mirror of
https://github.com/ziglang/zig.git
synced 2025-12-06 14:23:09 +00:00
ff3bf98345
Found while fuzzing. Previously 1.1897314953572317650857593266280070162E4932 was parsed as +inf, which caused issues for round-trip serialization of floats. Only f128 had issues, but have added other tests for all floating point large normals. The max_exponent for f128 was wrong, it is subtly different in the decimal code-path as it is based on where the decimal digit should go. This needs to be 2 greater than the max exponent (e.g. 308 or 4932) to work correctly (greater by 1, then we use a >= comparision). In addition, I've removed the redundant `optimize` constant which was only use for testing the slow path locally.
494 lines
28 KiB
Zig
494 lines
28 KiB
Zig
const std = @import("std");
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const math = std.math;
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const common = @import("common.zig");
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const FloatStream = @import("FloatStream.zig");
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const isEightDigits = @import("common.zig").isEightDigits;
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const mantissaType = common.mantissaType;
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// Arbitrary-precision decimal class for fallback algorithms.
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//
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// This is only used if the fast-path (native floats) and
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// the Eisel-Lemire algorithm are unable to unambiguously
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// determine the float.
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//
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// The technique used is "Simple Decimal Conversion", developed
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// by Nigel Tao and Ken Thompson. A detailed description of the
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// algorithm can be found in "ParseNumberF64 by Simple Decimal Conversion",
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// available online: <https://nigeltao.github.io/blog/2020/parse-number-f64-simple.html>.
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//
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// Big-decimal implementation. We do not use the big.Int routines since we only require a maximum
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// fixed region of memory. Further, we require only a small subset of operations.
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//
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// This accepts a floating point parameter and will generate a Decimal which can correctly parse
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// the input with sufficient accuracy. Internally this means either a u64 mantissa (f16, f32 or f64)
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// or a u128 mantissa (f128).
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pub fn Decimal(comptime T: type) type {
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const MantissaT = mantissaType(T);
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std.debug.assert(MantissaT == u64 or MantissaT == u128);
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return struct {
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const Self = @This();
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/// The maximum number of digits required to unambiguously round a float.
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///
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/// For a double-precision IEEE-754 float, this required 767 digits,
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/// so we store the max digits + 1.
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///
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/// We can exactly represent a float in base `b` from base 2 if
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/// `b` is divisible by 2. This function calculates the exact number of
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/// digits required to exactly represent that float.
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///
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/// According to the "Handbook of Floating Point Arithmetic",
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/// for IEEE754, with emin being the min exponent, p2 being the
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/// precision, and b being the base, the number of digits follows as:
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///
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/// `−emin + p2 + ⌊(emin + 1) log(2, b) − log(1 − 2^(−p2), b)⌋`
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///
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/// For f32, this follows as:
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/// emin = -126
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/// p2 = 24
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///
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/// For f64, this follows as:
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/// emin = -1022
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/// p2 = 53
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///
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/// For f128, this follows as:
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/// emin = -16383
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/// p2 = 112
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///
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/// In Python:
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/// `-emin + p2 + math.floor((emin+ 1)*math.log(2, b)-math.log(1-2**(-p2), b))`
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pub const max_digits = if (MantissaT == u64) 768 else 11564;
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/// The max digits that can be exactly represented in a 64-bit integer.
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pub const max_digits_without_overflow = if (MantissaT == u64) 19 else 38;
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pub const decimal_point_range = if (MantissaT == u64) 2047 else 32767;
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pub const min_exponent = if (MantissaT == u64) -324 else -4966;
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pub const max_exponent = if (MantissaT == u64) 310 else 4934;
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pub const max_decimal_digits = if (MantissaT == u64) 18 else 37;
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/// The number of significant digits in the decimal.
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num_digits: usize,
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/// The offset of the decimal point in the significant digits.
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decimal_point: i32,
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/// If the number of significant digits stored in the decimal is truncated.
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truncated: bool,
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/// buffer of the raw digits, in the range [0, 9].
