commit 31791ae15bfa8590cb235ce9d7c87a97d5136eef (tree)
parent afdc41cfd61db23f545d9239b61695e2ae991713
Author: Marc Tiehuis <marc@tiehu.is>
Date: Thu, 21 Mar 2024 13:57:57 +1300
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
Diffstat:
4 files changed, 1150 insertions(+), 1147 deletions(-)
diff --git a/CMakeLists.txt b/CMakeLists.txt
@@ -235,7 +235,7 @@ set(ZIG_STAGE2_SOURCES
"${CMAKE_SOURCE_DIR}/lib/std/elf.zig"
"${CMAKE_SOURCE_DIR}/lib/std/fifo.zig"
"${CMAKE_SOURCE_DIR}/lib/std/fmt.zig"
- "${CMAKE_SOURCE_DIR}/lib/std/fmt/ryu128.zig"
+ "${CMAKE_SOURCE_DIR}/lib/std/fmt/format_float.zig"
"${CMAKE_SOURCE_DIR}/lib/std/fmt/parse_float.zig"
"${CMAKE_SOURCE_DIR}/lib/std/fs.zig"
"${CMAKE_SOURCE_DIR}/lib/std/fs/AtomicFile.zig"
diff --git a/lib/std/fmt.zig b/lib/std/fmt.zig
@@ -9,7 +9,6 @@ const assert = std.debug.assert;
const mem = std.mem;
const unicode = std.unicode;
const meta = std.meta;
-const ryu128 = @import("fmt/ryu128.zig");
const lossyCast = std.math.lossyCast;
const expectFmt = std.testing.expectFmt;
@@ -757,21 +756,25 @@ pub fn formatIntValue(
return formatInt(int_value, base, case, options, writer);
}
+pub const format_float = @import("fmt/format_float.zig");
+pub const formatFloat = format_float.formatFloat;
+pub const FormatFloatError = format_float.FormatError;
+
fn formatFloatValue(
value: anytype,
comptime fmt: []const u8,
options: FormatOptions,
writer: anytype,
) !void {
- var buf: [ryu128.bufferSize(.decimal, f64)]u8 = undefined;
+ var buf: [format_float.bufferSize(.decimal, f64)]u8 = undefined;
if (fmt.len == 0 or comptime std.mem.eql(u8, fmt, "e")) {
- const s = ryu128.format(&buf, value, .{ .mode = .scientific, .precision = options.precision }) catch |err| switch (err) {
+ const s = formatFloat(&buf, value, .{ .mode = .scientific, .precision = options.precision }) catch |err| switch (err) {
error.BufferTooSmall => "(float)",
};
return formatBuf(s, options, writer);
} else if (comptime std.mem.eql(u8, fmt, "d")) {
- const s = ryu128.format(&buf, value, .{ .mode = .decimal, .precision = options.precision }) catch |err| switch (err) {
+ const s = formatFloat(&buf, value, .{ .mode = .decimal, .precision = options.precision }) catch |err| switch (err) {
error.BufferTooSmall => "(float)",
};
return formatBuf(s, options, writer);
@@ -787,7 +790,7 @@ fn formatFloatValue(
}
test {
- _ = &ryu128;
+ _ = &format_float;
}
pub const Case = enum { lower, upper };
@@ -890,7 +893,7 @@ fn formatSizeImpl(comptime base: comptime_int) type {
return formatBuf("0B", options, writer);
}
// The worst case in terms of space needed is 32 bytes + 3 for the suffix.
- var buf: [ryu128.min_buffer_size + 3]u8 = undefined;
+ var buf: [format_float.min_buffer_size + 3]u8 = undefined;
const mags_si = " kMGTPEZY";
const mags_iec = " KMGTPEZY";
@@ -908,7 +911,7 @@ fn formatSizeImpl(comptime base: comptime_int) type {
else => unreachable,
};
- const s = ryu128.format(&buf, new_value, .{ .mode = .decimal, .precision = options.precision }) catch |err| switch (err) {
+ const s = formatFloat(&buf, new_value, .{ .mode = .decimal, .precision = options.precision }) catch |err| switch (err) {
error.BufferTooSmall => unreachable,
};
diff --git a/lib/std/fmt/format_float.zig b/lib/std/fmt/format_float.zig
@@ -0,0 +1,1139 @@
+//! This file implements the ryu floating point conversion algorithm:
+//! https://dl.acm.org/doi/pdf/10.1145/3360595
+
+const std = @import("std");
+const expectFmt = std.testing.expectFmt;
+
+const special_exponent = 0x7fffffff;
+
+/// Any buffer used for `format` must be at least this large. This is asserted. A runtime check will
+/// additionally be performed if more bytes are required.
+pub const min_buffer_size = 53;
+
+/// Returns the minimum buffer size needed to print every float of a specific type and format.
+pub fn bufferSize(comptime mode: Format, comptime T: type) comptime_int {
+ comptime std.debug.assert(@typeInfo(T) == .Float);
+ return switch (mode) {
+ .scientific => 53,
+ // Based on minimum subnormal values.
+ .decimal => switch (@bitSizeOf(T)) {
+ 16 => @max(15, min_buffer_size),
+ 32 => 55,
+ 64 => 347,
+ 80 => 4996,
+ 128 => 5011,
+ else => unreachable,
+ },
+ };
+}
+
+pub const FormatError = error{
+ BufferTooSmall,
+};
+
+pub const Format = enum {
+ scientific,
+ decimal,
+};
+
+pub const FormatOptions = struct {
+ mode: Format = .scientific,
+ precision: ?usize = null,
+};
+
+/// Format a floating-point value and write it to buffer. Returns a slice to the buffer containing
+/// the string representation.
+///
+/// Full precision is the default. Any full precision float can be reparsed with std.fmt.parseFloat
+/// unambiguously.
+///
+/// Scientific mode is recommended generally as the output is more compact and any type can be
+/// written in full precision using a buffer of only `min_buffer_size`.
+///
+/// When printing full precision decimals, use `bufferSize` to get the required space. It is
+/// recommended to bound decimal output with a fixed precision to reduce the required buffer size.
+pub fn formatFloat(buf: []u8, v_: anytype, options: FormatOptions) FormatError![]const u8 {
+ const v = switch (@TypeOf(v_)) {
+ // comptime_float internally is a f128; this preserves precision.
+ comptime_float => @as(f128, v_),
+ else => v_,
+ };
+
+ const T = @TypeOf(v);
+ comptime std.debug.assert(@typeInfo(T) == .Float);
+ const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
+
+ const has_explicit_leading_bit = std.math.floatMantissaBits(T) - std.math.floatFractionalBits(T) != 0;
+ const d = binaryToDecimal(@as(I, @bitCast(v)), std.math.floatMantissaBits(T), std.math.floatExponentBits(T), has_explicit_leading_bit);
+
+ return switch (options.mode) {
+ .scientific => formatScientific(buf, d, options.precision),
+ .decimal => formatDecimal(buf, d, options.precision),
+ };
+}
+
+pub const FloatDecimal128 = struct {
+ mantissa: u128,
+ exponent: i32,
+ sign: bool,
+};
+
+fn copySpecialStr(buf: []u8, f: FloatDecimal128) []const u8 {
+ if (f.sign) {
+ buf[0] = '-';
+ }
+ const offset: usize = @intFromBool(f.sign);
+ if (f.mantissa != 0) {
+ @memcpy(buf[offset..][0..3], "nan");
+ return buf[0 .. 3 + offset];
+ }
+ @memcpy(buf[offset..][0..3], "inf");
+ return buf[0 .. 3 + offset];
+}
+
+fn writeDecimal(buf: []u8, value: anytype, count: usize) void {
+ var i: usize = 0;
+
+ while (i + 2 < count) : (i += 2) {
+ const c: u8 = @intCast(value.* % 100);
+ value.* /= 100;
+ const d = std.fmt.digits2(c);
+ buf[count - i - 1] = d[1];
+ buf[count - i - 2] = d[0];
+ }
+
+ while (i < count) : (i += 1) {
+ const c: u8 = @intCast(value.* % 10);
+ value.* /= 10;
+ buf[count - i - 1] = '0' + c;
+ }
+}
+
+fn isPowerOf10(n_: u128) bool {
+ var n = n_;
+ while (n != 0) : (n /= 10) {
+ if (n % 10 != 0) return false;
+ }
+ return true;
+}
+
+const RoundMode = enum {
+ /// 1234.56 = precision 2
+ decimal,
+ /// 1.23456e3 = precision 5
+ scientific,
+};
+
+fn round(f: FloatDecimal128, mode: RoundMode, precision: usize) FloatDecimal128 {
+ var round_digit: usize = 0;
+ var output = f.mantissa;
+ var exp = f.exponent;
+ const olength = decimalLength(output);
+
+ switch (mode) {
+ .decimal => {
+ if (f.exponent > 0) {
+ round_digit = (olength - 1) + precision + @as(usize, @intCast(f.exponent));
+ } else {
+ const min_exp_required = @as(usize, @intCast(-f.exponent));
+ if (precision + olength > min_exp_required) {
+ round_digit = precision + olength - min_exp_required;
+ }
+ }
+ },
+ .scientific => {
+ round_digit = 1 + precision;
+ },
+ }
+
+ if (round_digit < olength) {
+ var nlength = olength;
+ for (round_digit + 1..olength) |_| {
+ output /= 10;
+ exp += 1;
+ nlength -= 1;
+ }
+
+ if (output % 10 >= 5) {
+ output /= 10;
+ output += 1;
+ exp += 1;
+
+ // e.g. 9999 -> 10000
+ if (isPowerOf10(output)) {
+ output /= 10;
+ exp += 1;
+ }
+ }
+ }
+
+ return .{
+ .mantissa = output,
+ .exponent = exp,
+ .sign = f.sign,
+ };
+}
+
+/// Write a FloatDecimal128 to a buffer in scientific form.
+///
+/// The buffer provided must be greater than `min_buffer_size` in length. If no precision is
+/// specified, this function will never return an error. If a precision is specified, up to
+/// `8 + precision` bytes will be written to the buffer. An error will be returned if the content
+/// will not fit.
+///
+/// It is recommended to bound decimal formatting with an exact precision.
+pub fn formatScientific(buf: []u8, f_: FloatDecimal128, precision: ?usize) FormatError![]const u8 {
+ std.debug.assert(buf.len >= min_buffer_size);
+ var f = f_;
+
+ if (f.exponent == special_exponent) {
+ return copySpecialStr(buf, f);
+ }
+
+ if (precision) |prec| {
+ f = round(f, .scientific, prec);
+ }
+
+ var output = f.mantissa;
+ const olength = decimalLength(output);
+
+ if (precision) |prec| {
+ // fixed bound: sign(1) + leading_digit(1) + point(1) + exp_sign(1) + exp_max(4)
+ const req_bytes = 8 + prec;
+ if (buf.len < req_bytes) {
+ return error.BufferTooSmall;
+ }
+ }
+
+ // Step 5: Print the scientific representation
+ var index: usize = 0;
+ if (f.sign) {
+ buf[index] = '-';
+ index += 1;
+ }
+
+ // 1.12345
+ writeDecimal(buf[index + 2 ..], &output, olength - 1);
+ buf[index] = '0' + @as(u8, @intCast(output % 10));
+ buf[index + 1] = '.';
+ index += 2;
+ const dp_index = index;
+ if (olength > 1) index += olength - 1 else index -= 1;
+
+ if (precision) |prec| {
+ index += @intFromBool(olength == 1);
+ if (prec > olength - 1) {
+ const len = prec - (olength - 1);
+ @memset(buf[index..][0..len], '0');
+ index += len;
+ } else {
+ index = dp_index + prec - @intFromBool(prec == 0);
+ }
+ }
+
+ // e100
+ buf[index] = 'e';
+ index += 1;
+ var exp = f.exponent + @as(i32, @intCast(olength)) - 1;
+ if (exp < 0) {
+ buf[index] = '-';
+ index += 1;
+ exp = -exp;
+ }
+ var uexp: u32 = @intCast(exp);
+ const elength = decimalLength(uexp);
+ writeDecimal(buf[index..], &uexp, elength);
+ index += elength;
+
+ return buf[0..index];
+}
+
+/// Write a FloatDecimal128 to a buffer in decimal form.
+///
+/// The buffer provided must be greater than `min_buffer_size` bytes in length. If no precision is
+/// specified, this may still return an error. If precision is specified, `2 + precision` bytes will
+/// always be written.
+pub fn formatDecimal(buf: []u8, f_: FloatDecimal128, precision: ?usize) FormatError![]const u8 {
+ std.debug.assert(buf.len >= min_buffer_size);
+ var f = f_;
+
+ if (f.exponent == special_exponent) {
+ return copySpecialStr(buf, f);
+ }
+
+ if (precision) |prec| {
+ f = round(f, .decimal, prec);
+ }
+
+ var output = f.mantissa;
+ const olength = decimalLength(output);
+
+ // fixed bound: leading_digit(1) + point(1)
+ const req_bytes = if (f.exponent >= 0)
+ 2 + @abs(f.exponent) + olength + (precision orelse 0)
+ else
+ 2 + @max(@abs(f.exponent) + olength, precision orelse 0);
+ if (buf.len < req_bytes) {
+ return error.BufferTooSmall;
+ }
+
+ // Step 5: Print the decimal representation
+ var index: usize = 0;
+ if (f.sign) {
+ buf[index] = '-';
+ index += 1;
+ }
+
+ const dp_offset = f.exponent + cast_i32(olength);
+ if (dp_offset <= 0) {
+ // 0.000001234
+ buf[index] = '0';
+ buf[index + 1] = '.';
+ index += 2;
+ const dp_index = index;
+
+ const dp_poffset: u32 = @intCast(-dp_offset);
+ @memset(buf[index..][0..dp_poffset], '0');
+ index += dp_poffset;
+ writeDecimal(buf[index..], &output, olength);
+ index += olength;
+
+ if (precision) |prec| {
+ const dp_written = index - dp_index;
+ if (prec > dp_written) {
+ @memset(buf[index..][0 .. prec - dp_written], '0');
+ }
+ index = dp_index + prec - @intFromBool(prec == 0);
+ }
+ } else {
+ // 123456000
+ const dp_uoffset: usize = @intCast(dp_offset);
+ if (dp_uoffset >= olength) {
+ writeDecimal(buf[index..], &output, olength);
+ index += olength;
+ @memset(buf[index..][0 .. dp_uoffset - olength], '0');
+ index += dp_uoffset - olength;
+
+ if (precision) |prec| {
+ if (prec != 0) {
+ buf[index] = '.';
+ index += 1;
+ @memset(buf[index..][0..prec], '0');
+ index += prec;
+ }
+ }
+ } else {
+ // 12345.6789
+ writeDecimal(buf[index + dp_uoffset + 1 ..], &output, olength - dp_uoffset);
+ buf[index + dp_uoffset] = '.';
+ const dp_index = index + dp_uoffset + 1;
+ writeDecimal(buf[index..], &output, dp_uoffset);
+ index += olength + 1;
+
+ if (precision) |prec| {
+ const dp_written = olength - dp_uoffset;
+ if (prec > dp_written) {
+ @memset(buf[index..][0 .. prec - dp_written], '0');
+ }
+ index = dp_index + prec - @intFromBool(prec == 0);
+ }
+ }
+ }
+
+ return buf[0..index];
+}
+
+fn cast_i32(v: anytype) i32 {
+ return @intCast(v);
+}
+
+/// Convert a binary float representation to decimal.
+pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explicit_leading_bit: bool) FloatDecimal128 {
+ const bias = (@as(u32, 1) << (exponent_bits - 1)) - 1;
+ const ieee_sign = ((bits >> (mantissa_bits + exponent_bits)) & 1) != 0;
+ const ieee_mantissa = bits & ((@as(u128, 1) << mantissa_bits) - 1);
+ const ieee_exponent: u32 = @intCast((bits >> mantissa_bits) & ((@as(u128, 1) << exponent_bits) - 1));
+
+ if (ieee_exponent == 0 and ieee_mantissa == 0) {
+ return .{
+ .mantissa = 0,
+ .exponent = 0,
+ .sign = ieee_sign,
+ };
+ }
+ if (ieee_exponent == ((@as(u32, 1) << exponent_bits) - 1)) {
+ return .{
+ .mantissa = if (explicit_leading_bit) ieee_mantissa & ((@as(u128, 1) << (mantissa_bits - 1)) - 1) else ieee_mantissa,
+ .exponent = 0x7fffffff,
+ .sign = ieee_sign,
+ };
+ }
+
+ var e2: i32 = undefined;
+ var m2: u128 = undefined;
+ if (explicit_leading_bit) {
+ if (ieee_exponent == 0) {
+ e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
+ } else {
+ e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
+ }
+ m2 = ieee_mantissa;
+ } else {
+ if (ieee_exponent == 0) {
+ e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
+ m2 = ieee_mantissa;
+ } else {
+ e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
+ m2 = (@as(u128, 1) << mantissa_bits) | ieee_mantissa;
+ }
+ }
+ const even = (m2 & 1) == 0;
+ const accept_bounds = even;
+
+ // Step 2: Determine the interval of legal decimal representations.
+ const mv = 4 * m2;
+ const mm_shift: u1 = @intFromBool((ieee_mantissa != if (explicit_leading_bit) (@as(u128, 1) << (mantissa_bits - 1)) else 0) or (ieee_exponent == 0));
+
+ // Step 3: Convert to a decimal power base using 128-bit arithmetic.
+ var vr: u128 = undefined;
+ var vp: u128 = undefined;
+ var vm: u128 = undefined;
+ var e10: i32 = undefined;
+ var vm_is_trailing_zeros = false;
+ var vr_is_trailing_zeros = false;
+ if (e2 >= 0) {
+ const q: u32 = log10Pow2(@intCast(e2)) - @intFromBool(e2 > 3);
+ e10 = cast_i32(q);
+ const k: i32 = @intCast(FLOAT_128_POW5_INV_BITCOUNT + pow5Bits(q) - 1);
+ const i: u32 = @intCast(-e2 + cast_i32(q) + k);
+
+ const pow5 = computeInvPow5(q);
+ vr = mulShift(4 * m2, &pow5, i);
+ vp = mulShift(4 * m2 + 2, &pow5, i);
+ vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, i);
+
+ if (q <= 55) {
+ if (mv % 5 == 0) {
+ vr_is_trailing_zeros = multipleOfPowerOf5(mv, q -% 1);
+ } else if (accept_bounds) {
+ vm_is_trailing_zeros = multipleOfPowerOf5(mv - 1 - mm_shift, q);
+ } else {
+ vp -= @intFromBool(multipleOfPowerOf5(mv + 2, q));
+ }
+ }
+ } else {
+ const q: u32 = log10Pow5(@intCast(-e2)) - @intFromBool(-e2 > 1);
+ e10 = cast_i32(q) + e2;
+ const i: i32 = -e2 - cast_i32(q);
+ const k: i32 = cast_i32(pow5Bits(@intCast(i))) - FLOAT_128_POW5_BITCOUNT;
+ const j: u32 = @intCast(cast_i32(q) - k);
+
+ const pow5 = computePow5(@intCast(i));
+ vr = mulShift(4 * m2, &pow5, j);
+ vp = mulShift(4 * m2 + 2, &pow5, j);
+ vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, j);
+
+ if (q <= 1) {
+ vr_is_trailing_zeros = true;
+ if (accept_bounds) {
+ vm_is_trailing_zeros = mm_shift == 1;
+ } else {
+ vp -= 1;
+ }
+ } else if (q < 127) {
+ vr_is_trailing_zeros = multipleOfPowerOf2(mv, q - 1);
+ }
+ }
+
+ // Step 4: Find the shortest decimal representation in the interval of legal representations.
+ var removed: u32 = 0;
+ var last_removed_digit: u8 = 0;
+
+ while (vp / 10 > vm / 10) {
+ vm_is_trailing_zeros = vm_is_trailing_zeros and vm % 10 == 0;
+ vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
+ last_removed_digit = @intCast(vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ removed += 1;
+ }
+
+ if (vm_is_trailing_zeros) {
+ while (vm % 10 == 0) {
+ vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
+ last_removed_digit = @intCast(vr % 10);
+ vr /= 10;
+ vp /= 10;
+ vm /= 10;
+ removed += 1;
+ }
+ }
+
+ if (vr_is_trailing_zeros and (last_removed_digit == 5) and (vr % 2 == 0)) {
+ last_removed_digit = 4;
+ }
+
+ return .{
+ .mantissa = vr + @intFromBool((vr == vm and (!accept_bounds or !vm_is_trailing_zeros)) or last_removed_digit >= 5),
+ .exponent = e10 + cast_i32(removed),
+ .sign = ieee_sign,
+ };
+}
+
+fn decimalLength(v: u128) u32 {
+ const LARGEST_POW10 = (@as(u128, 5421010862427522170) << 64) | 687399551400673280;
+ var p10 = LARGEST_POW10;
+ var i: u32 = 39;
+ while (i > 0) : (i -= 1) {
+ if (v >= p10) return i;
+ p10 /= 10;
+ }
+ return 1;
+}
+
+// floor(log_10(2^e))
+fn log10Pow2(e: u32) u32 {
+ std.debug.assert(e <= 1 << 15);
+ return @intCast((@as(u64, @intCast(e)) * 169464822037455) >> 49);
+}
+
+// floor(log_10(5^e))
+fn log10Pow5(e: u32) u32 {
+ std.debug.assert(e <= 1 << 15);
+ return @intCast((@as(u64, @intCast(e)) * 196742565691928) >> 48);
+}
+
+// if (e == 0) 1 else ceil(log_2(5^e))
+fn pow5Bits(e: u32) u32 {
+ std.debug.assert(e <= 1 << 15);
+ return @intCast(((@as(u64, @intCast(e)) * 163391164108059) >> 46) + 1);
+}
+
+fn pow5Factor(value_: u128) u32 {
+ var count: u32 = 0;
+ var value = value_;
+ while (value > 0) : ({
+ count += 1;
+ value /= 5;
+ }) {
+ if (value % 5 != 0) return count;
+ }
+ return 0;
+}
+
+fn multipleOfPowerOf5(value: u128, p: u32) bool {
+ return pow5Factor(value) >= p;
+}
+
+fn multipleOfPowerOf2(value: u128, p: u32) bool {
+ return (value & ((@as(u128, 1) << @as(u7, @intCast(p))) - 1)) == 0;
+}
+
+fn computeInvPow5(i: u32) [4]u64 {
+ const base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
+ const base2 = base * POW5_TABLE_SIZE;
+ const mul = &GENERIC_POW5_INV_SPLIT[base]; // 1 / 5^base2
+ if (i == base2) {
+ return .{ mul[0] + 1, mul[1], mul[2], mul[3] };
+ } else {
+ const offset = base2 - i;
+ const m = &GENERIC_POW5_TABLE[offset]; // 5^offset
+ const delta = pow5Bits(base2) - pow5Bits(i);
+
+ const shift: u6 = @intCast(2 * (i % 32));
+ const corr: u32 = @intCast(((POW5_INV_ERRORS[i / 32] >> shift) & 3) + 1);
+ return mul_128_256_shift(m, mul, delta, corr);
+ }
+}
+
+fn computePow5(i: u32) [4]u64 {
+ const base = i / POW5_TABLE_SIZE;
+ const base2 = base * POW5_TABLE_SIZE;
+ const mul = &GENERIC_POW5_SPLIT[base];
+ if (i == base2) {
+ return mul.*;
+ } else {
+ const offset = i - base2;
+ const m = &GENERIC_POW5_TABLE[offset];
+ const delta = pow5Bits(i) - pow5Bits(base2);
+
+ const shift: u6 = @intCast(2 * (i % 32));
+ const corr: u32 = @intCast((POW5_ERRORS[i / 32] >> shift) & 3);
+ return mul_128_256_shift(m, mul, delta, corr);
+ }
+}
+
+fn mulShift(m: u128, mul: *const [4]u64, j: u32) u128 {
+ std.debug.assert(j > 128);
+ const a: [2]u64 = .{ @truncate(m), @truncate(m >> 64) };
+ const r = mul_128_256_shift(&a, mul, j, 0);
+ return (@as(u128, r[1]) << 64) | r[0];
+}
+
+fn mul_128_256_shift(a: *const [2]u64, b: *const [4]u64, shift: u32, corr: u32) [4]u64 {
+ std.debug.assert(shift > 0);
+ std.debug.assert(shift < 256);
+
+ const b00 = @as(u128, a[0]) * b[0];
+ const b01 = @as(u128, a[0]) * b[1];
+ const b02 = @as(u128, a[0]) * b[2];
+ const b03 = @as(u128, a[0]) * b[3];
+ const b10 = @as(u128, a[1]) * b[0];
+ const b11 = @as(u128, a[1]) * b[1];
+ const b12 = @as(u128, a[1]) * b[2];
+ const b13 = @as(u128, a[1]) * b[3];
+
+ const s0 = b00;
+ const s1 = b01 +% b10;
+ const c1: u128 = @intFromBool(s1 < b01);
+ const s2 = b02 +% b11;
+ const c2: u128 = @intFromBool(s2 < b02);
+ const s3 = b03 +% b12;
+ const c3: u128 = @intFromBool(s3 < b03);
+
+ const p0 = s0 +% (s1 << 64);
+ const d0: u128 = @intFromBool(p0 < b00);
+ const q1 = s2 +% (s1 >> 64) +% (s3 << 64);
+ const d1: u128 = @intFromBool(q1 < s2);
+ const p1 = q1 +% (c1 << 64) +% d0;
+ const d2: u128 = @intFromBool(p1 < q1);
+ const p2 = b13 +% (s3 >> 64) +% c2 +% (c3 << 64) +% d1 +% d2;
+
+ var r0: u128 = undefined;
+ var r1: u128 = undefined;
+ if (shift < 128) {
+ const cshift: u7 = @intCast(shift);
+ const sshift: u7 = @intCast(128 - shift);
+ r0 = corr +% ((p0 >> cshift) | (p1 << sshift));
+ r1 = ((p1 >> cshift) | (p2 << sshift)) +% @intFromBool(r0 < corr);
+ } else if (shift == 128) {
+ r0 = corr +% p1;
+ r1 = p2 +% @intFromBool(r0 < corr);
+ } else {
+ const ashift: u7 = @intCast(shift - 128);
+ const sshift: u7 = @intCast(256 - shift);
+ r0 = corr +% ((p1 >> ashift) | (p2 << sshift));
+ r1 = (p2 >> ashift) +% @intFromBool(r0 < corr);
+ }
+
+ return .{ @truncate(r0), @truncate(r0 >> 64), @truncate(r1), @truncate(r1 >> 64) };
+}
+
+// zig fmt: off
+//
+// 4.5KiB of tables.
+
+const FLOAT_128_POW5_INV_BITCOUNT = 249;
+const FLOAT_128_POW5_BITCOUNT = 249;
+const POW5_TABLE_SIZE = 56;
+
+const GENERIC_POW5_TABLE: [POW5_TABLE_SIZE][2]u64 = .{
+ .{ 1, 0 },
+ .{ 5, 0 },
+ .{ 25, 0 },
+ .{ 125, 0 },
+ .{ 625, 0 },
+ .{ 3125, 0 },
+ .{ 15625, 0 },
+ .{ 78125, 0 },
+ .{ 390625, 0 },
+ .{ 1953125, 0 },
+ .{ 9765625, 0 },
+ .{ 48828125, 0 },
+ .{ 244140625, 0 },
+ .{ 1220703125, 0 },
+ .{ 6103515625, 0 },
+ .{ 30517578125, 0 },
+ .{ 152587890625, 0 },
+ .{ 762939453125, 0 },
+ .{ 3814697265625, 0 },
+ .{ 19073486328125, 0 },
+ .{ 95367431640625, 0 },
+ .{ 476837158203125, 0 },
+ .{ 2384185791015625, 0 },
+ .{ 11920928955078125, 0 },
+ .{ 59604644775390625, 0 },
+ .{ 298023223876953125, 0 },
+ .{ 1490116119384765625, 0 },
+ .{ 7450580596923828125, 0 },
+ .{ 359414837200037393, 2 },
+ .{ 1797074186000186965, 10 },
+ .{ 8985370930000934825, 50 },
+ .{ 8033366502585570893, 252 },
+ .{ 3273344365508751233, 1262 },
+ .{ 16366721827543756165, 6310 },
+ .{ 8046632842880574361, 31554 },
+ .{ 3339676066983768573, 157772 },
+ .{ 16698380334918842865, 788860 },
+ .{ 9704925379756007861, 3944304 },
+ .{ 11631138751360936073, 19721522 },
+ .{ 2815461535676025517, 98607613 },
+ .{ 14077307678380127585, 493038065 },
+ .{ 15046306170771983077, 2465190328 },
+ .{ 1444554559021708921, 12325951644 },
+ .{ 7222772795108544605, 61629758220 },
+ .{ 17667119901833171409, 308148791101 },
+ .{ 14548623214327650581, 1540743955509 },
+ .{ 17402883850509598057, 7703719777548 },
+ .{ 13227442957709783821, 38518598887744 },
+ .{ 10796982567420264257, 192592994438723 },
+ .{ 17091424689682218053, 962964972193617 },
+ .{ 11670147153572883801, 4814824860968089 },
+ .{ 3010503546735764157, 24074124304840448 },
+ .{ 15052517733678820785, 120370621524202240 },
+ .{ 1475612373555897461, 601853107621011204 },
+ .{ 7378061867779487305, 3009265538105056020 },
+ .{ 18443565265187884909, 15046327690525280101 },
+};
+
+const GENERIC_POW5_SPLIT: [89][4]u64 = .{
+ .{ 0, 0, 0, 72057594037927936 },
+ .{ 0, 5206161169240293376, 4575641699882439235, 73468396926392969 },
+ .{ 3360510775605221349, 6983200512169538081, 4325643253124434363, 74906821675075173 },
+ .{ 11917660854915489451, 9652941469841108803, 946308467778435600, 76373409087490117 },
+ .{ 1994853395185689235, 16102657350889591545, 6847013871814915412, 77868710555449746 },
+ .{ 958415760277438274, 15059347134713823592, 7329070255463483331, 79393288266368765 },
+ .{ 2065144883315240188, 7145278325844925976, 14718454754511147343, 80947715414629833 },
+ .{ 8980391188862868935, 13709057401304208685, 8230434828742694591, 82532576417087045 },
+ .{ 432148644612782575, 7960151582448466064, 12056089168559840552, 84148467132788711 },
+ .{ 484109300864744403, 15010663910730448582, 16824949663447227068, 85795995087002057 },
+ .{ 14793711725276144220, 16494403799991899904, 10145107106505865967, 87475779699624060 },
+ .{ 15427548291869817042, 12330588654550505203, 13980791795114552342, 89188452518064298 },
+ .{ 9979404135116626552, 13477446383271537499, 14459862802511591337, 90934657454687378 },
+ .{ 12385121150303452775, 9097130814231585614, 6523855782339765207, 92715051028904201 },
+ .{ 1822931022538209743, 16062974719797586441, 3619180286173516788, 94530302614003091 },
+ .{ 12318611738248470829, 13330752208259324507, 10986694768744162601, 96381094688813589 },
+ .{ 13684493829640282333, 7674802078297225834, 15208116197624593182, 98268123094297527 },
+ .{ 5408877057066295332, 6470124174091971006, 15112713923117703147, 100192097295163851 },
+ .{ 11407083166564425062, 18189998238742408185, 4337638702446708282, 102153740646605557 },
+ .{ 4112405898036935485, 924624216579956435, 14251108172073737125, 104153790666259019 },
+ .{ 16996739107011444789, 10015944118339042475, 2395188869672266257, 106192999311487969 },
+ .{ 4588314690421337879, 5339991768263654604, 15441007590670620066, 108272133262096356 },
+ .{ 2286159977890359825, 14329706763185060248, 5980012964059367667, 110391974208576409 },
+ .{ 9654767503237031099, 11293544302844823188, 11739932712678287805, 112553319146000238 },
+ .{ 11362964448496095896, 7990659682315657680, 251480263940996374, 114756980673665505 },
+ .{ 1423410421096377129, 14274395557581462179, 16553482793602208894, 117003787300607788 },
+ .{ 2070444190619093137, 11517140404712147401, 11657844572835578076, 119294583757094535 },
+ .{ 7648316884775828921, 15264332483297977688, 247182277434709002, 121630231312217685 },
+ .{ 17410896758132241352, 10923914482914417070, 13976383996795783649, 124011608097704390 },
+ .{ 9542674537907272703, 3079432708831728956, 14235189590642919676, 126439609438067572 },
+ .{ 10364666969937261816, 8464573184892924210, 12758646866025101190, 128915148187220428 },
+ .{ 14720354822146013883, 11480204489231511423, 7449876034836187038, 131439155071681461 },
+ .{ 1692907053653558553, 17835392458598425233, 1754856712536736598, 134012579040499057 },
+ .{ 5620591334531458755, 11361776175667106627, 13350215315297937856, 136636387622027174 },
+ .{ 17455759733928092601, 10362573084069962561, 11246018728801810510, 139311567287686283 },
+ .{ 2465404073814044982, 17694822665274381860, 1509954037718722697, 142039123822846312 },
+ .{ 2152236053329638369, 11202280800589637091, 16388426812920420176, 72410041352485523 },
