742565691928) >> 48);
	505	}
	506
	507	// if (e == 0) 1 else ceil(log_2(5^e))
	508	fn pow5Bits(e: u32) u32 {
	509	std.debug.assert(e <= 1 << 15);
	510	return @intCast(((@as(u64, @intCast(e)) * 163391164108059) >> 46) + 1);
	511	}
	512
	513	fn pow5Factor(value_: u128) u32 {
	514	var count: u32 = 0;
	515	var value = value_;
	516	while (value > 0) : ({
	517	count += 1;
	518	value /= 5;
	519	}) {
	520	if (value % 5 != 0) return count;
	521	}
	522	return 0;
	523	}
	524
	525	fn multipleOfPowerOf5(value: u128, p: u32) bool {
	526	return pow5Factor(value) >= p;
	527	}
	528
	529	fn multipleOfPowerOf2(value: u128, p: u32) bool {
	530	return (value & ((@as(u128, 1) << @as(u7, @intCast(p))) - 1)) == 0;
	531	}
	532
	533	fn computeInvPow5(i: u32) [4]u64 {
	534	const base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
	535	const base2 = base * POW5_TABLE_SIZE;
	536	const mul = &GENERIC_POW5_INV_SPLIT[base]; // 1 / 5^base2
	537	if (i == base2) {
	538	return .{ mul[0] + 1, mul[1], mul[2], mul[3] };
	539	} else {
	540	const offset = base2 - i;
	541	const m = &GENERIC_POW5_TABLE[offset]; // 5^offset
	542	const delta = pow5Bits(base2) - pow5Bits(i);
	543
	544	const shift: u6 = @intCast(2 * (i % 32));
	545	const corr: u32 = @intCast(((POW5_INV_ERRORS[i / 32] >> shift) & 3) + 1);
	546	return mul_128_256_shift(m, mul, delta, corr);
	547	}
	548	}
	549
	550	fn computePow5(i: u32) [4]u64 {
	551	const base = i / POW5_TABLE_SIZE;
	552	const base2 = base * POW5_TABLE_SIZE;
	553	const mul = &GENERIC_POW5_SPLIT[base];
	554	if (i == base2) {
	555	return mul.*;
	556	} else {
	557	const offset = i - base2;
	558	const m = &GENERIC_POW5_TABLE[offset];
	559	const delta = pow5Bits(i) - pow5Bits(base2);
	560
	561	const shift: u6 = @intCast(2 * (i % 32));
	562	const corr: u32 = @intCast((POW5_ERRORS[i / 32] >> shift) & 3);
	563	return mul_128_256_shift(m, mul, delta, corr);
	564	}
	565	}
	566
	567	fn mulShift(m: u128, mul: *const [4]u64, j: u32) u128 {
	568	std.debug.assert(j > 128);
	569	const a: [2]u64 = .{ @truncate(m), @truncate(m >> 64) };
	570	const r = mul_128_256_shift(&a, mul, j, 0);
	571	return (@as(u128, r[1]) << 64) \| r[0];
	572	}
	573
	574	fn mul_128_256_shift(a: const [2]u64, b: const [4]u64, shift: u32, corr: u32) [4]u64 {
	575	std.debug.assert(shift > 0);
	576	std.debug.assert(shift < 256);
	577
	578	const b00 = @as(u128, a[0]) * b[0];
	579	const b01 = @as(u128, a[0]) * b[1];
	580	const b02 = @as(u128, a[0]) * b[2];
	581	const b03 = @as(u128, a[0]) * b[3];
	582	const b10 = @as(u128, a[1]) * b[0];
	583	const b11 = @as(u128, a[1]) * b[1];
	584	const b12 = @as(u128, a[1]) * b[2];
	585	const b13 = @as(u128, a[1]) * b[3];
	586
	587	const s0 = b00;
	588	const s1 = b01 +% b10;
	589	const c1: u128 = @intFromBool(s1 < b01);
	590	const s2 = b02 +% b11;
	591	const c2: u128 = @intFromBool(s2 < b02);
	592	const s3 = b03 +% b12;
	593	const c3: u128 = @intFromBool(s3 < b03);
	594
	595	const p0 = s0 +% (s1 << 64);
	596	const d0: u128 = @intFromBool(p0 < b00);
	597	const q1 = s2 +% (s1 >> 64) +% (s3 << 64);
	598	const d1: u128 = @intFromBool(q1 < s2);
	599	const p1 = q1 +% (c1 << 64) +% d0;
	600	const d2: u128 = @intFromBool(p1 < q1);
	601	const p2 = b13 +% (s3 >> 64) +% c2 +% (c3 << 64) +% d1 +% d2;
	602
	603	var r0: u128 = undefined;
	604	var r1: u128 = undefined;
	605	if (shift < 128) {
	606	const cshift: u7 = @intCast(shift);
	607	const sshift: u7 = @intCast(128 - shift);
	608	r0 = corr +% ((p0 >> cshift) \| (p1 << sshift));
	609	r1 = ((p1 >> cshift) \| (p2 << sshift)) +% @intFromBool(r0 < corr);
	610	} else if (shift == 128) {
	611	r0 = corr +% p1;
	612	r1 = p2 +% @intFromBool(r0 < corr);
	613	} else {
	614	const ashift: u7 = @intCast(shift - 128);
	615	const sshift: u7 = @intCast(256 - shift);
	616	r0 = corr +% ((p1 >> ashift) \| (p2 << sshift));
	617	r1 = (p2 >> ashift) +% @intFromBool(r0 < corr);
	618	}
	619
	620	return .{ @truncate(r0), @truncate(r0 >> 64), @truncate(r1), @truncate(r1 >> 64) };
	621	}
	622
	623	// zig fmt: off
	624	//
	625	// 4.5KiB of tables.
	626
	627	const FLOAT_128_POW5_INV_BITCOUNT = 249;
	628	const FLOAT_128_POW5_BITCOUNT = 249;
	629	const POW5_TABLE_SIZE = 56;
	630
	631	const GENERIC_POW5_TABLE: [POW5_TABLE_SIZE][2]u64 = .{
	632	.{ 1, 0 },
	633	.{ 5, 0 },
	634	.{ 25, 0 },
	635	.{ 125, 0 },
	636	.{ 625, 0 },
	637	.{ 3125, 0 },
	638	.{ 15625, 0 },
	639	.{ 78125, 0 },
	640	.{ 390625, 0 },
	641	.{ 1953125, 0 },
	642	.{ 9765625, 0 },
	643	.{ 48828125, 0 },
	644	.{ 244140625, 0 },
	645	.{ 1220703125, 0 },
	646	.{ 6103515625, 0 },
	647	.{ 30517578125, 0 },
	648	.{ 152587890625, 0 },
	649	.{ 762939453125, 0 },
	650	.{ 3814697265625, 0 },
	651	.{ 19073486328125, 0 },
	652	.{ 95367431640625, 0 },
	653	.{ 476837158203125, 0 },
	654	.{ 2384185791015625, 0 },
	655	.{ 11920928955078125, 0 },
	656	.{ 59604644775390625, 0 },
	657	.{ 298023223876953125, 0 },
	658	.{ 1490116119384765625, 0 },
	659	.{ 7450580596923828125, 0 },
	660	.{ 359414837200037393, 2 },
	661	.{ 1797074186000186965, 10 },
	662	.{ 8985370930000934825, 50 },
	663	.{ 8033366502585570893, 252 },
	664	.{ 3273344365508751233, 1262 },
	665	.{ 16366721827543756165, 6310 },
	666	.{ 8046632842880574361, 31554 },
	667	.{ 3339676066983768573, 157772 },
	668	.{ 16698380334918842865, 788860 },
	669	.{ 9704925379756007861, 3944304 },
	670	.{ 11631138751360936073, 19721522 },
	671	.{ 2815461535676025517, 98607613 },
	672	.{ 14077307678380127585, 493038065 },
	673	.{ 15046306170771983077, 2465190328 },
	674	.{ 1444554559021708921, 12325951644 },
	675	.{ 7222772795108544605, 61629758220 },
	676	.{ 17667119901833171409, 308148791101 },
	677	.{ 14548623214327650581, 1540743955509 },
	678	.{ 17402883850509598057, 7703719777548 },
	679	.{ 13227442957709783821, 38518598887744 },
	680	.{ 10796982567420264257, 192592994438723 },
	681	.{ 17091424689682218053, 962964972193617 },
	682	.{ 11670147153572883801, 4814824860968089 },
	683	.{ 3010503546735764157, 24074124304840448 },
	684	.{ 15052517733678820785, 120370621524202240 },
	685	.{ 1475612373555897461, 601853107621011204 },
	686	.{ 7378061867779487305, 3009265538105056020 },
	687	.{ 18443565265187884909, 15046327690525280101 },
	688	};
	689
	690	const GENERIC_POW5_SPLIT: [89][4]u64 = .{
	691	.{ 0, 0, 0, 72057594037927936 },
	692	.{ 0, 5206161169240293376, 4575641699882439235, 73468396926392969 },
	693	.{ 3360510775605221349, 6983200512169538081, 4325643253124434363, 74906821675075173 },
	694	.{ 11917660854915489451, 9652941469841108803, 946308467778435600, 76373409087490117 },
	695	.{ 1994853395185689235, 16102657350889591545, 6847013871814915412, 77868710555449746 },
	696	.{ 958415760277438274, 15059347134713823592, 7329070255463483331, 79393288266368765 },
	697	.{ 2065144883315240188, 7145278325844925976, 14718454754511147343, 80947715414629833 },
	698	.{ 8980391188862868935, 13709057401304208685, 8230434828742694591, 82532576417087045 },
	699	.{ 432148644612782575, 7960151582448466064, 12056089168559840552, 84148467132788711 },
	700	.{ 484109300864744403, 15010663910730448582, 16824949663447227068, 85795995087002057 },
	701	.{ 14793711725276144220, 16494403799991899904, 10145107106505865967, 87475779699624060 },
	702	.{ 15427548291869817042, 12330588654550505203, 13980791795114552342, 89188452518064298 },
	703	.{ 9979404135116626552, 13477446383271537499, 14459862802511591337, 90934657454687378 },
	704	.{ 12385121150303452775, 9097130814231585614, 6523855782339765207, 92715051028904201 },
	705	.{ 1822931022538209743, 16062974719797586441, 3619180286173516788, 94530302614003091 },
	706	.{ 12318611738248470829, 13330752208259324507, 10986694768744162601, 96381094688813589 },
	707	.{ 13684493829640282333, 7674802078297225834, 15208116197624593182, 98268123094297527 },
	708	.{ 5408877057066295332, 6470124174091971006, 15112713923117703147, 100192097295163851 },
	709	.{ 11407083166564425062, 18189998238742408185, 4337638702446708282, 102153740646605557 },
	710	.{ 4112405898036935485, 924624216579956435, 14251108172073737125, 104153790666259019 },
	711	.{ 16996739107011444789, 10015944118339042475, 2395188869672266257, 106192999311487969 },
	712	.{ 4588314690421337879, 5339991768263654604, 15441007590670620066, 108272133262096356 },
	713	.{ 2286159977890359825, 14329706763185060248, 5980012964059367667, 110391974208576409 },
	714	.{ 9654767503237031099, 11293544302844823188, 11739932712678287805, 112553319146000238 },
	715	.{ 11362964448496095896, 7990659682315657680, 251480263940996374, 114756980673665505 },
	716	.{ 1423410421096377129, 14274395557581462179, 16553482793602208894, 117003787300607788 },
	717	.{ 2070444190619093137, 11517140404712147401, 11657844572835578076, 119294583757094535 },
	718	.{ 7648316884775828921, 15264332483297977688, 247182277434709002, 121630231312217685 },
	719	.{ 17410896758132241352, 10923914482914417070, 13976383996795783649, 124011608097704390 },
	720	.{ 9542674537907272703, 3079432708831728956, 14235189590642919676, 126439609438067572 },
	721	.{ 10364666969937261816, 8464573184892924210, 12758646866025101190, 128915148187220428 },
	722	.{ 14720354822146013883, 11480204489231511423, 7449876034836187038, 131439155071681461 },
	723	.{ 1692907053653558553, 17835392458598425233, 1754856712536736598, 134012579040499057 },
	724	.{ 5620591334531458755, 11361776175667106627, 13350215315297937856, 136636387622027174 },
	725	.{ 17455759733928092601, 10362573084069962561, 11246018728801810510, 139311567287686283 },
	726	.{ 2465404073814044982, 17694822665274381860, 1509954037718722697, 142039123822846312 },
	727	.{ 2152236053329638369, 11202280800589637091, 16388426812920420176, 72410041352485523 },
	728	.{ 17319024055671609028, 10944982848661280484, 2457150158022562661, 73827744744583080 },
	729	.{ 17511219308535248024, 5122059497846768077, 2089605804219668451, 75273205100637900 },
	730	.{ 10082673333144031533, 14429008783411894887, 12842832230171903890, 76746965869337783 },
	731	.{ 16196653406315961184, 10260180891682904501, 10537411930446752461, 78249581139456266 },
	732	.{ 15084422041749743389, 234835370106753111, 16662517110286225617, 79781615848172976 },
	733	.{ 8199644021067702606, 3787318116274991885, 7438130039325743106, 81343645993472659 },
	734	.{ 12039493937039359765, 9773822153580393709, 5945428874398357806, 82936258850702722 },
	735	.{ 984543865091303961, 7975107621689454830, 6556665988501773347, 84560053193370726 },
	736	.{ 9633317878125234244, 16099592426808915028, 9706674539190598200, 86215639518264828 },
	737	.{ 6860695058870476186, 4471839111886709592, 7828342285492709568, 87903640274981819 },
	738	.{ 14583324717644598331, 4496120889473451238, 5290040788305728466, 89624690099949049 },
	739	.{ 18093669366515003715, 12879506572606942994, 18005739787089675377, 91379436055028227 },
	740	.{ 17997493966862379937, 14646222655265145582, 10265023312844161858, 93168537870790806 },
	741	.{ 12283848109039722318, 11290258077250314935, 9878160025624946825, 94992668194556404 },
	742	.{ 8087752761883078164, 5262596608437575693, 11093553063763274413, 96852512843287537 },
	743	.{ 15027787746776840781, 12250273651168257752, 9290470558712181914, 98748771061435726 },
	744	.{ 15003915578366724489, 2937334162439764327, 5404085603526796602, 100682155783835929 },
	745	.{ 5225610465224746757, 14932114897406142027, 2774647558180708010, 102653393903748137 },
