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zig/lib/std/fmt/errol.zig

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// SPDX-License-Identifier: MIT
// Copyright (c) 2015-2020 Zig Contributors
// This file is part of [zig](https://ziglang.org/), which is MIT licensed.
// The MIT license requires this copyright notice to be included in all copies
// and substantial portions of the software.
const std = @import("../std.zig");
const enum3 = @import("errol/enum3.zig").enum3;
const enum3_data = @import("errol/enum3.zig").enum3_data;
const lookup_table = @import("errol/lookup.zig").lookup_table;
const HP = @import("errol/lookup.zig").HP;
const math = std.math;
const mem = std.mem;
const assert = std.debug.assert;
pub const FloatDecimal = struct {
digits: []u8,
exp: i32,
};
pub const RoundMode = enum {
// Round only the fractional portion (e.g. 1234.23 has precision 2)
Decimal,
// Round the entire whole/fractional portion (e.g. 1.23423e3 has precision 5)
Scientific,
};
/// Round a FloatDecimal as returned by errol3 to the specified fractional precision.
/// All digits after the specified precision should be considered invalid.
pub fn roundToPrecision(float_decimal: *FloatDecimal, precision: usize, mode: RoundMode) void {
// The round digit refers to the index which we should look at to determine
// whether we need to round to match the specified precision.
var round_digit: usize = 0;
switch (mode) {
RoundMode.Decimal => {
if (float_decimal.exp >= 0) {
round_digit = precision + @intCast(usize, float_decimal.exp);
} else {
// if a small negative exp, then adjust we need to offset by the number
// of leading zeros that will occur.
const min_exp_required = @intCast(usize, -float_decimal.exp);
if (precision > min_exp_required) {
round_digit = precision - min_exp_required;
}
}
},
RoundMode.Scientific => {
round_digit = 1 + precision;
},
}
// It suffices to look at just this digit. We don't round and propagate say 0.04999 to 0.05
// first, and then to 0.1 in the case of a {.1} single precision.
// Find the digit which will signify the round point and start rounding backwards.
if (round_digit < float_decimal.digits.len and float_decimal.digits[round_digit] - '0' >= 5) {
assert(round_digit >= 0);
var i = round_digit;
while (true) {
if (i == 0) {
// Rounded all the way past the start. This was of the form 9.999...
// Slot the new digit in place and increase the exponent.
float_decimal.exp += 1;
// Re-size the buffer to use the reserved leading byte.
const one_before = @intToPtr([*]u8, @ptrToInt(&float_decimal.digits[0]) - 1);
float_decimal.digits = one_before[0 .. float_decimal.digits.len + 1];
float_decimal.digits[0] = '1';
return;
}
i -= 1;
const new_value = (float_decimal.digits[i] - '0' + 1) % 10;
float_decimal.digits[i] = new_value + '0';
// must continue rounding until non-9
if (new_value != 0) {
return;
}
}
}
}
/// Corrected Errol3 double to ASCII conversion.
pub fn errol3(value: f64, buffer: []u8) FloatDecimal {
const bits = @bitCast(u64, value);
const i = tableLowerBound(bits);
if (i < enum3.len and enum3[i] == bits) {
const data = enum3_data[i];
const digits = buffer[1 .. data.str.len + 1];
mem.copy(u8, digits, data.str);
return FloatDecimal{
.digits = digits,
.exp = data.exp,
};
}
return errol3u(value, buffer);
}
/// Uncorrected Errol3 double to ASCII conversion.