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digits: [max_digits]u8,
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pub fn new() Self {
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return .{
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.num_digits = 0,
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.decimal_point = 0,
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.truncated = false,
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.digits = [_]u8{0} ** max_digits,
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};
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}
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/// Append a digit to the buffer
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pub fn tryAddDigit(self: *Self, digit: u8) void {
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if (self.num_digits < max_digits) {
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self.digits[self.num_digits] = digit;
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}
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self.num_digits += 1;
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}
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/// Trim trailing zeroes from the buffer
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pub fn trim(self: *Self) void {
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// All of the following calls to `Self::trim` can't panic because:
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//
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// 1. `parse_decimal` sets `num_digits` to a max of `max_digits`.
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// 2. `right_shift` sets `num_digits` to `write_index`, which is bounded by `num_digits`.
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// 3. `left_shift` `num_digits` to a max of `max_digits`.
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//
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// Trim is only called in `right_shift` and `left_shift`.
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std.debug.assert(self.num_digits <= max_digits);
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while (self.num_digits != 0 and self.digits[self.num_digits - 1] == 0) {
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self.num_digits -= 1;
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}
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}
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pub fn round(self: *Self) MantissaT {
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if (self.num_digits == 0 or self.decimal_point < 0) {
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return 0;
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} else if (self.decimal_point > max_decimal_digits) {
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return math.maxInt(MantissaT);
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}
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const dp = @as(usize, @intCast(self.decimal_point));
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var n: MantissaT = 0;
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var i: usize = 0;
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while (i < dp) : (i += 1) {
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n *= 10;
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if (i < self.num_digits) {
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n += @as(MantissaT, self.digits[i]);
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}
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}
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var round_up = false;
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if (dp < self.num_digits) {
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round_up = self.digits[dp] >= 5;
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if (self.digits[dp] == 5 and dp + 1 == self.num_digits) {
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round_up = self.truncated or ((dp != 0) and (1 & self.digits[dp - 1] != 0));
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}
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}
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if (round_up) {
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n += 1;
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}
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return n;
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}
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/// Computes decimal * 2^shift.
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pub fn leftShift(self: *Self, shift: usize) void {
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if (self.num_digits == 0) {
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return;
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}
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const num_new_digits = self.numberOfDigitsLeftShift(shift);
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var read_index = self.num_digits;
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var write_index = self.num_digits + num_new_digits;
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var n: MantissaT = 0;
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while (read_index != 0) {
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read_index -= 1;
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write_index -= 1;
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n += math.shl(MantissaT, self.digits[read_index], shift);
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const quotient = n / 10;
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const remainder = n - (10 * quotient);
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if (write_index < max_digits) {
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self.digits[write_index] = @as(u8, @intCast(remainder));
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} else if (remainder > 0) {
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self.truncated = true;
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}
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n = quotient;
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}
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while (n > 0) {
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write_index -= 1;
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const quotient = n / 10;
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const remainder = n - (10 * quotient);
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if (write_index < max_digits) {
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self.digits[write_index] = @as(u8, @intCast(remainder));
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} else if (remainder > 0) {
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self.truncated = true;
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}
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n = quotient;
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}
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self.num_digits += num_new_digits;
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if (self.num_digits > max_digits) {
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self.num_digits = max_digits;
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}
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self.decimal_point += @as(i32, @intCast(num_new_digits));
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self.trim();
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}
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/// Computes decimal * 2^-shift.
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pub fn rightShift(self: *Self, shift: usize) void {
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var read_index: usize = 0;
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var write_index: usize = 0;
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var n: MantissaT = 0;
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while (math.shr(MantissaT, n, shift) == 0) {
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if (read_index < self.num_digits) {
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n = (10 * n) + self.digits[read_index];
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read_index += 1;
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} else if (n == 0) {
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return;
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} else {
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while (math.shr(MantissaT, n, shift) == 0) {
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n *= 10;
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read_index += 1;
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}
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break;
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}
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}
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self.decimal_point -= @as(i32, @intCast(read_index)) - 1;
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if (self.decimal_point < -decimal_point_range) {
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self.num_digits = 0;
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self.decimal_point = 0;
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self.truncated = false;
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return;
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}
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const mask = math.shl(MantissaT, 1, shift) - 1;
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while (read_index < self.num_digits) {
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const new_digit = @as(u8, @intCast(math.shr(MantissaT, n, shift)));
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n = (10 * (n & mask)) + self.digits[read_index];
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read_index += 1;
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self.digits[write_index] = new_digit;
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write_index += 1;
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}
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while (n > 0) {
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const new_digit = @as(u8, @intCast(math.shr(MantissaT, n, shift)));
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n = 10 * (n & mask);
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if (write_index < max_digits) {
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self.digits[write_index] = new_digit;
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write_index += 1;
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} else if (new_digit > 0) {
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self.truncated = true;
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}
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}
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self.num_digits = write_index;
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self.trim();
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}
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/// Parse a bit integer representation of the float as a decimal.