	746	.{ 17112957703385190360, 12069082008339002412, 3901112447086388439, 104663226546146909 },
	747	.{ 4062324464323300238, 3992768146772240329, 15757196565593695724, 106712409346361594 },
	748	.{ 5525364615810306701, 11855206026704935156, 11344868740897365300, 108801712734172003 },
	749	.{ 9274143661888462646, 4478365862348432381, 18010077872551661771, 110931922223466333 },
	750	.{ 12604141221930060148, 8930937759942591500, 9382183116147201338, 113103838707570263 },
	751	.{ 14513929377491886653, 1410646149696279084, 587092196850797612, 115318278760358235 },
	752	.{ 2226851524999454362, 7717102471110805679, 7187441550995571734, 117576074943260147 },
	753	.{ 5527526061344932763, 2347100676188369132, 16976241418824030445, 119878076118278875 },
	754	.{ 6088479778147221611, 17669593130014777580, 10991124207197663546, 122225147767136307 },
	755	.{ 11107734086759692041, 3391795220306863431, 17233960908859089158, 124618172316667879 },
	756	.{ 7913172514655155198, 17726879005381242552, 641069866244011540, 127058049470587962 },
	757	.{ 12596991768458713949, 15714785522479904446, 6035972567136116512, 129545696547750811 },
	758	.{ 16901996933781815980, 4275085211437148707, 14091642539965169063, 132082048827034281 },
	759	.{ 7524574627987869240, 15661204384239316051, 2444526454225712267, 134668059898975949 },
	760	.{ 8199251625090479942, 6803282222165044067, 16064817666437851504, 137304702024293857 },
	761	.{ 4453256673338111920, 15269922543084434181, 3139961729834750852, 139992966499426682 },
	762	.{ 15841763546372731299, 3013174075437671812, 4383755396295695606, 142733864029230733 },
	763	.{ 9771896230907310329, 4900659362437687569, 12386126719044266361, 72764212553486967 },
	764	.{ 9420455527449565190, 1859606122611023693, 6555040298902684281, 74188850200884818 },
	765	.{ 5146105983135678095, 2287300449992174951, 4325371679080264751, 75641380576797959 },
	766	.{ 11019359372592553360, 8422686425957443718, 7175176077944048210, 77122349788024458 },
	767	.{ 11005742969399620716, 4132174559240043701, 9372258443096612118, 78632314633490790 },
	768	.{ 8887589641394725840, 8029899502466543662, 14582206497241572853, 80171842813591127 },
	769	.{ 360247523705545899, 12568341805293354211, 14653258284762517866, 81741513143625247 },
	770	.{ 12314272731984275834, 4740745023227177044, 6141631472368337539, 83341915771415304 },
	771	.{ 441052047733984759, 7940090120939869826, 11750200619921094248, 84973652399183278 },
	772	.{ 3436657868127012749, 9187006432149937667, 16389726097323041290, 86637336509772529 },
	773	.{ 13490220260784534044, 15339072891382896702, 8846102360835316895, 88333593597298497 },
	774	.{ 4125672032094859833, 158347675704003277, 10592598512749774447, 90063061402315272 },
	775	.{ 12189928252974395775, 2386931199439295891, 7009030566469913276, 91826390151586454 },
	776	.{ 9256479608339282969, 2844900158963599229, 11148388908923225596, 93624242802550437 },
	777	.{ 11584393507658707408, 2863659090805147914, 9873421561981063551, 95457295292572042 },
	778	.{ 13984297296943171390, 1931468383973130608, 12905719743235082319, 97326236793074198 },
	779	.{ 5837045222254987499, 10213498696735864176, 14893951506257020749, 99231769968645227 },
	780	};
	781
	782	// Unfortunately, the results are sometimes off by one or two. We use an additional
	783	// lookup table to store those cases and adjust the result.
	784	const POW5_ERRORS: [156]u64 = .{
	785	0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9555596400000000,
	786	0x65a6569525565555, 0x4415551445449655, 0x5105015504144541, 0x65a69969a6965964,
	787	0x5054955969959656, 0x5105154515554145, 0x4055511051591555, 0x5500514455550115,
	788	0x0041140014145515, 0x1005440545511051, 0x0014405450411004, 0x0414440010500000,
	789	0x0044000440010040, 0x5551155000004001, 0x4554555454544114, 0x5150045544005441,
	790	0x0001111400054501, 0x6550955555554554, 0x1504159645559559, 0x4105055141454545,
	791	0x1411541410405454, 0x0415555044545555, 0x0014154115405550, 0x1540055040411445,
	792	0x0000000500000000, 0x5644000000000000, 0x1155555591596555, 0x0410440054569565,
	793	0x5145100010010005, 0x0555041405500150, 0x4141450455140450, 0x0000000144000140,
	794	0x5114004001105410, 0x4444100404005504, 0x0414014410001015, 0x5145055155555015,
	795	0x0141041444445540, 0x0000100451541414, 0x4105041104155550, 0x0500501150451145,
	796	0x1001050000004114, 0x5551504400141045, 0x5110545410151454, 0x0100001400004040,
	797	0x5040010111040000, 0x0140000150541100, 0x4400140400104110, 0x5011014405545004,
	798	0x0000000044155440, 0x0000000010000000, 0x1100401444440001, 0x0040401010055111,
	799	0x5155155551405454, 0x0444440015514411, 0x0054505054014101, 0x0451015441115511,
	800	0x1541411401140551, 0x4155104514445110, 0x4141145450145515, 0x5451445055155050,
	801	0x4400515554110054, 0x5111145104501151, 0x565a655455500501, 0x5565555555525955,
	802	0x0550511500405695, 0x4415504051054544, 0x6555595965555554, 0x0100915915555655,
	803	0x5540001510001001, 0x5450051414000544, 0x1405010555555551, 0x5555515555644155,
	804	0x5555055595496555, 0x5451045004415000, 0x5450510144040144, 0x5554155555556455,
	805	0x5051555495415555, 0x5555554555555545, 0x0000000010005455, 0x4000005000040000,
	806	0x5565555555555954, 0x5554559555555505, 0x9645545495552555, 0x4000400055955564,
	807	0x0040000000000001, 0x4004100100000000, 0x5540040440000411, 0x4565555955545644,
	808	0x1140659549651556, 0x0100000410010000, 0x5555515400004001, 0x5955545555155255,
	809	0x5151055545505556, 0x5051454510554515, 0x0501500050415554, 0x5044154005441005,
	810	0x1455445450550455, 0x0010144055144545, 0x0000401100000004, 0x1050145050000010,
	811	0x0415004554011540, 0x1000510100151150, 0x0100040400001144, 0x0000000000000000,
	812	0x0550004400000100, 0x0151145041451151, 0x0000400400005450, 0x0000100044010004,
	813	0x0100054100050040, 0x0504400005410010, 0x4011410445500105, 0x0000404000144411,
	814	0x0101504404500000, 0x0000005044400400, 0x0000000014000100, 0x0404440414000000,
	815	0x5554100410000140, 0x4555455544505555, 0x5454105055455455, 0x0115454155454015,
	816	0x4404110000045100, 0x4400001100101501, 0x6596955956966a94, 0x0040655955665965,
	817	0x5554144400100155, 0xa549495401011041, 0x5596555565955555, 0x5569965959549555,
	818	0x969565a655555456, 0x0000001000000000, 0x0000000040000140, 0x0000040100000000,
	819	0x1415454400000000, 0x5410415411454114, 0x0400040104000154, 0x0504045000000411,
	820	0x0000001000000010, 0x5554000000001040, 0x5549155551556595, 0x1455541055515555,
	821	0x0510555454554541, 0x9555555555540455, 0x6455456555556465, 0x4524565555654514,
	822	0x5554655255559545, 0x9555455441155556, 0x0000000051515555, 0x0010005040000550,
	823	0x5044044040000000, 0x1045040440010500, 0x0000400000040000, 0x0000000000000000,
	824	};
	825
	826	const GENERIC_POW5_INV_SPLIT: [89][4]u64 = .{
	827	.{ 0, 0, 0, 144115188075855872 },
	828	.{ 1573859546583440065, 2691002611772552616, 6763753280790178510, 141347765182270746 },
	829	.{ 12960290449513840412, 12345512957918226762, 18057899791198622765, 138633484706040742 },
	830	.{ 7615871757716765416, 9507132263365501332, 4879801712092008245, 135971326161092377 },
	831	.{ 7869961150745287587, 5804035291554591636, 8883897266325833928, 133360288657597085 },
	832	.{ 2942118023529634767, 15128191429820565086, 10638459445243230718, 130799390525667397 },
	833	.{ 14188759758411913794, 5362791266439207815, 8068821289119264054, 128287668946279217 },
	834	.{ 7183196927902545212, 1952291723540117099, 12075928209936341512, 125824179589281448 },
	835	.{ 5672588001402349748, 17892323620748423487, 9874578446960390364, 123407996258356868 },
	836	.{ 4442590541217566325, 4558254706293456445, 10343828952663182727, 121038210542800766 },
	837	.{ 3005560928406962566, 2082271027139057888, 13961184524927245081, 118713931475986426 },
	838	.{ 13299058168408384786, 17834349496131278595, 9029906103900731664, 116434285200389047 },
	839	.{ 5414878118283973035, 13079825470227392078, 17897304791683760280, 114198414639042157 },
	840	.{ 14609755883382484834, 14991702445765844156, 3269802549772755411, 112005479173303009 },
	841	.{ 15967774957605076027, 2511532636717499923, 16221038267832563171, 109854654326805788 },
	842	.{ 9269330061621627145, 3332501053426257392, 16223281189403734630, 107745131455483836 },
	843	.{ 16739559299223642282, 1873986623300664530, 6546709159471442872, 105676117443544318 },
	844	.{ 17116435360051202055, 1359075105581853924, 2038341371621886470, 103646834405281051 },
	845	.{ 17144715798009627550, 3201623802661132408, 9757551605154622431, 101656519392613377 },
	846	.{ 17580479792687825857, 6546633380567327312, 15099972427870912398, 99704424108241124 },
	847	.{ 9726477118325522902, 14578369026754005435, 11728055595254428803, 97789814624307808 },
	848	.{ 134593949518343635, 5715151379816901985, 1660163707976377376, 95911971106466306 },
	849	.{ 5515914027713859358, 7124354893273815720, 5548463282858794077, 94070187543243255 },
	850	.{ 6188403395862945512, 5681264392632320838, 15417410852121406654, 92263771480600430 },
	851	.{ 15908890877468271457, 10398888261125597540, 4817794962769172309, 90492043761593298 },
	852	.{ 1413077535082201005, 12675058125384151580, 7731426132303759597, 88754338271028867 },
	853	.{ 1486733163972670293, 11369385300195092554, 11610016711694864110, 87050001685026843 },
	854	.{ 8788596583757589684, 3978580923851924802, 9255162428306775812, 85378393225389919 },
	855	.{ 7203518319660962120, 15044736224407683725, 2488132019818199792, 83738884418690858 },
	856	.{ 4004175967662388707, 18236988667757575407, 15613100370957482671, 82130858859985791 },
	857	.{ 18371903370586036463, 53497579022921640, 16465963977267203307, 80553711981064899 },
	858	.{ 10170778323887491315, 1999668801648976001, 10209763593579456445, 79006850823153334 },
	859	.{ 17108131712433974546, 16825784443029944237, 2078700786753338945, 77489693813976938 },
	860	.{ 17221789422665858532, 12145427517550446164, 5391414622238668005, 76001670549108934 },
	861	.{ 4859588996898795878, 1715798948121313204, 3950858167455137171, 74542221577515387 },
	862	.{ 13513469241795711526, 631367850494860526, 10517278915021816160, 73110798191218799 },
	863	.{ 11757513142672073111, 2581974932255022228, 17498959383193606459, 143413724438001539 },
	864	.{ 14524355192525042817, 5640643347559376447, 1309659274756813016, 140659771648132296 },
	865	.{ 2765095348461978538, 11021111021896007722, 3224303603779962366, 137958702611185230 },
	866	.{ 12373410389187981037, 13679193545685856195, 11644609038462631561, 135309501808182158 },
	867	.{ 12813176257562780151, 3754199046160268020, 9954691079802960722, 132711173221007413 },
	868	.{ 17557452279667723458, 3237799193992485824, 17893947919029030695, 130162739957935629 },
	869	.{ 14634200999559435155, 4123869946105211004, 6955301747350769239, 127663243886350468 },
	870	.{ 2185352760627740240, 2864813346878886844, 13049218671329690184, 125211745272516185 },
	871	.{ 6143438674322183002, 10464733336980678750, 6982925169933978309, 122807322428266620 },
	872	.{ 1099509117817174576, 10202656147550524081, 754997032816608484, 120449071364478757 },
	873	.{ 2410631293559367023, 17407273750261453804, 15307291918933463037, 118136105451200587 },
	874	.{ 12224968375134586697, 1664436604907828062, 11506086230137787358, 115867555084305488 },
	875	.{ 3495926216898000888, 18392536965197424288, 10992889188570643156, 113642567358547782 },