+ .{ 17319024055671609028, 10944982848661280484, 2457150158022562661, 73827744744583080 },
+ .{ 17511219308535248024, 5122059497846768077, 2089605804219668451, 75273205100637900 },
+ .{ 10082673333144031533, 14429008783411894887, 12842832230171903890, 76746965869337783 },
+ .{ 16196653406315961184, 10260180891682904501, 10537411930446752461, 78249581139456266 },
+ .{ 15084422041749743389, 234835370106753111, 16662517110286225617, 79781615848172976 },
+ .{ 8199644021067702606, 3787318116274991885, 7438130039325743106, 81343645993472659 },
+ .{ 12039493937039359765, 9773822153580393709, 5945428874398357806, 82936258850702722 },
+ .{ 984543865091303961, 7975107621689454830, 6556665988501773347, 84560053193370726 },
+ .{ 9633317878125234244, 16099592426808915028, 9706674539190598200, 86215639518264828 },
+ .{ 6860695058870476186, 4471839111886709592, 7828342285492709568, 87903640274981819 },
+ .{ 14583324717644598331, 4496120889473451238, 5290040788305728466, 89624690099949049 },
+ .{ 18093669366515003715, 12879506572606942994, 18005739787089675377, 91379436055028227 },
+ .{ 17997493966862379937, 14646222655265145582, 10265023312844161858, 93168537870790806 },
+ .{ 12283848109039722318, 11290258077250314935, 9878160025624946825, 94992668194556404 },
+ .{ 8087752761883078164, 5262596608437575693, 11093553063763274413, 96852512843287537 },
+ .{ 15027787746776840781, 12250273651168257752, 9290470558712181914, 98748771061435726 },
+ .{ 15003915578366724489, 2937334162439764327, 5404085603526796602, 100682155783835929 },
+ .{ 5225610465224746757, 14932114897406142027, 2774647558180708010, 102653393903748137 },
+ .{ 17112957703385190360, 12069082008339002412, 3901112447086388439, 104663226546146909 },
+ .{ 4062324464323300238, 3992768146772240329, 15757196565593695724, 106712409346361594 },
+ .{ 5525364615810306701, 11855206026704935156, 11344868740897365300, 108801712734172003 },
+ .{ 9274143661888462646, 4478365862348432381, 18010077872551661771, 110931922223466333 },
+ .{ 12604141221930060148, 8930937759942591500, 9382183116147201338, 113103838707570263 },
+ .{ 14513929377491886653, 1410646149696279084, 587092196850797612, 115318278760358235 },
+ .{ 2226851524999454362, 7717102471110805679, 7187441550995571734, 117576074943260147 },
+ .{ 5527526061344932763, 2347100676188369132, 16976241418824030445, 119878076118278875 },
+ .{ 6088479778147221611, 17669593130014777580, 10991124207197663546, 122225147767136307 },
+ .{ 11107734086759692041, 3391795220306863431, 17233960908859089158, 124618172316667879 },
+ .{ 7913172514655155198, 17726879005381242552, 641069866244011540, 127058049470587962 },
+ .{ 12596991768458713949, 15714785522479904446, 6035972567136116512, 129545696547750811 },
+ .{ 16901996933781815980, 4275085211437148707, 14091642539965169063, 132082048827034281 },
+ .{ 7524574627987869240, 15661204384239316051, 2444526454225712267, 134668059898975949 },
+ .{ 8199251625090479942, 6803282222165044067, 16064817666437851504, 137304702024293857 },
+ .{ 4453256673338111920, 15269922543084434181, 3139961729834750852, 139992966499426682 },
+ .{ 15841763546372731299, 3013174075437671812, 4383755396295695606, 142733864029230733 },
+ .{ 9771896230907310329, 4900659362437687569, 12386126719044266361, 72764212553486967 },
+ .{ 9420455527449565190, 1859606122611023693, 6555040298902684281, 74188850200884818 },
+ .{ 5146105983135678095, 2287300449992174951, 4325371679080264751, 75641380576797959 },
+ .{ 11019359372592553360, 8422686425957443718, 7175176077944048210, 77122349788024458 },
+ .{ 11005742969399620716, 4132174559240043701, 9372258443096612118, 78632314633490790 },
+ .{ 8887589641394725840, 8029899502466543662, 14582206497241572853, 80171842813591127 },
+ .{ 360247523705545899, 12568341805293354211, 14653258284762517866, 81741513143625247 },
+ .{ 12314272731984275834, 4740745023227177044, 6141631472368337539, 83341915771415304 },
+ .{ 441052047733984759, 7940090120939869826, 11750200619921094248, 84973652399183278 },
+ .{ 3436657868127012749, 9187006432149937667, 16389726097323041290, 86637336509772529 },
+ .{ 13490220260784534044, 15339072891382896702, 8846102360835316895, 88333593597298497 },
+ .{ 4125672032094859833, 158347675704003277, 10592598512749774447, 90063061402315272 },
+ .{ 12189928252974395775, 2386931199439295891, 7009030566469913276, 91826390151586454 },
+ .{ 9256479608339282969, 2844900158963599229, 11148388908923225596, 93624242802550437 },
+ .{ 11584393507658707408, 2863659090805147914, 9873421561981063551, 95457295292572042 },
+ .{ 13984297296943171390, 1931468383973130608, 12905719743235082319, 97326236793074198 },
+ .{ 5837045222254987499, 10213498696735864176, 14893951506257020749, 99231769968645227 },
+};
+
+// Unfortunately, the results are sometimes off by one or two. We use an additional
+// lookup table to store those cases and adjust the result.
+const POW5_ERRORS: [156]u64 = .{
+ 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9555596400000000,
+ 0x65a6569525565555, 0x4415551445449655, 0x5105015504144541, 0x65a69969a6965964,
+ 0x5054955969959656, 0x5105154515554145, 0x4055511051591555, 0x5500514455550115,
+ 0x0041140014145515, 0x1005440545511051, 0x0014405450411004, 0x0414440010500000,
+ 0x0044000440010040, 0x5551155000004001, 0x4554555454544114, 0x5150045544005441,
+ 0x0001111400054501, 0x6550955555554554, 0x1504159645559559, 0x4105055141454545,
+ 0x1411541410405454, 0x0415555044545555, 0x0014154115405550, 0x1540055040411445,
+ 0x0000000500000000, 0x5644000000000000, 0x1155555591596555, 0x0410440054569565,
+ 0x5145100010010005, 0x0555041405500150, 0x4141450455140450, 0x0000000144000140,
+ 0x5114004001105410, 0x4444100404005504, 0x0414014410001015, 0x5145055155555015,
+ 0x0141041444445540, 0x0000100451541414, 0x4105041104155550, 0x0500501150451145,
+ 0x1001050000004114, 0x5551504400141045, 0x5110545410151454, 0x0100001400004040,
+ 0x5040010111040000, 0x0140000150541100, 0x4400140400104110, 0x5011014405545004,
+ 0x0000000044155440, 0x0000000010000000, 0x1100401444440001, 0x0040401010055111,
+ 0x5155155551405454, 0x0444440015514411, 0x0054505054014101, 0x0451015441115511,
+ 0x1541411401140551, 0x4155104514445110, 0x4141145450145515, 0x5451445055155050,
+ 0x4400515554110054, 0x5111145104501151, 0x565a655455500501, 0x5565555555525955,
+ 0x0550511500405695, 0x4415504051054544, 0x6555595965555554, 0x0100915915555655,
+ 0x5540001510001001, 0x5450051414000544, 0x1405010555555551, 0x5555515555644155,
+ 0x5555055595496555, 0x5451045004415000, 0x5450510144040144, 0x5554155555556455,
+ 0x5051555495415555, 0x5555554555555545, 0x0000000010005455, 0x4000005000040000,
+ 0x5565555555555954, 0x5554559555555505, 0x9645545495552555, 0x4000400055955564,
+ 0x0040000000000001, 0x4004100100000000, 0x5540040440000411, 0x4565555955545644,
+ 0x1140659549651556, 0x0100000410010000, 0x5555515400004001, 0x5955545555155255,
+ 0x5151055545505556, 0x5051454510554515, 0x0501500050415554, 0x5044154005441005,
+ 0x1455445450550455, 0x0010144055144545, 0x0000401100000004, 0x1050145050000010,
+ 0x0415004554011540, 0x1000510100151150, 0x0100040400001144, 0x0000000000000000,
+ 0x0550004400000100, 0x0151145041451151, 0x0000400400005450, 0x0000100044010004,
+ 0x0100054100050040, 0x0504400005410010, 0x4011410445500105, 0x0000404000144411,
+ 0x0101504404500000, 0x0000005044400400, 0x0000000014000100, 0x0404440414000000,
+ 0x5554100410000140, 0x4555455544505555, 0x5454105055455455, 0x0115454155454015,
+ 0x4404110000045100, 0x4400001100101501, 0x6596955956966a94, 0x0040655955665965,
+ 0x5554144400100155, 0xa549495401011041, 0x5596555565955555, 0x5569965959549555,
+ 0x969565a655555456, 0x0000001000000000, 0x0000000040000140, 0x0000040100000000,
+ 0x1415454400000000, 0x5410415411454114, 0x0400040104000154, 0x0504045000000411,
+ 0x0000001000000010, 0x5554000000001040, 0x5549155551556595, 0x1455541055515555,
+ 0x0510555454554541, 0x9555555555540455, 0x6455456555556465, 0x4524565555654514,
+ 0x5554655255559545, 0x9555455441155556, 0x0000000051515555, 0x0010005040000550,
+ 0x5044044040000000, 0x1045040440010500, 0x0000400000040000, 0x0000000000000000,
+};
+
+const GENERIC_POW5_INV_SPLIT: [89][4]u64 = .{
+ .{ 0, 0, 0, 144115188075855872 },
+ .{ 1573859546583440065, 2691002611772552616, 6763753280790178510, 141347765182270746 },
+ .{ 12960290449513840412, 12345512957918226762, 18057899791198622765, 138633484706040742 },
+ .{ 7615871757716765416, 9507132263365501332, 4879801712092008245, 135971326161092377 },
+ .{ 7869961150745287587, 5804035291554591636, 8883897266325833928, 133360288657597085 },
+ .{ 2942118023529634767, 15128191429820565086, 10638459445243230718, 130799390525667397 },
+ .{ 14188759758411913794, 5362791266439207815, 8068821289119264054, 128287668946279217 },
+ .{ 7183196927902545212, 1952291723540117099, 12075928209936341512, 125824179589281448 },
+ .{ 5672588001402349748, 17892323620748423487, 9874578446960390364, 123407996258356868 },
+ .{ 4442590541217566325, 4558254706293456445, 10343828952663182727, 121038210542800766 },
+ .{ 3005560928406962566, 2082271027139057888, 13961184524927245081, 118713931475986426 },
+ .{ 13299058168408384786, 17834349496131278595, 9029906103900731664, 116434285200389047 },
+ .{ 5414878118283973035, 13079825470227392078, 17897304791683760280, 114198414639042157 },
+ .{ 14609755883382484834, 14991702445765844156, 3269802549772755411, 112005479173303009 },
+ .{ 15967774957605076027, 2511532636717499923, 16221038267832563171, 109854654326805788 },
+ .{ 9269330061621627145, 3332501053426257392, 16223281189403734630, 107745131455483836 },
+ .{ 16739559299223642282, 1873986623300664530, 6546709159471442872, 105676117443544318 },
+ .{ 17116435360051202055, 1359075105581853924, 2038341371621886470, 103646834405281051 },
+ .{ 17144715798009627550, 3201623802661132408, 9757551605154622431, 101656519392613377 },
+ .{ 17580479792687825857, 6546633380567327312, 15099972427870912398, 99704424108241124 },
+ .{ 9726477118325522902, 14578369026754005435, 11728055595254428803, 97789814624307808 },
+ .{ 134593949518343635, 5715151379816901985, 1660163707976377376, 95911971106466306 },
+ .{ 5515914027713859358, 7124354893273815720, 5548463282858794077, 94070187543243255 },
+ .{ 6188403395862945512, 5681264392632320838, 15417410852121406654, 92263771480600430 },
+ .{ 15908890877468271457, 10398888261125597540, 4817794962769172309, 90492043761593298 },
+ .{ 1413077535082201005, 12675058125384151580, 7731426132303759597, 88754338271028867 },
+ .{ 1486733163972670293, 11369385300195092554, 11610016711694864110, 87050001685026843 },
+ .{ 8788596583757589684, 3978580923851924802, 9255162428306775812, 85378393225389919 },
+ .{ 7203518319660962120, 15044736224407683725, 2488132019818199792, 83738884418690858 },
+ .{ 4004175967662388707, 18236988667757575407, 15613100370957482671, 82130858859985791 },
+ .{ 18371903370586036463, 53497579022921640, 16465963977267203307, 80553711981064899 },
+ .{ 10170778323887491315, 1999668801648976001, 10209763593579456445, 79006850823153334 },
+ .{ 17108131712433974546, 16825784443029944237, 2078700786753338945, 77489693813976938 },
+ .{ 17221789422665858532, 12145427517550446164, 5391414622238668005, 76001670549108934 },
+ .{ 4859588996898795878, 1715798948121313204, 3950858167455137171, 74542221577515387 },
+ .{ 13513469241795711526, 631367850494860526, 10517278915021816160, 73110798191218799 },
+ .{ 11757513142672073111, 2581974932255022228, 17498959383193606459, 143413724438001539 },
+ .{ 14524355192525042817, 5640643347559376447, 1309659274756813016, 140659771648132296 },
+ .{ 2765095348461978538, 11021111021896007722, 3224303603779962366, 137958702611185230 },
+ .{ 12373410389187981037, 13679193545685856195, 11644609038462631561, 135309501808182158 },
+ .{ 12813176257562780151, 3754199046160268020, 9954691079802960722, 132711173221007413 },
+ .{ 17557452279667723458, 3237799193992485824, 17893947919029030695, 130162739957935629 },
+ .{ 14634200999559435155, 4123869946105211004, 6955301747350769239, 127663243886350468 },
+ .{ 2185352760627740240, 2864813346878886844, 13049218671329690184, 125211745272516185 },
+ .{ 6143438674322183002, 10464733336980678750, 6982925169933978309, 122807322428266620 },
+ .{ 1099509117817174576, 10202656147550524081, 754997032816608484, 120449071364478757 },
+ .{ 2410631293559367023, 17407273750261453804, 15307291918933463037, 118136105451200587 },
+ .{ 12224968375134586697, 1664436604907828062, 11506086230137787358, 115867555084305488 },
+ .{ 3495926216898000888, 18392536965197424288, 10992889188570643156, 113642567358547782 },
+ .{ 8744506286256259680, 3966568369496879937, 18342264969761820037, 111460305746896569 },
+ .{ 7689600520560455039, 5254331190877624630, 9628558080573245556, 109319949786027263 },
+ .{ 11862637625618819436, 3456120362318976488, 14690471063106001082, 107220694767852583 },
+ .{ 5697330450030126444, 12424082405392918899, 358204170751754904, 105161751436977040 },
+ .{ 11257457505097373622, 15373192700214208870, 671619062372033814, 103142345693961148 },
+ .{ 16850355018477166700, 1913910419361963966, 4550257919755970531, 101161718304283822 },
+ .{ 9670835567561997011, 10584031339132130638, 3060560222974851757, 99219124612893520 },
+ .{ 7698686577353054710, 11689292838639130817, 11806331021588878241, 97313834264240819 },
+ .{ 12233569599615692137, 3347791226108469959, 10333904326094451110, 95445130927687169 },
+ .{ 13049400362825383933, 17142621313007799680, 3790542585289224168, 93612312028186576 },
+ .{ 12430457242474442072, 5625077542189557960, 14765055286236672238, 91814688482138969 },
+ .{ 4759444137752473128, 2230562561567025078, 4954443037339580076, 90051584438315940 },
