v/vlib/strconv/ftoa/f64_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 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 = 0
	e int = 0
}

// support union for convert f64 to u64
union Uf64 {
mut:
	f f64 = 0
	u u64
}

// pow of ten table used by n_digit reduction
const(
	ten_pow_table_64 = [
		u64(1),
		u64(10),
		u64(100),
		u64(1000),
		u64(10000),
		u64(100000),
		u64(1000000),
		u64(10000000),
		u64(100000000),
		u64(1000000000),
		u64(10000000000),
		u64(100000000000),
		u64(1000000000000),
		u64(10000000000000),
		u64(100000000000000),
		u64(1000000000000000),
		u64(10000000000000000),
		u64(100000000000000000),
		u64(1000000000000000000),
		u64(10000000000000000000),
	]
)

/******************************************************************************
*
* Conversion Functions
*
******************************************************************************/
const(
	mantbits64  = u32(52)
	expbits64   = u32(11)
	bias64      = 1023 // f64 exponent bias
	maxexp64    = 2047
)

fn (d Dec64) get_string_64(neg bool, i_n_digit int, i_pad_digit int) string {
	mut n_digit          := i_n_digit + 1
	pad_digit        := i_pad_digit + 1
	mut out          := d.m
	mut d_exp        := d.e
	mut out_len      := decimal_len_64(out)
	out_len_original := out_len

	mut fw_zeros := 0
	if pad_digit > out_len {
		fw_zeros = pad_digit - out_len
	}

	mut buf := [byte(0)].repeat(out_len + 6 + 1 +1 + fw_zeros) // 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
	}

	// rounding last used digit
	if n_digit < out_len {
		//println("out:[$out]")
		out += ten_pow_table_64[out_len - n_digit - 1] * 5   // round to up
		out /= ten_pow_table_64[out_len - n_digit ]
		//println("out1:[$out] ${d.m / ten_pow_table_64[out_len - n_digit ]}")
		if d.m / ten_pow_table_64[out_len - n_digit ] < out {
			d_exp += 1
			n_digit += 1
		}

		//println("cmp: ${d.m/ten_pow_table_64[out_len - n_digit ]} ${out/ten_pow_table_64[out_len - n_digit ]}")

		out_len = n_digit
		//println("orig: ${out_len_original} new len: ${out_len} out:[$out]")
	}

	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++
	}

	for fw_zeros > 0 {
		buf[i++] = `0`
		fw_zeros--
	}

	/*
	x=0
	for x<buf.len {
		C.printf("d:%c\n",buf[x])
		x++
	}
	C.printf("\n")
	*/

	buf[i]=`e`
	i++

	mut exp := d_exp + out_len_original - 1
	if exp < 0 {
		buf[i]=`-`
		i++
		exp = -exp
	} else {
		buf[i]=`+`
		i++
	}

	// 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 | u64(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 - int(mantbits64) - 2
		m2 = mant
	} else {
		e2 = int(exp) - bias64 - int(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, 0)
}

// f64_to_str return a string in scientific notation with max n_digit after the dot
pub fn f64_to_str_pad(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("DEBUG: ${d.m} ${d.e}")
	return d.get_string_64(neg, n_digit, n_digit)
}