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ftoa in V (#3831)

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penguindark
2020-02-25 11:12:37 +01:00
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vlib/strconv/ftoa/f64_str.v Normal file
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/**********************************************************************
*
* f32 to string
*
* Copyright (c) 2019-2020 Dario Deledda. All rights reserved.
* Use of this source code is governed by an MIT license
* that can be found in the LICENSE file.
*
* This file contains the f64 to string functions
*
* These functions are based on the work of:
* Publication:PLDI 2018: Proceedings of the 39th ACM SIGPLAN
* Conference on Programming Language Design and ImplementationJune 2018
* Pages 270–282 https://doi.org/10.1145/3192366.3192369
*
* inspired by the Go version here:
* https://github.com/cespare/ryu/tree/ba56a33f39e3bbbfa409095d0f9ae168a595feea
*
**********************************************************************/
module ftoa
struct Uint128 {
mut:
lo u64 = u64(0)
hi u64 = u64(0)
}
// dec64 is a floating decimal type representing m * 10^e.
struct Dec64 {
mut:
m u64 = u64(0)
e int = 0
}
// support union for convert f64 to u64
union Uf64 {
mut:
f f64 = f64(0)
u u64
}
/******************************************************************************
*
* Conversion Functions
*
******************************************************************************/
const(
mantbits64 = u32(52)
expbits64 = u32(11)
bias64 = u32(1023) // f64 exponent bias
maxexp64 = 2047
)
fn (d Dec64) get_string_64(neg bool, n_digit int) string {
mut out := d.m
mut out_len := decimal_len_64(out)
mut buf := [byte(0)].repeat(out_len + 6 + 1 +1) // sign + mant_len + . + e + e_sign + exp_len(2) + \0
mut i := 0
if n_digit > 0 && out_len > n_digit {
out_len = n_digit+1
}
if neg {
buf[i]=`-`
i++
}
mut disp := 0
if out_len <= 1 {
disp = 1
}
y := i + out_len
mut x := 0
for x < (out_len-disp-1) {
buf[y - x] = `0` + byte(out%10)
out /= 10
i++
x++
}
if out_len >= 1 {
buf[y - x] = `.`
x++
i++
}
if y-x >= 0 {
buf[y - x] = `0` + byte(out%10)
i++
}
/*
x=0
for x<buf.len {
C.printf("d:%c\n",buf[x])
x++
}
C.printf("\n")
*/
buf[i]=`e`
i++
mut exp := d.e + out_len - 1
if exp < 0 {
buf[i]=`-`
i++
exp = -exp
} else {
buf[i]=`+`
i++
}
// Always print two digits to match strconv's formatting.
/* d1 := exp % 10
d0 := exp / 10
buf[i]=`0` + byte(d0)
i++
buf[i]=`0` + byte(d1)
i++
buf[i]=0
*/
// Always print at least two digits to match strconv's formatting.
d2 := exp % 10
exp /= 10
d1 := exp % 10
d0 := exp / 10
if d0 > 0 {
buf[i]=`0` + byte(d0)
i++
}
buf[i]=`0` + byte(d1)
i++
buf[i]=`0` + byte(d2)
i++
buf[i]=0
/*
x=0
for x<buf.len {
C.printf("d:%c\n",buf[x])
x++
}
*/
return tos(byteptr(&buf[0]), i)
}
fn f64_to_decimal_exact_int(i_mant u64, exp u64) (Dec64, bool) {
mut d := Dec64{}
e := exp - bias64
if e > mantbits64 {
return d, false
}
shift := mantbits64 - e
mant := i_mant | 0x0010_0000_0000_0000 // implicit 1
//mant := i_mant | (1 << mantbits64) // implicit 1
d.m = mant >> shift
if (d.m << shift) != mant {
return d, false
}
for (d.m % 10) == 0 {
d.m /= 10
d.e++
}
return d, true
}
fn f64_to_decimal(mant u64, exp u64) Dec64 {
mut e2 := 0
mut m2 := u64(0)
if exp == 0 {
// We subtract 2 so that the bounds computation has
// 2 additional bits.
e2 = 1 - bias64 - mantbits64 - 2
m2 = mant
} else {
e2 = int(exp) - bias64 - mantbits64 - 2
m2 = (u64(1)<<mantbits64) | mant
}
even := (m2 & 1) == 0
accept_bounds := even
// Step 2: Determine the interval of valid decimal representations.
mv := u64(4 * m2)
mm_shift := bool_to_u64(mant != 0 || exp <= 1)
// Step 3: Convert to a decimal power base uing 128-bit arithmetic.
mut vr := u64(0)
mut vp := u64(0)
mut vm := u64(0)
mut e10 := 0
mut vm_is_trailing_zeros := false
mut vr_is_trailing_zeros := false
if e2 >= 0 {
// This expression is slightly faster than max(0, log10Pow2(e2) - 1).
q := log10_pow2(e2) - bool_to_u32(e2 > 3)
e10 = int(q)
k := pow5_inv_num_bits_64 + pow5_bits(int(q)) - 1
i := -e2 + int(q) + k
mul := pow5_inv_split_64[q]
vr = mul_shift_64(u64(4) * m2 , mul, i)
vp = mul_shift_64(u64(4) * m2 + u64(2) , mul, i)
vm = mul_shift_64(u64(4) * m2 - u64(1) - mm_shift, mul, i)
if q <= 21 {
// This should use q <= 22, but I think 21 is also safe.
