/* -*- Mode: C; c-file-style: "python" -*- */

#include <Python.h>

#include "pycore_dtoa.h"          // _Py_dg_strtod()

#include "pycore_pymath.h"        // _PY_SHORT_FLOAT_REPR

#include <locale.h>               // localeconv()

/* Case-insensitive string match used for nan and inf detection; t should be

   lower-case.  Returns 1 for a successful match, 0 otherwise. */

static int

case_insensitive_match(const char *s, const char *t)

{

    while(*t && Py_TOLOWER(*s) == *t) {

        s++;

        t++;

    }

    return *t ? 0 : 1;

}

/* _Py_parse_inf_or_nan: Attempt to parse a string of the form "nan", "inf" or

   "infinity", with an optional leading sign of "+" or "-".  On success,

   return the NaN or Infinity as a double and set *endptr to point just beyond

   the successfully parsed portion of the string.  On failure, return -1.0 and

   set *endptr to point to the start of the string. */

double

_Py_parse_inf_or_nan(const char *p, char **endptr)

{

    double retval;

    const char *s;

    int negate = 0;

    s = p;

    if (*s == '-') {

        negate = 1;

        s++;

    }

    else if (*s == '+') {

        s++;

    }

    if (case_insensitive_match(s, "inf")) {

        s += 3;

        if (case_insensitive_match(s, "inity"))

            s += 5;

        retval = negate ? -Py_INFINITY : Py_INFINITY;

    }

    else if (case_insensitive_match(s, "nan")) {

        s += 3;

        retval = negate ? -fabs(Py_NAN) : fabs(Py_NAN);

    }

    else {

        s = p;

        retval = -1.0;

    }

    *endptr = (char *)s;

    return retval;

}

/**

 * _PyOS_ascii_strtod:

 * @nptr:    the string to convert to a numeric value.

 * @endptr:  if non-%NULL, it returns the character after

 *           the last character used in the conversion.

 *

 * Converts a string to a #gdouble value.

 * This function behaves like the standard strtod() function

 * does in the C locale. It does this without actually

 * changing the current locale, since that would not be

 * thread-safe.

 *

 * This function is typically used when reading configuration

 * files or other non-user input that should be locale independent.

 * To handle input from the user you should normally use the

 * locale-sensitive system strtod() function.

 *

 * If the correct value would cause overflow, plus or minus %HUGE_VAL

 * is returned (according to the sign of the value), and %ERANGE is

 * stored in %errno. If the correct value would cause underflow,

 * zero is returned and %ERANGE is stored in %errno.

 * If memory allocation fails, %ENOMEM is stored in %errno.

 *

 * This function resets %errno before calling strtod() so that

 * you can reliably detect overflow and underflow.

 *

 * Return value: the #gdouble value.

 **/

#if _PY_SHORT_FLOAT_REPR == 1

static double

_PyOS_ascii_strtod(const char *nptr, char **endptr)

{

    double result;

    _Py_SET_53BIT_PRECISION_HEADER;

    assert(nptr != NULL);

    /* Set errno to zero, so that we can distinguish zero results

       and underflows */

    errno = 0;

    _Py_SET_53BIT_PRECISION_START;

    result = _Py_dg_strtod(nptr, endptr);

    _Py_SET_53BIT_PRECISION_END;

    if (*endptr == nptr)

        /* string might represent an inf or nan */

        result = _Py_parse_inf_or_nan(nptr, endptr);

    return result;

}

#else

/*

   Use system strtod;  since strtod is locale aware, we may

   have to first fix the decimal separator.

   Note that unlike _Py_dg_strtod, the system strtod may not always give

   correctly rounded results.