	876	.{ 8744506286256259680, 3966568369496879937, 18342264969761820037, 111460305746896569 },
	877	.{ 7689600520560455039, 5254331190877624630, 9628558080573245556, 109319949786027263 },
	878	.{ 11862637625618819436, 3456120362318976488, 14690471063106001082, 107220694767852583 },
	879	.{ 5697330450030126444, 12424082405392918899, 358204170751754904, 105161751436977040 },
	880	.{ 11257457505097373622, 15373192700214208870, 671619062372033814, 103142345693961148 },
	881	.{ 16850355018477166700, 1913910419361963966, 4550257919755970531, 101161718304283822 },
	882	.{ 9670835567561997011, 10584031339132130638, 3060560222974851757, 99219124612893520 },
	883	.{ 7698686577353054710, 11689292838639130817, 11806331021588878241, 97313834264240819 },
	884	.{ 12233569599615692137, 3347791226108469959, 10333904326094451110, 95445130927687169 },
	885	.{ 13049400362825383933, 17142621313007799680, 3790542585289224168, 93612312028186576 },
	886	.{ 12430457242474442072, 5625077542189557960, 14765055286236672238, 91814688482138969 },
	887	.{ 4759444137752473128, 2230562561567025078, 4954443037339580076, 90051584438315940 },
	888	.{ 7246913525170274758, 8910297835195760709, 4015904029508858381, 88322337023761438 },
	889	.{ 12854430245836432067, 8135139748065431455, 11548083631386317976, 86626296094571907 },
	890	.{ 4848827254502687803, 4789491250196085625, 3988192420450664125, 84962823991462151 },
	891	.{ 7435538409611286684, 904061756819742353, 14598026519493048444, 83331295300025028 },
	892	.{ 11042616160352530997, 8948390828345326218, 10052651191118271927, 81731096615594853 },
	893	.{ 11059348291563778943, 11696515766184685544, 3783210511290897367, 80161626312626082 },
	894	.{ 7020010856491885826, 5025093219346041680, 8960210401638911765, 78622294318500592 },
	895	.{ 17732844474490699984, 7820866704994446502, 6088373186798844243, 77112521891678506 },
	896	.{ 688278527545590501, 3045610706602776618, 8684243536999567610, 75631741404109150 },
	897	.{ 2734573255120657297, 3903146411440697663, 9470794821691856713, 74179396127820347 },
	898	.{ 15996457521023071259, 4776627823451271680, 12394856457265744744, 72754940025605801 },
	899	.{ 13492065758834518331, 7390517611012222399, 1630485387832860230, 142715675091463768 },
	900	.{ 13665021627282055864, 9897834675523659302, 17907668136755296849, 139975126841173266 },
	901	.{ 9603773719399446181, 10771916301484339398, 10672699855989487527, 137287204938390542 },
	902	.{ 3630218541553511265, 8139010004241080614, 2876479648932814543, 134650898807055963 },
	903	.{ 8318835909686377084, 9525369258927993371, 2796120270400437057, 132065217277054270 },
	904	.{ 11190003059043290163, 12424345635599592110, 12539346395388933763, 129529188211565064 },
	905	.{ 8701968833973242276, 820569587086330727, 2315591597351480110, 127041858141569228 },
	906	.{ 5115113890115690487, 16906305245394587826, 9899749468931071388, 124602291907373862 },
	907	.{ 15543535488939245974, 10945189844466391399, 3553863472349432246, 122209572307020975 },
	908	.{ 7709257252608325038, 1191832167690640880, 15077137020234258537, 119862799751447719 },
	909	.{ 7541333244210021737, 9790054727902174575, 5160944773155322014, 117561091926268545 },
	910	.{ 12297384708782857832, 1281328873123467374, 4827925254630475769, 115303583460052092 },
	911	.{ 13243237906232367265, 15873887428139547641, 3607993172301799599, 113089425598968120 },
	912	.{ 11384616453739611114, 15184114243769211033, 13148448124803481057, 110917785887682141 },
	913	.{ 17727970963596660683, 1196965221832671990, 14537830463956404138, 108787847856377790 },
	914	.{ 17241367586707330931, 8880584684128262874, 11173506540726547818, 106698810713789254 },
	915	.{ 7184427196661305643, 14332510582433188173, 14230167953789677901, 104649889046128358 },
	916	};
	917
	918	const POW5_INV_ERRORS: [154]u64 = .{
	919	0x1144155514145504, 0x0000541555401141, 0x0000000000000000, 0x0154454000000000,
	920	0x4114105515544440, 0x0001001111500415, 0x4041411410011000, 0x5550114515155014,
	921	0x1404100041554551, 0x0515000450404410, 0x5054544401140004, 0x5155501005555105,
	922	0x1144141000105515, 0x0541500000500000, 0x1104105540444140, 0x4000015055514110,
	923	0x0054010450004005, 0x4155515404100005, 0x5155145045155555, 0x1511555515440558,
	924	0x5558544555515555, 0x0000000000000010, 0x5004000000000050, 0x1415510100000010,
	925	0x4545555444514500, 0x5155151555555551, 0x1441540144044554, 0x5150104045544400,
	926	0x5450545401444040, 0x5554455045501400, 0x4655155555555145, 0x1000010055455055,
	927	0x1000004000055004, 0x4455405104000005, 0x4500114504150545, 0x0000000014000000,
	928	0x5450000000000000, 0x5514551511445555, 0x4111501040555451, 0x4515445500054444,
	929	0x5101500104100441, 0x1545115155545055, 0x0000000000000000, 0x1554000000100000,
	930	0x5555545595551555, 0x5555051851455955, 0x5555555555555559, 0x0000400011001555,
	931	0x0000004400040000, 0x5455511555554554, 0x5614555544115445, 0x6455156145555155,
	932	0x5455855455415455, 0x5515555144555545, 0x0114400000145155, 0x0000051000450511,
	933	0x4455154554445100, 0x4554150141544455, 0x65955555559a5965, 0x5555555854559559,
	934	0x9569654559616595, 0x1040044040005565, 0x1010010500011044, 0x1554015545154540,
	935	0x4440555401545441, 0x1014441450550105, 0x4545400410504145, 0x5015111541040151,
	936	0x5145051154000410, 0x1040001044545044, 0x4001400000151410, 0x0540000044040000,
	937	0x0510555454411544, 0x0400054054141550, 0x1001041145001100, 0x0000000140000000,
	938	0x0000000014100000, 0x1544005454000140, 0x4050055505445145, 0x0011511104504155,
	939	0x5505544415045055, 0x1155154445515554, 0x0000000000004555, 0x0000000000000000,
	940	0x5101010510400004, 0x1514045044440400, 0x5515519555515555, 0x4554545441555545,
	941	0x1551055955551515, 0x0150000011505515, 0x0044005040400000, 0x0004001004010050,
	942	0x0000051004450414, 0x0114001101001144, 0x0401000001000001, 0x4500010001000401,
	943	0x0004100000005000, 0x0105000441101100, 0x0455455550454540, 0x5404050144105505,
	944	0x4101510540555455, 0x1055541411451555, 0x5451445110115505, 0x1154110010101545,
	945	0x1145140450054055, 0x5555565415551554, 0x1550559555555555, 0x5555541545045141,
	946	0x4555455450500100, 0x5510454545554555, 0x1510140115045455, 0x1001050040111510,
	947	0x5555454555555504, 0x9954155545515554, 0x6596656555555555, 0x0140410051555559,
	948	0x0011104010001544, 0x965669659a680501, 0x5655a55955556955, 0x4015111014404514,
	949	0x1414155554505145, 0x0540040011051404, 0x1010000000015005, 0x0010054050004410,
	950	0x5041104014000100, 0x4440010500100001, 0x1155510504545554, 0x0450151545115541,
	951	0x4000100400110440, 0x1004440010514440, 0x0000115050450000, 0x0545404455541500,
	952	0x1051051555505101, 0x5505144554544144, 0x4550545555515550, 0x0015400450045445,
	953	0x4514155400554415, 0x4555055051050151, 0x1511441450001014, 0x4544554510404414,
	954	0x4115115545545450, 0x5500541555551555, 0x5550010544155015, 0x0144414045545500,
	955	0x4154050001050150, 0x5550511111000145, 0x1114504055000151, 0x5104041101451040,
	956	0x0010501401051441, 0x0010501450504401, 0x4554585440044444, 0x5155555951450455,
	957	0x0040000400105555, 0x0000000000000001,
	958	};
	959
	960	// zig fmt: on
	961
	962	fn check(comptime T: type, value: T, comptime expected: []const u8) !void {
	963	const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
	964
	965	var buf: [6000]u8 = undefined;
	966	const value_bits: I = @bitCast(value);
	967	const s = try formatFloat(&buf, value, .{});
	968	try std.testing.expectEqualStrings(expected, s);
	969
	970	if (@bitSizeOf(T) != 80) {
	971	const o = try std.fmt.parseFloat(T, s);
	972	const o_bits: I = @bitCast(o);
	973
	974	if (std.math.isNan(value)) {
	975	try std.testing.expect(std.math.isNan(o));
	976	} else {
	977	try std.testing.expectEqual(value_bits, o_bits);
	978	}
	979	}
	980	}
	981
	982	test "format f32" {
	983	try check(f32, 0.0, "0e0");
	984	try check(f32, -0.0, "-0e0");
	985	try check(f32, 1.0, "1e0");
	986	try check(f32, -1.0, "-1e0");
	987	try check(f32, std.math.nan(f32), "nan");
	988	try check(f32, std.math.inf(f32), "inf");
	989	try check(f32, -std.math.inf(f32), "-inf");
	990	try check(f32, 1.1754944e-38, "1.1754944e-38");
	991	try check(f32, @bitCast(@as(u32, 0x7f7fffff)), "3.4028235e38");
	992	try check(f32, @bitCast(@as(u32, 1)), "1e-45");
	993	try check(f32, 3.355445E7, "3.355445e7");
	994	try check(f32, 8.999999e9, "9e9");
	995	try check(f32, 3.4366717e10, "3.436672e10");
	996	try check(f32, 3.0540412e5, "3.0540412e5");
	997	try check(f32, 8.0990312e3, "8.0990312e3");
	998	try check(f32, 2.4414062e-4, "2.4414062e-4");
	999	try check(f32, 2.4414062e-3, "2.4414062e-3");
	1000	try check(f32, 4.3945312e-3, "4.3945312e-3");
	1001	try check(f32, 6.3476562e-3, "6.3476562e-3");
	1002	try check(f32, 4.7223665e21, "4.7223665e21");
	1003	try check(f32, 8388608.0, "8.388608e6");
	1004	try check(f32, 1.6777216e7, "1.6777216e7");
	1005	try check(f32, 3.3554436e7, "3.3554436e7");
	1006	try check(f32, 6.7131496e7, "6.7131496e7");
	1007	try check(f32, 1.9310392e-38, "1.9310392e-38");
	1008	try check(f32, -2.47e-43, "-2.47e-43");
	1009	try check(f32, 1.993244e-38, "1.993244e-38");
	1010	try check(f32, 4103.9003, "4.1039004e3");
	1011	try check(f32, 5.3399997e9, "5.3399997e9");
	1012	try check(f32, 6.0898e-39, "6.0898e-39");
	1013	try check(f32, 0.0010310042, "1.0310042e-3");
	1014	try check(f32, 2.8823261e17, "2.882326e17");
	1015	try check(f32, 7.038531e-26, "7.038531e-26");
	1016	try check(f32, 9.2234038e17, "9.223404e17");
	1017	try check(f32, 6.7108872e7, "6.710887e7");
	1018	try check(f32, 1.0e-44, "1e-44");
	1019	try check(f32, 2.816025e14, "2.816025e14");
	1020	try check(f32, 9.223372e18, "9.223372e18");
	1021	try check(f32, 1.5846085e29, "1.5846086e29");
	1022	try check(f32, 1.1811161e19, "1.1811161e19");
	1023	try check(f32, 5.368709e18, "5.368709e18");
	1024	try check(f32, 4.6143165e18, "4.6143166e18");
	1025	try check(f32, 0.007812537, "7.812537e-3");
	1026	try check(f32, 1.4e-45, "1e-45");
	1027	try check(f32, 1.18697724e20, "1.18697725e20");
	1028	try check(f32, 1.00014165e-36, "1.00014165e-36");
	1029	try check(f32, 200.0, "2e2");
	1030	try check(f32, 3.3554432e7, "3.3554432e7");
	1031
	1032	try check(f32, 1.0, "1e0");
	1033	try check(f32, 1.2, "1.2e0");
	1034	try check(f32, 1.23, "1.23e0");
	1035	try check(f32, 1.234, "1.234e0");
	1036	try check(f32, 1.2345, "1.2345e0");
	1037	try check(f32, 1.23456, "1.23456e0");
	1038	try check(f32, 1.234567, "1.234567e0");
	1039	try check(f32, 1.2345678, "1.2345678e0");
	1040	try check(f32, 1.23456735e-36, "1.23456735e-36");
	1041	}
	1042
	1043	test "format f64" {
	1044	try check(f64, 0.0, "0e0");
	1045	try check(f64, -0.0, "-0e0");
	1046	try check(f64, 1.0, "1e0");
	1047	try check(f64, -1.0, "-1e0");
	1048	try check(f64, std.math.nan(f64), "nan");
	1049	try check(f64, std.math.inf(f64), "inf");
	1050	try check(f64, -std.math.inf(f64), "-inf");
	1051	try check(f64, 2.2250738585072014e-308, "2.2250738585072014e-308");
	1052	try check(f64, @bitCast(@as(u64, 0x7fefffffffffffff)), "1.7976931348623157e308");
	1053	try check(f64, @bitCast(@as(u64, 1)), "5e-324");
	1054	try check(f64, 2.98023223876953125e-8, "2.9802322387695312e-8");
	1055	try check(f64, -2.109808898695963e16, "-2.109808898695963e16");
	1056	try check(f64, 4.940656e-318, "4.940656e-318");
	1057	try check(f64, 1.18575755e-316, "1.18575755e-316");
