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384 lines
9.1 KiB
V
384 lines
9.1 KiB
V
/**********************************************************************
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*
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* f32 to string
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*
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* Copyright (c) 2019-2020 Dario Deledda. All rights reserved.
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* Use of this source code is governed by an MIT license
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* that can be found in the LICENSE file.
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*
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* This file contains the f32 to string functions
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*
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* These functions are based on the work of:
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* Publication:PLDI 2018: Proceedings of the 39th ACM SIGPLAN
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* Conference on Programming Language Design and ImplementationJune 2018
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* Pages 270–282 https://doi.org/10.1145/3192366.3192369
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*
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* inspired by the Go version here:
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* https://github.com/cespare/ryu/tree/ba56a33f39e3bbbfa409095d0f9ae168a595feea
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*
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**********************************************************************/
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module ftoa
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// dec32 is a floating decimal type representing m * 10^e.
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struct Dec32 {
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mut:
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m u32 = 0
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e int = 0
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}
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// support union for convert f32 to u32
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union Uf32 {
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mut:
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f f32 = 0
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u u32
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}
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// pow of ten table used by n_digit reduction
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const(
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ten_pow_table_32 = [
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u32(1),
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u32(10),
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u32(100),
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u32(1000),
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u32(10000),
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u32(100000),
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u32(1000000),
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u32(10000000),
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u32(100000000),
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u32(1000000000),
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u32(10000000000),
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u32(100000000000),
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]
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)
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/******************************************************************************
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*
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* Conversion Functions
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*
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******************************************************************************/
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const(
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mantbits32 = u32(23)
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expbits32 = u32(8)
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bias32 = u32(127) // f32 exponent bias
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maxexp32 = 255
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)
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// max 46 char
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// -3.40282346638528859811704183484516925440e+38
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fn (d Dec32) get_string_32(neg bool, i_n_digit int, i_pad_digit int) string {
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n_digit := i_n_digit + 1
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pad_digit := i_pad_digit + 1
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mut out := d.m
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mut out_len := decimal_len_32(out)
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out_len_original := out_len
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mut fw_zeros := 0
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if pad_digit > out_len {
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fw_zeros = pad_digit -out_len
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}
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mut buf := [byte(0)].repeat(out_len + 5 + 1 +1) // sign + mant_len + . + e + e_sign + exp_len(2) + \0
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mut i := 0
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if neg {
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buf[i]=`-`
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i++
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}
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mut disp := 0
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if out_len <= 1 {
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disp = 1
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}
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if n_digit < out_len {
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//println("orig: ${out_len_original}")
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out += ten_pow_table_32[out_len - n_digit - 1] * 5 // round to up
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out /= ten_pow_table_32[out_len - n_digit]
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out_len = n_digit
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}
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y := i + out_len
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mut x := 0
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for x < (out_len-disp-1) {
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buf[y - x] = `0` + byte(out%10)
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out /= 10
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i++
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x++
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}
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if out_len >= 1 {
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buf[y - x] = `.`
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x++
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i++
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}
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if y-x >= 0 {
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buf[y - x] = `0` + byte(out%10)
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i++
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}
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for fw_zeros > 0 {
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buf[i++] = `0`
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fw_zeros--
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}
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/*
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x=0
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for x<buf.len {
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C.printf("d:%c\n",buf[x])
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x++
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}
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C.printf("\n")
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*/
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buf[i]=`e`
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i++
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mut exp := d.e + out_len_original - 1
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if exp < 0 {
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buf[i]=`-`
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i++
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exp = -exp
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} else {
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buf[i]=`+`
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i++
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}
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// Always print two digits to match strconv's formatting.