// Smaller values may still be safe, but it's more
// difficult to reason about them. Only one of mp, mv,
// and mm can be a multiple of 5, if any.
if mv%5 == 0 {
vr_is_trailing_zeros = multiple_of_power_of_five_64(mv, q)
} else if accept_bounds {
// Same as min(e2 + (^mm & 1), pow5Factor64(mm)) >= q
// <=> e2 + (^mm & 1) >= q && pow5Factor64(mm) >= q
// <=> true && pow5Factor64(mm) >= q, since e2 >= q.
vm_is_trailing_zeros = multiple_of_power_of_five_64(mv-1-mm_shift, q)
} else if multiple_of_power_of_five_64(mv+2, q) {
vp--
}
}
} else {
// This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
q := log10_pow5(-e2) - bool_to_u32(-e2 > 1)
e10 = int(q) + e2
i := -e2 - int(q)
k := pow5_bits(i) - pow5_num_bits_64
mut j := int(q) - k
mul := pow5_split_64[i]
vr = mul_shift_64(u64(4) * m2 , mul, j)
vp = mul_shift_64(u64(4) * m2 + u64(2) , mul, j)
vm = mul_shift_64(u64(4) * m2 - u64(1) - mm_shift, mul, j)
if q <= 1 {
// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
// mv = 4 * m2, so it always has at least two trailing 0 bits.
vr_is_trailing_zeros = true
if accept_bounds {
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
vm_is_trailing_zeros = (mm_shift == 1)
} else {
// mp = mv + 2, so it always has at least one trailing 0 bit.
vp--
}
} else if q < 63 { // TODO(ulfjack/cespare): Use a tighter bound here.
// We need to compute min(ntz(mv), pow5Factor64(mv) - e2) >= q - 1
// <=> ntz(mv) >= q - 1 && pow5Factor64(mv) - e2 >= q - 1
// <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q)
// <=> (mv & ((1 << (q - 1)) - 1)) == 0
// We also need to make sure that the left shift does not overflow.
vr_is_trailing_zeros = multiple_of_power_of_two_64(mv, q - 1)
}
}
// Step 4: Find the shortest decimal representation
// in the interval of valid representations.
mut removed := 0
mut last_removed_digit := byte(0)
mut out := u64(0)
// On average, we remove ~2 digits.
if vm_is_trailing_zeros || vr_is_trailing_zeros {
// General case, which happens rarely (~0.7%).
for {
vp_div_10 := vp / 10
vm_div_10 := vm / 10
if vp_div_10 <= vm_div_10 {
break
}
vm_mod_10 := vm % 10
vr_div_10 := vr / 10
vr_mod_10 := vr % 10
vm_is_trailing_zeros = vm_is_trailing_zeros && vm_mod_10 == 0
vr_is_trailing_zeros = vr_is_trailing_zeros && (last_removed_digit == 0)
last_removed_digit = byte(vr_mod_10)
vr = vr_div_10
vp = vp_div_10
vm = vm_div_10
removed++
}
if vm_is_trailing_zeros {
for {
vm_div_10 := vm / 10
vm_mod_10 := vm % 10
if vm_mod_10 != 0 {
break
}
vp_div_10 := vp / 10
vr_div_10 := vr / 10
vr_mod_10 := vr % 10
vr_is_trailing_zeros = vr_is_trailing_zeros && (last_removed_digit == 0)
last_removed_digit = byte(vr_mod_10)
vr = vr_div_10
vp = vp_div_10
vm = vm_div_10
removed++
}
}
if vr_is_trailing_zeros && (last_removed_digit == 5) && (vr % 2) == 0 {
// Round even if the exact number is .....50..0.
last_removed_digit = 4
}
out = vr
// We need to take vr + 1 if vr is outside bounds
// or we need to round up.
if (vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5 {
out++
}
} else {
// Specialized for the common case (~99.3%).
// Percentages below are relative to this.
mut round_up := false
for vp / 100 > vm / 100 {
// Optimization: remove two digits at a time (~86.2%).
round_up = (vr % 100) >= 50
vr /= 100
vp /= 100
vm /= 100
removed += 2
}
// Loop iterations below (approximately), without optimization above:
// 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
// Loop iterations below (approximately), with optimization above:
// 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
for vp / 10 > vm / 10 {
round_up = (vr % 10) >= 5
vr /= 10
vp /= 10
vm /= 10
removed++
}
// We need to take vr + 1 if vr is outside bounds
// or we need to round up.
out = vr + bool_to_u64(vr == vm || round_up)
}
return Dec64{m: out, e: e10 + removed}
}
// f64_to_str return a string in scientific notation with max n_digit after the dot
pub fn f64_to_str(f f64, n_digit int) string {
mut u1 := Uf64{}
u1.f = f
u := u1.u
neg := (u>>(mantbits64+expbits64)) != 0
mant := u & ((u64(1)<<mantbits64) - u64(1))
exp := (u >> mantbits64) & ((u64(1)<<expbits64) - u64(1))
//println("s:${neg} mant:${mant} exp:${exp} float:${f} byte:${u1.u:016lx}")
// Exit early for easy cases.
if (exp == maxexp64) || (exp == 0 && mant == 0) {
return get_string_special(neg, exp == 0, mant == 0)
}
mut d, ok := f64_to_decimal_exact_int(mant, exp)
if !ok {
//println("to_decimal")
d = f64_to_decimal(mant, exp)
}
//println("${d.m} ${d.e}")
return d.get_string_64(neg, n_digit)
}