fast convert string_view to floating point

Question

The code makes following assumptions:

• std::string_view is not null-terminated
• there are no exponents, all floating point inputs are in the way 123.123
• limiting digits before and after decimal point
• <ctype.h> free. No locale. Uses own isspace() and isdigits()

---

  #include <cstdint>
  #include <string_view>
  #include <limits>
  
  // based on http://www.jbox.dk/sanos/source/lib/strtod.c.html
  
  namespace to_fp_impl_{
    namespace{
        constexpr char decimal_point = '.';
  
        auto isspace(char c){
            return c == ' ' || c == '\t';
        };
  
        auto isdigit(char c){
            return c >= '0' && c <= '9';
        }
  
        template<typename FP>
        void add_char(FP &number, char c){
            number = number * 10 + (c - '0');
        }
    }
  
    template<typename FP>
    struct ResultFP{
        FP  num;
        bool    ok  = true;
  
        static auto err(){
            return ResultFP{ 0, false };
        }
    };
  } // namespace to_fp_impl_
  
  
  template<
    typename FP,
    uint8_t digits      = std::numeric_limits<FP>::digits10,
    uint8_t decimals    = digits
  >
  auto to_fp(std::string_view const str){
    static_assert(
        std::is_floating_point_v<FP>            &&
        digits   <= std::numeric_limits<FP>::digits10   &&
        decimals <= std::numeric_limits<FP>::digits10
    );
  
    // -----
  
    using namespace to_fp_impl_;
  
    using Result = ResultFP<FP>;
  
    auto it  = std::begin(str);
    auto end = std::end(str);
  
    // -----
  
    // Skip leading whitespace
    while (it != end && isspace(*it))
        ++it;
  
    // -----
  
    // Handle optional sign
    int8_t sign = +1;
  
    if (it != end){
        if (*it == '-'){
            sign = -1;
  
            ++it;
        }else if (*it == '+'){
        //  sign = +1;
  
            ++it;
        }
    }
  
    // -----
  
    FP number = 0.0;
  
    uint8_t total_digits = 0;
  
    // Process digits
    {
        uint8_t num_digits = 0;
        while (it != end && isdigit(*it)){
            if (++num_digits > digits)
                return Result::err();
  
            add_char(number, *it);
            ++it;
        }
  
        total_digits += num_digits;
    }
  
    // -----
  
    // Process decimal part
    if (it != end && *it == decimal_point){
        ++it;
  
        FP exp = 1;
  
        uint8_t num_digits = 0;
        while (it != end && isdigit(*it)){
            if (++num_digits > decimals)
                return Result::err();
  
            add_char(number, *it);
            ++it;
            exp *= 0.1;
        }
  
        total_digits += num_digits;
  
        number *= exp;
    }
  
    // -----
  
    return Result{ number * sign, total_digits != 0 };
  }
  
  template<
    typename FP,
    uint8_t digits      = std::numeric_limits<FP>::digits10,
    uint8_t decimals    = digits
  >
  auto to_fp_def(std::string_view const str, FP def = 0){
    auto[num, ok] = to_fp<FP, digits, decimals>(str);
  
    return ok ? num : def;
  }
  
  template<
    uint8_t digits      = std::numeric_limits<double>::digits10,
    uint8_t decimals    = digits
  >
  auto to_double_def(std::string_view const str, double def = 0){
    return to_fp_def<double, digits, decimals>(str, def);
  }
  
  template<
    uint8_t digits      = std::numeric_limits<float>::digits10,
    uint8_t decimals    = digits
  >
  auto to_float_def(std::string_view const str, float def = 0){
    return to_fp_def<float, digits, decimals>(str, def);
  }
  
  #include <cstdio>
  
  int main(){
    auto _ = [](const char *s){
        const char *mask = ">%32.15f<\n";
        constexpr double def = -0.111111111111111;
        printf(mask, to_double_def(s, def));
    };
  
    _("    ."               ); //error
    _("   -."               ); //error
    _("   +."               ); //error
  
    _("    .0"              );
    _("   -.0"              );
    _("   +.0"              );
  
    _("   0."               );
    _("  -0."               );
    _("  +0."               );
  
    _("   0"                );
    _("  -0"                );
    _("  +0"                );
  