	1058	try check(f64, 2.989102097996e-312, "2.989102097996e-312");
	1059	try check(f64, 9.0608011534336e15, "9.0608011534336e15");
	1060	try check(f64, 4.708356024711512e18, "4.708356024711512e18");
	1061	try check(f64, 9.409340012568248e18, "9.409340012568248e18");
	1062	try check(f64, 1.2345678, "1.2345678e0");
	1063	try check(f64, @bitCast(@as(u64, 0x4830f0cf064dd592)), "5.764607523034235e39");
	1064	try check(f64, @bitCast(@as(u64, 0x4840f0cf064dd592)), "1.152921504606847e40");
	1065	try check(f64, @bitCast(@as(u64, 0x4850f0cf064dd592)), "2.305843009213694e40");
	1066
	1067	try check(f64, 1, "1e0");
	1068	try check(f64, 1.2, "1.2e0");
	1069	try check(f64, 1.23, "1.23e0");
	1070	try check(f64, 1.234, "1.234e0");
	1071	try check(f64, 1.2345, "1.2345e0");
	1072	try check(f64, 1.23456, "1.23456e0");
	1073	try check(f64, 1.234567, "1.234567e0");
	1074	try check(f64, 1.2345678, "1.2345678e0");
	1075	try check(f64, 1.23456789, "1.23456789e0");
	1076	try check(f64, 1.234567895, "1.234567895e0");
	1077	try check(f64, 1.2345678901, "1.2345678901e0");
	1078	try check(f64, 1.23456789012, "1.23456789012e0");
	1079	try check(f64, 1.234567890123, "1.234567890123e0");
	1080	try check(f64, 1.2345678901234, "1.2345678901234e0");
	1081	try check(f64, 1.23456789012345, "1.23456789012345e0");
	1082	try check(f64, 1.234567890123456, "1.234567890123456e0");
	1083	try check(f64, 1.2345678901234567, "1.2345678901234567e0");
	1084
	1085	try check(f64, 4.294967294, "4.294967294e0");
	1086	try check(f64, 4.294967295, "4.294967295e0");
	1087	try check(f64, 4.294967296, "4.294967296e0");
	1088	try check(f64, 4.294967297, "4.294967297e0");
	1089	try check(f64, 4.294967298, "4.294967298e0");
	1090	}
	1091
	1092	test "format f80" {
	1093	try check(f80, 0.0, "0e0");
	1094	try check(f80, -0.0, "-0e0");
	1095	try check(f80, 1.0, "1e0");
	1096	try check(f80, -1.0, "-1e0");
	1097	try check(f80, std.math.nan(f80), "nan");
	1098	try check(f80, std.math.inf(f80), "inf");
	1099	try check(f80, -std.math.inf(f80), "-inf");
	1100
	1101	try check(f80, 2.2250738585072014e-308, "2.2250738585072014e-308");
	1102	try check(f80, 2.98023223876953125e-8, "2.98023223876953125e-8");
	1103	try check(f80, -2.109808898695963e16, "-2.109808898695963e16");
	1104	try check(f80, 4.940656e-318, "4.940656e-318");
	1105	try check(f80, 1.18575755e-316, "1.18575755e-316");
	1106	try check(f80, 2.989102097996e-312, "2.989102097996e-312");
	1107	try check(f80, 9.0608011534336e15, "9.0608011534336e15");
	1108	try check(f80, 4.708356024711512e18, "4.708356024711512e18");
	1109	try check(f80, 9.409340012568248e18, "9.409340012568248e18");
	1110	try check(f80, 1.2345678, "1.2345678e0");
	1111	}
	1112
	1113	test "format f128" {
	1114	try check(f128, 0.0, "0e0");
	1115	try check(f128, -0.0, "-0e0");
	1116	try check(f128, 1.0, "1e0");
	1117	try check(f128, -1.0, "-1e0");
	1118	try check(f128, std.math.nan(f128), "nan");
	1119	try check(f128, std.math.inf(f128), "inf");
	1120	try check(f128, -std.math.inf(f128), "-inf");
	1121
	1122	try check(f128, 2.2250738585072014e-308, "2.2250738585072014e-308");
	1123	try check(f128, 2.98023223876953125e-8, "2.98023223876953125e-8");
	1124	try check(f128, -2.109808898695963e16, "-2.109808898695963e16");
	1125	try check(f128, 4.940656e-318, "4.940656e-318");
	1126	try check(f128, 1.18575755e-316, "1.18575755e-316");
	1127	try check(f128, 2.989102097996e-312, "2.989102097996e-312");
	1128	try check(f128, 9.0608011534336e15, "9.0608011534336e15");
	1129	try check(f128, 4.708356024711512e18, "4.708356024711512e18");
	1130	try check(f128, 9.409340012568248e18, "9.409340012568248e18");
	1131	try check(f128, 1.2345678, "1.2345678e0");
	1132	}
	1133
	1134	test "format float to decimal with zero precision" {
	1135	try expectFmt("5", "{d:.0}", .{5});
	1136	try expectFmt("6", "{d:.0}", .{6});
	1137	try expectFmt("7", "{d:.0}", .{7});
	1138	try expectFmt("8", "{d:.0}", .{8});
	1139	}

lib/std/fmt/ryu128.zig deleted-1139

...	...	@@ -1,1139 +0,0 @@
1		//! This file implements the ryu floating point conversion algorithm:
2		//! https://dl.acm.org/doi/pdf/10.1145/3360595
3
4		const std = @import("std");
5		const expectFmt = std.testing.expectFmt;
6
7		const special_exponent = 0x7fffffff;
8
9		/// Any buffer used for `format` must be at least this large. This is asserted. A runtime check will
10		/// additionally be performed if more bytes are required.
11		pub const min_buffer_size = 53;
12
13		/// Returns the minimum buffer size needed to print every float of a specific type and format.
14		pub fn bufferSize(comptime mode: Format, comptime T: type) comptime_int {
15		comptime std.debug.assert(@typeInfo(T) == .Float);
16		return switch (mode) {
17		.scientific => 53,
18		// Based on minimum subnormal values.
19		.decimal => switch (@bitSizeOf(T)) {
20		16 => @max(15, min_buffer_size),
21		32 => 55,
22		64 => 347,
23		80 => 4996,
24		128 => 5011,
25		else => unreachable,
26		},
27		};
28		}
29
30		pub const RyuError = error{
31		BufferTooSmall,
32		};
33
34		pub const Format = enum {
35		scientific,
36		decimal,
37		};
38
39		pub const FormatOptions = struct {
40		mode: Format = .scientific,
41		precision: ?usize = null,
42		};
43
44		/// Format a floating-point value and write it to buffer. Returns a slice to the buffer containing
45		/// the string representation.
46		///
47		/// Full precision is the default. Any full precision float can be reparsed with std.fmt.parseFloat
48		/// unambiguously.
49		///
50		/// Scientific mode is recommended generally as the output is more compact and any type can be
51		/// written in full precision using a buffer of only `min_buffer_size`.
52		///
53		/// When printing full precision decimals, use `bufferSize` to get the required space. It is
54		/// recommended to bound decimal output with a fixed precision to reduce the required buffer size.
55		pub fn format(buf: []u8, v_: anytype, options: FormatOptions) RyuError![]const u8 {
56		const v = switch (@TypeOf(v_)) {
57		// comptime_float internally is a f128; this preserves precision.
58		comptime_float => @as(f128, v_),
59		else => v_,
60		};
61
62		const T = @TypeOf(v);
63		comptime std.debug.assert(@typeInfo(T) == .Float);
64		const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
65
66		const has_explicit_leading_bit = std.math.floatMantissaBits(T) - std.math.floatFractionalBits(T) != 0;
67		const d = binaryToDecimal(@as(I, @bitCast(v)), std.math.floatMantissaBits(T), std.math.floatExponentBits(T), has_explicit_leading_bit);
68
69		return switch (options.mode) {
70		.scientific => formatScientific(buf, d, options.precision),
71		.decimal => formatDecimal(buf, d, options.precision),
72		};
73		}
74
75		pub const FloatDecimal128 = struct {
76		mantissa: u128,
77		exponent: i32,
78		sign: bool,
79		};
80
81		fn copySpecialStr(buf: []u8, f: FloatDecimal128) []const u8 {
82		if (f.sign) {
83		buf[0] = '-';
84		}
85		const offset: usize = @intFromBool(f.sign);
86		if (f.mantissa != 0) {
87		@memcpy(buf[offset..][0..3], "nan");
88		return buf[0 .. 3 + offset];
89		}
90		@memcpy(buf[offset..][0..3], "inf");
91		return buf[0 .. 3 + offset];
92		}
93
94		fn writeDecimal(buf: []u8, value: anytype, count: usize) void {
95		var i: usize = 0;
96
97		while (i + 2 < count) : (i += 2) {
98		const c: u8 = @intCast(value.* % 100);
99		value.* /= 100;
100		const d = std.fmt.digits2(c);
101		buf[count - i - 1] = d[1];
102		buf[count - i - 2] = d[0];
103		}
104
105		while (i < count) : (i += 1) {
106		const c: u8 = @intCast(value.* % 10);
107		value.* /= 10;
108		buf[count - i - 1] = '0' + c;
109		}
110		}
111
112		fn isPowerOf10(n_: u128) bool {
113		var n = n_;
114		while (n != 0) : (n /= 10) {
115		if (n % 10 != 0) return false;
116		}
117		return true;
118		}
119
120		const RoundMode = enum {
121		/// 1234.56 = precision 2
122		decimal,
123		/// 1.23456e3 = precision 5
124		scientific,
125		};
126
127		fn round(f: FloatDecimal128, mode: RoundMode, precision: usize) FloatDecimal128 {
128		var round_digit: usize = 0;
129		var output = f.mantissa;
130		var exp = f.exponent;
131		const olength = decimalLength(output);
132
133		switch (mode) {
134		.decimal => {
135		if (f.exponent > 0) {
136		round_digit = (olength - 1) + precision + @as(usize, @intCast(f.exponent));
137		} else {
138		const min_exp_required = @as(usize, @intCast(-f.exponent));
139		if (precision + olength > min_exp_required) {
140		round_digit = precision + olength - min_exp_required;
141		}
142		}
143		},
144		.scientific => {
145		round_digit = 1 + precision;
146		},
147		}
148
149		if (round_digit < olength) {
150		var nlength = olength;
151		for (round_digit + 1..olength) \|_\| {
152		output /= 10;
153		exp += 1;
154		nlength -= 1;
155		}
156
157		if (output % 10 >= 5) {
158		output /= 10;
159		output += 1;
160		exp += 1;
161
162		// e.g. 9999 -> 10000
163		if (isPowerOf10(output)) {
164		output /= 10;
165		exp += 1;
166		}
167		}
168		}
169
170		return .{
171		.mantissa = output,
172		.exponent = exp,
173		.sign = f.sign,
174		};
175		}
176
177		/// Write a FloatDecimal128 to a buffer in scientific form.
178		///
179		/// The buffer provided must be greater than `min_buffer_size` in length. If no precision is
180		/// specified, this function will never return an error. If a precision is specified, up to
181		/// `8 + precision` bytes will be written to the buffer. An error will be returned if the content
182		/// will not fit.
183		///
184		/// It is recommended to bound decimal formatting with an exact precision.
185		pub fn formatScientific(buf: []u8, f_: FloatDecimal128, precision: ?usize) RyuError![]const u8 {
186		std.debug.assert(buf.len >= min_buffer_size);
187		var f = f_;
188
189		if (f.exponent == special_exponent) {
190		return copySpecialStr(buf, f);
191		}
192
193		if (precision) \|prec\| {
194		f = round(f, .scientific, prec);
195		}
196
197		var output = f.mantissa;
198		const olength = decimalLength(output);
199
200		if (precision) \|prec\| {
201		// fixed bound: sign(1) + leading_digit(1) + point(1) + exp_sign(1) + exp_max(4)
202		const req_bytes = 8 + prec;
203		if (buf.len < req_bytes) {
204		return error.BufferTooSmall;
205		}
206		}
207
208		// Step 5: Print the scientific representation
209		var index: usize = 0;
210		if (f.sign) {
211		buf[index] = '-';
212		index += 1;
213		}
214
215		// 1.12345
216		writeDecimal(buf[index + 2 ..], &output, olength - 1);
217		buf[index] = '0' + @as(u8, @intCast(output % 10));
218		buf[index + 1] = '.';
219		index += 2;
220		const dp_index = index;
221		if (olength > 1) index += olength - 1 else index -= 1;
222
223		if (precision) \|prec\| {
224		index += @intFromBool(olength == 1);
225		if (prec > olength - 1) {
226		const len = prec - (olength - 1);
227		@memset(buf[index..][0..len], '0');
228		index += len;
229		} else {
230		index = dp_index + prec - @intFromBool(prec == 0);
231		}
232		}
233
234		// e100
235		buf[index] = 'e';
236		index += 1;
237		var exp = f.exponent + @as(i32, @intCast(olength)) - 1;
238		if (exp < 0) {
239		buf[index] = '-';
240		index += 1;
241		exp = -exp;
242		}
243		var uexp: u32 = @intCast(exp);
244		const elength = decimalLength(uexp);
245		writeDecimal(buf[index..], &uexp, elength);
246		index += elength;
247
248		return buf[0..index];
249		}
250
251		/// Write a FloatDecimal128 to a buffer in decimal form.