*/

static double

_PyOS_ascii_strtod(const char *nptr, char **endptr)

{

    char *fail_pos;

    double val;

    struct lconv *locale_data;

    const char *decimal_point;

    size_t decimal_point_len;

    const char *p, *decimal_point_pos;

    const char *end = NULL; /* Silence gcc */

    const char *digits_pos = NULL;

    int negate = 0;

    assert(nptr != NULL);

    fail_pos = NULL;

    locale_data = localeconv();

    decimal_point = locale_data->decimal_point;

    decimal_point_len = strlen(decimal_point);

    assert(decimal_point_len != 0);

    decimal_point_pos = NULL;

    /* Parse infinities and nans */

    val = _Py_parse_inf_or_nan(nptr, endptr);

    if (*endptr != nptr)

        return val;

    /* Set errno to zero, so that we can distinguish zero results

       and underflows */

    errno = 0;

    /* We process the optional sign manually, then pass the remainder to

       the system strtod.  This ensures that the result of an underflow

       has the correct sign. (bug #1725)  */

    p = nptr;

    /* Process leading sign, if present */

    if (*p == '-') {

        negate = 1;

        p++;

    }

    else if (*p == '+') {

        p++;

    }

    /* Some platform strtods accept hex floats; Python shouldn't (at the

       moment), so we check explicitly for strings starting with '0x'. */

    if (*p == '0' && (*(p+1) == 'x' || *(p+1) == 'X'))

        goto invalid_string;

    /* Check that what's left begins with a digit or decimal point */

    if (!Py_ISDIGIT(*p) && *p != '.')

        goto invalid_string;

    digits_pos = p;

    if (decimal_point[0] != '.' ||

        decimal_point[1] != 0)

    {

        /* Look for a '.' in the input; if present, it'll need to be

           swapped for the current locale's decimal point before we

           call strtod.  On the other hand, if we find the current

           locale's decimal point then the input is invalid. */

        while (Py_ISDIGIT(*p))

            p++;

        if (*p == '.')

        {

            decimal_point_pos = p++;

            /* locate end of number */

            while (Py_ISDIGIT(*p))

                p++;

            if (*p == 'e' || *p == 'E')

                p++;

            if (*p == '+' || *p == '-')

                p++;

            while (Py_ISDIGIT(*p))

                p++;

            end = p;

        }

        else if (strncmp(p, decimal_point, decimal_point_len) == 0)

            /* Python bug #1417699 */

            goto invalid_string;

        /* For the other cases, we need not convert the decimal

           point */

    }

    if (decimal_point_pos) {

        char *copy, *c;

        /* Create a copy of the input, with the '.' converted to the

           locale-specific decimal point */

        copy = (char *)PyMem_Malloc(end - digits_pos +

                                    1 + decimal_point_len);

        if (copy == NULL) {

            *endptr = (char *)nptr;

            errno = ENOMEM;

            return val;

        }

        c = copy;

        memcpy(c, digits_pos, decimal_point_pos - digits_pos);

        c += decimal_point_pos - digits_pos;

        memcpy(c, decimal_point, decimal_point_len);

        c += decimal_point_len;

        memcpy(c, decimal_point_pos + 1,

               end - (decimal_point_pos + 1));

        c += end - (decimal_point_pos + 1);

        *c = 0;

        val = strtod(copy, &fail_pos);

        if (fail_pos)

        {

            if (fail_pos > decimal_point_pos)

                fail_pos = (char *)digits_pos +

                    (fail_pos - copy) -

                    (decimal_point_len - 1);

            else

                fail_pos = (char *)digits_pos +

                    (fail_pos - copy);

        }

        PyMem_Free(copy);

    }

    else {

        val = strtod(digits_pos, &fail_pos);

    }

    if (fail_pos == digits_pos)

        goto invalid_string;

    if (negate && fail_pos != nptr)

        val = -val;

    *endptr = fail_pos;

    return val;

  invalid_string:

    *endptr = (char*)nptr;

    errno = EINVAL;

    return -1.0;

}

#endif

/* PyOS_string_to_double converts a null-terminated byte string s (interpreted

   as a string of ASCII characters) to a float.  The string should not have

   leading or trailing whitespace.  The conversion is independent of the

   current locale.

   If endptr is NULL, try to convert the whole string.  Raise ValueError and

   return -1.0 if the string is not a valid representation of a floating-point

   number.

