module strconv // Copyright (c) 2019-2022 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 utilities for converting a string to a f64 variable. // IEEE 754 standard is used. // Know limitation: limited to 18 significant digits // // The code is inspired by: // Grzegorz Kraszewski krashan@teleinfo.pb.edu.pl // URL: http://krashan.ppa.pl/articles/stringtofloat/ // Original license: MIT // 96 bit operation utilities // // Note: when u128 will be available, these function can be refactored. // f32 constants pub const ( single_plus_zero = u32(0x0000_0000) single_minus_zero = u32(0x8000_0000) single_plus_infinity = u32(0x7F80_0000) single_minus_infinity = u32(0xFF80_0000) ) // f64 constants pub const ( digits = 18 double_plus_zero = u64(0x0000000000000000) double_minus_zero = u64(0x8000000000000000) double_plus_infinity = u64(0x7FF0000000000000) double_minus_infinity = u64(0xFFF0000000000000) ) // char constants pub const ( c_dpoint = `.` c_plus = `+` c_minus = `-` c_zero = `0` c_nine = `9` c_ten = u32(10) ) // right logical shift 96 bit fn lsr96(s2 u32, s1 u32, s0 u32) (u32, u32, u32) { mut r0 := u32(0) mut r1 := u32(0) mut r2 := u32(0) r0 = (s0 >> 1) | ((s1 & u32(1)) << 31) r1 = (s1 >> 1) | ((s2 & u32(1)) << 31) r2 = s2 >> 1 return r2, r1, r0 } // left logical shift 96 bit fn lsl96(s2 u32, s1 u32, s0 u32) (u32, u32, u32) { mut r0 := u32(0) mut r1 := u32(0) mut r2 := u32(0) r2 = (s2 << 1) | ((s1 & (u32(1) << 31)) >> 31) r1 = (s1 << 1) | ((s0 & (u32(1) << 31)) >> 31) r0 = s0 << 1 return r2, r1, r0 } // sum on 96 bit fn add96(s2 u32, s1 u32, s0 u32, d2 u32, d1 u32, d0 u32) (u32, u32, u32) { mut w := u64(0) mut r0 := u32(0) mut r1 := u32(0) mut r2 := u32(0) w = u64(s0) + u64(d0) r0 = u32(w) w >>= 32 w += u64(s1) + u64(d1) r1 = u32(w) w >>= 32 w += u64(s2) + u64(d2) r2 = u32(w) return r2, r1, r0 } // subtraction on 96 bit fn sub96(s2 u32, s1 u32, s0 u32, d2 u32, d1 u32, d0 u32) (u32, u32, u32) { mut w := u64(0) mut r0 := u32(0) mut r1 := u32(0) mut r2 := u32(0) w = u64(s0) - u64(d0) r0 = u32(w) w >>= 32 w += u64(s1) - u64(d1) r1 = u32(w) w >>= 32 w += u64(s2) - u64(d2) r2 = u32(w) return r2, r1, r0 } // Utility functions fn is_digit(x u8) bool { return x >= strconv.c_zero && x <= strconv.c_nine } fn is_space(x u8) bool { return x == `\t` || x == `\n` || x == `\v` || x == `\f` || x == `\r` || x == ` ` } fn is_exp(x u8) bool { return x == `E` || x == `e` } // Possible parser return values. enum ParserState { ok // parser finished OK pzero // no digits or number is smaller than +-2^-1022 mzero // number is negative, module smaller pinf // number is higher than +HUGE_VAL minf // number is lower than -HUGE_VAL invalid_number // invalid number, used for '#@%^' for example } // parser tries to parse the given string into a number // NOTE: #TOFIX need one char after the last char of the number [direct_array_access] fn parser(s string) (ParserState, PrepNumber) { mut digx := 0 mut result := ParserState.ok mut expneg := false mut expexp := 0 mut i := 0 mut pn := PrepNumber{} // skip spaces for i < s.len && s[i].is_space() { i++ } // check negatives if s[i] == `-` { pn.negative = true i++ } // positive sign ignore it if s[i] == `+` { i++ } // read mantissa for i < s.len && s[i].is_digit() { // println("$i => ${s[i]}") if digx < strconv.digits { pn.mantissa *= 10 pn.mantissa += u64(s[i] - strconv.c_zero) digx++ } else if pn.exponent < 2147483647 { pn.exponent++ } i++ } // read mantissa decimals if (i < s.len) && (s[i] == `.`) { i++ for i < s.len && s[i].is_digit() { if digx < strconv.digits { pn.mantissa *= 10 pn.mantissa += u64(s[i] - strconv.c_zero) pn.exponent-- digx++ } i++ } } // read exponent if (i < s.len) && ((s[i] == `e`) || (s[i] == `E`)) { i++ if i < s.len { // esponent sign if s[i] == strconv.c_plus { i++ } else if s[i] == strconv.c_minus { expneg = true i++ } for i < s.len && s[i].is_digit() { if expexp < 214748364 { expexp *= 10 expexp += int(s[i] - strconv.c_zero) } i++ } } } if expneg { expexp = -expexp } pn.exponent += expexp if pn.mantissa == 0 { if pn.negative { result = .mzero } else { result = .pzero } } else if pn.exponent > 309 { if pn.negative { result = .minf } else { result = .pinf } } else if pn.exponent < -328 { if pn.negative { result = .mzero } else { result = .pzero } } if i == 0 && s.len > 0 { return ParserState.invalid_number, pn } return result, pn } // converter returns a u64 with the bit image of the f64 number fn converter(mut pn PrepNumber) u64 { mut binexp := 92 // s0,s1,s2 are the parts of a 96-bit precision integer mut s2 := u32(0) mut s1 := u32(0) mut s0 := u32(0) // q0,q1,q2 are the parts of a 96-bit precision integer mut q2 := u32(0) mut q1 := u32(0) mut q0 := u32(0) // r0,r1,r2 are the parts of a 96-bit precision integer mut r2 := u32(0) mut r1 := u32(0) mut r0 := u32(0) // mask28 := u32(u64(0xF) << 28) mut result := u64(0) // working on 3 u32 to have 96 bit precision s0 = u32(pn.mantissa & u64(0x00000000FFFFFFFF)) s1 = u32(pn.mantissa >> 32) s2 = u32(0) // so we take the decimal exponent off for pn.exponent > 0 { q2, q1, q0 = lsl96(s2, s1, s0) // q = s * 2 r2, r1, r0 = lsl96(q2, q1, q0) // r = s * 4 <=> q * 2 s2, s1, s0 = lsl96(r2, r1, r0) // s = s * 8 <=> r * 2 s2, s1, s0 = add96(s2, s1, s0, q2, q1, q0) // s = (s * 8) + (s * 2) <=> s*10 pn.exponent-- for (s2 & mask28) != 0 { q2, q1, q0 = lsr96(s2, s1, s0) binexp++ s2 = q2 s1 = q1 s0 = q0 } } for pn.exponent < 0 { for !((s2 & (u32(1) << 31)) != 0) { q2, q1, q0 = lsl96(s2, s1, s0) binexp-- s2 = q2 s1 = q1 s0 = q0 } q2 = s2 / strconv.c_ten r1 = s2 % strconv.c_ten r2 = (s1 >> 8) | (r1 << 24) q1 = r2 / strconv.c_ten r1 = r2 % strconv.c_ten r2 = ((s1 & u32(0xFF)) << 16) | (s0 >> 16) | (r1 << 24) r0 = r2 / strconv.c_ten r1 = r2 % strconv.c_ten q1 = (q1 << 8) | ((r0 & u32(0x00FF0000)) >> 16) q0 = r0 << 16 r2 = (s0 & u32(0xFFFF)) | (r1 << 16) q0 |= r2 / strconv.c_ten s2 = q2 s1 = q1 s0 = q0 pn.exponent++ } // C.printf(c"mantissa