252		///
253		/// The buffer provided must be greater than `min_buffer_size` bytes in length. If no precision is
254		/// specified, this may still return an error. If precision is specified, `2 + precision` bytes will
255		/// always be written.
256		pub fn formatDecimal(buf: []u8, f_: FloatDecimal128, precision: ?usize) RyuError![]const u8 {
257		std.debug.assert(buf.len >= min_buffer_size);
258		var f = f_;
259
260		if (f.exponent == special_exponent) {
261		return copySpecialStr(buf, f);
262		}
263
264		if (precision) \|prec\| {
265		f = round(f, .decimal, prec);
266		}
267
268		var output = f.mantissa;
269		const olength = decimalLength(output);
270
271		// fixed bound: leading_digit(1) + point(1)
272		const req_bytes = if (f.exponent >= 0)
273		2 + @abs(f.exponent) + olength + (precision orelse 0)
274		else
275		2 + @max(@abs(f.exponent) + olength, precision orelse 0);
276		if (buf.len < req_bytes) {
277		return error.BufferTooSmall;
278		}
279
280		// Step 5: Print the decimal representation
281		var index: usize = 0;
282		if (f.sign) {
283		buf[index] = '-';
284		index += 1;
285		}
286
287		const dp_offset = f.exponent + cast_i32(olength);
288		if (dp_offset <= 0) {
289		// 0.000001234
290		buf[index] = '0';
291		buf[index + 1] = '.';
292		index += 2;
293		const dp_index = index;
294
295		const dp_poffset: u32 = @intCast(-dp_offset);
296		@memset(buf[index..][0..dp_poffset], '0');
297		index += dp_poffset;
298		writeDecimal(buf[index..], &output, olength);
299		index += olength;
300
301		if (precision) \|prec\| {
302		const dp_written = index - dp_index;
303		if (prec > dp_written) {
304		@memset(buf[index..][0 .. prec - dp_written], '0');
305		}
306		index = dp_index + prec - @intFromBool(prec == 0);
307		}
308		} else {
309		// 123456000
310		const dp_uoffset: usize = @intCast(dp_offset);
311		if (dp_uoffset >= olength) {
312		writeDecimal(buf[index..], &output, olength);
313		index += olength;
314		@memset(buf[index..][0 .. dp_uoffset - olength], '0');
315		index += dp_uoffset - olength;
316
317		if (precision) \|prec\| {
318		if (prec != 0) {
319		buf[index] = '.';
320		index += 1;
321		@memset(buf[index..][0..prec], '0');
322		index += prec;
323		}
324		}
325		} else {
326		// 12345.6789
327		writeDecimal(buf[index + dp_uoffset + 1 ..], &output, olength - dp_uoffset);
328		buf[index + dp_uoffset] = '.';
329		const dp_index = index + dp_uoffset + 1;
330		writeDecimal(buf[index..], &output, dp_uoffset);
331		index += olength + 1;
332
333		if (precision) \|prec\| {
334		const dp_written = olength - dp_uoffset;
335		if (prec > dp_written) {
336		@memset(buf[index..][0 .. prec - dp_written], '0');
337		}
338		index = dp_index + prec - @intFromBool(prec == 0);
339		}
340		}
341		}
342
343		return buf[0..index];
344		}
345
346		fn cast_i32(v: anytype) i32 {
347		return @intCast(v);
348		}
349
350		/// Convert a binary float representation to decimal.
351		pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explicit_leading_bit: bool) FloatDecimal128 {
352		const bias = (@as(u32, 1) << (exponent_bits - 1)) - 1;
353		const ieee_sign = ((bits >> (mantissa_bits + exponent_bits)) & 1) != 0;
354		const ieee_mantissa = bits & ((@as(u128, 1) << mantissa_bits) - 1);
355		const ieee_exponent: u32 = @intCast((bits >> mantissa_bits) & ((@as(u128, 1) << exponent_bits) - 1));
356
357		if (ieee_exponent == 0 and ieee_mantissa == 0) {
358		return .{
359		.mantissa = 0,
360		.exponent = 0,
361		.sign = ieee_sign,
362		};
363		}
364		if (ieee_exponent == ((@as(u32, 1) << exponent_bits) - 1)) {
365		return .{
366		.mantissa = if (explicit_leading_bit) ieee_mantissa & ((@as(u128, 1) << (mantissa_bits - 1)) - 1) else ieee_mantissa,
367		.exponent = 0x7fffffff,
368		.sign = ieee_sign,
369		};
370		}
371
372		var e2: i32 = undefined;
373		var m2: u128 = undefined;
374		if (explicit_leading_bit) {
375		if (ieee_exponent == 0) {
376		e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
377		} else {
378		e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
379		}
380		m2 = ieee_mantissa;
381		} else {
382		if (ieee_exponent == 0) {
383		e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
384		m2 = ieee_mantissa;
385		} else {
386		e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
387		m2 = (@as(u128, 1) << mantissa_bits) \| ieee_mantissa;
388		}
389		}
390		const even = (m2 & 1) == 0;
391		const accept_bounds = even;
392
393		// Step 2: Determine the interval of legal decimal representations.
394		const mv = 4 * m2;
395		const mm_shift: u1 = @intFromBool((ieee_mantissa != if (explicit_leading_bit) (@as(u128, 1) << (mantissa_bits - 1)) else 0) or (ieee_exponent == 0));
396
397		// Step 3: Convert to a decimal power base using 128-bit arithmetic.
398		var vr: u128 = undefined;
399		var vp: u128 = undefined;
400		var vm: u128 = undefined;
401		var e10: i32 = undefined;
402		var vm_is_trailing_zeros = false;
403		var vr_is_trailing_zeros = false;
404		if (e2 >= 0) {
405		const q: u32 = log10Pow2(@intCast(e2)) - @intFromBool(e2 > 3);
406		e10 = cast_i32(q);
407		const k: i32 = @intCast(FLOAT_128_POW5_INV_BITCOUNT + pow5Bits(q) - 1);
408		const i: u32 = @intCast(-e2 + cast_i32(q) + k);
409
410		const pow5 = computeInvPow5(q);
411		vr = mulShift(4 * m2, &pow5, i);
412		vp = mulShift(4 * m2 + 2, &pow5, i);
413		vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, i);
414
415		if (q <= 55) {
416		if (mv % 5 == 0) {
417		vr_is_trailing_zeros = multipleOfPowerOf5(mv, q -% 1);
418		} else if (accept_bounds) {
419		vm_is_trailing_zeros = multipleOfPowerOf5(mv - 1 - mm_shift, q);
420		} else {
421		vp -= @intFromBool(multipleOfPowerOf5(mv + 2, q));
422		}
423		}
424		} else {
425		const q: u32 = log10Pow5(@intCast(-e2)) - @intFromBool(-e2 > 1);
426		e10 = cast_i32(q) + e2;
427		const i: i32 = -e2 - cast_i32(q);
428		const k: i32 = cast_i32(pow5Bits(@intCast(i))) - FLOAT_128_POW5_BITCOUNT;
429		const j: u32 = @intCast(cast_i32(q) - k);
430
431		const pow5 = computePow5(@intCast(i));
432		vr = mulShift(4 * m2, &pow5, j);
433		vp = mulShift(4 * m2 + 2, &pow5, j);
434		vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, j);
435
436		if (q <= 1) {
437		vr_is_trailing_zeros = true;
438		if (accept_bounds) {
439		vm_is_trailing_zeros = mm_shift == 1;
440		} else {
441		vp -= 1;
442		}
443		} else if (q < 127) {
444		vr_is_trailing_zeros = multipleOfPowerOf2(mv, q - 1);
445		}
446		}
447
448		// Step 4: Find the shortest decimal representation in the interval of legal representations.
449		var removed: u32 = 0;
450		var last_removed_digit: u8 = 0;
451
452		while (vp / 10 > vm / 10) {
453		vm_is_trailing_zeros = vm_is_trailing_zeros and vm % 10 == 0;
454		vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
455		last_removed_digit = @intCast(vr % 10);
456		vr /= 10;
457		vp /= 10;
458		vm /= 10;
459		removed += 1;
460		}
461
462		if (vm_is_trailing_zeros) {
463		while (vm % 10 == 0) {
464		vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
465		last_removed_digit = @intCast(vr % 10);
466		vr /= 10;
467		vp /= 10;
468		vm /= 10;
469		removed += 1;
470		}
471		}
472
473		if (vr_is_trailing_zeros and (last_removed_digit == 5) and (vr % 2 == 0)) {
474		last_removed_digit = 4;
475		}
476
477		return .{
478		.mantissa = vr + @intFromBool((vr == vm and (!accept_bounds or !vm_is_trailing_zeros)) or last_removed_digit >= 5),
479		.exponent = e10 + cast_i32(removed),
480		.sign = ieee_sign,
481		};
482		}
483
484		fn decimalLength(v: u128) u32 {
485		const LARGEST_POW10 = (@as(u128, 5421010862427522170) << 64) \| 687399551400673280;
486		var p10 = LARGEST_POW10;
487		var i: u32 = 39;
488		while (i > 0) : (i -= 1) {
489		if (v >= p10) return i;
490		p10 /= 10;
491		}
492		return 1;
493		}
494
495		// floor(log_10(2^e))
496		fn log10Pow2(e: u32) u32 {
497		std.debug.assert(e <= 1 << 15);
498		return @intCast((@as(u64, @intCast(e)) * 169464822037455) >> 49);
499		}
500
501		// floor(log_10(5^e))
502		fn log10Pow5(e: u32) u32 {
503		std.debug.assert(e <= 1 << 15);
504		return @intCast((@as(u64, @intCast(e)) * 196742565691928) >> 48);
505		}
506
507		// if (e == 0) 1 else ceil(log_2(5^e))
508		fn pow5Bits(e: u32) u32 {
509		std.debug.assert(e <= 1 << 15);
510		return @intCast(((@as(u64, @intCast(e)) * 163391164108059) >> 46) + 1);
511		}
512
513		fn pow5Factor(value_: u128) u32 {
514		var count: u32 = 0;
515		var value = value_;
516		while (value > 0) : ({
517		count += 1;
518		value /= 5;
519		}) {
520		if (value % 5 != 0) return count;
521		}
522		return 0;
523		}
524
525		fn multipleOfPowerOf5(value: u128, p: u32) bool {
526		return pow5Factor(value) >= p;
527		}
528
529		fn multipleOfPowerOf2(value: u128, p: u32) bool {
530		return (value & ((@as(u128, 1) << @as(u7, @intCast(p))) - 1)) == 0;
531		}
532
533		fn computeInvPow5(i: u32) [4]u64 {
534		const base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
535		const base2 = base * POW5_TABLE_SIZE;
536		const mul = &GENERIC_POW5_INV_SPLIT[base]; // 1 / 5^base2
537		if (i == base2) {
538		return .{ mul[0] + 1, mul[1], mul[2], mul[3] };
539		} else {
540		const offset = base2 - i;
541		const m = &GENERIC_POW5_TABLE[offset]; // 5^offset
542		const delta = pow5Bits(base2) - pow5Bits(i);
543
544		const shift: u6 = @intCast(2 * (i % 32));
545		const corr: u32 = @intCast(((POW5_INV_ERRORS[i / 32] >> shift) & 3) + 1);
546		return mul_128_256_shift(m, mul, delta, corr);
547		}
548		}
549
550		fn computePow5(i: u32) [4]u64 {
551		const base = i / POW5_TABLE_SIZE;
552		const base2 = base * POW5_TABLE_SIZE;
553		const mul = &GENERIC_POW5_SPLIT[base];
554		if (i == base2) {
555		return mul.*;
556		} else {
557		const offset = i - base2;
558		const m = &GENERIC_POW5_TABLE[offset];
559		const delta = pow5Bits(i) - pow5Bits(base2);
560
561		const shift: u6 = @intCast(2 * (i % 32));
562		const corr: u32 = @intCast((POW5_ERRORS[i / 32] >> shift) & 3);
563		return mul_128_256_shift(m, mul, delta, corr);
564		}
565		}
566
567		fn mulShift(m: u128, mul: *const [4]u64, j: u32) u128 {
568		std.debug.assert(j > 128);
569		const a: [2]u64 = .{ @truncate(m), @truncate(m >> 64) };
570		const r = mul_128_256_shift(&a, mul, j, 0);
571		return (@as(u128, r[1]) << 64) \| r[0];
572		}
573
574		fn mul_128_256_shift(a: const [2]u64, b: const [4]u64, shift: u32, corr: u32) [4]u64 {
575		std.debug.assert(shift > 0);
576		std.debug.assert(shift < 256);
577
578		const b00 = @as(u128, a[0]) * b[0];
579		const b01 = @as(u128, a[0]) * b[1];
580		const b02 = @as(u128, a[0]) * b[2];
581		const b03 = @as(u128, a[0]) * b[3];
582		const b10 = @as(u128, a[1]) * b[0];
583		const b11 = @as(u128, a[1]) * b[1];
584		const b12 = @as(u128, a[1]) * b[2];
585		const b13 = @as(u128, a[1]) * b[3];
586
587		const s0 = b00;
588		const s1 = b01 +% b10;
589		const c1: u128 = @intFromBool(s1 < b01);
590		const s2 = b02 +% b11;
591		const c2: u128 = @intFromBool(s2 < b02);
592		const s3 = b03 +% b12;
593		const c3: u128 = @intFromBool(s3 < b03);
594
595		const p0 = s0 +% (s1 << 64);
596		const d0: u128 = @intFromBool(p0 < b00);
597		const q1 = s2 +% (s1 >> 64) +% (s3 << 64);
598		const d1: u128 = @intFromBool(q1 < s2);
599		const p1 = q1 +% (c1 << 64) +% d0;
600		const d2: u128 = @intFromBool(p1 < q1);
601		const p2 = b13 +% (s3 >> 64) +% c2 +% (c3 << 64) +% d1 +% d2;
602
603		var r0: u128 = undefined;
604		var r1: u128 = undefined;
605		if (shift < 128) {
606		const cshift: u7 = @intCast(shift);
607		const sshift: u7 = @intCast(128 - shift);
608		r0 = corr +% ((p0 >> cshift) \| (p1 << sshift));
609		r1 = ((p1 >> cshift) \| (p2 << sshift)) +% @intFromBool(r0 < corr);
610		} else if (shift == 128) {
611		r0 = corr +% p1;
612		r1 = p2 +% @intFromBool(r0 < corr);
613		} else {
614		const ashift: u7 = @intCast(shift - 128);
615		const sshift: u7 = @intCast(256 - shift);
616		r0 = corr +% ((p1 >> ashift) \| (p2 << sshift));
617		r1 = (p2 >> ashift) +% @intFromBool(r0 < corr);
618		}
619
620		return .{ @truncate(r0), @truncate(r0 >> 64), @truncate(r1), @truncate(r1 >> 64) };
621		}
622
623		// zig fmt: off
624		//
625		// 4.5KiB of tables.