fn errol3u(val: f64, buffer: []u8) FloatDecimal {
// check if in integer or fixed range
if (val > 9.007199254740992e15 and val < 3.40282366920938e+38) {
return errolInt(val, buffer);
} else if (val >= 16.0 and val < 9.007199254740992e15) {
return errolFixed(val, buffer);
}
// normalize the midpoint
const e = math.frexp(val).exponent;
var exp = @floatToInt(i16, math.floor(307 + @intToFloat(f64, e) * 0.30103));
if (exp < 20) {
exp = 20;
} else if (@intCast(usize, exp) >= lookup_table.len) {
exp = @intCast(i16, lookup_table.len - 1);
}
var mid = lookup_table[@intCast(usize, exp)];
mid = hpProd(mid, val);
const lten = lookup_table[@intCast(usize, exp)].val;
exp -= 307;
var ten: f64 = 1.0;
while (mid.val > 10.0 or (mid.val == 10.0 and mid.off >= 0.0)) {
exp += 1;
hpDiv10(&mid);
ten /= 10.0;
}
while (mid.val < 1.0 or (mid.val == 1.0 and mid.off < 0.0)) {
exp -= 1;
hpMul10(&mid);
ten *= 10.0;
}
// compute boundaries
var high = HP{
.val = mid.val,
.off = mid.off + (fpnext(val) - val) * lten * ten / 2.0,
};
var low = HP{
.val = mid.val,
.off = mid.off + (fpprev(val) - val) * lten * ten / 2.0,
};
hpNormalize(&high);
hpNormalize(&low);
// normalized boundaries
while (high.val > 10.0 or (high.val == 10.0 and high.off >= 0.0)) {
exp += 1;
hpDiv10(&high);
hpDiv10(&low);
}
while (high.val < 1.0 or (high.val == 1.0 and high.off < 0.0)) {
exp -= 1;
hpMul10(&high);
hpMul10(&low);
}
// digit generation
// We generate digits starting at index 1. If rounding a buffer later then it may be
// required to generate a preceding digit in some cases (9.999) in which case we use
// the 0-index for this extra digit.
var buf_index: usize = 1;
while (true) {
var hdig = @floatToInt(u8, math.floor(high.val));
if ((high.val == @intToFloat(f64, hdig)) and (high.off < 0)) hdig -= 1;
var ldig = @floatToInt(u8, math.floor(low.val));
if ((low.val == @intToFloat(f64, ldig)) and (low.off < 0)) ldig -= 1;
if (ldig != hdig) break;
buffer[buf_index] = hdig + '0';
buf_index += 1;
high.val -= @intToFloat(f64, hdig);
low.val -= @intToFloat(f64, ldig);
hpMul10(&high);
hpMul10(&low);
}
const tmp = (high.val + low.val) / 2.0;
var mdig = @floatToInt(u8, math.floor(tmp + 0.5));
if ((@intToFloat(f64, mdig) - tmp) == 0.5 and (mdig & 0x1) != 0) mdig -= 1;
buffer[buf_index] = mdig + '0';
buf_index += 1;
return FloatDecimal{
.digits = buffer[1..buf_index],
.exp = exp,
};
}
fn tableLowerBound(k: u64) usize {
var i = enum3.len;
var j: usize = 0;
while (j < enum3.len) {
if (enum3[j] < k) {
j = 2 * j + 2;
} else {
i = j;
j = 2 * j + 1;
}
}
return i;
}
/// Compute the product of an HP number and a double.
/// @in: The HP number.
/// @val: The double.
/// &returns: The HP number.
fn hpProd(in: HP, val: f64) HP {
var hi: f64 = undefined;
var lo: f64 = undefined;
split(in.val, &hi, &lo);
var hi2: f64 = undefined;
var lo2: f64 = undefined;
split(val, &hi2, &lo2);
const p = in.val * val;
const e = ((hi * hi2 - p) + lo * hi2 + hi * lo2) + lo * lo2;
return HP{
.val = p,
.off = in.off * val + e,
};
}
/// Split a double into two halves.
/// @val: The double.
/// @hi: The high bits.
/// @lo: The low bits.
fn split(val: f64, hi: *f64, lo: *f64) void {
hi.* = gethi(val);
lo.* = val - hi.*;
}
fn gethi(in: f64) f64 {
const bits = @bitCast(u64, in);
const new_bits = bits & 0xFFFFFFFFF8000000;
return @bitCast(f64, new_bits);
}
/// Normalize the number by factoring in the error.