    _(" 100.1"              );
    _("-100.1"              );
    _("+100.1"              );
  
    _("  123456789012345"           );
    _("  123456789012345."          );
    _("                 .123456789012345"   );
    _("  123456789012345.123456789012345"   ); // OK, but truncated
  
    _("  -123456789012345"          );
    _("  -123456789012345."         );
    _("                 -.123456789012345"  );
    _("  -123456789012345.123456789012345"  ); // OK, but truncated
  
    _(" 1234567890123456."          ); //error, too long
    _("                 .1234567890123456"  ); //error, too long
    _(" 1234567890123456.1234567890123456"  ); //error, too long
  }

---

Result:

>              -0.111111111111111<
>              -0.111111111111111<
>              -0.111111111111111<
>               0.000000000000000<
>              -0.000000000000000<
>               0.000000000000000<
>               0.000000000000000<
>              -0.000000000000000<
>               0.000000000000000<
>               0.000000000000000<
>              -0.000000000000000<
>               0.000000000000000<
>             100.100000000000009<
>            -100.100000000000009<
>             100.100000000000009<
> 123456789012345.000000000000000<
> 123456789012345.000000000000000<
>               0.123456789012345<
> 123456789012345.250000000000000<
>-123456789012345.000000000000000<
>-123456789012345.000000000000000<
>              -0.123456789012345<
>-123456789012345.250000000000000<
>              -0.111111111111111<
>              -0.111111111111111<
>              -0.111111111111111<

---

Benchmark:

the code is 4.6 x faster than std::strtod(), but slower than std::from_chars()
https://quick-bench.com/q/cHVL5PW9m4WSp6OvPnrF-ApCrG4

Answer 1

hoist out of loop

Consider comparing num_digits to decimals at the very end, so you bench quicker.

FP accumulated error

This expression concerns me:

            exp *= 0.1;

We're supposed to be able to roundtrip any expression between FP and string, losslessly. Yet this is an inexact representation of 1/10th.

Consider incrementing an integer and then computing the exp multiplier afresh each time from that integer.

EDIT

Actually, it turns out that this is pretty terrible:

        number *= exp;

Why? Because exp is inexact. It is 10 ** -N, e.g. 10 ** -6. A much better approach would be to assign it 10 ** N, e.g. a million, and compute

        number /= exp;

In this case we're dividing an exact quantity, an integer (many integers fit fine within a double), by another exact quantity: number / exp. Only then do we round-off to 53 bits.

In contrast, the OP code suffers from a pair of rounding operations:

1. infinite repeating binary fraction for 10 ** -N
2. division

Truncating twice, to 53 bits, leads to worse errors. Try it and see. Good examples are 0.3 and 0.7. We don't want to obtain a result like 0.30000000000000004 or 0.7000000000000001 -- we'd much rather be able to roundtrip back and forth without such noise creeping in.

---

There is a subtler difficulty with this computation. The spec requires rounding toward an even number in some cases.

Let's back up a moment. A 64-bit double doesn't quite represent a number. Rather, it represents an interval on the real number line, bounded by adjacent bit patterns. Here, "adjacent" pretty much corresponds to C cast punning where you treat the significand bits as an int and use the ++ increment operator. While the real number line is infinitely divisible, FP space consists of a finite number of adjacent intervals (plus NaNs, infinities, and that whole -0.0 thing).

So the double 1.0 covers 1 through 1+ϵ, and 2.0 covers 2 through 2 plus a slightly bigger epsilon. If our division result falls within that ϵ interval, then we can roundtrip back and forth all day long without noise, going from string to double to string to double. Many numbers are amenable to this, such as 0.2 and even 0.3. They are infinite repeating binary fractions which we truncate to 53 bits and obtain a perfectly nice result. The fraction goes on infinitely but it lands squarely within an interval. The truncation can be viewed as appending an infinite number of zeros on the end.

For a number that appears to land right on an interval boundary, when rounding to 53 bits we're required to round to even. Kind of a tricky requirement. Again, this is like having infinite zeros to the right.

Here is an example ASCII string which illustrates this: "0.8750000000582075". The correct to_fp() result would be
0.8750000000582076 rather than
0.8750000000582075. Once we see that ...76 ending in the double, we can roundtrip to string to double to string all day long and it remains ...76.