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// We do not verify underscores in this path since these will have been verified
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// via parse.parseNumber so can assume the number is well-formed.
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// This code-path does not have to handle hex-floats since these will always be handled via another
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// function prior to this.
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pub fn parse(s: []const u8) Self {
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var d = Self.new();
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var stream = FloatStream.init(s);
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stream.skipChars2('0', '_');
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while (stream.scanDigit(10)) |digit| {
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d.tryAddDigit(digit);
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}
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if (stream.firstIs('.')) {
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stream.advance(1);
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const marker = stream.offsetTrue();
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// Skip leading zeroes
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if (d.num_digits == 0) {
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stream.skipChars('0');
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}
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while (stream.hasLen(8) and d.num_digits + 8 < max_digits) {
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const v = stream.readU64Unchecked();
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if (!isEightDigits(v)) {
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break;
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}
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std.mem.writeInt(u64, d.digits[d.num_digits..][0..8], v - 0x3030_3030_3030_3030, .little);
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d.num_digits += 8;
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stream.advance(8);
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}
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while (stream.scanDigit(10)) |digit| {
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d.tryAddDigit(digit);
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}
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d.decimal_point = @as(i32, @intCast(marker)) - @as(i32, @intCast(stream.offsetTrue()));
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}
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if (d.num_digits != 0) {
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// Ignore trailing zeros if any
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var n_trailing_zeros: usize = 0;
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var i = stream.offsetTrue() - 1;
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while (true) {
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if (s[i] == '0') {
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n_trailing_zeros += 1;
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} else if (s[i] != '.') {
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break;
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}
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i -= 1;
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if (i == 0) break;
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}
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d.decimal_point += @as(i32, @intCast(n_trailing_zeros));
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d.num_digits -= n_trailing_zeros;
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d.decimal_point += @as(i32, @intCast(d.num_digits));
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if (d.num_digits > max_digits) {
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d.truncated = true;
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d.num_digits = max_digits;
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}
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}
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if (stream.firstIsLower('e')) {
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stream.advance(1);
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var neg_exp = false;
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if (stream.firstIs('-')) {
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neg_exp = true;
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stream.advance(1);
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} else if (stream.firstIs('+')) {
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stream.advance(1);
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}
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var exp_num: i32 = 0;
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while (stream.scanDigit(10)) |digit| {
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if (exp_num < 0x10000) {
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exp_num = 10 * exp_num + digit;
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}
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}
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d.decimal_point += if (neg_exp) -exp_num else exp_num;
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}
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var i = d.num_digits;
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while (i < max_digits_without_overflow) : (i += 1) {
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d.digits[i] = 0;
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}
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return d;
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}
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// Compute the number decimal digits introduced by a base-2 shift. This is performed
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// by storing the leading digits of 1/2^i = 5^i and using these along with the cut-off
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// value to quickly determine the decimal shift from binary.
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//
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// See also https://github.com/golang/go/blob/go1.15.3/src/strconv/decimal.go#L163 for
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// another description of the method.
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pub fn numberOfDigitsLeftShift(self: *Self, shift: usize) usize {
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const ShiftCutoff = struct {
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delta: u8,
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cutoff: []const u8,
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};
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// Leading digits of 1/2^i = 5^i.