before normalization: %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp) // normalization, the 28 bit in s2 must the leftest one in the variable if s2 != 0 || s1 != 0 || s0 != 0 { for (s2 & mask28) == 0 { q2, q1, q0 = lsl96(s2, s1, s0) binexp-- s2 = q2 s1 = q1 s0 = q0 } } // rounding if needed /* * "round half to even" algorithm * Example for f32, just a reminder * * If bit 54 is 0, round down * If bit 54 is 1 * If any bit beyond bit 54 is 1, round up * If all bits beyond bit 54 are 0 (meaning the number is halfway between two floating-point numbers) * If bit 53 is 0, round down * If bit 53 is 1, round up */ /* test case 1 complete s2=0x1FFFFFFF s1=0xFFFFFF80 s0=0x0 */ /* test case 1 check_round_bit s2=0x18888888 s1=0x88888880 s0=0x0 */ /* test case check_round_bit + normalization s2=0x18888888 s1=0x88888F80 s0=0x0 */ // C.printf(c"mantissa before rounding: %08x%08x%08x binexp: %d \n", s2,s1,s0,binexp) // s1 => 0xFFFFFFxx only F are rapresented nbit := 7 check_round_bit := u32(1) << u32(nbit) check_round_mask := u32(0xFFFFFFFF) << u32(nbit) if (s1 & check_round_bit) != 0 { // C.printf(c"need round!! check mask: %08x\n", s1 & ~check_round_mask ) if (s1 & ~check_round_mask) != 0 { // C.printf(c"Add 1!\n") s2, s1, s0 = add96(s2, s1, s0, 0, check_round_bit, 0) } else { // C.printf(c"All 0!\n") if (s1 & (check_round_bit << u32(1))) != 0 { // C.printf(c"Add 1 form -1 bit control!\n") s2, s1, s0 = add96(s2, s1, s0, 0, check_round_bit, 0) } } s1 = s1 & check_round_mask s0 = u32(0) // recheck normalization if s2 & (mask28 << u32(1)) != 0 { // C.printf(c"Renormalize!!\n") q2, q1, q0 = lsr96(s2, s1, s0) binexp++ // dump(binexp) s2 = q2 s1 = q1 s0 = q0 } } // tmp := ( u64(s2 & ~mask28) << 24) | ((u64(s1) + u64(128)) >> 8) // C.printf(c"mantissa after rounding : %08x %08x %08x binexp: %d \n", s2,s1,s0,binexp) // C.printf(c"Tmp result: %016x\n",tmp) // end rounding // offset the binary exponent IEEE 754 binexp += 1023 if binexp > 2046 { if pn.negative { result = strconv.double_minus_infinity } else { result = strconv.double_plus_infinity } } else if binexp < 1 { if pn.negative { result = strconv.double_minus_zero } else { result = strconv.double_plus_zero } } else if s2 != 0 { mut q := u64(0) binexs2 := u64(binexp) << 52 q = (u64(s2 & ~mask28) << 24) | ((u64(s1) + u64(128)) >> 8) | binexs2 if pn.negative { q |= (u64(1) << 63) } result = q } return result } // atof64 parses the string `s`, and if possible, converts it into a f64 number pub fn atof64(s string) !f64 { if s.len == 0 { return error('expected a number found an empty string') } mut res := Float64u{} mut res_parsing, mut pn := parser(s) match res_parsing { .ok { res.u = converter(mut pn) } .pzero { res.u = strconv.double_plus_zero } .mzero { res.u = strconv.double_minus_zero } .pinf { res.u = strconv.double_plus_infinity } .minf { res.u = strconv.double_minus_infinity } .invalid_number { return error('not a number') } } return unsafe { res.f } }