+ .{ 7246913525170274758, 8910297835195760709, 4015904029508858381, 88322337023761438 },
+ .{ 12854430245836432067, 8135139748065431455, 11548083631386317976, 86626296094571907 },
+ .{ 4848827254502687803, 4789491250196085625, 3988192420450664125, 84962823991462151 },
+ .{ 7435538409611286684, 904061756819742353, 14598026519493048444, 83331295300025028 },
+ .{ 11042616160352530997, 8948390828345326218, 10052651191118271927, 81731096615594853 },
+ .{ 11059348291563778943, 11696515766184685544, 3783210511290897367, 80161626312626082 },
+ .{ 7020010856491885826, 5025093219346041680, 8960210401638911765, 78622294318500592 },
+ .{ 17732844474490699984, 7820866704994446502, 6088373186798844243, 77112521891678506 },
+ .{ 688278527545590501, 3045610706602776618, 8684243536999567610, 75631741404109150 },
+ .{ 2734573255120657297, 3903146411440697663, 9470794821691856713, 74179396127820347 },
+ .{ 15996457521023071259, 4776627823451271680, 12394856457265744744, 72754940025605801 },
+ .{ 13492065758834518331, 7390517611012222399, 1630485387832860230, 142715675091463768 },
+ .{ 13665021627282055864, 9897834675523659302, 17907668136755296849, 139975126841173266 },
+ .{ 9603773719399446181, 10771916301484339398, 10672699855989487527, 137287204938390542 },
+ .{ 3630218541553511265, 8139010004241080614, 2876479648932814543, 134650898807055963 },
+ .{ 8318835909686377084, 9525369258927993371, 2796120270400437057, 132065217277054270 },
+ .{ 11190003059043290163, 12424345635599592110, 12539346395388933763, 129529188211565064 },
+ .{ 8701968833973242276, 820569587086330727, 2315591597351480110, 127041858141569228 },
+ .{ 5115113890115690487, 16906305245394587826, 9899749468931071388, 124602291907373862 },
+ .{ 15543535488939245974, 10945189844466391399, 3553863472349432246, 122209572307020975 },
+ .{ 7709257252608325038, 1191832167690640880, 15077137020234258537, 119862799751447719 },
+ .{ 7541333244210021737, 9790054727902174575, 5160944773155322014, 117561091926268545 },
+ .{ 12297384708782857832, 1281328873123467374, 4827925254630475769, 115303583460052092 },
+ .{ 13243237906232367265, 15873887428139547641, 3607993172301799599, 113089425598968120 },
+ .{ 11384616453739611114, 15184114243769211033, 13148448124803481057, 110917785887682141 },
+ .{ 17727970963596660683, 1196965221832671990, 14537830463956404138, 108787847856377790 },
+ .{ 17241367586707330931, 8880584684128262874, 11173506540726547818, 106698810713789254 },
+ .{ 7184427196661305643, 14332510582433188173, 14230167953789677901, 104649889046128358 },
+};
+
+const POW5_INV_ERRORS: [154]u64 = .{
+ 0x1144155514145504, 0x0000541555401141, 0x0000000000000000, 0x0154454000000000,
+ 0x4114105515544440, 0x0001001111500415, 0x4041411410011000, 0x5550114515155014,
+ 0x1404100041554551, 0x0515000450404410, 0x5054544401140004, 0x5155501005555105,
+ 0x1144141000105515, 0x0541500000500000, 0x1104105540444140, 0x4000015055514110,
+ 0x0054010450004005, 0x4155515404100005, 0x5155145045155555, 0x1511555515440558,
+ 0x5558544555515555, 0x0000000000000010, 0x5004000000000050, 0x1415510100000010,
+ 0x4545555444514500, 0x5155151555555551, 0x1441540144044554, 0x5150104045544400,
+ 0x5450545401444040, 0x5554455045501400, 0x4655155555555145, 0x1000010055455055,
+ 0x1000004000055004, 0x4455405104000005, 0x4500114504150545, 0x0000000014000000,
+ 0x5450000000000000, 0x5514551511445555, 0x4111501040555451, 0x4515445500054444,
+ 0x5101500104100441, 0x1545115155545055, 0x0000000000000000, 0x1554000000100000,
+ 0x5555545595551555, 0x5555051851455955, 0x5555555555555559, 0x0000400011001555,
+ 0x0000004400040000, 0x5455511555554554, 0x5614555544115445, 0x6455156145555155,
+ 0x5455855455415455, 0x5515555144555545, 0x0114400000145155, 0x0000051000450511,
+ 0x4455154554445100, 0x4554150141544455, 0x65955555559a5965, 0x5555555854559559,
+ 0x9569654559616595, 0x1040044040005565, 0x1010010500011044, 0x1554015545154540,
+ 0x4440555401545441, 0x1014441450550105, 0x4545400410504145, 0x5015111541040151,
+ 0x5145051154000410, 0x1040001044545044, 0x4001400000151410, 0x0540000044040000,
+ 0x0510555454411544, 0x0400054054141550, 0x1001041145001100, 0x0000000140000000,
+ 0x0000000014100000, 0x1544005454000140, 0x4050055505445145, 0x0011511104504155,
+ 0x5505544415045055, 0x1155154445515554, 0x0000000000004555, 0x0000000000000000,
+ 0x5101010510400004, 0x1514045044440400, 0x5515519555515555, 0x4554545441555545,
+ 0x1551055955551515, 0x0150000011505515, 0x0044005040400000, 0x0004001004010050,
+ 0x0000051004450414, 0x0114001101001144, 0x0401000001000001, 0x4500010001000401,
+ 0x0004100000005000, 0x0105000441101100, 0x0455455550454540, 0x5404050144105505,
+ 0x4101510540555455, 0x1055541411451555, 0x5451445110115505, 0x1154110010101545,
+ 0x1145140450054055, 0x5555565415551554, 0x1550559555555555, 0x5555541545045141,
+ 0x4555455450500100, 0x5510454545554555, 0x1510140115045455, 0x1001050040111510,
+ 0x5555454555555504, 0x9954155545515554, 0x6596656555555555, 0x0140410051555559,
+ 0x0011104010001544, 0x965669659a680501, 0x5655a55955556955, 0x4015111014404514,
+ 0x1414155554505145, 0x0540040011051404, 0x1010000000015005, 0x0010054050004410,
+ 0x5041104014000100, 0x4440010500100001, 0x1155510504545554, 0x0450151545115541,
+ 0x4000100400110440, 0x1004440010514440, 0x0000115050450000, 0x0545404455541500,
+ 0x1051051555505101, 0x5505144554544144, 0x4550545555515550, 0x0015400450045445,
+ 0x4514155400554415, 0x4555055051050151, 0x1511441450001014, 0x4544554510404414,
+ 0x4115115545545450, 0x5500541555551555, 0x5550010544155015, 0x0144414045545500,
+ 0x4154050001050150, 0x5550511111000145, 0x1114504055000151, 0x5104041101451040,
+ 0x0010501401051441, 0x0010501450504401, 0x4554585440044444, 0x5155555951450455,
+ 0x0040000400105555, 0x0000000000000001,
+};
+
+// zig fmt: on
+
+fn check(comptime T: type, value: T, comptime expected: []const u8) !void {
+ const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
+
+ var buf: [6000]u8 = undefined;
+ const value_bits: I = @bitCast(value);
+ const s = try formatFloat(&buf, value, .{});
+ try std.testing.expectEqualStrings(expected, s);
+
+ if (@bitSizeOf(T) != 80) {
+ const o = try std.fmt.parseFloat(T, s);
+ const o_bits: I = @bitCast(o);
+
+ if (std.math.isNan(value)) {
+ try std.testing.expect(std.math.isNan(o));
+ } else {
+ try std.testing.expectEqual(value_bits, o_bits);
+ }
+ }
+}
+
+test "format f32" {
+ try check(f32, 0.0, "0e0");
+ try check(f32, -0.0, "-0e0");
+ try check(f32, 1.0, "1e0");
+ try check(f32, -1.0, "-1e0");
+ try check(f32, std.math.nan(f32), "nan");
+ try check(f32, std.math.inf(f32), "inf");
+ try check(f32, -std.math.inf(f32), "-inf");
+ try check(f32, 1.1754944e-38, "1.1754944e-38");
+ try check(f32, @bitCast(@as(u32, 0x7f7fffff)), "3.4028235e38");
+ try check(f32, @bitCast(@as(u32, 1)), "1e-45");
+ try check(f32, 3.355445E7, "3.355445e7");
+ try check(f32, 8.999999e9, "9e9");
+ try check(f32, 3.4366717e10, "3.436672e10");
+ try check(f32, 3.0540412e5, "3.0540412e5");
+ try check(f32, 8.0990312e3, "8.0990312e3");
+ try check(f32, 2.4414062e-4, "2.4414062e-4");
+ try check(f32, 2.4414062e-3, "2.4414062e-3");
+ try check(f32, 4.3945312e-3, "4.3945312e-3");
+ try check(f32, 6.3476562e-3, "6.3476562e-3");
+ try check(f32, 4.7223665e21, "4.7223665e21");
+ try check(f32, 8388608.0, "8.388608e6");
+ try check(f32, 1.6777216e7, "1.6777216e7");
+ try check(f32, 3.3554436e7, "3.3554436e7");
+ try check(f32, 6.7131496e7, "6.7131496e7");
+ try check(f32, 1.9310392e-38, "1.9310392e-38");
+ try check(f32, -2.47e-43, "-2.47e-43");
+ try check(f32, 1.993244e-38, "1.993244e-38");
+ try check(f32, 4103.9003, "4.1039004e3");
+ try check(f32, 5.3399997e9, "5.3399997e9");
+ try check(f32, 6.0898e-39, "6.0898e-39");
+ try check(f32, 0.0010310042, "1.0310042e-3");
+ try check(f32, 2.8823261e17, "2.882326e17");
+ try check(f32, 7.038531e-26, "7.038531e-26");
+ try check(f32, 9.2234038e17, "9.223404e17");
+ try check(f32, 6.7108872e7, "6.710887e7");
+ try check(f32, 1.0e-44, "1e-44");
+ try check(f32, 2.816025e14, "2.816025e14");
+ try check(f32, 9.223372e18, "9.223372e18");
+ try check(f32, 1.5846085e29, "1.5846086e29");
+ try check(f32, 1.1811161e19, "1.1811161e19");
+ try check(f32, 5.368709e18, "5.368709e18");
+ try check(f32, 4.6143165e18, "4.6143166e18");
+ try check(f32, 0.007812537, "7.812537e-3");
+ try check(f32, 1.4e-45, "1e-45");
+ try check(f32, 1.18697724e20, "1.18697725e20");
+ try check(f32, 1.00014165e-36, "1.00014165e-36");
+ try check(f32, 200.0, "2e2");
+ try check(f32, 3.3554432e7, "3.3554432e7");
+
+ try check(f32, 1.0, "1e0");
+ try check(f32, 1.2, "1.2e0");
+ try check(f32, 1.23, "1.23e0");
+ try check(f32, 1.234, "1.234e0");
+ try check(f32, 1.2345, "1.2345e0");
+ try check(f32, 1.23456, "1.23456e0");
+ try check(f32, 1.234567, "1.234567e0");
+ try check(f32, 1.2345678, "1.2345678e0");
+ try check(f32, 1.23456735e-36, "1.23456735e-36");
+}
+
+test "format f64" {
+ try check(f64, 0.0, "0e0");
+ try check(f64, -0.0, "-0e0");
+ try check(f64, 1.0, "1e0");
+ try check(f64, -1.0, "-1e0");
+ try check(f64, std.math.nan(f64), "nan");
+ try check(f64, std.math.inf(f64), "inf");
+ try check(f64, -std.math.inf(f64), "-inf");
+ try check(f64, 2.2250738585072014e-308, "2.2250738585072014e-308");
+ try check(f64, @bitCast(@as(u64, 0x7fefffffffffffff)), "1.7976931348623157e308");
+ try check(f64, @bitCast(@as(u64, 1)), "5e-324");
+ try check(f64, 2.98023223876953125e-8, "2.9802322387695312e-8");
+ try check(f64, -2.109808898695963e16, "-2.109808898695963e16");
+ try check(f64, 4.940656e-318, "4.940656e-318");
+ try check(f64, 1.18575755e-316, "1.18575755e-316");
+ try check(f64, 2.989102097996e-312, "2.989102097996e-312");
+ try check(f64, 9.0608011534336e15, "9.0608011534336e15");
+ try check(f64, 4.708356024711512e18, "4.708356024711512e18");
+ try check(f64, 9.409340012568248e18, "9.409340012568248e18");
+ try check(f64, 1.2345678, "1.2345678e0");
+ try check(f64, @bitCast(@as(u64, 0x4830f0cf064dd592)), "5.764607523034235e39");
+ try check(f64, @bitCast(@as(u64, 0x4840f0cf064dd592)), "1.152921504606847e40");
+ try check(f64, @bitCast(@as(u64, 0x4850f0cf064dd592)), "2.305843009213694e40");
+
+ try check(f64, 1, "1e0");
+ try check(f64, 1.2, "1.2e0");
+ try check(f64, 1.23, "1.23e0");
+ try check(f64, 1.234, "1.234e0");
+ try check(f64, 1.2345, "1.2345e0");
+ try check(f64, 1.23456, "1.23456e0");
+ try check(f64, 1.234567, "1.234567e0");
+ try check(f64, 1.2345678, "1.2345678e0");
+ try check(f64, 1.23456789, "1.23456789e0");
+ try check(f64, 1.234567895, "1.234567895e0");
+ try check(f64, 1.2345678901, "1.2345678901e0");
+ try check(f64, 1.23456789012, "1.23456789012e0");
+ try check(f64, 1.234567890123, "1.234567890123e0");
+ try check(f64, 1.2345678901234, "1.2345678901234e0");
+ try check(f64, 1.23456789012345, "1.23456789012345e0");
+ try check(f64, 1.234567890123456, "1.234567890123456e0");
+ try check(f64, 1.2345678901234567, "1.2345678901234567e0");
+
+ try check(f64, 4.294967294, "4.294967294e0");
+ try check(f64, 4.294967295, "4.294967295e0");
+ try check(f64, 4.294967296, "4.294967296e0");
+ try check(f64, 4.294967297, "4.294967297e0");
+ try check(f64, 4.294967298, "4.294967298e0");
+}
+
+test "format f80" {
+ try check(f80, 0.0, "0e0");
+ try check(f80, -0.0, "-0e0");
+ try check(f80, 1.0, "1e0");
+ try check(f80, -1.0, "-1e0");
+ try check(f80, std.math.nan(f80), "nan");
+ try check(f80, std.math.inf(f80), "inf");
+ try check(f80, -std.math.inf(f80), "-inf");
+
+ try check(f80, 2.2250738585072014e-308, "2.2250738585072014e-308");
+ try check(f80, 2.98023223876953125e-8, "2.98023223876953125e-8");
+ try check(f80, -2.109808898695963e16, "-2.109808898695963e16");
+ try check(f80, 4.940656e-318, "4.940656e-318");
+ try check(f80, 1.18575755e-316, "1.18575755e-316");
+ try check(f80, 2.989102097996e-312, "2.989102097996e-312");
+ try check(f80, 9.0608011534336e15, "9.0608011534336e15");
+ try check(f80, 4.708356024711512e18, "4.708356024711512e18");
+ try check(f80, 9.409340012568248e18, "9.409340012568248e18");
+ try check(f80, 1.2345678, "1.2345678e0");
+}
+
+test "format f128" {
+ try check(f128, 0.0, "0e0");
+ try check(f128, -0.0, "-0e0");
+ try check(f128, 1.0, "1e0");
+ try check(f128, -1.0, "-1e0");
+ try check(f128, std.math.nan(f128), "nan");
+ try check(f128, std.math.inf(f128), "inf");
+ try check(f128, -std.math.inf(f128), "-inf");
+
+ try check(f128, 2.2250738585072014e-308, "2.2250738585072014e-308");
+ try check(f128, 2.98023223876953125e-8, "2.98023223876953125e-8");
+ try check(f128, -2.109808898695963e16, "-2.109808898695963e16");
+ try check(f128, 4.940656e-318, "4.940656e-318");
+ try check(f128, 1.18575755e-316, "1.18575755e-316");
+ try check(f128, 2.989102097996e-312, "2.989102097996e-312");
+ try check(f128, 9.0608011534336e15, "9.0608011534336e15");
+ try check(f128, 4.708356024711512e18, "4.708356024711512e18");
+ try check(f128, 9.409340012568248e18, "9.409340012568248e18");
+ try check(f128, 1.2345678, "1.2345678e0");
+}
+
+test "format float to decimal with zero precision" {
+ try expectFmt("5", "{d:.0}", .{5});
+ try expectFmt("6", "{d:.0}", .{6});
+ try expectFmt("7", "{d:.0}", .{7});
+ try expectFmt("8", "{d:.0}", .{8});
+}
diff --git a/lib/std/fmt/ryu128.zig b/lib/std/fmt/ryu128.zig
@@ -1,1139 +0,0 @@
-//! This file implements the ryu floating point conversion algorithm:
-//! https://dl.acm.org/doi/pdf/10.1145/3360595
-
-const std = @import("std");
-const expectFmt = std.testing.expectFmt;
-
-const special_exponent = 0x7fffffff;
-
-/// Any buffer used for `format` must be at least this large. This is asserted. A runtime check will
-/// additionally be performed if more bytes are required.