The underlying representation for ...75, and for ...76, is
0x1.c00000007ffffp-1, while for ...77 it is
0x1.c000000080000p-1.

Answer 2

I don't see any benefit to ResultFP over simply using a std::optional type, which is already familiar to users rather than something new to learn.

The helper functions could (and probably should) be declared constexpr.

std::uint8_t is written throughout as uint8_t as if we'd included <stdint.h> rather than <cstdint>. Also, in the test program, std::printf is similarly misspelt.

Is std::uint8_t really the appropriate type for counting? std::uint_fast8_t seems a better choice, since it's guaranteed to exist. Or perhaps just use int for consistency with std::numeric_limits<FP>::digits10.

I'm not sure why we limit the integral and fractional components to digits10. That restricts us to quite a small portion of the floating-point range; consider max_exponent10 and digits10-min_exponent10 respectively for full coverage.

I'd prefer separate static_assert()s for the three tests - that gives more informative feedback to client code which violates them. We should also test that digits and decimals aren't both zero.

We're missing an include of <iterator> for the declarations of std::begin() and std::end(). However, it's simpler just to use std::string_view's member begin() and end() here.

As J_H's answer points out, we should avoid inexact numbers such as 0.1 or 1 / 10. The easy way to do this is to maintain FP divisor{1} and multiply that by 10.0 each time we read a digit from the fractional part. And at the end, return number / divisor.

The test program is better than nothing, but we have a ready-made source of truth we can compare against in the standard library, so we could make sure that we get the same results as std::strtod() and similar, and make the tests self-checking. We don't test any template arguments other than the defaults, so it's quite a weak test. Also, we don't test enough invalid inputs (the empty string would generally be my first test, when I'm deciding on the interface, for example).

I'm not a big fan of the name _ for the test function.

My suggested replacement:

#include <limits>
#include <optional>
#include <string_view>

template<
    typename FP = double,
    int digits = std::numeric_limits<FP>::digits10,
    int decimals = digits
    >
std::optional<FP> to_fp(std::string_view const str) {
    static_assert(std::is_floating_point_v<FP>);
    static_assert(0 <= digits);
    static_assert(0 <= decimals);
    static_assert(digits + decimals);
    static_assert(digits   <= std::numeric_limits<FP>::max_exponent10);
    static_assert(decimals <= std::numeric_limits<FP>::digits10-std::numeric_limits<FP>::min_exponent10);

    static auto const isspace = [](char c){
        return c == ' ' || c == '\t';
    };

    static auto const isdigit = [](char c){
            return c >= '0' && c <= '9';
    };

    static auto const add_char = [](FP &number, char c){
        number = number * 10 + (c - '0');
    };

    // -----

    auto it = str.begin();
    auto const end = str.end();

    // Skip leading whitespace
    while (it != end && isspace(*it)) {
        ++it;
    }
    if (it == end) { return {}; }

    // Handle optional sign
    FP sign = +1;
    if (*it == '-') {
        sign = -1;
        ++it;
    } else if (*it == '+') {
        ++it;
    }

    FP number = 0.0;
    bool digits_seen = false;
    // Process integer part
    for (int num_digits = 0;  it != end && isdigit(*it);  ++it) {
        if (++num_digits > digits) { return {}; }
        add_char(number, *it);
        digits_seen = true;
    }

    // Process decimal part
    if (it == end || *it != '.') { return sign * number; }
    ++it;

    FP divisor = 1;
    for (int num_digits = 0;  it != end && isdigit(*it);  ++it) {
        if (++num_digits > decimals) { return {}; }
        add_char(number, *it);
        digits_seen = true;
        divisor *= 10;
    }

    if (!digits_seen) { return {}; }

    return sign * number / divisor;
}

template<
    typename FP,
    int digits      = std::numeric_limits<FP>::digits10,
    int decimals    = digits
    >
auto to_fp_def(std::string_view const str, FP def = 0){
    return to_fp<FP, digits, decimals>(str).value_or(def);
}

There's still a tiny optimisation that can be made by tweaking the sign bit instead of multiplying by sign.

And it still fails to round correctly in the least-significant digit.