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//
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// ```
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// import math
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//
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// bits = 128
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// for i in range(bits):
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// log2 = math.log(2)/math.log(10)
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// print(f'.{{ .delta = {int(log2*i+1)}, .cutoff = "{5**i}" }}, // {2**i}')
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// ```
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const pow2_to_pow5_table = [_]ShiftCutoff{
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.{ .delta = 0, .cutoff = "" },
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.{ .delta = 1, .cutoff = "5" }, // 2
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.{ .delta = 1, .cutoff = "25" }, // 4
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.{ .delta = 1, .cutoff = "125" }, // 8
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.{ .delta = 2, .cutoff = "625" }, // 16
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.{ .delta = 2, .cutoff = "3125" }, // 32
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.{ .delta = 2, .cutoff = "15625" }, // 64
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.{ .delta = 3, .cutoff = "78125" }, // 128
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.{ .delta = 3, .cutoff = "390625" }, // 256
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.{ .delta = 3, .cutoff = "1953125" }, // 512
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.{ .delta = 4, .cutoff = "9765625" }, // 1024
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.{ .delta = 4, .cutoff = "48828125" }, // 2048
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.{ .delta = 4, .cutoff = "244140625" }, // 4096
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.{ .delta = 4, .cutoff = "1220703125" }, // 8192
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.{ .delta = 5, .cutoff = "6103515625" }, // 16384
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.{ .delta = 5, .cutoff = "30517578125" }, // 32768
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.{ .delta = 5, .cutoff = "152587890625" }, // 65536
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.{ .delta = 6, .cutoff = "762939453125" }, // 131072
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.{ .delta = 6, .cutoff = "3814697265625" }, // 262144
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.{ .delta = 6, .cutoff = "19073486328125" }, // 524288
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.{ .delta = 7, .cutoff = "95367431640625" }, // 1048576
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.{ .delta = 7, .cutoff = "476837158203125" }, // 2097152
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.{ .delta = 7, .cutoff = "2384185791015625" }, // 4194304
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.{ .delta = 7, .cutoff = "11920928955078125" }, // 8388608
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.{ .delta = 8, .cutoff = "59604644775390625" }, // 16777216
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.{ .delta = 8, .cutoff = "298023223876953125" }, // 33554432
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.{ .delta = 8, .cutoff = "1490116119384765625" }, // 67108864
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.{ .delta = 9, .cutoff = "7450580596923828125" }, // 134217728
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.{ .delta = 9, .cutoff = "37252902984619140625" }, // 268435456
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.{ .delta = 9, .cutoff = "186264514923095703125" }, // 536870912
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.{ .delta = 10, .cutoff = "931322574615478515625" }, // 1073741824
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.{ .delta = 10, .cutoff = "4656612873077392578125" }, // 2147483648
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.{ .delta = 10, .cutoff = "23283064365386962890625" }, // 4294967296
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.{ .delta = 10, .cutoff = "116415321826934814453125" }, // 8589934592
