v/vlib/strconv/ftoa/f32_str.v

/**********************************************************************
*
* 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 = 0
	e int = 0
}

// support union for convert f32 to u32
union Uf32 {
mut:
	f f32 = 0
	u u32
}

// pow of ten table used by n_digit reduction
const(
	ten_pow_table_32 = [
		u32(1),
		u32(10),
		u32(100),
		u32(1000),
		u32(10000),
		u32(100000),
		u32(1000000),
		u32(10000000),
		u32(100000000),
		u32(1000000000),
		u32(10000000000),
		u32(100000000000),
	]
)

/******************************************************************************
*
* 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, i_n_digit int) string {
	n_digit          := i_n_digit + 1
	mut out          := d.m
	mut out_len      := decimal_len_32(out)
	out_len_original := out_len

	mut buf := [byte(0)].repeat(out_len + 5 + 1 +1) // sign + mant_len + . +  e + e_sign + exp_len(2) + \0
	mut i := 0

	if neg {
		buf[i]=`-`
		i++
	}

	mut disp := 0
	if out_len <= 1 {
		disp = 1
	}

	if n_digit < out_len {
		//println("orig: ${out_len_original}")
		out += ten_pow_table_32[out_len - n_digit] + 1  // round to up
		out /= ten_pow_table_32[out_len - n_digit]
		out_len = n_digit
	}

	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_original - 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)
}