-pub const min_buffer_size = 53;
-
-/// Returns the minimum buffer size needed to print every float of a specific type and format.
-pub fn bufferSize(comptime mode: Format, comptime T: type) comptime_int {
- comptime std.debug.assert(@typeInfo(T) == .Float);
- return switch (mode) {
- .scientific => 53,
- // Based on minimum subnormal values.
- .decimal => switch (@bitSizeOf(T)) {
- 16 => @max(15, min_buffer_size),
- 32 => 55,
- 64 => 347,
- 80 => 4996,
- 128 => 5011,
- else => unreachable,
- },
- };
-}
-
-pub const RyuError = error{
- BufferTooSmall,
-};
-
-pub const Format = enum {
- scientific,
- decimal,
-};
-
-pub const FormatOptions = struct {
- mode: Format = .scientific,
- precision: ?usize = null,
-};
-
-/// Format a floating-point value and write it to buffer. Returns a slice to the buffer containing
-/// the string representation.
-///
-/// Full precision is the default. Any full precision float can be reparsed with std.fmt.parseFloat
-/// unambiguously.
-///
-/// Scientific mode is recommended generally as the output is more compact and any type can be
-/// written in full precision using a buffer of only `min_buffer_size`.
-///
-/// When printing full precision decimals, use `bufferSize` to get the required space. It is
-/// recommended to bound decimal output with a fixed precision to reduce the required buffer size.
-pub fn format(buf: []u8, v_: anytype, options: FormatOptions) RyuError![]const u8 {
- const v = switch (@TypeOf(v_)) {
- // comptime_float internally is a f128; this preserves precision.
- comptime_float => @as(f128, v_),
- else => v_,
- };
-
- const T = @TypeOf(v);
- comptime std.debug.assert(@typeInfo(T) == .Float);
- const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
-
- const has_explicit_leading_bit = std.math.floatMantissaBits(T) - std.math.floatFractionalBits(T) != 0;
- const d = binaryToDecimal(@as(I, @bitCast(v)), std.math.floatMantissaBits(T), std.math.floatExponentBits(T), has_explicit_leading_bit);
-
- return switch (options.mode) {
- .scientific => formatScientific(buf, d, options.precision),
- .decimal => formatDecimal(buf, d, options.precision),
- };
-}
-
-pub const FloatDecimal128 = struct {
- mantissa: u128,
- exponent: i32,
- sign: bool,
-};
-
-fn copySpecialStr(buf: []u8, f: FloatDecimal128) []const u8 {
- if (f.sign) {
- buf[0] = '-';
- }
- const offset: usize = @intFromBool(f.sign);
- if (f.mantissa != 0) {
- @memcpy(buf[offset..][0..3], "nan");
- return buf[0 .. 3 + offset];
- }
- @memcpy(buf[offset..][0..3], "inf");
- return buf[0 .. 3 + offset];
-}
-
-fn writeDecimal(buf: []u8, value: anytype, count: usize) void {
- var i: usize = 0;
-
- while (i + 2 < count) : (i += 2) {
- const c: u8 = @intCast(value.* % 100);
- value.* /= 100;
- const d = std.fmt.digits2(c);
- buf[count - i - 1] = d[1];
- buf[count - i - 2] = d[0];
- }
-
- while (i < count) : (i += 1) {
- const c: u8 = @intCast(value.* % 10);
- value.* /= 10;
- buf[count - i - 1] = '0' + c;
- }
-}
-
-fn isPowerOf10(n_: u128) bool {
- var n = n_;
- while (n != 0) : (n /= 10) {
- if (n % 10 != 0) return false;
- }
- return true;
-}
-
-const RoundMode = enum {
- /// 1234.56 = precision 2
- decimal,
- /// 1.23456e3 = precision 5
- scientific,
-};
-
-fn round(f: FloatDecimal128, mode: RoundMode, precision: usize) FloatDecimal128 {
- var round_digit: usize = 0;
- var output = f.mantissa;
- var exp = f.exponent;
- const olength = decimalLength(output);
-
- switch (mode) {
- .decimal => {
- if (f.exponent > 0) {
- round_digit = (olength - 1) + precision + @as(usize, @intCast(f.exponent));
- } else {
- const min_exp_required = @as(usize, @intCast(-f.exponent));
- if (precision + olength > min_exp_required) {
- round_digit = precision + olength - min_exp_required;
- }
- }
- },
- .scientific => {
- round_digit = 1 + precision;
- },
- }
-
- if (round_digit < olength) {
- var nlength = olength;
- for (round_digit + 1..olength) |_| {
- output /= 10;
- exp += 1;
- nlength -= 1;
- }
-
- if (output % 10 >= 5) {
- output /= 10;
- output += 1;
- exp += 1;
-
- // e.g. 9999 -> 10000
- if (isPowerOf10(output)) {
- output /= 10;
- exp += 1;
- }
- }
- }
-
- return .{
- .mantissa = output,
- .exponent = exp,
- .sign = f.sign,
- };
-}
-
-/// Write a FloatDecimal128 to a buffer in scientific form.
-///
-/// The buffer provided must be greater than `min_buffer_size` in length. If no precision is
-/// specified, this function will never return an error. If a precision is specified, up to
-/// `8 + precision` bytes will be written to the buffer. An error will be returned if the content
-/// will not fit.
-///
-/// It is recommended to bound decimal formatting with an exact precision.
-pub fn formatScientific(buf: []u8, f_: FloatDecimal128, precision: ?usize) RyuError![]const u8 {
- std.debug.assert(buf.len >= min_buffer_size);
- var f = f_;
-
- if (f.exponent == special_exponent) {
- return copySpecialStr(buf, f);
- }
-
- if (precision) |prec| {
- f = round(f, .scientific, prec);
- }
-
- var output = f.mantissa;
- const olength = decimalLength(output);
-
- if (precision) |prec| {
- // fixed bound: sign(1) + leading_digit(1) + point(1) + exp_sign(1) + exp_max(4)
- const req_bytes = 8 + prec;
- if (buf.len < req_bytes) {
- return error.BufferTooSmall;
- }
- }
-
- // Step 5: Print the scientific representation
- var index: usize = 0;
- if (f.sign) {
- buf[index] = '-';
- index += 1;
- }
-
- // 1.12345
- writeDecimal(buf[index + 2 ..], &output, olength - 1);
- buf[index] = '0' + @as(u8, @intCast(output % 10));
- buf[index + 1] = '.';
- index += 2;
- const dp_index = index;
- if (olength > 1) index += olength - 1 else index -= 1;
-
- if (precision) |prec| {
- index += @intFromBool(olength == 1);
- if (prec > olength - 1) {
- const len = prec - (olength - 1);
- @memset(buf[index..][0..len], '0');
- index += len;
- } else {
- index = dp_index + prec - @intFromBool(prec == 0);
- }
- }
-
- // e100
- buf[index] = 'e';
- index += 1;
- var exp = f.exponent + @as(i32, @intCast(olength)) - 1;
- if (exp < 0) {
- buf[index] = '-';
- index += 1;
- exp = -exp;
- }
- var uexp: u32 = @intCast(exp);
- const elength = decimalLength(uexp);
- writeDecimal(buf[index..], &uexp, elength);
- index += elength;
-
- return buf[0..index];
-}
-
-/// Write a FloatDecimal128 to a buffer in decimal form.
-///
-/// The buffer provided must be greater than `min_buffer_size` bytes in length. If no precision is
-/// specified, this may still return an error. If precision is specified, `2 + precision` bytes will
-/// always be written.
-pub fn formatDecimal(buf: []u8, f_: FloatDecimal128, precision: ?usize) RyuError![]const u8 {
- std.debug.assert(buf.len >= min_buffer_size);
- var f = f_;
-
- if (f.exponent == special_exponent) {
- return copySpecialStr(buf, f);
- }
-
- if (precision) |prec| {
- f = round(f, .decimal, prec);
- }
-
- var output = f.mantissa;
- const olength = decimalLength(output);
-
- // fixed bound: leading_digit(1) + point(1)
- const req_bytes = if (f.exponent >= 0)
- 2 + @abs(f.exponent) + olength + (precision orelse 0)
- else
- 2 + @max(@abs(f.exponent) + olength, precision orelse 0);
- if (buf.len < req_bytes) {
- return error.BufferTooSmall;
- }
-
- // Step 5: Print the decimal representation
- var index: usize = 0;
- if (f.sign) {
- buf[index] = '-';
- index += 1;
- }
-
- const dp_offset = f.exponent + cast_i32(olength);
- if (dp_offset <= 0) {
- // 0.000001234
- buf[index] = '0';
- buf[index + 1] = '.';
- index += 2;
- const dp_index = index;
-
- const dp_poffset: u32 = @intCast(-dp_offset);
- @memset(buf[index..][0..dp_poffset], '0');
- index += dp_poffset;
- writeDecimal(buf[index..], &output, olength);
- index += olength;
-
- if (precision) |prec| {
- const dp_written = index - dp_index;
- if (prec > dp_written) {
- @memset(buf[index..][0 .. prec - dp_written], '0');
- }
- index = dp_index + prec - @intFromBool(prec == 0);
- }
- } else {
- // 123456000
- const dp_uoffset: usize = @intCast(dp_offset);
- if (dp_uoffset >= olength) {
- writeDecimal(buf[index..], &output, olength);
- index += olength;
- @memset(buf[index..][0 .. dp_uoffset - olength], '0');
- index += dp_uoffset - olength;
-
- if (precision) |prec| {
- if (prec != 0) {
- buf[index] = '.';
- index += 1;
- @memset(buf[index..][0..prec], '0');
- index += prec;
- }
- }
- } else {
- // 12345.6789
- writeDecimal(buf[index + dp_uoffset + 1 ..], &output, olength - dp_uoffset);
- buf[index + dp_uoffset] = '.';
- const dp_index = index + dp_uoffset + 1;
- writeDecimal(buf[index..], &output, dp_uoffset);
- index += olength + 1;
-
- if (precision) |prec| {
- const dp_written = olength - dp_uoffset;
- if (prec > dp_written) {
- @memset(buf[index..][0 .. prec - dp_written], '0');
- }
- index = dp_index + prec - @intFromBool(prec == 0);
- }
- }
- }
-
- return buf[0..index];
-}
-
-fn cast_i32(v: anytype) i32 {
- return @intCast(v);
-}
-
-/// Convert a binary float representation to decimal.
-pub fn binaryToDecimal(bits: u128, mantissa_bits: u7, exponent_bits: u5, explicit_leading_bit: bool) FloatDecimal128 {
- const bias = (@as(u32, 1) << (exponent_bits - 1)) - 1;
- const ieee_sign = ((bits >> (mantissa_bits + exponent_bits)) & 1) != 0;
- const ieee_mantissa = bits & ((@as(u128, 1) << mantissa_bits) - 1);
- const ieee_exponent: u32 = @intCast((bits >> mantissa_bits) & ((@as(u128, 1) << exponent_bits) - 1));
-
- if (ieee_exponent == 0 and ieee_mantissa == 0) {
- return .{
- .mantissa = 0,
- .exponent = 0,
- .sign = ieee_sign,
- };
- }
- if (ieee_exponent == ((@as(u32, 1) << exponent_bits) - 1)) {
- return .{
- .mantissa = if (explicit_leading_bit) ieee_mantissa & ((@as(u128, 1) << (mantissa_bits - 1)) - 1) else ieee_mantissa,
- .exponent = 0x7fffffff,
- .sign = ieee_sign,
- };
- }
-
- var e2: i32 = undefined;
- var m2: u128 = undefined;
- if (explicit_leading_bit) {
- if (ieee_exponent == 0) {
- e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
- } else {
- e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) + 1 - 2;
- }
- m2 = ieee_mantissa;
- } else {
- if (ieee_exponent == 0) {
- e2 = 1 - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
- m2 = ieee_mantissa;
- } else {
- e2 = cast_i32(ieee_exponent) - cast_i32(bias) - cast_i32(mantissa_bits) - 2;
- m2 = (@as(u128, 1) << mantissa_bits) | ieee_mantissa;
- }
- }
- const even = (m2 & 1) == 0;
- const accept_bounds = even;
-
- // Step 2: Determine the interval of legal decimal representations.
- const mv = 4 * m2;
- const mm_shift: u1 = @intFromBool((ieee_mantissa != if (explicit_leading_bit) (@as(u128, 1) << (mantissa_bits - 1)) else 0) or (ieee_exponent == 0));
-
- // Step 3: Convert to a decimal power base using 128-bit arithmetic.