626
627		const FLOAT_128_POW5_INV_BITCOUNT = 249;
628		const FLOAT_128_POW5_BITCOUNT = 249;
629		const POW5_TABLE_SIZE = 56;
630
631		const GENERIC_POW5_TABLE: [POW5_TABLE_SIZE][2]u64 = .{
632		.{ 1, 0 },
633		.{ 5, 0 },
634		.{ 25, 0 },
635		.{ 125, 0 },
636		.{ 625, 0 },
637		.{ 3125, 0 },
638		.{ 15625, 0 },
639		.{ 78125, 0 },
640		.{ 390625, 0 },
641		.{ 1953125, 0 },
642		.{ 9765625, 0 },
643		.{ 48828125, 0 },
644		.{ 244140625, 0 },
645		.{ 1220703125, 0 },
646		.{ 6103515625, 0 },
647		.{ 30517578125, 0 },
648		.{ 152587890625, 0 },
649		.{ 762939453125, 0 },
650		.{ 3814697265625, 0 },
651		.{ 19073486328125, 0 },
652		.{ 95367431640625, 0 },
653		.{ 476837158203125, 0 },
654		.{ 2384185791015625, 0 },
655		.{ 11920928955078125, 0 },
656		.{ 59604644775390625, 0 },
657		.{ 298023223876953125, 0 },
658		.{ 1490116119384765625, 0 },
659		.{ 7450580596923828125, 0 },
660		.{ 359414837200037393, 2 },
661		.{ 1797074186000186965, 10 },
662		.{ 8985370930000934825, 50 },
663		.{ 8033366502585570893, 252 },
664		.{ 3273344365508751233, 1262 },
665		.{ 16366721827543756165, 6310 },
666		.{ 8046632842880574361, 31554 },
667		.{ 3339676066983768573, 157772 },
668		.{ 16698380334918842865, 788860 },
669		.{ 9704925379756007861, 3944304 },
670		.{ 11631138751360936073, 19721522 },
671		.{ 2815461535676025517, 98607613 },
672		.{ 14077307678380127585, 493038065 },
673		.{ 15046306170771983077, 2465190328 },
674		.{ 1444554559021708921, 12325951644 },
675		.{ 7222772795108544605, 61629758220 },
676		.{ 17667119901833171409, 308148791101 },
677		.{ 14548623214327650581, 1540743955509 },
678		.{ 17402883850509598057, 7703719777548 },
679		.{ 13227442957709783821, 38518598887744 },
680		.{ 10796982567420264257, 192592994438723 },
681		.{ 17091424689682218053, 962964972193617 },
682		.{ 11670147153572883801, 4814824860968089 },
683		.{ 3010503546735764157, 24074124304840448 },
684		.{ 15052517733678820785, 120370621524202240 },
685		.{ 1475612373555897461, 601853107621011204 },
686		.{ 7378061867779487305, 3009265538105056020 },
687		.{ 18443565265187884909, 15046327690525280101 },
688		};
689
690		const GENERIC_POW5_SPLIT: [89][4]u64 = .{
691		.{ 0, 0, 0, 72057594037927936 },
692		.{ 0, 5206161169240293376, 4575641699882439235, 73468396926392969 },
693		.{ 3360510775605221349, 6983200512169538081, 4325643253124434363, 74906821675075173 },
694		.{ 11917660854915489451, 9652941469841108803, 946308467778435600, 76373409087490117 },
695		.{ 1994853395185689235, 16102657350889591545, 6847013871814915412, 77868710555449746 },
696		.{ 958415760277438274, 15059347134713823592, 7329070255463483331, 79393288266368765 },
697		.{ 2065144883315240188, 7145278325844925976, 14718454754511147343, 80947715414629833 },
698		.{ 8980391188862868935, 13709057401304208685, 8230434828742694591, 82532576417087045 },
699		.{ 432148644612782575, 7960151582448466064, 12056089168559840552, 84148467132788711 },
700		.{ 484109300864744403, 15010663910730448582, 16824949663447227068, 85795995087002057 },
701		.{ 14793711725276144220, 16494403799991899904, 10145107106505865967, 87475779699624060 },
702		.{ 15427548291869817042, 12330588654550505203, 13980791795114552342, 89188452518064298 },
703		.{ 9979404135116626552, 13477446383271537499, 14459862802511591337, 90934657454687378 },
704		.{ 12385121150303452775, 9097130814231585614, 6523855782339765207, 92715051028904201 },
705		.{ 1822931022538209743, 16062974719797586441, 3619180286173516788, 94530302614003091 },
706		.{ 12318611738248470829, 13330752208259324507, 10986694768744162601, 96381094688813589 },
707		.{ 13684493829640282333, 7674802078297225834, 15208116197624593182, 98268123094297527 },
708		.{ 5408877057066295332, 6470124174091971006, 15112713923117703147, 100192097295163851 },
709		.{ 11407083166564425062, 18189998238742408185, 4337638702446708282, 102153740646605557 },
710		.{ 4112405898036935485, 924624216579956435, 14251108172073737125, 104153790666259019 },
711		.{ 16996739107011444789, 10015944118339042475, 2395188869672266257, 106192999311487969 },
712		.{ 4588314690421337879, 5339991768263654604, 15441007590670620066, 108272133262096356 },
713		.{ 2286159977890359825, 14329706763185060248, 5980012964059367667, 110391974208576409 },
714		.{ 9654767503237031099, 11293544302844823188, 11739932712678287805, 112553319146000238 },
715		.{ 11362964448496095896, 7990659682315657680, 251480263940996374, 114756980673665505 },
716		.{ 1423410421096377129, 14274395557581462179, 16553482793602208894, 117003787300607788 },
717		.{ 2070444190619093137, 11517140404712147401, 11657844572835578076, 119294583757094535 },
718		.{ 7648316884775828921, 15264332483297977688, 247182277434709002, 121630231312217685 },
719		.{ 17410896758132241352, 10923914482914417070, 13976383996795783649, 124011608097704390 },
720		.{ 9542674537907272703, 3079432708831728956, 14235189590642919676, 126439609438067572 },
721		.{ 10364666969937261816, 8464573184892924210, 12758646866025101190, 128915148187220428 },
722		.{ 14720354822146013883, 11480204489231511423, 7449876034836187038, 131439155071681461 },
723		.{ 1692907053653558553, 17835392458598425233, 1754856712536736598, 134012579040499057 },
724		.{ 5620591334531458755, 11361776175667106627, 13350215315297937856, 136636387622027174 },
725		.{ 17455759733928092601, 10362573084069962561, 11246018728801810510, 139311567287686283 },
726		.{ 2465404073814044982, 17694822665274381860, 1509954037718722697, 142039123822846312 },
727		.{ 2152236053329638369, 11202280800589637091, 16388426812920420176, 72410041352485523 },
728		.{ 17319024055671609028, 10944982848661280484, 2457150158022562661, 73827744744583080 },
729		.{ 17511219308535248024, 5122059497846768077, 2089605804219668451, 75273205100637900 },
730		.{ 10082673333144031533, 14429008783411894887, 12842832230171903890, 76746965869337783 },
731		.{ 16196653406315961184, 10260180891682904501, 10537411930446752461, 78249581139456266 },
732		.{ 15084422041749743389, 234835370106753111, 16662517110286225617, 79781615848172976 },
733		.{ 8199644021067702606, 3787318116274991885, 7438130039325743106, 81343645993472659 },
734		.{ 12039493937039359765, 9773822153580393709, 5945428874398357806, 82936258850702722 },
735		.{ 984543865091303961, 7975107621689454830, 6556665988501773347, 84560053193370726 },
736		.{ 9633317878125234244, 16099592426808915028, 9706674539190598200, 86215639518264828 },
737		.{ 6860695058870476186, 4471839111886709592, 7828342285492709568, 87903640274981819 },
738		.{ 14583324717644598331, 4496120889473451238, 5290040788305728466, 89624690099949049 },
739		.{ 18093669366515003715, 12879506572606942994, 18005739787089675377, 91379436055028227 },
740		.{ 17997493966862379937, 14646222655265145582, 10265023312844161858, 93168537870790806 },
741		.{ 12283848109039722318, 11290258077250314935, 9878160025624946825, 94992668194556404 },
742		.{ 8087752761883078164, 5262596608437575693, 11093553063763274413, 96852512843287537 },
743		.{ 15027787746776840781, 12250273651168257752, 9290470558712181914, 98748771061435726 },
744		.{ 15003915578366724489, 2937334162439764327, 5404085603526796602, 100682155783835929 },
745		.{ 5225610465224746757, 14932114897406142027, 2774647558180708010, 102653393903748137 },
746		.{ 17112957703385190360, 12069082008339002412, 3901112447086388439, 104663226546146909 },
747		.{ 4062324464323300238, 3992768146772240329, 15757196565593695724, 106712409346361594 },
748		.{ 5525364615810306701, 11855206026704935156, 11344868740897365300, 108801712734172003 },
749		.{ 9274143661888462646, 4478365862348432381, 18010077872551661771, 110931922223466333 },
750		.{ 12604141221930060148, 8930937759942591500, 9382183116147201338, 113103838707570263 },
751		.{ 14513929377491886653, 1410646149696279084, 587092196850797612, 115318278760358235 },
752		.{ 2226851524999454362, 7717102471110805679, 7187441550995571734, 117576074943260147 },
753		.{ 5527526061344932763, 2347100676188369132, 16976241418824030445, 119878076118278875 },
754		.{ 6088479778147221611, 17669593130014777580, 10991124207197663546, 122225147767136307 },
755		.{ 11107734086759692041, 3391795220306863431, 17233960908859089158, 124618172316667879 },
756		.{ 7913172514655155198, 17726879005381242552, 641069866244011540, 127058049470587962 },
757		.{ 12596991768458713949, 15714785522479904446, 6035972567136116512, 129545696547750811 },
758		.{ 16901996933781815980, 4275085211437148707, 14091642539965169063, 132082048827034281 },
759		.{ 7524574627987869240, 15661204384239316051, 2444526454225712267, 134668059898975949 },
760		.{ 8199251625090479942, 6803282222165044067, 16064817666437851504, 137304702024293857 },
761		.{ 4453256673338111920, 15269922543084434181, 3139961729834750852, 139992966499426682 },
762		.{ 15841763546372731299, 3013174075437671812, 4383755396295695606, 142733864029230733 },
763		.{ 9771896230907310329, 4900659362437687569, 12386126719044266361, 72764212553486967 },
764		.{ 9420455527449565190, 1859606122611023693, 6555040298902684281, 74188850200884818 },
765		.{ 5146105983135678095, 2287300449992174951, 4325371679080264751, 75641380576797959 },
766		.{ 11019359372592553360, 8422686425957443718, 7175176077944048210, 77122349788024458 },
767		.{ 11005742969399620716, 4132174559240043701, 9372258443096612118, 78632314633490790 },
768		.{ 8887589641394725840, 8029899502466543662, 14582206497241572853, 80171842813591127 },
769		.{ 360247523705545899, 12568341805293354211, 14653258284762517866, 81741513143625247 },
770		.{ 12314272731984275834, 4740745023227177044, 6141631472368337539, 83341915771415304 },
771		.{ 441052047733984759, 7940090120939869826, 11750200619921094248, 84973652399183278 },
772		.{ 3436657868127012749, 9187006432149937667, 16389726097323041290, 86637336509772529 },
773		.{ 13490220260784534044, 15339072891382896702, 8846102360835316895, 88333593597298497 },
774		.{ 4125672032094859833, 158347675704003277, 10592598512749774447, 90063061402315272 },
775		.{ 12189928252974395775, 2386931199439295891, 7009030566469913276, 91826390151586454 },
776		.{ 9256479608339282969, 2844900158963599229, 11148388908923225596, 93624242802550437 },
777		.{ 11584393507658707408, 2863659090805147914, 9873421561981063551, 95457295292572042 },
778		.{ 13984297296943171390, 1931468383973130608, 12905719743235082319, 97326236793074198 },
779		.{ 5837045222254987499, 10213498696735864176, 14893951506257020749, 99231769968645227 },
780		};
781
782		// Unfortunately, the results are sometimes off by one or two. We use an additional
783		// lookup table to store those cases and adjust the result.