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d1 := exp % 10
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d0 := exp / 10
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buf[i]=`0` + byte(d0)
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i++
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buf[i]=`0` + byte(d1)
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i++
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buf[i]=0
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/*
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x=0
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for x<buf.len {
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C.printf("d:%c\n",buf[x])
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x++
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}
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*/
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return tos(byteptr(&buf[0]), i)
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}
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fn f32_to_decimal_exact_int(i_mant u32, exp u32) (Dec32,bool) {
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mut d := Dec32{}
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e := exp - bias32
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if e > mantbits32 {
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return d, false
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}
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shift := mantbits32 - e
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mant := i_mant | 0x0080_0000 // implicit 1
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//mant := i_mant | (1 << mantbits32) // implicit 1
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d.m = mant >> shift
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if (d.m << shift) != mant {
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return d, false
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}
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for (d.m % 10) == 0 {
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d.m /= 10
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d.e++
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}
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return d, true
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}
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pub fn f32_to_decimal(mant u32, exp u32) Dec32 {
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mut e2 := 0
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mut m2 := u32(0)
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if exp == 0 {
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// We subtract 2 so that the bounds computation has
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// 2 additional bits.
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e2 = 1 - bias32 - mantbits32 - 2
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m2 = mant
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} else {
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e2 = int(exp) - bias32 - mantbits32 - 2
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m2 = (u32(1) << mantbits32) | mant
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}
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even := (m2 & 1) == 0
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accept_bounds := even
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// Step 2: Determine the interval of valid decimal representations.
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mv := u32(4 * m2)
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mp := u32(4 * m2 + 2)
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mm_shift := bool_to_u32(mant != 0 || exp <= 1)
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mm := u32(4 * m2 - 1 - mm_shift)
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mut vr := u32(0)
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mut vp := u32(0)
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mut vm := u32(0)
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mut e10 := 0
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mut vm_is_trailing_zeros := false
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mut vr_is_trailing_zeros := false
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mut last_removed_digit := byte(0)
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if e2 >= 0 {
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q := log10_pow2(e2)
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e10 = int(q)
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k := pow5_inv_num_bits_32 + pow5_bits(int(q)) - 1
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i := -e2 + int(q) + k
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vr = mul_pow5_invdiv_pow2(mv, q, i)
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vp = mul_pow5_invdiv_pow2(mp, q, i)
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vm = mul_pow5_invdiv_pow2(mm, q, i)
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if q != 0 && (vp-1)/10 <= vm/10 {
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// We need to know one removed digit even if we are not
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// going to loop below. We could use q = X - 1 above,
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// except that would require 33 bits for the result, and
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// we've found that 32-bit arithmetic is faster even on
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// 64-bit machines.
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l := pow5_inv_num_bits_32 + pow5_bits(int(q - 1)) - 1
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last_removed_digit = byte(mul_pow5_invdiv_pow2(mv, q - 1, -e2 + int(q - 1) + l) % 10)
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}
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if q <= 9 {
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// The largest power of 5 that fits in 24 bits is 5^10,
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// but q <= 9 seems to be safe as well. Only one of mp,
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// mv, and mm can be a multiple of 5, if any.
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if mv%5 == 0 {
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vr_is_trailing_zeros = multiple_of_power_of_five_32(mv, q)
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} else if accept_bounds {
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vm_is_trailing_zeros = multiple_of_power_of_five_32(mm, q)
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} else if multiple_of_power_of_five_32(mp, q) {
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vp--
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}
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}
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} else {
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q := log10_pow5(-e2)
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e10 = int(q) + e2
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i := -e2 - int(q)
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k := pow5_bits(i) - pow5_num_bits_32
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mut j := int(q) - k
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vr = mul_pow5_div_pow2(mv, u32(i), j)
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vp = mul_pow5_div_pow2(mp, u32(i), j)
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vm = mul_pow5_div_pow2(mm, u32(i), j)
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if q != 0 && ((vp-1)/10) <= vm/10 {
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j = int(q) - 1 - (pow5_bits(i + 1) - pow5_num_bits_32)
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last_removed_digit = byte(mul_pow5_div_pow2(mv, u32(i + 1), j) % 10)
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}
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if q <= 1 {
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// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at
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// least q trailing 0 bits. mv = 4 * m2, so it always
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// has at least two trailing 0 bits.
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vr_is_trailing_zeros = true
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if accept_bounds {
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// mm = mv - 1 - mm_shift, so it has 1 trailing 0 bit
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// if mm_shift == 1.