- var vr: u128 = undefined;
- var vp: u128 = undefined;
- var vm: u128 = undefined;
- var e10: i32 = undefined;
- var vm_is_trailing_zeros = false;
- var vr_is_trailing_zeros = false;
- if (e2 >= 0) {
- const q: u32 = log10Pow2(@intCast(e2)) - @intFromBool(e2 > 3);
- e10 = cast_i32(q);
- const k: i32 = @intCast(FLOAT_128_POW5_INV_BITCOUNT + pow5Bits(q) - 1);
- const i: u32 = @intCast(-e2 + cast_i32(q) + k);
-
- const pow5 = computeInvPow5(q);
- vr = mulShift(4 * m2, &pow5, i);
- vp = mulShift(4 * m2 + 2, &pow5, i);
- vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, i);
-
- if (q <= 55) {
- if (mv % 5 == 0) {
- vr_is_trailing_zeros = multipleOfPowerOf5(mv, q -% 1);
- } else if (accept_bounds) {
- vm_is_trailing_zeros = multipleOfPowerOf5(mv - 1 - mm_shift, q);
- } else {
- vp -= @intFromBool(multipleOfPowerOf5(mv + 2, q));
- }
- }
- } else {
- const q: u32 = log10Pow5(@intCast(-e2)) - @intFromBool(-e2 > 1);
- e10 = cast_i32(q) + e2;
- const i: i32 = -e2 - cast_i32(q);
- const k: i32 = cast_i32(pow5Bits(@intCast(i))) - FLOAT_128_POW5_BITCOUNT;
- const j: u32 = @intCast(cast_i32(q) - k);
-
- const pow5 = computePow5(@intCast(i));
- vr = mulShift(4 * m2, &pow5, j);
- vp = mulShift(4 * m2 + 2, &pow5, j);
- vm = mulShift(4 * m2 - 1 - mm_shift, &pow5, j);
-
- if (q <= 1) {
- vr_is_trailing_zeros = true;
- if (accept_bounds) {
- vm_is_trailing_zeros = mm_shift == 1;
- } else {
- vp -= 1;
- }
- } else if (q < 127) {
- vr_is_trailing_zeros = multipleOfPowerOf2(mv, q - 1);
- }
- }
-
- // Step 4: Find the shortest decimal representation in the interval of legal representations.
- var removed: u32 = 0;
- var last_removed_digit: u8 = 0;
-
- while (vp / 10 > vm / 10) {
- vm_is_trailing_zeros = vm_is_trailing_zeros and vm % 10 == 0;
- vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
- last_removed_digit = @intCast(vr % 10);
- vr /= 10;
- vp /= 10;
- vm /= 10;
- removed += 1;
- }
-
- if (vm_is_trailing_zeros) {
- while (vm % 10 == 0) {
- vr_is_trailing_zeros = vr_is_trailing_zeros and last_removed_digit == 0;
- last_removed_digit = @intCast(vr % 10);
- vr /= 10;
- vp /= 10;
- vm /= 10;
- removed += 1;
- }
- }
-
- if (vr_is_trailing_zeros and (last_removed_digit == 5) and (vr % 2 == 0)) {
- last_removed_digit = 4;
- }
-
- return .{
- .mantissa = vr + @intFromBool((vr == vm and (!accept_bounds or !vm_is_trailing_zeros)) or last_removed_digit >= 5),
- .exponent = e10 + cast_i32(removed),
- .sign = ieee_sign,
- };
-}
-
-fn decimalLength(v: u128) u32 {
- const LARGEST_POW10 = (@as(u128, 5421010862427522170) << 64) | 687399551400673280;
- var p10 = LARGEST_POW10;
- var i: u32 = 39;
- while (i > 0) : (i -= 1) {
- if (v >= p10) return i;
- p10 /= 10;
- }
- return 1;
-}
-
-// floor(log_10(2^e))
-fn log10Pow2(e: u32) u32 {
- std.debug.assert(e <= 1 << 15);
- return @intCast((@as(u64, @intCast(e)) * 169464822037455) >> 49);
-}
-
-// floor(log_10(5^e))
-fn log10Pow5(e: u32) u32 {
- std.debug.assert(e <= 1 << 15);
- return @intCast((@as(u64, @intCast(e)) * 196742565691928) >> 48);
-}
-
-// if (e == 0) 1 else ceil(log_2(5^e))
-fn pow5Bits(e: u32) u32 {
- std.debug.assert(e <= 1 << 15);
- return @intCast(((@as(u64, @intCast(e)) * 163391164108059) >> 46) + 1);
-}
-
-fn pow5Factor(value_: u128) u32 {
- var count: u32 = 0;
- var value = value_;
- while (value > 0) : ({
- count += 1;
- value /= 5;
- }) {
- if (value % 5 != 0) return count;
- }
- return 0;
-}
-
-fn multipleOfPowerOf5(value: u128, p: u32) bool {
- return pow5Factor(value) >= p;
-}
-
-fn multipleOfPowerOf2(value: u128, p: u32) bool {
- return (value & ((@as(u128, 1) << @as(u7, @intCast(p))) - 1)) == 0;
-}
-
-fn computeInvPow5(i: u32) [4]u64 {
- const base = (i + POW5_TABLE_SIZE - 1) / POW5_TABLE_SIZE;
- const base2 = base * POW5_TABLE_SIZE;
- const mul = &GENERIC_POW5_INV_SPLIT[base]; // 1 / 5^base2
- if (i == base2) {
- return .{ mul[0] + 1, mul[1], mul[2], mul[3] };
- } else {
- const offset = base2 - i;
- const m = &GENERIC_POW5_TABLE[offset]; // 5^offset
- const delta = pow5Bits(base2) - pow5Bits(i);
-
- const shift: u6 = @intCast(2 * (i % 32));
- const corr: u32 = @intCast(((POW5_INV_ERRORS[i / 32] >> shift) & 3) + 1);
- return mul_128_256_shift(m, mul, delta, corr);
- }
-}
-
-fn computePow5(i: u32) [4]u64 {
- const base = i / POW5_TABLE_SIZE;
- const base2 = base * POW5_TABLE_SIZE;
- const mul = &GENERIC_POW5_SPLIT[base];
- if (i == base2) {
- return mul.*;
- } else {
- const offset = i - base2;
- const m = &GENERIC_POW5_TABLE[offset];
- const delta = pow5Bits(i) - pow5Bits(base2);
-
- const shift: u6 = @intCast(2 * (i % 32));
- const corr: u32 = @intCast((POW5_ERRORS[i / 32] >> shift) & 3);
- return mul_128_256_shift(m, mul, delta, corr);
- }
-}
-
-fn mulShift(m: u128, mul: *const [4]u64, j: u32) u128 {
- std.debug.assert(j > 128);
- const a: [2]u64 = .{ @truncate(m), @truncate(m >> 64) };
- const r = mul_128_256_shift(&a, mul, j, 0);
- return (@as(u128, r[1]) << 64) | r[0];
-}
-
-fn mul_128_256_shift(a: *const [2]u64, b: *const [4]u64, shift: u32, corr: u32) [4]u64 {
- std.debug.assert(shift > 0);
- std.debug.assert(shift < 256);
-
- const b00 = @as(u128, a[0]) * b[0];
- const b01 = @as(u128, a[0]) * b[1];
- const b02 = @as(u128, a[0]) * b[2];
- const b03 = @as(u128, a[0]) * b[3];
- const b10 = @as(u128, a[1]) * b[0];
- const b11 = @as(u128, a[1]) * b[1];
- const b12 = @as(u128, a[1]) * b[2];
- const b13 = @as(u128, a[1]) * b[3];
-
- const s0 = b00;
- const s1 = b01 +% b10;
- const c1: u128 = @intFromBool(s1 < b01);
- const s2 = b02 +% b11;
- const c2: u128 = @intFromBool(s2 < b02);
- const s3 = b03 +% b12;
- const c3: u128 = @intFromBool(s3 < b03);
-
- const p0 = s0 +% (s1 << 64);
- const d0: u128 = @intFromBool(p0 < b00);
- const q1 = s2 +% (s1 >> 64) +% (s3 << 64);
- const d1: u128 = @intFromBool(q1 < s2);
- const p1 = q1 +% (c1 << 64) +% d0;
- const d2: u128 = @intFromBool(p1 < q1);
- const p2 = b13 +% (s3 >> 64) +% c2 +% (c3 << 64) +% d1 +% d2;
-
- var r0: u128 = undefined;
- var r1: u128 = undefined;
- if (shift < 128) {
- const cshift: u7 = @intCast(shift);
- const sshift: u7 = @intCast(128 - shift);
- r0 = corr +% ((p0 >> cshift) | (p1 << sshift));
- r1 = ((p1 >> cshift) | (p2 << sshift)) +% @intFromBool(r0 < corr);
- } else if (shift == 128) {
- r0 = corr +% p1;
- r1 = p2 +% @intFromBool(r0 < corr);
- } else {
- const ashift: u7 = @intCast(shift - 128);
- const sshift: u7 = @intCast(256 - shift);
- r0 = corr +% ((p1 >> ashift) | (p2 << sshift));
- r1 = (p2 >> ashift) +% @intFromBool(r0 < corr);
- }
-
- return .{ @truncate(r0), @truncate(r0 >> 64), @truncate(r1), @truncate(r1 >> 64) };
-}
-
-// zig fmt: off
-//
-// 4.5KiB of tables.
-
-const FLOAT_128_POW5_INV_BITCOUNT = 249;
-const FLOAT_128_POW5_BITCOUNT = 249;
-const POW5_TABLE_SIZE = 56;
-
-const GENERIC_POW5_TABLE: [POW5_TABLE_SIZE][2]u64 = .{
- .{ 1, 0 },
- .{ 5, 0 },
- .{ 25, 0 },
- .{ 125, 0 },
- .{ 625, 0 },
- .{ 3125, 0 },
- .{ 15625, 0 },
- .{ 78125, 0 },
- .{ 390625, 0 },
- .{ 1953125, 0 },
- .{ 9765625, 0 },
- .{ 48828125, 0 },
- .{ 244140625, 0 },
- .{ 1220703125, 0 },
- .{ 6103515625, 0 },
- .{ 30517578125, 0 },
- .{ 152587890625, 0 },
- .{ 762939453125, 0 },
- .{ 3814697265625, 0 },
- .{ 19073486328125, 0 },
- .{ 95367431640625, 0 },
- .{ 476837158203125, 0 },
- .{ 2384185791015625, 0 },
- .{ 11920928955078125, 0 },
- .{ 59604644775390625, 0 },
- .{ 298023223876953125, 0 },
- .{ 1490116119384765625, 0 },
- .{ 7450580596923828125, 0 },
- .{ 359414837200037393, 2 },
- .{ 1797074186000186965, 10 },
- .{ 8985370930000934825, 50 },
- .{ 8033366502585570893, 252 },
- .{ 3273344365508751233, 1262 },
- .{ 16366721827543756165, 6310 },
- .{ 8046632842880574361, 31554 },
- .{ 3339676066983768573, 157772 },
- .{ 16698380334918842865, 788860 },
- .{ 9704925379756007861, 3944304 },
- .{ 11631138751360936073, 19721522 },
- .{ 2815461535676025517, 98607613 },
- .{ 14077307678380127585, 493038065 },
- .{ 15046306170771983077, 2465190328 },
- .{ 1444554559021708921, 12325951644 },
- .{ 7222772795108544605, 61629758220 },
- .{ 17667119901833171409, 308148791101 },
- .{ 14548623214327650581, 1540743955509 },
- .{ 17402883850509598057, 7703719777548 },
- .{ 13227442957709783821, 38518598887744 },
- .{ 10796982567420264257, 192592994438723 },
- .{ 17091424689682218053, 962964972193617 },
- .{ 11670147153572883801, 4814824860968089 },
- .{ 3010503546735764157, 24074124304840448 },
- .{ 15052517733678820785, 120370621524202240 },
- .{ 1475612373555897461, 601853107621011204 },
- .{ 7378061867779487305, 3009265538105056020 },
- .{ 18443565265187884909, 15046327690525280101 },
-};
-
-const GENERIC_POW5_SPLIT: [89][4]u64 = .{
- .{ 0, 0, 0, 72057594037927936 },
- .{ 0, 5206161169240293376, 4575641699882439235, 73468396926392969 },
- .{ 3360510775605221349, 6983200512169538081, 4325643253124434363, 74906821675075173 },
- .{ 11917660854915489451, 9652941469841108803, 946308467778435600, 76373409087490117 },
- .{ 1994853395185689235, 16102657350889591545, 6847013871814915412, 77868710555449746 },
- .{ 958415760277438274, 15059347134713823592, 7329070255463483331, 79393288266368765 },
- .{ 2065144883315240188, 7145278325844925976, 14718454754511147343, 80947715414629833 },
- .{ 8980391188862868935, 13709057401304208685, 8230434828742694591, 82532576417087045 },
- .{ 432148644612782575, 7960151582448466064, 12056089168559840552, 84148467132788711 },
- .{ 484109300864744403, 15010663910730448582, 16824949663447227068, 85795995087002057 },
- .{ 14793711725276144220, 16494403799991899904, 10145107106505865967, 87475779699624060 },
- .{ 15427548291869817042, 12330588654550505203, 13980791795114552342, 89188452518064298 },
- .{ 9979404135116626552, 13477446383271537499, 14459862802511591337, 90934657454687378 },
- .{ 12385121150303452775, 9097130814231585614, 6523855782339765207, 92715051028904201 },
- .{ 1822931022538209743, 16062974719797586441, 3619180286173516788, 94530302614003091 },
- .{ 12318611738248470829, 13330752208259324507, 10986694768744162601, 96381094688813589 },
- .{ 13684493829640282333, 7674802078297225834, 15208116197624593182, 98268123094297527 },
- .{ 5408877057066295332, 6470124174091971006, 15112713923117703147, 100192097295163851 },
- .{ 11407083166564425062, 18189998238742408185, 4337638702446708282, 102153740646605557 },
- .{ 4112405898036935485, 924624216579956435, 14251108172073737125, 104153790666259019 },
- .{ 16996739107011444789, 10015944118339042475, 2395188869672266257, 106192999311487969 },
- .{ 4588314690421337879, 5339991768263654604, 15441007590670620066, 108272133262096356 },
- .{ 2286159977890359825, 14329706763185060248, 5980012964059367667, 110391974208576409 },
- .{ 9654767503237031099, 11293544302844823188, 11739932712678287805, 112553319146000238 },
- .{ 11362964448496095896, 7990659682315657680, 251480263940996374, 114756980673665505 },
- .{ 1423410421096377129, 14274395557581462179, 16553482793602208894, 117003787300607788 },
- .{ 2070444190619093137, 11517140404712147401, 11657844572835578076, 119294583757094535 },
- .{ 7648316884775828921, 15264332483297977688, 247182277434709002, 121630231312217685 },
- .{ 17410896758132241352, 10923914482914417070, 13976383996795783649, 124011608097704390 },
- .{ 9542674537907272703, 3079432708831728956, 14235189590642919676, 126439609438067572 },
- .{ 10364666969937261816, 8464573184892924210, 12758646866025101190, 128915148187220428 },
- .{ 14720354822146013883, 11480204489231511423, 7449876034836187038, 131439155071681461 },
- .{ 1692907053653558553, 17835392458598425233, 1754856712536736598, 134012579040499057 },
- .{ 5620591334531458755, 11361776175667106627, 13350215315297937856, 136636387622027174 },
- .{ 17455759733928092601, 10362573084069962561, 11246018728801810510, 139311567287686283 },
- .{ 2465404073814044982, 17694822665274381860, 1509954037718722697, 142039123822846312 },
- .{ 2152236053329638369, 11202280800589637091, 16388426812920420176, 72410041352485523 },
- .{ 17319024055671609028, 10944982848661280484, 2457150158022562661, 73827744744583080 },
- .{ 17511219308535248024, 5122059497846768077, 2089605804219668451, 75273205100637900 },
- .{ 10082673333144031533, 14429008783411894887, 12842832230171903890, 76746965869337783 },
- .{ 16196653406315961184, 10260180891682904501, 10537411930446752461, 78249581139456266 },
- .{ 15084422041749743389, 234835370106753111, 16662517110286225617, 79781615848172976 },
- .{ 8199644021067702606, 3787318116274991885, 7438130039325743106, 81343645993472659 },
- .{ 12039493937039359765, 9773822153580393709, 5945428874398357806, 82936258850702722 },
- .{ 984543865091303961, 7975107621689454830, 6556665988501773347, 84560053193370726 },
- .{ 9633317878125234244, 16099592426808915028, 9706674539190598200, 86215639518264828 },
- .{ 6860695058870476186, 4471839111886709592, 7828342285492709568, 87903640274981819 },
- .{ 14583324717644598331, 4496120889473451238, 5290040788305728466, 89624690099949049 },