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.{ .delta = 11, .cutoff = "582076609134674072265625" }, // 17179869184
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.{ .delta = 11, .cutoff = "2910383045673370361328125" }, // 34359738368
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.{ .delta = 11, .cutoff = "14551915228366851806640625" }, // 68719476736
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.{ .delta = 12, .cutoff = "72759576141834259033203125" }, // 137438953472
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.{ .delta = 12, .cutoff = "363797880709171295166015625" }, // 274877906944
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.{ .delta = 12, .cutoff = "1818989403545856475830078125" }, // 549755813888
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.{ .delta = 13, .cutoff = "9094947017729282379150390625" }, // 1099511627776
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.{ .delta = 13, .cutoff = "45474735088646411895751953125" }, // 2199023255552
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.{ .delta = 13, .cutoff = "227373675443232059478759765625" }, // 4398046511104
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.{ .delta = 13, .cutoff = "1136868377216160297393798828125" }, // 8796093022208
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.{ .delta = 14, .cutoff = "5684341886080801486968994140625" }, // 17592186044416
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.{ .delta = 14, .cutoff = "28421709430404007434844970703125" }, // 35184372088832
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.{ .delta = 14, .cutoff = "142108547152020037174224853515625" }, // 70368744177664
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.{ .delta = 15, .cutoff = "710542735760100185871124267578125" }, // 140737488355328
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.{ .delta = 15, .cutoff = "3552713678800500929355621337890625" }, // 281474976710656
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.{ .delta = 15, .cutoff = "17763568394002504646778106689453125" }, // 562949953421312
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.{ .delta = 16, .cutoff = "88817841970012523233890533447265625" }, // 1125899906842624
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.{ .delta = 16, .cutoff = "444089209850062616169452667236328125" }, // 2251799813685248
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.{ .delta = 16, .cutoff = "2220446049250313080847263336181640625" }, // 4503599627370496
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.{ .delta = 16, .cutoff = "11102230246251565404236316680908203125" }, // 9007199254740992
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.{ .delta = 17, .cutoff = "55511151231257827021181583404541015625" }, // 18014398509481984
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.{ .delta = 17, .cutoff = "277555756156289135105907917022705078125" }, // 36028797018963968
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.{ .delta = 17, .cutoff = "1387778780781445675529539585113525390625" }, // 72057594037927936
|
||
.{ .delta = 18, .cutoff = "6938893903907228377647697925567626953125" }, // 144115188075855872
|
||
.{ .delta = 18, .cutoff = "34694469519536141888238489627838134765625" }, // 288230376151711744
|
||
.{ .delta = 18, .cutoff = "173472347597680709441192448139190673828125" }, // 576460752303423488
|
||
.{ .delta = 19, .cutoff = "867361737988403547205962240695953369140625" }, // 1152921504606846976
|
||
.{ .delta = 19, .cutoff = "4336808689942017736029811203479766845703125" }, // 2305843009213693952
|
||
.{ .delta = 19, .cutoff = "21684043449710088680149056017398834228515625" }, // 4611686018427387904
|
||
.{ .delta = 19, .cutoff = "108420217248550443400745280086994171142578125" }, // 9223372036854775808
|
||
.{ .delta = 20, .cutoff = "542101086242752217003726400434970855712890625" }, // 18446744073709551616
|
||
.{ .delta = 20, .cutoff = "2710505431213761085018632002174854278564453125" }, // 36893488147419103232
|
||
.{ .delta = 20, .cutoff = "13552527156068805425093160010874271392822265625" }, // 73786976294838206464
|
||
.{ .delta = 21, .cutoff = "67762635780344027125465800054371356964111328125" }, // 147573952589676412928
|
||
.{ .delta = 21, .cutoff = "338813178901720135627329000271856784820556640625" }, // 295147905179352825856
|
||
.{ .delta = 21, .cutoff = "1694065894508600678136645001359283924102783203125" }, // 590295810358705651712