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vm_is_trailing_zeros = mm_shift == 1
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} else {
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// mp = mv + 2, so it always has at least one
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// trailing 0 bit.
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vp--
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}
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} else if q < 31 {
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vr_is_trailing_zeros = multiple_of_power_of_two_32(mv, q - 1)
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}
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}
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// Step 4: Find the shortest decimal representation
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// in the interval of valid representations.
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mut removed := 0
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mut out := u32(0)
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if vm_is_trailing_zeros || vr_is_trailing_zeros {
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// General case, which happens rarely (~4.0%).
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for vp/10 > vm/10 {
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vm_is_trailing_zeros = vm_is_trailing_zeros && (vm % 10) == 0
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vr_is_trailing_zeros = vr_is_trailing_zeros && (last_removed_digit == 0)
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last_removed_digit = byte(vr % 10)
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vr /= 10
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vp /= 10
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vm /= 10
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removed++
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}
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if vm_is_trailing_zeros {
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for vm%10 == 0 {
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vr_is_trailing_zeros = vr_is_trailing_zeros && (last_removed_digit == 0)
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last_removed_digit = byte(vr % 10)
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vr /= 10
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vp /= 10
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vm /= 10
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removed++
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}
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}
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if vr_is_trailing_zeros && (last_removed_digit == 5) && (vr % 2) == 0 {
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// Round even if the exact number is .....50..0.
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last_removed_digit = 4
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}
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out = vr
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// We need to take vr + 1 if vr is outside bounds
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// or we need to round up.
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if (vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5 {
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out++
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}
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} else {
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// Specialized for the common case (~96.0%). Percentages below
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// are relative to this. Loop iterations below (approximately):
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// 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
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for vp/10 > vm/10 {
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last_removed_digit = byte(vr % 10)
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vr /= 10
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vp /= 10
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vm /= 10
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removed++
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}
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// We need to take vr + 1 if vr is outside bounds
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// or we need to round up.
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out = vr + bool_to_u32(vr == vm || last_removed_digit >= 5)
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}
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return Dec32{m: out e: e10 + removed}
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}
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// f32_to_str return a string in scientific notation with max n_digit after the dot
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pub fn f32_to_str(f f32, n_digit int) string {
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mut u1 := Uf32{}
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u1.f = f
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u := u1.u
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neg := (u>>(mantbits32+expbits32)) != 0
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mant := u & ((u32(1)<<mantbits32) - u32(1))
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exp := (u >> mantbits32) & ((u32(1)<<expbits32) - u32(1))
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//println("${neg} ${mant} e ${exp-bias32}")
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// Exit early for easy cases.
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if (exp == maxexp32) || (exp == 0 && mant == 0) {
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return get_string_special(neg, exp == 0, mant == 0)
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}
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mut d, ok := f32_to_decimal_exact_int(mant, exp)
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if !ok {
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//println("with exp form")
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d = f32_to_decimal(mant, exp)
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}
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//println("${d.m} ${d.e}")
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return d.get_string_32(neg, n_digit,0)
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}
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// f32_to_str return a string in scientific notation with max n_digit after the dot
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pub fn f32_to_str_pad(f f32, n_digit int) string {
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mut u1 := Uf32{}
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u1.f = f
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u := u1.u
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neg := (u>>(mantbits32+expbits32)) != 0
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mant := u & ((u32(1)<<mantbits32) - u32(1))
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exp := (u >> mantbits32) & ((u32(1)<<expbits32) - u32(1))
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//println("${neg} ${mant} e ${exp-bias32}")
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// Exit early for easy cases.
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if (exp == maxexp32) || (exp == 0 && mant == 0) {
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return get_string_special(neg, exp == 0, mant == 0)
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}
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mut d, ok := f32_to_decimal_exact_int(mant, exp)
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if !ok {
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//println("with exp form")
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d = f32_to_decimal(mant, exp)
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}
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//println("${d.m} ${d.e}")
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return d.get_string_32(neg, n_digit, n_digit)
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}
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