- .{ 18093669366515003715, 12879506572606942994, 18005739787089675377, 91379436055028227 },
- .{ 17997493966862379937, 14646222655265145582, 10265023312844161858, 93168537870790806 },
- .{ 12283848109039722318, 11290258077250314935, 9878160025624946825, 94992668194556404 },
- .{ 8087752761883078164, 5262596608437575693, 11093553063763274413, 96852512843287537 },
- .{ 15027787746776840781, 12250273651168257752, 9290470558712181914, 98748771061435726 },
- .{ 15003915578366724489, 2937334162439764327, 5404085603526796602, 100682155783835929 },
- .{ 5225610465224746757, 14932114897406142027, 2774647558180708010, 102653393903748137 },
- .{ 17112957703385190360, 12069082008339002412, 3901112447086388439, 104663226546146909 },
- .{ 4062324464323300238, 3992768146772240329, 15757196565593695724, 106712409346361594 },
- .{ 5525364615810306701, 11855206026704935156, 11344868740897365300, 108801712734172003 },
- .{ 9274143661888462646, 4478365862348432381, 18010077872551661771, 110931922223466333 },
- .{ 12604141221930060148, 8930937759942591500, 9382183116147201338, 113103838707570263 },
- .{ 14513929377491886653, 1410646149696279084, 587092196850797612, 115318278760358235 },
- .{ 2226851524999454362, 7717102471110805679, 7187441550995571734, 117576074943260147 },
- .{ 5527526061344932763, 2347100676188369132, 16976241418824030445, 119878076118278875 },
- .{ 6088479778147221611, 17669593130014777580, 10991124207197663546, 122225147767136307 },
- .{ 11107734086759692041, 3391795220306863431, 17233960908859089158, 124618172316667879 },
- .{ 7913172514655155198, 17726879005381242552, 641069866244011540, 127058049470587962 },
- .{ 12596991768458713949, 15714785522479904446, 6035972567136116512, 129545696547750811 },
- .{ 16901996933781815980, 4275085211437148707, 14091642539965169063, 132082048827034281 },
- .{ 7524574627987869240, 15661204384239316051, 2444526454225712267, 134668059898975949 },
- .{ 8199251625090479942, 6803282222165044067, 16064817666437851504, 137304702024293857 },
- .{ 4453256673338111920, 15269922543084434181, 3139961729834750852, 139992966499426682 },
- .{ 15841763546372731299, 3013174075437671812, 4383755396295695606, 142733864029230733 },
- .{ 9771896230907310329, 4900659362437687569, 12386126719044266361, 72764212553486967 },
- .{ 9420455527449565190, 1859606122611023693, 6555040298902684281, 74188850200884818 },
- .{ 5146105983135678095, 2287300449992174951, 4325371679080264751, 75641380576797959 },
- .{ 11019359372592553360, 8422686425957443718, 7175176077944048210, 77122349788024458 },
- .{ 11005742969399620716, 4132174559240043701, 9372258443096612118, 78632314633490790 },
- .{ 8887589641394725840, 8029899502466543662, 14582206497241572853, 80171842813591127 },
- .{ 360247523705545899, 12568341805293354211, 14653258284762517866, 81741513143625247 },
- .{ 12314272731984275834, 4740745023227177044, 6141631472368337539, 83341915771415304 },
- .{ 441052047733984759, 7940090120939869826, 11750200619921094248, 84973652399183278 },
- .{ 3436657868127012749, 9187006432149937667, 16389726097323041290, 86637336509772529 },
- .{ 13490220260784534044, 15339072891382896702, 8846102360835316895, 88333593597298497 },
- .{ 4125672032094859833, 158347675704003277, 10592598512749774447, 90063061402315272 },
- .{ 12189928252974395775, 2386931199439295891, 7009030566469913276, 91826390151586454 },
- .{ 9256479608339282969, 2844900158963599229, 11148388908923225596, 93624242802550437 },
- .{ 11584393507658707408, 2863659090805147914, 9873421561981063551, 95457295292572042 },
- .{ 13984297296943171390, 1931468383973130608, 12905719743235082319, 97326236793074198 },
- .{ 5837045222254987499, 10213498696735864176, 14893951506257020749, 99231769968645227 },
-};
-
-// Unfortunately, the results are sometimes off by one or two. We use an additional
-// lookup table to store those cases and adjust the result.
-const POW5_ERRORS: [156]u64 = .{
- 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x9555596400000000,
- 0x65a6569525565555, 0x4415551445449655, 0x5105015504144541, 0x65a69969a6965964,
- 0x5054955969959656, 0x5105154515554145, 0x4055511051591555, 0x5500514455550115,
- 0x0041140014145515, 0x1005440545511051, 0x0014405450411004, 0x0414440010500000,
- 0x0044000440010040, 0x5551155000004001, 0x4554555454544114, 0x5150045544005441,
- 0x0001111400054501, 0x6550955555554554, 0x1504159645559559, 0x4105055141454545,
- 0x1411541410405454, 0x0415555044545555, 0x0014154115405550, 0x1540055040411445,
- 0x0000000500000000, 0x5644000000000000, 0x1155555591596555, 0x0410440054569565,
- 0x5145100010010005, 0x0555041405500150, 0x4141450455140450, 0x0000000144000140,
- 0x5114004001105410, 0x4444100404005504, 0x0414014410001015, 0x5145055155555015,
- 0x0141041444445540, 0x0000100451541414, 0x4105041104155550, 0x0500501150451145,
- 0x1001050000004114, 0x5551504400141045, 0x5110545410151454, 0x0100001400004040,
- 0x5040010111040000, 0x0140000150541100, 0x4400140400104110, 0x5011014405545004,
- 0x0000000044155440, 0x0000000010000000, 0x1100401444440001, 0x0040401010055111,
- 0x5155155551405454, 0x0444440015514411, 0x0054505054014101, 0x0451015441115511,
- 0x1541411401140551, 0x4155104514445110, 0x4141145450145515, 0x5451445055155050,
- 0x4400515554110054, 0x5111145104501151, 0x565a655455500501, 0x5565555555525955,
- 0x0550511500405695, 0x4415504051054544, 0x6555595965555554, 0x0100915915555655,
- 0x5540001510001001, 0x5450051414000544, 0x1405010555555551, 0x5555515555644155,
- 0x5555055595496555, 0x5451045004415000, 0x5450510144040144, 0x5554155555556455,
- 0x5051555495415555, 0x5555554555555545, 0x0000000010005455, 0x4000005000040000,
- 0x5565555555555954, 0x5554559555555505, 0x9645545495552555, 0x4000400055955564,
- 0x0040000000000001, 0x4004100100000000, 0x5540040440000411, 0x4565555955545644,
- 0x1140659549651556, 0x0100000410010000, 0x5555515400004001, 0x5955545555155255,
- 0x5151055545505556, 0x5051454510554515, 0x0501500050415554, 0x5044154005441005,
- 0x1455445450550455, 0x0010144055144545, 0x0000401100000004, 0x1050145050000010,
- 0x0415004554011540, 0x1000510100151150, 0x0100040400001144, 0x0000000000000000,
- 0x0550004400000100, 0x0151145041451151, 0x0000400400005450, 0x0000100044010004,
- 0x0100054100050040, 0x0504400005410010, 0x4011410445500105, 0x0000404000144411,
- 0x0101504404500000, 0x0000005044400400, 0x0000000014000100, 0x0404440414000000,
- 0x5554100410000140, 0x4555455544505555, 0x5454105055455455, 0x0115454155454015,
- 0x4404110000045100, 0x4400001100101501, 0x6596955956966a94, 0x0040655955665965,
- 0x5554144400100155, 0xa549495401011041, 0x5596555565955555, 0x5569965959549555,
- 0x969565a655555456, 0x0000001000000000, 0x0000000040000140, 0x0000040100000000,
- 0x1415454400000000, 0x5410415411454114, 0x0400040104000154, 0x0504045000000411,
- 0x0000001000000010, 0x5554000000001040, 0x5549155551556595, 0x1455541055515555,
- 0x0510555454554541, 0x9555555555540455, 0x6455456555556465, 0x4524565555654514,
- 0x5554655255559545, 0x9555455441155556, 0x0000000051515555, 0x0010005040000550,
- 0x5044044040000000, 0x1045040440010500, 0x0000400000040000, 0x0000000000000000,
-};
-
-const GENERIC_POW5_INV_SPLIT: [89][4]u64 = .{
- .{ 0, 0, 0, 144115188075855872 },
- .{ 1573859546583440065, 2691002611772552616, 6763753280790178510, 141347765182270746 },
- .{ 12960290449513840412, 12345512957918226762, 18057899791198622765, 138633484706040742 },
- .{ 7615871757716765416, 9507132263365501332, 4879801712092008245, 135971326161092377 },
- .{ 7869961150745287587, 5804035291554591636, 8883897266325833928, 133360288657597085 },
- .{ 2942118023529634767, 15128191429820565086, 10638459445243230718, 130799390525667397 },
- .{ 14188759758411913794, 5362791266439207815, 8068821289119264054, 128287668946279217 },
- .{ 7183196927902545212, 1952291723540117099, 12075928209936341512, 125824179589281448 },
- .{ 5672588001402349748, 17892323620748423487, 9874578446960390364, 123407996258356868 },
- .{ 4442590541217566325, 4558254706293456445, 10343828952663182727, 121038210542800766 },
- .{ 3005560928406962566, 2082271027139057888, 13961184524927245081, 118713931475986426 },
- .{ 13299058168408384786, 17834349496131278595, 9029906103900731664, 116434285200389047 },
- .{ 5414878118283973035, 13079825470227392078, 17897304791683760280, 114198414639042157 },
- .{ 14609755883382484834, 14991702445765844156, 3269802549772755411, 112005479173303009 },
- .{ 15967774957605076027, 2511532636717499923, 16221038267832563171, 109854654326805788 },
- .{ 9269330061621627145, 3332501053426257392, 16223281189403734630, 107745131455483836 },
- .{ 16739559299223642282, 1873986623300664530, 6546709159471442872, 105676117443544318 },
- .{ 17116435360051202055, 1359075105581853924, 2038341371621886470, 103646834405281051 },
- .{ 17144715798009627550, 3201623802661132408, 9757551605154622431, 101656519392613377 },
- .{ 17580479792687825857, 6546633380567327312, 15099972427870912398, 99704424108241124 },
- .{ 9726477118325522902, 14578369026754005435, 11728055595254428803, 97789814624307808 },
- .{ 134593949518343635, 5715151379816901985, 1660163707976377376, 95911971106466306 },
- .{ 5515914027713859358, 7124354893273815720, 5548463282858794077, 94070187543243255 },
- .{ 6188403395862945512, 5681264392632320838, 15417410852121406654, 92263771480600430 },
- .{ 15908890877468271457, 10398888261125597540, 4817794962769172309, 90492043761593298 },
- .{ 1413077535082201005, 12675058125384151580, 7731426132303759597, 88754338271028867 },
- .{ 1486733163972670293, 11369385300195092554, 11610016711694864110, 87050001685026843 },
- .{ 8788596583757589684, 3978580923851924802, 9255162428306775812, 85378393225389919 },
- .{ 7203518319660962120, 15044736224407683725, 2488132019818199792, 83738884418690858 },
- .{ 4004175967662388707, 18236988667757575407, 15613100370957482671, 82130858859985791 },
- .{ 18371903370586036463, 53497579022921640, 16465963977267203307, 80553711981064899 },
- .{ 10170778323887491315, 1999668801648976001, 10209763593579456445, 79006850823153334 },
- .{ 17108131712433974546, 16825784443029944237, 2078700786753338945, 77489693813976938 },
- .{ 17221789422665858532, 12145427517550446164, 5391414622238668005, 76001670549108934 },
- .{ 4859588996898795878, 1715798948121313204, 3950858167455137171, 74542221577515387 },
- .{ 13513469241795711526, 631367850494860526, 10517278915021816160, 73110798191218799 },
- .{ 11757513142672073111, 2581974932255022228, 17498959383193606459, 143413724438001539 },
- .{ 14524355192525042817, 5640643347559376447, 1309659274756813016, 140659771648132296 },
- .{ 2765095348461978538, 11021111021896007722, 3224303603779962366, 137958702611185230 },
- .{ 12373410389187981037, 13679193545685856195, 11644609038462631561, 135309501808182158 },
- .{ 12813176257562780151, 3754199046160268020, 9954691079802960722, 132711173221007413 },
- .{ 17557452279667723458, 3237799193992485824, 17893947919029030695, 130162739957935629 },
- .{ 14634200999559435155, 4123869946105211004, 6955301747350769239, 127663243886350468 },
- .{ 2185352760627740240, 2864813346878886844, 13049218671329690184, 125211745272516185 },
- .{ 6143438674322183002, 10464733336980678750, 6982925169933978309, 122807322428266620 },
- .{ 1099509117817174576, 10202656147550524081, 754997032816608484, 120449071364478757 },
- .{ 2410631293559367023, 17407273750261453804, 15307291918933463037, 118136105451200587 },
- .{ 12224968375134586697, 1664436604907828062, 11506086230137787358, 115867555084305488 },
- .{ 3495926216898000888, 18392536965197424288, 10992889188570643156, 113642567358547782 },
- .{ 8744506286256259680, 3966568369496879937, 18342264969761820037, 111460305746896569 },
- .{ 7689600520560455039, 5254331190877624630, 9628558080573245556, 109319949786027263 },
- .{ 11862637625618819436, 3456120362318976488, 14690471063106001082, 107220694767852583 },
- .{ 5697330450030126444, 12424082405392918899, 358204170751754904, 105161751436977040 },
- .{ 11257457505097373622, 15373192700214208870, 671619062372033814, 103142345693961148 },
- .{ 16850355018477166700, 1913910419361963966, 4550257919755970531, 101161718304283822 },
- .{ 9670835567561997011, 10584031339132130638, 3060560222974851757, 99219124612893520 },
- .{ 7698686577353054710, 11689292838639130817, 11806331021588878241, 97313834264240819 },
- .{ 12233569599615692137, 3347791226108469959, 10333904326094451110, 95445130927687169 },
- .{ 13049400362825383933, 17142621313007799680, 3790542585289224168, 93612312028186576 },
- .{ 12430457242474442072, 5625077542189557960, 14765055286236672238, 91814688482138969 },
- .{ 4759444137752473128, 2230562561567025078, 4954443037339580076, 90051584438315940 },
- .{ 7246913525170274758, 8910297835195760709, 4015904029508858381, 88322337023761438 },
- .{ 12854430245836432067, 8135139748065431455, 11548083631386317976, 86626296094571907 },
- .{ 4848827254502687803, 4789491250196085625, 3988192420450664125, 84962823991462151 },
