/**********************************************************************
*
* 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 f32 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
// dec32 is a floating decimal type representing m * 10^e.
struct Dec32 {
mut:
m u32 = u32(0)
e int = 0
}
// support union for convert f32 to u32
union Uf32 {
mut:
f f32 = f32(0)
u u32
}
/******************************************************************************
*
* Conversion Functions
*
******************************************************************************/
const(
mantbits32 = u32(23)
expbits32 = u32(8)
bias32 = u32(127) // f32 exponent bias
maxexp32 = 255
)
// max 46 char
// -3.40282346638528859811704183484516925440e+38
fn (d Dec32) get_string_32(neg bool, n_digit int) string {
mut out := d.m
mut out_len := decimal_len_32(out)
mut buf := [byte(0)].repeat(out_len + 5 + 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
/*
x=0
for x<buf.len {
C.printf("d:%c\n",buf[x])
x++
}
*/
return tos(byteptr(&buf[0]), i)
}
fn f32_to_decimal_exact_int(i_mant u32, exp u32) (Dec32,bool) {
mut d := Dec32{}
e := exp - bias32
if e > mantbits32 {
return d, false
}
shift := mantbits32 - e
mant := i_mant | 0x0080_0000 // implicit 1
//mant := i_mant | (1 << mantbits32) // 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
}
pub fn f32_to_decimal(mant u32, exp u32) Dec32 {
mut e2 := 0
mut m2 := u32(0)
if exp == 0 {
// We subtract 2 so that the bounds computation has
// 2 additional bits.
e2 = 1 - bias32 - mantbits32 - 2
m2 = mant
} else {
e2 = int(exp) - bias32 - mantbits32 - 2
m2 = (u32(1) << mantbits32) | mant
}
even := (m2 & 1) == 0
accept_bounds := even
// Step 2: Determine the interval of valid decimal representations.
mv := u32(4 * m2)
mp := u32(4 * m2 + 2)
mm_shift := bool_to_u32(mant != 0 || exp <= 1)
mm := u32(4 * m2 - 1 - mm_shift)
mut vr := u32(0)
mut vp := u32(0)
mut vm := u32(0)
mut e10 := 0
mut vm_is_trailing_zeros := false
mut vr_is_trailing_zeros := false
mut last_removed_digit := byte(0)
if e2 >= 0 {
q := log10_pow2(e2)
e10 = int(q)
k := pow5_inv_num_bits_32 + pow5_bits(int(q)) - 1
i := -e2 + int(q) + k
vr = mul_pow5_invdiv_pow2(mv, q, i)
vp = mul_pow5_invdiv_pow2(mp, q, i)
vm = mul_pow5_invdiv_pow2(mm, q, i)
if q != 0 && (vp-1)/10 <= vm/10 {
// We need to know one removed digit even if we are not
// going to loop below. We could use q = X - 1 above,
// except that would require 33 bits for the result, and
// we've found that 32-bit arithmetic is faster even on
// 64-bit machines.
l := pow5_inv_num_bits_32 + pow5_bits(int(q - 1)) - 1
last_removed_digit = byte(mul_pow5_invdiv_pow2(mv, q - 1, -e2 + int(q - 1) + l) % 10)
}
if q <= 9 {
// The largest power of 5 that fits in 24 bits is 5^10,
// but q <= 9 seems to be safe as well. 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_32(mv, q)
} else if accept_bounds {
vm_is_trailing_zeros = multiple_of_power_of_five_32(mm, q)
} else if multiple_of_power_of_five_32(mp, q) {
vp--
}
}
} else {
q := log10_pow5(-e2)
e10 = int(q) + e2
i := -e2 - int(q)
k := pow5_bits(i) - pow5_num_bits_32
mut j := int(q) - k
vr = mul_pow5_div_pow2(mv, u32(i), j)
vp = mul_pow5_div_pow2(mp, u32(i), j)
vm = mul_pow5_div_pow2(mm, u32(i), j)
if q != 0 && ((vp-1)/10) <= vm/10 {
j = int(q) - 1 - (pow5_bits(i + 1) - pow5_num_bits_32)
last_removed_digit = byte(mul_pow5_div_pow2(mv, u32(i + 1), j) % 10)
}
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 - mm_shift, so it has 1 trailing 0 bit
// if mm_shift == 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 < 31 {
vr_is_trailing_zeros = multiple_of_power_of_two_32(mv, q - 1)
}
}
// Step 4: Find the shortest decimal representation
// in the interval of valid representations.
mut removed := 0
mut out := u32(0)
if vm_is_trailing_zeros || vr_is_trailing_zeros {
// General case, which happens rarely (~4.0%).
for vp/10 > vm/10 {
vm_is_trailing_zeros = vm_is_trailing_zeros && (vm % 10) == 0
vr_is_trailing_zeros = vr_is_trailing_zeros && (last_removed_digit == 0)
last_removed_digit = byte(vr % 10)
vr /= 10
vp /= 10
vm /= 10
removed++
}
if vm_is_trailing_zeros {
for vm%10 == 0 {
vr_is_trailing_zeros = vr_is_trailing_zeros && (last_removed_digit == 0)
last_removed_digit = byte(vr % 10)
vr /= 10
vp /= 10
vm /= 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 (~96.0%). Percentages below
// are relative to this. Loop iterations below (approximately):
// 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
for vp/10 > vm/10 {
last_removed_digit = byte(vr % 10)
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_u32(vr == vm || last_removed_digit >= 5)
}
return Dec32{m: out e: e10 + removed}
}
// f32_to_str return a string in scientific notation with max n_digit after the dot
pub fn f32_to_str(f f32, n_digit int) string {
mut u1 := Uf32{}
u1.f = f
u := u1.u
neg := (u>>(mantbits32+expbits32)) != 0
mant := u & ((u32(1)<<mantbits32) - u32(1))
exp := (u >> mantbits32) & ((u32(1)<<expbits32) - u32(1))
//println("${neg} ${mant} e ${exp-bias32}")
// Exit early for easy cases.
if (exp == maxexp32) || (exp == 0 && mant == 0) {
return get_string_special(neg, exp == 0, mant == 0)
}
mut d, ok := f32_to_decimal_exact_int(mant, exp)
if !ok {
//println("with exp form")
d = f32_to_decimal(mant, exp)
}
//println("${d.m} ${d.e}")
return d.get_string_32(neg, n_digit)
}