|
||
.{ .delta = 22, .cutoff = "8470329472543003390683225006796419620513916015625" }, // 1180591620717411303424
|
||
.{ .delta = 22, .cutoff = "42351647362715016953416125033982098102569580078125" }, // 2361183241434822606848
|
||
.{ .delta = 22, .cutoff = "211758236813575084767080625169910490512847900390625" }, // 4722366482869645213696
|
||
.{ .delta = 22, .cutoff = "1058791184067875423835403125849552452564239501953125" }, // 9444732965739290427392
|
||
.{ .delta = 23, .cutoff = "5293955920339377119177015629247762262821197509765625" }, // 18889465931478580854784
|
||
.{ .delta = 23, .cutoff = "26469779601696885595885078146238811314105987548828125" }, // 37778931862957161709568
|
||
.{ .delta = 23, .cutoff = "132348898008484427979425390731194056570529937744140625" }, // 75557863725914323419136
|
||
.{ .delta = 24, .cutoff = "661744490042422139897126953655970282852649688720703125" }, // 151115727451828646838272
|
||
.{ .delta = 24, .cutoff = "3308722450212110699485634768279851414263248443603515625" }, // 302231454903657293676544
|
||
.{ .delta = 24, .cutoff = "16543612251060553497428173841399257071316242218017578125" }, // 604462909807314587353088
|
||
.{ .delta = 25, .cutoff = "82718061255302767487140869206996285356581211090087890625" }, // 1208925819614629174706176
|
||
.{ .delta = 25, .cutoff = "413590306276513837435704346034981426782906055450439453125" }, // 2417851639229258349412352
|
||
.{ .delta = 25, .cutoff = "2067951531382569187178521730174907133914530277252197265625" }, // 4835703278458516698824704
|
||
.{ .delta = 25, .cutoff = "10339757656912845935892608650874535669572651386260986328125" }, // 9671406556917033397649408
|
||
.{ .delta = 26, .cutoff = "51698788284564229679463043254372678347863256931304931640625" }, // 19342813113834066795298816
|
||
.{ .delta = 26, .cutoff = "258493941422821148397315216271863391739316284656524658203125" }, // 38685626227668133590597632
|
||
.{ .delta = 26, .cutoff = "1292469707114105741986576081359316958696581423282623291015625" }, // 77371252455336267181195264
|
||
.{ .delta = 27, .cutoff = "6462348535570528709932880406796584793482907116413116455078125" }, // 154742504910672534362390528
|
||
.{ .delta = 27, .cutoff = "32311742677852643549664402033982923967414535582065582275390625" }, // 309485009821345068724781056
|
||
.{ .delta = 27, .cutoff = "161558713389263217748322010169914619837072677910327911376953125" }, // 618970019642690137449562112
|
||
.{ .delta = 28, .cutoff = "807793566946316088741610050849573099185363389551639556884765625" }, // 1237940039285380274899124224
|
||
.{ .delta = 28, .cutoff = "4038967834731580443708050254247865495926816947758197784423828125" }, // 2475880078570760549798248448
|
||
.{ .delta = 28, .cutoff = "20194839173657902218540251271239327479634084738790988922119140625" }, // 4951760157141521099596496896
|
||
.{ .delta = 28, .cutoff = "100974195868289511092701256356196637398170423693954944610595703125" }, // 9903520314283042199192993792
|
||
.{ .delta = 29, .cutoff = "504870979341447555463506281780983186990852118469774723052978515625" }, // 19807040628566084398385987584
|
||
.{ .delta = 29, .cutoff = "2524354896707237777317531408904915934954260592348873615264892578125" }, // 39614081257132168796771975168
|
||
.{ .delta = 29, .cutoff = "12621774483536188886587657044524579674771302961744368076324462890625" }, // 79228162514264337593543950336
|
||
.{ .delta = 30, .cutoff = "63108872417680944432938285222622898373856514808721840381622314453125" }, // 158456325028528675187087900672
|
||
.{ .delta = 30, .cutoff = "315544362088404722164691426113114491869282574043609201908111572265625" }, // 316912650057057350374175801344
|
||
.{ .delta = 30, .cutoff = "1577721810442023610823457130565572459346412870218046009540557861328125" }, // 633825300114114700748351602688
|
||
.{ .delta = 31, .cutoff = "7888609052210118054117285652827862296732064351090230047702789306640625" }, // 1267650600228229401496703205376
|
||
.{ .delta = 31, .cutoff = "39443045261050590270586428264139311483660321755451150238513946533203125" }, // 2535301200456458802993406410752
|
||
.{ .delta = 31, .cutoff = "197215226305252951352932141320696557418301608777255751192569732666015625" }, // 5070602400912917605986812821504
|
||
.{ .delta = 32, .cutoff = "986076131526264756764660706603482787091508043886278755962848663330078125" }, // 10141204801825835211973625643008