/// @hp: The float pair.
fn hpNormalize(hp: *HP) void {
const val = hp.val;
hp.val += hp.off;
hp.off += val - hp.val;
}
/// Divide the high-precision number by ten.
/// @hp: The high-precision number
fn hpDiv10(hp: *HP) void {
var val = hp.val;
hp.val /= 10.0;
hp.off /= 10.0;
val -= hp.val * 8.0;
val -= hp.val * 2.0;
hp.off += val / 10.0;
hpNormalize(hp);
}
/// Multiply the high-precision number by ten.
/// @hp: The high-precision number
fn hpMul10(hp: *HP) void {
const val = hp.val;
hp.val *= 10.0;
hp.off *= 10.0;
var off = hp.val;
off -= val * 8.0;
off -= val * 2.0;
hp.off -= off;
hpNormalize(hp);
}
/// Integer conversion algorithm, guaranteed correct, optimal, and best.
/// @val: The val.
/// @buf: The output buffer.
/// &return: The exponent.
fn errolInt(val: f64, buffer: []u8) FloatDecimal {
const pow19 = @as(u128, 1e19);
assert((val > 9.007199254740992e15) and val < (3.40282366920938e38));
var mid = @floatToInt(u128, val);
var low: u128 = mid - fpeint((fpnext(val) - val) / 2.0);
var high: u128 = mid + fpeint((val - fpprev(val)) / 2.0);
if (@bitCast(u64, val) & 0x1 != 0) {
high -= 1;
} else {
low -= 1;
}
var l64 = @intCast(u64, low % pow19);
const lf = @intCast(u64, (low / pow19) % pow19);
var h64 = @intCast(u64, high % pow19);
const hf = @intCast(u64, (high / pow19) % pow19);
if (lf != hf) {
l64 = lf;
h64 = hf;
mid = mid / (pow19 / 10);
}
var mi: i32 = mismatch10(l64, h64);
var x: u64 = 1;
{
var i: i32 = @boolToInt(lf == hf);
while (i < mi) : (i += 1) {
x *= 10;
}
}
const m64 = @truncate(u64, @divTrunc(mid, x));
if (lf != hf) mi += 19;
var buf_index = u64toa(m64, buffer) - 1;
if (mi != 0) {
buffer[buf_index - 1] += @boolToInt(buffer[buf_index] >= '5');
} else {
buf_index += 1;
}
return FloatDecimal{
.digits = buffer[0..buf_index],
.exp = @intCast(i32, buf_index) + mi,
};
}
/// Fixed point conversion algorithm, guaranteed correct, optimal, and best.
/// @val: The val.
/// @buf: The output buffer.
/// &return: The exponent.
fn errolFixed(val: f64, buffer: []u8) FloatDecimal {
assert((val >= 16.0) and (val < 9.007199254740992e15));
const u = @floatToInt(u64, val);
const n = @intToFloat(f64, u);
var mid = val - n;
var lo = ((fpprev(val) - n) + mid) / 2.0;
var hi = ((fpnext(val) - n) + mid) / 2.0;
var buf_index = u64toa(u, buffer);
var exp = @intCast(i32, buf_index);
var j = buf_index;
buffer[j] = 0;
if (mid != 0.0) {
while (mid != 0.0) {
lo *= 10.0;
const ldig = @floatToInt(i32, lo);
lo -= @intToFloat(f64, ldig);
mid *= 10.0;
const mdig = @floatToInt(i32, mid);
mid -= @intToFloat(f64, mdig);
hi *= 10.0;
const hdig = @floatToInt(i32, hi);
hi -= @intToFloat(f64, hdig);
buffer[j] = @intCast(u8, mdig + '0');
j += 1;
if (hdig != ldig or j > 50) break;
}
if (mid > 0.5) {
buffer[j - 1] += 1;
} else if ((mid == 0.5) and (buffer[j - 1] & 0x1) != 0) {
buffer[j - 1] += 1;
}
} else {
while (buffer[j - 1] == '0') {
buffer[j - 1] = 0;
j -= 1;
}
}
buffer[j] = 0;
return FloatDecimal{
.digits = buffer[0..j],
.exp = exp,
};
}
fn fpnext(val: f64) f64 {
return @bitCast(f64, @bitCast(u64, val) +% 1);
}
fn fpprev(val: f64) f64 {
return @bitCast(f64, @bitCast(u64, val) -% 1);
}
pub const c_digits_lut = [_]u8{
'0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6',
'0', '7', '0', '8', '0', '9', '1', '0', '1', '1', '1', '2', '1', '3',
'1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9', '2', '0',
'2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7',
'2', '8', '2', '9', '3', '0', '3', '1', '3', '2', '3', '3', '3', '4',