784		const POW5_ERRORS: [156]u64 = .{
785		0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9555596400000000,
786		0x65a6569525565555, 0x4415551445449655, 0x5105015504144541, 0x65a69969a6965964,
787		0x5054955969959656, 0x5105154515554145, 0x4055511051591555, 0x5500514455550115,
788		0x0041140014145515, 0x1005440545511051, 0x0014405450411004, 0x0414440010500000,
789		0x0044000440010040, 0x5551155000004001, 0x4554555454544114, 0x5150045544005441,
790		0x0001111400054501, 0x6550955555554554, 0x1504159645559559, 0x4105055141454545,
791		0x1411541410405454, 0x0415555044545555, 0x0014154115405550, 0x1540055040411445,
792		0x0000000500000000, 0x5644000000000000, 0x1155555591596555, 0x0410440054569565,
793		0x5145100010010005, 0x0555041405500150, 0x4141450455140450, 0x0000000144000140,
794		0x5114004001105410, 0x4444100404005504, 0x0414014410001015, 0x5145055155555015,
795		0x0141041444445540, 0x0000100451541414, 0x4105041104155550, 0x0500501150451145,
796		0x1001050000004114, 0x5551504400141045, 0x5110545410151454, 0x0100001400004040,
797		0x5040010111040000, 0x0140000150541100, 0x4400140400104110, 0x5011014405545004,
798		0x0000000044155440, 0x0000000010000000, 0x1100401444440001, 0x0040401010055111,
799		0x5155155551405454, 0x0444440015514411, 0x0054505054014101, 0x0451015441115511,
800		0x1541411401140551, 0x4155104514445110, 0x4141145450145515, 0x5451445055155050,
801		0x4400515554110054, 0x5111145104501151, 0x565a655455500501, 0x5565555555525955,
802		0x0550511500405695, 0x4415504051054544, 0x6555595965555554, 0x0100915915555655,
803		0x5540001510001001, 0x5450051414000544, 0x1405010555555551, 0x5555515555644155,
804		0x5555055595496555, 0x5451045004415000, 0x5450510144040144, 0x5554155555556455,
805		0x5051555495415555, 0x5555554555555545, 0x0000000010005455, 0x4000005000040000,
806		0x5565555555555954, 0x5554559555555505, 0x9645545495552555, 0x4000400055955564,
807		0x0040000000000001, 0x4004100100000000, 0x5540040440000411, 0x4565555955545644,
808		0x1140659549651556, 0x0100000410010000, 0x5555515400004001, 0x5955545555155255,
809		0x5151055545505556, 0x5051454510554515, 0x0501500050415554, 0x5044154005441005,
810		0x1455445450550455, 0x0010144055144545, 0x0000401100000004, 0x1050145050000010,
811		0x0415004554011540, 0x1000510100151150, 0x0100040400001144, 0x0000000000000000,
812		0x0550004400000100, 0x0151145041451151, 0x0000400400005450, 0x0000100044010004,
813		0x0100054100050040, 0x0504400005410010, 0x4011410445500105, 0x0000404000144411,
814		0x0101504404500000, 0x0000005044400400, 0x0000000014000100, 0x0404440414000000,
815		0x5554100410000140, 0x4555455544505555, 0x5454105055455455, 0x0115454155454015,
816		0x4404110000045100, 0x4400001100101501, 0x6596955956966a94, 0x0040655955665965,
817		0x5554144400100155, 0xa549495401011041, 0x5596555565955555, 0x5569965959549555,
818		0x969565a655555456, 0x0000001000000000, 0x0000000040000140, 0x0000040100000000,
819		0x1415454400000000, 0x5410415411454114, 0x0400040104000154, 0x0504045000000411,
820		0x0000001000000010, 0x5554000000001040, 0x5549155551556595, 0x1455541055515555,
821		0x0510555454554541, 0x9555555555540455, 0x6455456555556465, 0x4524565555654514,
822		0x5554655255559545, 0x9555455441155556, 0x0000000051515555, 0x0010005040000550,
823		0x5044044040000000, 0x1045040440010500, 0x0000400000040000, 0x0000000000000000,
824		};
825
826		const GENERIC_POW5_INV_SPLIT: [89][4]u64 = .{
827		.{ 0, 0, 0, 144115188075855872 },
828		.{ 1573859546583440065, 2691002611772552616, 6763753280790178510, 141347765182270746 },
829		.{ 12960290449513840412, 12345512957918226762, 18057899791198622765, 138633484706040742 },
830		.{ 7615871757716765416, 9507132263365501332, 4879801712092008245, 135971326161092377 },
831		.{ 7869961150745287587, 5804035291554591636, 8883897266325833928, 133360288657597085 },
832		.{ 2942118023529634767, 15128191429820565086, 10638459445243230718, 130799390525667397 },
833		.{ 14188759758411913794, 5362791266439207815, 8068821289119264054, 128287668946279217 },
834		.{ 7183196927902545212, 1952291723540117099, 12075928209936341512, 125824179589281448 },
835		.{ 5672588001402349748, 17892323620748423487, 9874578446960390364, 123407996258356868 },
836		.{ 4442590541217566325, 4558254706293456445, 10343828952663182727, 121038210542800766 },
837		.{ 3005560928406962566, 2082271027139057888, 13961184524927245081, 118713931475986426 },
838		.{ 13299058168408384786, 17834349496131278595, 9029906103900731664, 116434285200389047 },
839		.{ 5414878118283973035, 13079825470227392078, 17897304791683760280, 114198414639042157 },
840		.{ 14609755883382484834, 14991702445765844156, 3269802549772755411, 112005479173303009 },
841		.{ 15967774957605076027, 2511532636717499923, 16221038267832563171, 109854654326805788 },
842		.{ 9269330061621627145, 3332501053426257392, 16223281189403734630, 107745131455483836 },
843		.{ 16739559299223642282, 1873986623300664530, 6546709159471442872, 105676117443544318 },
844		.{ 17116435360051202055, 1359075105581853924, 2038341371621886470, 103646834405281051 },
845		.{ 17144715798009627550, 3201623802661132408, 9757551605154622431, 101656519392613377 },
846		.{ 17580479792687825857, 6546633380567327312, 15099972427870912398, 99704424108241124 },
847		.{ 9726477118325522902, 14578369026754005435, 11728055595254428803, 97789814624307808 },
848		.{ 134593949518343635, 5715151379816901985, 1660163707976377376, 95911971106466306 },
849		.{ 5515914027713859358, 7124354893273815720, 5548463282858794077, 94070187543243255 },
850		.{ 6188403395862945512, 5681264392632320838, 15417410852121406654, 92263771480600430 },
851		.{ 15908890877468271457, 10398888261125597540, 4817794962769172309, 90492043761593298 },
852		.{ 1413077535082201005, 12675058125384151580, 7731426132303759597, 88754338271028867 },
853		.{ 1486733163972670293, 11369385300195092554, 11610016711694864110, 87050001685026843 },
854		.{ 8788596583757589684, 3978580923851924802, 9255162428306775812, 85378393225389919 },
855		.{ 7203518319660962120, 15044736224407683725, 2488132019818199792, 83738884418690858 },
856		.{ 4004175967662388707, 18236988667757575407, 15613100370957482671, 82130858859985791 },
857		.{ 18371903370586036463, 53497579022921640, 16465963977267203307, 80553711981064899 },
858		.{ 10170778323887491315, 1999668801648976001, 10209763593579456445, 79006850823153334 },
859		.{ 17108131712433974546, 16825784443029944237, 2078700786753338945, 77489693813976938 },
860		.{ 17221789422665858532, 12145427517550446164, 5391414622238668005, 76001670549108934 },
861		.{ 4859588996898795878, 1715798948121313204, 3950858167455137171, 74542221577515387 },
862		.{ 13513469241795711526, 631367850494860526, 10517278915021816160, 73110798191218799 },
863		.{ 11757513142672073111, 2581974932255022228, 17498959383193606459, 143413724438001539 },
864		.{ 14524355192525042817, 5640643347559376447, 1309659274756813016, 140659771648132296 },
865		.{ 2765095348461978538, 11021111021896007722, 3224303603779962366, 137958702611185230 },
866		.{ 12373410389187981037, 13679193545685856195, 11644609038462631561, 135309501808182158 },
867		.{ 12813176257562780151, 3754199046160268020, 9954691079802960722, 132711173221007413 },
868		.{ 17557452279667723458, 3237799193992485824, 17893947919029030695, 130162739957935629 },
869		.{ 14634200999559435155, 4123869946105211004, 6955301747350769239, 127663243886350468 },
870		.{ 2185352760627740240, 2864813346878886844, 13049218671329690184, 125211745272516185 },
871		.{ 6143438674322183002, 10464733336980678750, 6982925169933978309, 122807322428266620 },
872		.{ 1099509117817174576, 10202656147550524081, 754997032816608484, 120449071364478757 },
873		.{ 2410631293559367023, 17407273750261453804, 15307291918933463037, 118136105451200587 },
874		.{ 12224968375134586697, 1664436604907828062, 11506086230137787358, 115867555084305488 },
875		.{ 3495926216898000888, 18392536965197424288, 10992889188570643156, 113642567358547782 },
876		.{ 8744506286256259680, 3966568369496879937, 18342264969761820037, 111460305746896569 },
877		.{ 7689600520560455039, 5254331190877624630, 9628558080573245556, 109319949786027263 },
878		.{ 11862637625618819436, 3456120362318976488, 14690471063106001082, 107220694767852583 },
879		.{ 5697330450030126444, 12424082405392918899, 358204170751754904, 105161751436977040 },
880		.{ 11257457505097373622, 15373192700214208870, 671619062372033814, 103142345693961148 },
881		.{ 16850355018477166700, 1913910419361963966, 4550257919755970531, 101161718304283822 },
882		.{ 9670835567561997011, 10584031339132130638, 3060560222974851757, 99219124612893520 },
883		.{ 7698686577353054710, 11689292838639130817, 11806331021588878241, 97313834264240819 },
884		.{ 12233569599615692137, 3347791226108469959, 10333904326094451110, 95445130927687169 },
885		.{ 13049400362825383933, 17142621313007799680, 3790542585289224168, 93612312028186576 },
886		.{ 12430457242474442072, 5625077542189557960, 14765055286236672238, 91814688482138969 },
887		.{ 4759444137752473128, 2230562561567025078, 4954443037339580076, 90051584438315940 },
888		.{ 7246913525170274758, 8910297835195760709, 4015904029508858381, 88322337023761438 },
889		.{ 12854430245836432067, 8135139748065431455, 11548083631386317976, 86626296094571907 },
890		.{ 4848827254502687803, 4789491250196085625, 3988192420450664125, 84962823991462151 },
891		.{ 7435538409611286684, 904061756819742353, 14598026519493048444, 83331295300025028 },
892		.{ 11042616160352530997, 8948390828345326218, 10052651191118271927, 81731096615594853 },
893		.{ 11059348291563778943, 11696515766184685544, 3783210511290897367, 80161626312626082 },
894		.{ 7020010856491885826, 5025093219346041680, 8960210401638911765, 78622294318500592 },
895		.{ 17732844474490699984, 7820866704994446502, 6088373186798844243, 77112521891678506 },
896		.{ 688278527545590501, 3045610706602776618, 8684243536999567610, 75631741404109150 },
897		.{ 2734573255120657297, 3903146411440697663, 9470794821691856713, 74179396127820347 },
898		.{ 15996457521023071259, 4776627823451271680, 12394856457265744744, 72754940025605801 },
899		.{ 13492065758834518331, 7390517611012222399, 1630485387832860230, 142715675091463768 },
900		.{ 13665021627282055864, 9897834675523659302, 17907668136755296849, 139975126841173266 },
901		.{ 9603773719399446181, 10771916301484339398, 10672699855989487527, 137287204938390542 },
902		.{ 3630218541553511265, 8139010004241080614, 2876479648932814543, 134650898807055963 },
903		.{ 8318835909686377084, 9525369258927993371, 2796120270400437057, 132065217277054270 },
904		.{ 11190003059043290163, 12424345635599592110, 12539346395388933763, 129529188211565064 },
905		.{ 8701968833973242276, 820569587086330727, 2315591597351480110, 127041858141569228 },
906		.{ 5115113890115690487, 16906305245394587826, 9899749468931071388, 124602291907373862 },
907		.{ 15543535488939245974, 10945189844466391399, 3553863472349432246, 122209572307020975 },
908		.{ 7709257252608325038, 1191832167690640880, 15077137020234258537, 119862799751447719 },
909		.{ 7541333244210021737, 9790054727902174575, 5160944773155322014, 117561091926268545 },
910		.{ 12297384708782857832, 1281328873123467374, 4827925254630475769, 115303583460052092 },
911		.{ 13243237906232367265, 15873887428139547641, 3607993172301799599, 113089425598968120 },
912		.{ 11384616453739611114, 15184114243769211033, 13148448124803481057, 110917785887682141 },
913		.{ 17727970963596660683, 1196965221832671990, 14537830463956404138, 108787847856377790 },
914		.{ 17241367586707330931, 8880584684128262874, 11173506540726547818, 106698810713789254 },