|
||
.{ .delta = 32, .cutoff = "4930380657631323783823303533017413935457540219431393779814243316650390625" }, // 20282409603651670423947251286016
|
||
.{ .delta = 32, .cutoff = "24651903288156618919116517665087069677287701097156968899071216583251953125" }, // 40564819207303340847894502572032
|
||
.{ .delta = 32, .cutoff = "123259516440783094595582588325435348386438505485784844495356082916259765625" }, // 81129638414606681695789005144064
|
||
.{ .delta = 33, .cutoff = "616297582203915472977912941627176741932192527428924222476780414581298828125" }, // 162259276829213363391578010288128
|
||
.{ .delta = 33, .cutoff = "3081487911019577364889564708135883709660962637144621112383902072906494140625" }, // 324518553658426726783156020576256
|
||
.{ .delta = 33, .cutoff = "15407439555097886824447823540679418548304813185723105561919510364532470703125" }, // 649037107316853453566312041152512
|
||
.{ .delta = 34, .cutoff = "77037197775489434122239117703397092741524065928615527809597551822662353515625" }, // 1298074214633706907132624082305024
|
||
.{ .delta = 34, .cutoff = "385185988877447170611195588516985463707620329643077639047987759113311767578125" }, // 2596148429267413814265248164610048
|
||
.{ .delta = 34, .cutoff = "1925929944387235853055977942584927318538101648215388195239938795566558837890625" }, // 5192296858534827628530496329220096
|
||
.{ .delta = 35, .cutoff = "9629649721936179265279889712924636592690508241076940976199693977832794189453125" }, // 10384593717069655257060992658440192
|
||
.{ .delta = 35, .cutoff = "48148248609680896326399448564623182963452541205384704880998469889163970947265625" }, // 20769187434139310514121985316880384
|
||
.{ .delta = 35, .cutoff = "240741243048404481631997242823115914817262706026923524404992349445819854736328125" }, // 41538374868278621028243970633760768
|
||
.{ .delta = 35, .cutoff = "1203706215242022408159986214115579574086313530134617622024961747229099273681640625" }, // 83076749736557242056487941267521536
|
||
.{ .delta = 36, .cutoff = "6018531076210112040799931070577897870431567650673088110124808736145496368408203125" }, // 166153499473114484112975882535043072
|
||
.{ .delta = 36, .cutoff = "30092655381050560203999655352889489352157838253365440550624043680727481842041015625" }, // 332306998946228968225951765070086144
|
||
.{ .delta = 36, .cutoff = "150463276905252801019998276764447446760789191266827202753120218403637409210205078125" }, // 664613997892457936451903530140172288
|
||
.{ .delta = 37, .cutoff = "752316384526264005099991383822237233803945956334136013765601092018187046051025390625" }, // 1329227995784915872903807060280344576
|
||
.{ .delta = 37, .cutoff = "3761581922631320025499956919111186169019729781670680068828005460090935230255126953125" }, // 2658455991569831745807614120560689152
|
||
.{ .delta = 37, .cutoff = "18807909613156600127499784595555930845098648908353400344140027300454676151275634765625" }, // 5316911983139663491615228241121378304
|
||
.{ .delta = 38, .cutoff = "94039548065783000637498922977779654225493244541767001720700136502273380756378173828125" }, // 10633823966279326983230456482242756608
|
||
.{ .delta = 38, .cutoff = "470197740328915003187494614888898271127466222708835008603500682511366903781890869140625" }, // 21267647932558653966460912964485513216
|
||
.{ .delta = 38, .cutoff = "2350988701644575015937473074444491355637331113544175043017503412556834518909454345703125" }, // 42535295865117307932921825928971026432
|
||
.{ .delta = 38, .cutoff = "11754943508222875079687365372222456778186655567720875215087517062784172594547271728515625" }, // 85070591730234615865843651857942052864
|
||
.{ .delta = 39, .cutoff = "58774717541114375398436826861112283890933277838604376075437585313920862972736358642578125" }, // 170141183460469231731687303715884105728
|
||
};
|
||
|
||
std.debug.assert(shift < pow2_to_pow5_table.len);
|
||
const x = pow2_to_pow5_table[shift];
|
||
|
||
// Compare leading digits of current to check if lexicographically less than cutoff.
|
||
for (x.cutoff, 0..) |p5, i| {
|
||
if (i >= self.num_digits) {
|
||
return x.delta - 1;
|
||
} else if (self.digits[i] == p5 - '0') { // digits are stored as integers
|
||
continue;
|
||
} else if (self.digits[i] < p5 - '0') {
|
||
return x.delta - 1;
|
||
} else {
|
||
return x.delta;
|
||
}
|
||
return x.delta;
|
||
}
|
||
return x.delta;
|
||
}
|
||
};
|
||
}
|