- .{ 7435538409611286684, 904061756819742353, 14598026519493048444, 83331295300025028 },
- .{ 11042616160352530997, 8948390828345326218, 10052651191118271927, 81731096615594853 },
- .{ 11059348291563778943, 11696515766184685544, 3783210511290897367, 80161626312626082 },
- .{ 7020010856491885826, 5025093219346041680, 8960210401638911765, 78622294318500592 },
- .{ 17732844474490699984, 7820866704994446502, 6088373186798844243, 77112521891678506 },
- .{ 688278527545590501, 3045610706602776618, 8684243536999567610, 75631741404109150 },
- .{ 2734573255120657297, 3903146411440697663, 9470794821691856713, 74179396127820347 },
- .{ 15996457521023071259, 4776627823451271680, 12394856457265744744, 72754940025605801 },
- .{ 13492065758834518331, 7390517611012222399, 1630485387832860230, 142715675091463768 },
- .{ 13665021627282055864, 9897834675523659302, 17907668136755296849, 139975126841173266 },
- .{ 9603773719399446181, 10771916301484339398, 10672699855989487527, 137287204938390542 },
- .{ 3630218541553511265, 8139010004241080614, 2876479648932814543, 134650898807055963 },
- .{ 8318835909686377084, 9525369258927993371, 2796120270400437057, 132065217277054270 },
- .{ 11190003059043290163, 12424345635599592110, 12539346395388933763, 129529188211565064 },
- .{ 8701968833973242276, 820569587086330727, 2315591597351480110, 127041858141569228 },
- .{ 5115113890115690487, 16906305245394587826, 9899749468931071388, 124602291907373862 },
- .{ 15543535488939245974, 10945189844466391399, 3553863472349432246, 122209572307020975 },
- .{ 7709257252608325038, 1191832167690640880, 15077137020234258537, 119862799751447719 },
- .{ 7541333244210021737, 9790054727902174575, 5160944773155322014, 117561091926268545 },
- .{ 12297384708782857832, 1281328873123467374, 4827925254630475769, 115303583460052092 },
- .{ 13243237906232367265, 15873887428139547641, 3607993172301799599, 113089425598968120 },
- .{ 11384616453739611114, 15184114243769211033, 13148448124803481057, 110917785887682141 },
- .{ 17727970963596660683, 1196965221832671990, 14537830463956404138, 108787847856377790 },
- .{ 17241367586707330931, 8880584684128262874, 11173506540726547818, 106698810713789254 },
- .{ 7184427196661305643, 14332510582433188173, 14230167953789677901, 104649889046128358 },
-};
-
-const POW5_INV_ERRORS: [154]u64 = .{
- 0x1144155514145504, 0x0000541555401141, 0x0000000000000000, 0x0154454000000000,
- 0x4114105515544440, 0x0001001111500415, 0x4041411410011000, 0x5550114515155014,
- 0x1404100041554551, 0x0515000450404410, 0x5054544401140004, 0x5155501005555105,
- 0x1144141000105515, 0x0541500000500000, 0x1104105540444140, 0x4000015055514110,
- 0x0054010450004005, 0x4155515404100005, 0x5155145045155555, 0x1511555515440558,
- 0x5558544555515555, 0x0000000000000010, 0x5004000000000050, 0x1415510100000010,
- 0x4545555444514500, 0x5155151555555551, 0x1441540144044554, 0x5150104045544400,
- 0x5450545401444040, 0x5554455045501400, 0x4655155555555145, 0x1000010055455055,
- 0x1000004000055004, 0x4455405104000005, 0x4500114504150545, 0x0000000014000000,
- 0x5450000000000000, 0x5514551511445555, 0x4111501040555451, 0x4515445500054444,
- 0x5101500104100441, 0x1545115155545055, 0x0000000000000000, 0x1554000000100000,
- 0x5555545595551555, 0x5555051851455955, 0x5555555555555559, 0x0000400011001555,
- 0x0000004400040000, 0x5455511555554554, 0x5614555544115445, 0x6455156145555155,
- 0x5455855455415455, 0x5515555144555545, 0x0114400000145155, 0x0000051000450511,
- 0x4455154554445100, 0x4554150141544455, 0x65955555559a5965, 0x5555555854559559,
- 0x9569654559616595, 0x1040044040005565, 0x1010010500011044, 0x1554015545154540,
- 0x4440555401545441, 0x1014441450550105, 0x4545400410504145, 0x5015111541040151,
- 0x5145051154000410, 0x1040001044545044, 0x4001400000151410, 0x0540000044040000,
- 0x0510555454411544, 0x0400054054141550, 0x1001041145001100, 0x0000000140000000,
- 0x0000000014100000, 0x1544005454000140, 0x4050055505445145, 0x0011511104504155,
- 0x5505544415045055, 0x1155154445515554, 0x0000000000004555, 0x0000000000000000,
- 0x5101010510400004, 0x1514045044440400, 0x5515519555515555, 0x4554545441555545,
- 0x1551055955551515, 0x0150000011505515, 0x0044005040400000, 0x0004001004010050,
- 0x0000051004450414, 0x0114001101001144, 0x0401000001000001, 0x4500010001000401,
- 0x0004100000005000, 0x0105000441101100, 0x0455455550454540, 0x5404050144105505,
- 0x4101510540555455, 0x1055541411451555, 0x5451445110115505, 0x1154110010101545,
- 0x1145140450054055, 0x5555565415551554, 0x1550559555555555, 0x5555541545045141,
- 0x4555455450500100, 0x5510454545554555, 0x1510140115045455, 0x1001050040111510,
- 0x5555454555555504, 0x9954155545515554, 0x6596656555555555, 0x0140410051555559,
- 0x0011104010001544, 0x965669659a680501, 0x5655a55955556955, 0x4015111014404514,
- 0x1414155554505145, 0x0540040011051404, 0x1010000000015005, 0x0010054050004410,
- 0x5041104014000100, 0x4440010500100001, 0x1155510504545554, 0x0450151545115541,
- 0x4000100400110440, 0x1004440010514440, 0x0000115050450000, 0x0545404455541500,
- 0x1051051555505101, 0x5505144554544144, 0x4550545555515550, 0x0015400450045445,
- 0x4514155400554415, 0x4555055051050151, 0x1511441450001014, 0x4544554510404414,
- 0x4115115545545450, 0x5500541555551555, 0x5550010544155015, 0x0144414045545500,
- 0x4154050001050150, 0x5550511111000145, 0x1114504055000151, 0x5104041101451040,
- 0x0010501401051441, 0x0010501450504401, 0x4554585440044444, 0x5155555951450455,
- 0x0040000400105555, 0x0000000000000001,
-};
-
-// zig fmt: on
-
-fn check(comptime T: type, value: T, comptime expected: []const u8) !void {
- const I = @Type(.{ .Int = .{ .signedness = .unsigned, .bits = @bitSizeOf(T) } });
-
- var buf: [6000]u8 = undefined;
- const value_bits: I = @bitCast(value);
- const s = try format(&buf, value, .{});
- try std.testing.expectEqualStrings(expected, s);
-
- if (@bitSizeOf(T) != 80) {
- const o = try std.fmt.parseFloat(T, s);
- const o_bits: I = @bitCast(o);
-
- if (std.math.isNan(value)) {
- try std.testing.expect(std.math.isNan(o));
- } else {
- try std.testing.expectEqual(value_bits, o_bits);
- }
- }
-}
-
-test "format f32" {
- try check(f32, 0.0, "0e0");
- try check(f32, -0.0, "-0e0");
- try check(f32, 1.0, "1e0");
- try check(f32, -1.0, "-1e0");
- try check(f32, std.math.nan(f32), "nan");
- try check(f32, std.math.inf(f32), "inf");
- try check(f32, -std.math.inf(f32), "-inf");
- try check(f32, 1.1754944e-38, "1.1754944e-38");
- try check(f32, @bitCast(@as(u32, 0x7f7fffff)), "3.4028235e38");
- try check(f32, @bitCast(@as(u32, 1)), "1e-45");
- try check(f32, 3.355445E7, "3.355445e7");
- try check(f32, 8.999999e9, "9e9");
- try check(f32, 3.4366717e10, "3.436672e10");
- try check(f32, 3.0540412e5, "3.0540412e5");
- try check(f32, 8.0990312e3, "8.0990312e3");
- try check(f32, 2.4414062e-4, "2.4414062e-4");
- try check(f32, 2.4414062e-3, "2.4414062e-3");
- try check(f32, 4.3945312e-3, "4.3945312e-3");
- try check(f32, 6.3476562e-3, "6.3476562e-3");
- try check(f32, 4.7223665e21, "4.7223665e21");
- try check(f32, 8388608.0, "8.388608e6");
- try check(f32, 1.6777216e7, "1.6777216e7");
- try check(f32, 3.3554436e7, "3.3554436e7");
- try check(f32, 6.7131496e7, "6.7131496e7");
- try check(f32, 1.9310392e-38, "1.9310392e-38");
- try check(f32, -2.47e-43, "-2.47e-43");
- try check(f32, 1.993244e-38, "1.993244e-38");
- try check(f32, 4103.9003, "4.1039004e3");
- try check(f32, 5.3399997e9, "5.3399997e9");
- try check(f32, 6.0898e-39, "6.0898e-39");
- try check(f32, 0.0010310042, "1.0310042e-3");
- try check(f32, 2.8823261e17, "2.882326e17");
- try check(f32, 7.038531e-26, "7.038531e-26");
- try check(f32, 9.2234038e17, "9.223404e17");
- try check(f32, 6.7108872e7, "6.710887e7");
- try check(f32, 1.0e-44, "1e-44");
- try check(f32, 2.816025e14, "2.816025e14");
- try check(f32, 9.223372e18, "9.223372e18");
- try check(f32, 1.5846085e29, "1.5846086e29");
- try check(f32, 1.1811161e19, "1.1811161e19");
- try check(f32, 5.368709e18, "5.368709e18");
- try check(f32, 4.6143165e18, "4.6143166e18");
- try check(f32, 0.007812537, "7.812537e-3");
- try check(f32, 1.4e-45, "1e-45");
- try check(f32, 1.18697724e20, "1.18697725e20");
- try check(f32, 1.00014165e-36, "1.00014165e-36");
- try check(f32, 200.0, "2e2");
- try check(f32, 3.3554432e7, "3.3554432e7");
-
- try check(f32, 1.0, "1e0");
- try check(f32, 1.2, "1.2e0");
- try check(f32, 1.23, "1.23e0");
- try check(f32, 1.234, "1.234e0");
- try check(f32, 1.2345, "1.2345e0");
- try check(f32, 1.23456, "1.23456e0");
- try check(f32, 1.234567, "1.234567e0");
- try check(f32, 1.2345678, "1.2345678e0");
- try check(f32, 1.23456735e-36, "1.23456735e-36");
-}
-
-test "format f64" {
- try check(f64, 0.0, "0e0");
- try check(f64, -0.0, "-0e0");
- try check(f64, 1.0, "1e0");
- try check(f64, -1.0, "-1e0");
- try check(f64, std.math.nan(f64), "nan");
- try check(f64, std.math.inf(f64), "inf");
- try check(f64, -std.math.inf(f64), "-inf");
- try check(f64, 2.2250738585072014e-308, "2.2250738585072014e-308");
- try check(f64, @bitCast(@as(u64, 0x7fefffffffffffff)), "1.7976931348623157e308");
- try check(f64, @bitCast(@as(u64, 1)), "5e-324");
- try check(f64, 2.98023223876953125e-8, "2.9802322387695312e-8");
- try check(f64, -2.109808898695963e16, "-2.109808898695963e16");
- try check(f64, 4.940656e-318, "4.940656e-318");
- try check(f64, 1.18575755e-316, "1.18575755e-316");
- try check(f64, 2.989102097996e-312, "2.989102097996e-312");
- try check(f64, 9.0608011534336e15, "9.0608011534336e15");
- try check(f64, 4.708356024711512e18, "4.708356024711512e18");
- try check(f64, 9.409340012568248e18, "9.409340012568248e18");
- try check(f64, 1.2345678, "1.2345678e0");
- try check(f64, @bitCast(@as(u64, 0x4830f0cf064dd592)), "5.764607523034235e39");
- try check(f64, @bitCast(@as(u64, 0x4840f0cf064dd592)), "1.152921504606847e40");
- try check(f64, @bitCast(@as(u64, 0x4850f0cf064dd592)), "2.305843009213694e40");
-
- try check(f64, 1, "1e0");
- try check(f64, 1.2, "1.2e0");
- try check(f64, 1.23, "1.23e0");
- try check(f64, 1.234, "1.234e0");
- try check(f64, 1.2345, "1.2345e0");
- try check(f64, 1.23456, "1.23456e0");
- try check(f64, 1.234567, "1.234567e0");
- try check(f64, 1.2345678, "1.2345678e0");
- try check(f64, 1.23456789, "1.23456789e0");
- try check(f64, 1.234567895, "1.234567895e0");
- try check(f64, 1.2345678901, "1.2345678901e0");
- try check(f64, 1.23456789012, "1.23456789012e0");
- try check(f64, 1.234567890123, "1.234567890123e0");
- try check(f64, 1.2345678901234, "1.2345678901234e0");
- try check(f64, 1.23456789012345, "1.23456789012345e0");
- try check(f64, 1.234567890123456, "1.234567890123456e0");
- try check(f64, 1.2345678901234567, "1.2345678901234567e0");
-
- try check(f64, 4.294967294, "4.294967294e0");
- try check(f64, 4.294967295, "4.294967295e0");
- try check(f64, 4.294967296, "4.294967296e0");
- try check(f64, 4.294967297, "4.294967297e0");
- try check(f64, 4.294967298, "4.294967298e0");
-}
-
-test "format f80" {
- try check(f80, 0.0, "0e0");
- try check(f80, -0.0, "-0e0");
- try check(f80, 1.0, "1e0");
- try check(f80, -1.0, "-1e0");
- try check(f80, std.math.nan(f80), "nan");
- try check(f80, std.math.inf(f80), "inf");
- try check(f80, -std.math.inf(f80), "-inf");
-
- try check(f80, 2.2250738585072014e-308, "2.2250738585072014e-308");
- try check(f80, 2.98023223876953125e-8, "2.98023223876953125e-8");
- try check(f80, -2.109808898695963e16, "-2.109808898695963e16");
- try check(f80, 4.940656e-318, "4.940656e-318");
- try check(f80, 1.18575755e-316, "1.18575755e-316");
- try check(f80, 2.989102097996e-312, "2.989102097996e-312");
- try check(f80, 9.0608011534336e15, "9.0608011534336e15");
- try check(f80, 4.708356024711512e18, "4.708356024711512e18");
- try check(f80, 9.409340012568248e18, "9.409340012568248e18");
- try check(f80, 1.2345678, "1.2345678e0");
-}
-
-test "format f128" {
- try check(f128, 0.0, "0e0");
- try check(f128, -0.0, "-0e0");
- try check(f128, 1.0, "1e0");
- try check(f128, -1.0, "-1e0");
- try check(f128, std.math.nan(f128), "nan");
- try check(f128, std.math.inf(f128), "inf");
- try check(f128, -std.math.inf(f128), "-inf");
-
- try check(f128, 2.2250738585072014e-308, "2.2250738585072014e-308");
- try check(f128, 2.98023223876953125e-8, "2.98023223876953125e-8");
- try check(f128, -2.109808898695963e16, "-2.109808898695963e16");
- try check(f128, 4.940656e-318, "4.940656e-318");
- try check(f128, 1.18575755e-316, "1.18575755e-316");
- try check(f128, 2.989102097996e-312, "2.989102097996e-312");
- try check(f128, 9.0608011534336e15, "9.0608011534336e15");
- try check(f128, 4.708356024711512e18, "4.708356024711512e18");
- try check(f128, 9.409340012568248e18, "9.409340012568248e18");
- try check(f128, 1.2345678, "1.2345678e0");
-}
-
-test "format float to decimal with zero precision" {
- try expectFmt("5", "{d:.0}", .{5});
- try expectFmt("6", "{d:.0}", .{6});
- try expectFmt("7", "{d:.0}", .{7});
- try expectFmt("8", "{d:.0}", .{8});
-}