'3', '5', '3', '6', '3', '7', '3', '8', '3', '9', '4', '0', '4', '1',
'4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8',
'4', '9', '5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5',
'5', '6', '5', '7', '5', '8', '5', '9', '6', '0', '6', '1', '6', '2',
'6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
'7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6',
'7', '7', '7', '8', '7', '9', '8', '0', '8', '1', '8', '2', '8', '3',
'8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9', '9', '0',
'9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7',
'9', '8', '9', '9',
};
fn u64toa(value_param: u64, buffer: []u8) usize {
var value = value_param;
const kTen8: u64 = 100000000;
const kTen9: u64 = kTen8 * 10;
const kTen10: u64 = kTen8 * 100;
const kTen11: u64 = kTen8 * 1000;
const kTen12: u64 = kTen8 * 10000;
const kTen13: u64 = kTen8 * 100000;
const kTen14: u64 = kTen8 * 1000000;
const kTen15: u64 = kTen8 * 10000000;
const kTen16: u64 = kTen8 * kTen8;
var buf_index: usize = 0;
if (value < kTen8) {
const v = @intCast(u32, value);
if (v < 10000) {
const d1: u32 = (v / 100) << 1;
const d2: u32 = (v % 100) << 1;
if (v >= 1000) {
buffer[buf_index] = c_digits_lut[d1];
buf_index += 1;
}
if (v >= 100) {
buffer[buf_index] = c_digits_lut[d1 + 1];
buf_index += 1;
}
if (v >= 10) {
buffer[buf_index] = c_digits_lut[d2];
buf_index += 1;
}
buffer[buf_index] = c_digits_lut[d2 + 1];
buf_index += 1;
} else {
// value = bbbbcccc
const b: u32 = v / 10000;
const c: u32 = v % 10000;
const d1: u32 = (b / 100) << 1;
const d2: u32 = (b % 100) << 1;
const d3: u32 = (c / 100) << 1;
const d4: u32 = (c % 100) << 1;
if (value >= 10000000) {
buffer[buf_index] = c_digits_lut[d1];
buf_index += 1;
}
if (value >= 1000000) {
buffer[buf_index] = c_digits_lut[d1 + 1];
buf_index += 1;
}
if (value >= 100000) {
buffer[buf_index] = c_digits_lut[d2];
buf_index += 1;
}
buffer[buf_index] = c_digits_lut[d2 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d3];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d3 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d4];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d4 + 1];
buf_index += 1;
}
} else if (value < kTen16) {
const v0: u32 = @intCast(u32, value / kTen8);
const v1: u32 = @intCast(u32, value % kTen8);
const b0: u32 = v0 / 10000;
const c0: u32 = v0 % 10000;
const d1: u32 = (b0 / 100) << 1;
const d2: u32 = (b0 % 100) << 1;
const d3: u32 = (c0 / 100) << 1;
const d4: u32 = (c0 % 100) << 1;
const b1: u32 = v1 / 10000;
const c1: u32 = v1 % 10000;
const d5: u32 = (b1 / 100) << 1;
const d6: u32 = (b1 % 100) << 1;
const d7: u32 = (c1 / 100) << 1;
const d8: u32 = (c1 % 100) << 1;
if (value >= kTen15) {
buffer[buf_index] = c_digits_lut[d1];
buf_index += 1;
}
if (value >= kTen14) {
buffer[buf_index] = c_digits_lut[d1 + 1];
buf_index += 1;
}
if (value >= kTen13) {
buffer[buf_index] = c_digits_lut[d2];
buf_index += 1;
}
if (value >= kTen12) {
buffer[buf_index] = c_digits_lut[d2 + 1];
buf_index += 1;
}
if (value >= kTen11) {
buffer[buf_index] = c_digits_lut[d3];
buf_index += 1;
}
if (value >= kTen10) {
buffer[buf_index] = c_digits_lut[d3 + 1];
buf_index += 1;
}
if (value >= kTen9) {
buffer[buf_index] = c_digits_lut[d4];
buf_index += 1;
}
if (value >= kTen8) {
buffer[buf_index] = c_digits_lut[d4 + 1];
buf_index += 1;
}