915		.{ 7184427196661305643, 14332510582433188173, 14230167953789677901, 104649889046128358 },
916		};
917
918		const POW5_INV_ERRORS: [154]u64 = .{
919		0x1144155514145504, 0x0000541555401141, 0x0000000000000000, 0x0154454000000000,
920		0x4114105515544440, 0x0001001111500415, 0x4041411410011000, 0x5550114515155014,
921		0x1404100041554551, 0x0515000450404410, 0x5054544401140004, 0x5155501005555105,
922		0x1144141000105515, 0x0541500000500000, 0x1104105540444140, 0x4000015055514110,
923		0x0054010450004005, 0x4155515404100005, 0x5155145045155555, 0x1511555515440558,
924		0x5558544555515555, 0x0000000000000010, 0x5004000000000050, 0x1415510100000010,
925		0x4545555444514500, 0x5155151555555551, 0x1441540144044554, 0x5150104045544400,
926		0x5450545401444040, 0x5554455045501400, 0x4655155555555145, 0x1000010055455055,
927		0x1000004000055004, 0x4455405104000005, 0x4500114504150545, 0x0000000014000000,
928		0x5450000000000000, 0x5514551511445555, 0x4111501040555451, 0x4515445500054444,
929		0x5101500104100441, 0x1545115155545055, 0x0000000000000000, 0x1554000000100000,
930		0x5555545595551555, 0x5555051851455955, 0x5555555555555559, 0x0000400011001555,
931		0x0000004400040000, 0x5455511555554554, 0x5614555544115445, 0x6455156145555155,
932		0x5455855455415455, 0x5515555144555545, 0x0114400000145155, 0x0000051000450511,
933		0x4455154554445100, 0x4554150141544455, 0x65955555559a5965, 0x5555555854559559,
934		0x9569654559616595, 0x1040044040005565, 0x1010010500011044, 0x1554015545154540,
935		0x4440555401545441, 0x1014441450550105, 0x4545400410504145, 0x5015111541040151,
936		0x5145051154000410, 0x1040001044545044, 0x4001400000151410, 0x0540000044040000,
937		0x0510555454411544, 0x0400054054141550, 0x1001041145001100, 0x0000000140000000,
938		0x0000000014100000, 0x1544005454000140, 0x4050055505445145, 0x0011511104504155,
939		0x5505544415045055, 0x1155154445515554, 0x0000000000004555, 0x0000000000000000,
940		0x5101010510400004, 0x1514045044440400, 0x5515519555515555, 0x4554545441555545,
941		0x1551055955551515, 0x0150000011505515, 0x0044005040400000, 0x0004001004010050,
942		0x0000051004450414, 0x0114001101001144, 0x0401000001000001, 0x4500010001000401,
943		0x0004100000005000, 0x0105000441101100, 0x0455455550454540, 0x5404050144105505,
944		0x4101510540555455, 0x1055541411451555, 0x5451445110115505, 0x1154110010101545,
945		0x1145140450054055, 0x5555565415551554, 0x1550559555555555, 0x5555541545045141,
946		0x4555455450500100, 0x5510454545554555, 0x1510140115045455, 0x1001050040111510,
947		0x5555454555555504, 0x9954155545515554, 0x6596656555555555, 0x0140410051555559,
948		0x0011104010001544, 0x965669659a680501, 0x5655a55955556955, 0x4015111014404514,
949		0x1414155554505145, 0x0540040011051404, 0x1010000000015005, 0x0010054050004410,
950		0x5041104014000100, 0x4440010500100001, 0x1155510504545554, 0x0450151545115541,
951		0x4000100400110440, 0x1004440010514440, 0x0000115050450000, 0x0545404455541500,
952		0x1051051555505101, 0x5505144554544144, 0x4550545555515550, 0x0015400450045445,
953		0x4514155400554415, 0x4555055051050151, 0x1511441450001014, 0x4544554510404414,
954		0x4115115545545450, 0x5500541555551555, 0x5550010544155015, 0x0144414045545500,
955		0x4154050001050150, 0x5550511111000145, 0x1114504055000151, 0x5104041101451040,
956		0x0010501401051441, 0x0010501450504401, 0x4554585440044444, 0x5155555951450455,
957		0x0040000400105555, 0x0000000000000001,
958		};
959
960		// zig fmt: on
961
962		fn check(comptime T: type, value: T, comptime expected: []const u8) !void {
963		const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
964
965		var buf: [6000]u8 = undefined;
966		const value_bits: I = @bitCast(value);
967		const s = try format(&buf, value, .{});
968		try std.testing.expectEqualStrings(expected, s);
969
970		if (@bitSizeOf(T) != 80) {
971		const o = try std.fmt.parseFloat(T, s);
972		const o_bits: I = @bitCast(o);
973
974		if (std.math.isNan(value)) {
975		try std.testing.expect(std.math.isNan(o));
976		} else {
977		try std.testing.expectEqual(value_bits, o_bits);
978		}
979		}
980		}
981
982		test "format f32" {
983		try check(f32, 0.0, "0e0");
984		try check(f32, -0.0, "-0e0");
985		try check(f32, 1.0, "1e0");
986		try check(f32, -1.0, "-1e0");
987		try check(f32, std.math.nan(f32), "nan");
988		try check(f32, std.math.inf(f32), "inf");
989		try check(f32, -std.math.inf(f32), "-inf");
990		try check(f32, 1.1754944e-38, "1.1754944e-38");
991		try check(f32, @bitCast(@as(u32, 0x7f7fffff)), "3.4028235e38");
992		try check(f32, @bitCast(@as(u32, 1)), "1e-45");
993		try check(f32, 3.355445E7, "3.355445e7");
994		try check(f32, 8.999999e9, "9e9");
995		try check(f32, 3.4366717e10, "3.436672e10");
996		try check(f32, 3.0540412e5, "3.0540412e5");
997		try check(f32, 8.0990312e3, "8.0990312e3");
998		try check(f32, 2.4414062e-4, "2.4414062e-4");
999		try check(f32, 2.4414062e-3, "2.4414062e-3");
1000		try check(f32, 4.3945312e-3, "4.3945312e-3");
1001		try check(f32, 6.3476562e-3, "6.3476562e-3");
1002		try check(f32, 4.7223665e21, "4.7223665e21");
1003		try check(f32, 8388608.0, "8.388608e6");
1004		try check(f32, 1.6777216e7, "1.6777216e7");
1005		try check(f32, 3.3554436e7, "3.3554436e7");
1006		try check(f32, 6.7131496e7, "6.7131496e7");
1007		try check(f32, 1.9310392e-38, "1.9310392e-38");
1008		try check(f32, -2.47e-43, "-2.47e-43");
1009		try check(f32, 1.993244e-38, "1.993244e-38");
1010		try check(f32, 4103.9003, "4.1039004e3");
1011		try check(f32, 5.3399997e9, "5.3399997e9");
1012		try check(f32, 6.0898e-39, "6.0898e-39");
1013		try check(f32, 0.0010310042, "1.0310042e-3");
1014		try check(f32, 2.8823261e17, "2.882326e17");
1015		try check(f32, 7.038531e-26, "7.038531e-26");
1016		try check(f32, 9.2234038e17, "9.223404e17");
1017		try check(f32, 6.7108872e7, "6.710887e7");
1018		try check(f32, 1.0e-44, "1e-44");
1019		try check(f32, 2.816025e14, "2.816025e14");
1020		try check(f32, 9.223372e18, "9.223372e18");
1021		try check(f32, 1.5846085e29, "1.5846086e29");
1022		try check(f32, 1.1811161e19, "1.1811161e19");
1023		try check(f32, 5.368709e18, "5.368709e18");
1024		try check(f32, 4.6143165e18, "4.6143166e18");
1025		try check(f32, 0.007812537, "7.812537e-3");
1026		try check(f32, 1.4e-45, "1e-45");
1027		try check(f32, 1.18697724e20, "1.18697725e20");
1028		try check(f32, 1.00014165e-36, "1.00014165e-36");
1029		try check(f32, 200.0, "2e2");
1030		try check(f32, 3.3554432e7, "3.3554432e7");
1031
1032		try check(f32, 1.0, "1e0");
1033		try check(f32, 1.2, "1.2e0");
1034		try check(f32, 1.23, "1.23e0");
1035		try check(f32, 1.234, "1.234e0");
1036		try check(f32, 1.2345, "1.2345e0");
1037		try check(f32, 1.23456, "1.23456e0");
1038		try check(f32, 1.234567, "1.234567e0");
1039		try check(f32, 1.2345678, "1.2345678e0");
1040		try check(f32, 1.23456735e-36, "1.23456735e-36");
1041		}
1042
1043		test "format f64" {
1044		try check(f64, 0.0, "0e0");
1045		try check(f64, -0.0, "-0e0");
1046		try check(f64, 1.0, "1e0");
1047		try check(f64, -1.0, "-1e0");
1048		try check(f64, std.math.nan(f64), "nan");
1049		try check(f64, std.math.inf(f64), "inf");
1050		try check(f64, -std.math.inf(f64), "-inf");
1051		try check(f64, 2.2250738585072014e-308, "2.2250738585072014e-308");
1052		try check(f64, @bitCast(@as(u64, 0x7fefffffffffffff)), "1.7976931348623157e308");
1053		try check(f64, @bitCast(@as(u64, 1)), "5e-324");
1054		try check(f64, 2.98023223876953125e-8, "2.9802322387695312e-8");
1055		try check(f64, -2.109808898695963e16, "-2.109808898695963e16");
1056		try check(f64, 4.940656e-318, "4.940656e-318");
1057		try check(f64, 1.18575755e-316, "1.18575755e-316");
1058		try check(f64, 2.989102097996e-312, "2.989102097996e-312");
1059		try check(f64, 9.0608011534336e15, "9.0608011534336e15");
1060		try check(f64, 4.708356024711512e18, "4.708356024711512e18");
1061		try check(f64, 9.409340012568248e18, "9.409340012568248e18");
1062		try check(f64, 1.2345678, "1.2345678e0");
1063		try check(f64, @bitCast(@as(u64, 0x4830f0cf064dd592)), "5.764607523034235e39");
1064		try check(f64, @bitCast(@as(u64, 0x4840f0cf064dd592)), "1.152921504606847e40");
1065		try check(f64, @bitCast(@as(u64, 0x4850f0cf064dd592)), "2.305843009213694e40");
1066
1067		try check(f64, 1, "1e0");
1068		try check(f64, 1.2, "1.2e0");
1069		try check(f64, 1.23, "1.23e0");
1070		try check(f64, 1.234, "1.234e0");
1071		try check(f64, 1.2345, "1.2345e0");
1072		try check(f64, 1.23456, "1.23456e0");
1073		try check(f64, 1.234567, "1.234567e0");
1074		try check(f64, 1.2345678, "1.2345678e0");
1075		try check(f64, 1.23456789, "1.23456789e0");
1076		try check(f64, 1.234567895, "1.234567895e0");
1077		try check(f64, 1.2345678901, "1.2345678901e0");
1078		try check(f64, 1.23456789012, "1.23456789012e0");
1079		try check(f64, 1.234567890123, "1.234567890123e0");
1080		try check(f64, 1.2345678901234, "1.2345678901234e0");
1081		try check(f64, 1.23456789012345, "1.23456789012345e0");
1082		try check(f64, 1.234567890123456, "1.234567890123456e0");
1083		try check(f64, 1.2345678901234567, "1.2345678901234567e0");
1084
1085		try check(f64, 4.294967294, "4.294967294e0");
1086		try check(f64, 4.294967295, "4.294967295e0");
1087		try check(f64, 4.294967296, "4.294967296e0");
1088		try check(f64, 4.294967297, "4.294967297e0");
1089		try check(f64, 4.294967298, "4.294967298e0");
1090		}
1091
1092		test "format f80" {
1093		try check(f80, 0.0, "0e0");
1094		try check(f80, -0.0, "-0e0");
1095		try check(f80, 1.0, "1e0");
1096		try check(f80, -1.0, "-1e0");
1097		try check(f80, std.math.nan(f80), "nan");
1098		try check(f80, std.math.inf(f80), "inf");
1099		try check(f80, -std.math.inf(f80), "-inf");
1100
1101		try check(f80, 2.2250738585072014e-308, "2.2250738585072014e-308");
1102		try check(f80, 2.98023223876953125e-8, "2.98023223876953125e-8");
1103		try check(f80, -2.109808898695963e16, "-2.109808898695963e16");
1104		try check(f80, 4.940656e-318, "4.940656e-318");
1105		try check(f80, 1.18575755e-316, "1.18575755e-316");
1106		try check(f80, 2.989102097996e-312, "2.989102097996e-312");
1107		try check(f80, 9.0608011534336e15, "9.0608011534336e15");
1108		try check(f80, 4.708356024711512e18, "4.708356024711512e18");
1109		try check(f80, 9.409340012568248e18, "9.409340012568248e18");
1110		try check(f80, 1.2345678, "1.2345678e0");
1111		}
1112
1113		test "format f128" {
1114		try check(f128, 0.0, "0e0");
1115		try check(f128, -0.0, "-0e0");
1116		try check(f128, 1.0, "1e0");
1117		try check(f128, -1.0, "-1e0");
1118		try check(f128, std.math.nan(f128), "nan");
1119		try check(f128, std.math.inf(f128), "inf");
1120		try check(f128, -std.math.inf(f128), "-inf");
1121
1122		try check(f128, 2.2250738585072014e-308, "2.2250738585072014e-308");
1123		try check(f128, 2.98023223876953125e-8, "2.98023223876953125e-8");
1124		try check(f128, -2.109808898695963e16, "-2.109808898695963e16");
1125		try check(f128, 4.940656e-318, "4.940656e-318");
1126		try check(f128, 1.18575755e-316, "1.18575755e-316");
1127		try check(f128, 2.989102097996e-312, "2.989102097996e-312");
1128		try check(f128, 9.0608011534336e15, "9.0608011534336e15");
1129		try check(f128, 4.708356024711512e18, "4.708356024711512e18");
1130		try check(f128, 9.409340012568248e18, "9.409340012568248e18");
1131		try check(f128, 1.2345678, "1.2345678e0");
1132		}
1133
1134		test "format float to decimal with zero precision" {
1135		try expectFmt("5", "{d:.0}", .{5});
1136		try expectFmt("6", "{d:.0}", .{6});
1137		try expectFmt("7", "{d:.0}", .{7});
1138		try expectFmt("8", "{d:.0}", .{8});
1139		}