buffer[buf_index] = c_digits_lut[d5];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d5 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d6];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d6 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d7];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d7 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d8];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d8 + 1];
buf_index += 1;
} else {
const a = @intCast(u32, value / kTen16); // 1 to 1844
value %= kTen16;
if (a < 10) {
buffer[buf_index] = '0' + @intCast(u8, a);
buf_index += 1;
} else if (a < 100) {
const i: u32 = a << 1;
buffer[buf_index] = c_digits_lut[i];
buf_index += 1;
buffer[buf_index] = c_digits_lut[i + 1];
buf_index += 1;
} else if (a < 1000) {
buffer[buf_index] = '0' + @intCast(u8, a / 100);
buf_index += 1;
const i: u32 = (a % 100) << 1;
buffer[buf_index] = c_digits_lut[i];
buf_index += 1;
buffer[buf_index] = c_digits_lut[i + 1];
buf_index += 1;
} else {
const i: u32 = (a / 100) << 1;
const j: u32 = (a % 100) << 1;
buffer[buf_index] = c_digits_lut[i];
buf_index += 1;
buffer[buf_index] = c_digits_lut[i + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[j];
buf_index += 1;
buffer[buf_index] = c_digits_lut[j + 1];
buf_index += 1;
}
const v0 = @intCast(u32, value / kTen8);
const v1 = @intCast(u32, value % kTen8);
const b0: u32 = v0 / 10000;
const c0: u32 = v0 % 10000;
const d1: u32 = (b0 / 100) << 1;
const d2: u32 = (b0 % 100) << 1;
const d3: u32 = (c0 / 100) << 1;
const d4: u32 = (c0 % 100) << 1;
const b1: u32 = v1 / 10000;
const c1: u32 = v1 % 10000;
const d5: u32 = (b1 / 100) << 1;
const d6: u32 = (b1 % 100) << 1;
const d7: u32 = (c1 / 100) << 1;
const d8: u32 = (c1 % 100) << 1;
buffer[buf_index] = c_digits_lut[d1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d1 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d2];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d2 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d3];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d3 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d4];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d4 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d5];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d5 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d6];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d6 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d7];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d7 + 1];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d8];
buf_index += 1;
buffer[buf_index] = c_digits_lut[d8 + 1];
buf_index += 1;
}
return buf_index;
}
fn fpeint(from: f64) u128 {
const bits = @bitCast(u64, from);
assert((bits & ((1 << 52) - 1)) == 0);
return @as(u128, 1) << @truncate(u7, (bits >> 52) -% 1023);
}
/// Given two different integers with the same length in terms of the number
/// of decimal digits, index the digits from the right-most position starting
/// from zero, find the first index where the digits in the two integers
/// divergent starting from the highest index.
/// @a: Integer a.
/// @b: Integer b.
/// &returns: An index within [0, 19).
fn mismatch10(a: u64, b: u64) i32 {
const pow10 = 10000000000;
const af = a / pow10;
const bf = b / pow10;
var i: i32 = 0;
var a_copy = a;
var b_copy = b;
if (af != bf) {
i = 10;
a_copy = af;
b_copy = bf;
}
while (true) : (i += 1) {
a_copy /= 10;
b_copy /= 10;
if (a_copy == b_copy) return i;
}
}
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