   If endptr is non-NULL, try to convert as much of the string as possible.

   If no initial segment of the string is the valid representation of a

   floating-point number then *endptr is set to point to the beginning of the

   string, -1.0 is returned and again ValueError is raised.

   On overflow (e.g., when trying to convert '1e500' on an IEEE 754 machine),

   if overflow_exception is NULL then +-Py_INFINITY is returned, and no Python

   exception is raised.  Otherwise, overflow_exception should point to

   a Python exception, this exception will be raised, -1.0 will be returned,

   and *endptr will point just past the end of the converted value.

   If any other failure occurs (for example lack of memory), -1.0 is returned

   and the appropriate Python exception will have been set.

*/

double

PyOS_string_to_double(const char *s,

                      char **endptr,

                      PyObject *overflow_exception)

{

    double x, result=-1.0;

    char *fail_pos;

    errno = 0;

    x = _PyOS_ascii_strtod(s, &fail_pos);

    if (errno == ENOMEM) {

        PyErr_NoMemory();

        fail_pos = (char *)s;

    }

    else if (!endptr && (fail_pos == s || *fail_pos != '\0'))

        PyErr_Format(PyExc_ValueError,

                      "could not convert string to float: "

                      "'%.200s'", s);

    else if (fail_pos == s)

        PyErr_Format(PyExc_ValueError,

                      "could not convert string to float: "

                      "'%.200s'", s);

    else if (errno == ERANGE && fabs(x) >= 1.0 && overflow_exception)

        PyErr_Format(overflow_exception,

                      "value too large to convert to float: "

                      "'%.200s'", s);

    else

        result = x;

    if (endptr != NULL)

        *endptr = fail_pos;

    return result;

}

/* Remove underscores that follow the underscore placement rule from

   the string and then call the `innerfunc` function on the result.

   It should return a new object or NULL on exception.

   `what` is used for the error message emitted when underscores are detected

   that don't follow the rule. `arg` is an opaque pointer passed to the inner

   function.

   This is used to implement underscore-agnostic conversion for floats

   and complex numbers.

*/

PyObject *

_Py_string_to_number_with_underscores(

    const char *s, Py_ssize_t orig_len, const char *what, PyObject *obj, void *arg,

    PyObject *(*innerfunc)(const char *, Py_ssize_t, void *))

{

    char prev;

    const char *p, *last;

    char *dup, *end;

    PyObject *result;

    assert(s[orig_len] == '\0');

    if (strchr(s, '_') == NULL) {

        return innerfunc(s, orig_len, arg);

    }

    dup = PyMem_Malloc(orig_len + 1);

    if (dup == NULL) {

        return PyErr_NoMemory();

    }

    end = dup;

    prev = '\0';

    last = s + orig_len;

    for (p = s; *p; p++) {

        if (*p == '_') {

            /* Underscores are only allowed after digits. */

            if (!(prev >= '0' && prev <= '9')) {

                goto error;

            }

        }

        else {

            *end++ = *p;

            /* Underscores are only allowed before digits. */

            if (prev == '_' && !(*p >= '0' && *p <= '9')) {

                goto error;

            }

        }

        prev = *p;

    }

    /* Underscores are not allowed at the end. */

    if (prev == '_') {

        goto error;

    }

    /* No embedded NULs allowed. */

    if (p != last) {

        goto error;

    }

    *end = '\0';

    result = innerfunc(dup, end - dup, arg);

    PyMem_Free(dup);

    return result;

  error:

    PyMem_Free(dup);

    PyErr_Format(PyExc_ValueError,

                 "could not convert string to %s: "

                 "%R", what, obj);

    return NULL;

}

#if _PY_SHORT_FLOAT_REPR == 0

/* Given a string that may have a decimal point in the current

   locale, change it back to a dot.  Since the string cannot get

   longer, no need for a maximum buffer size parameter. */

Py_LOCAL_INLINE(void)

change_decimal_from_locale_to_dot(char* buffer)

{

    struct lconv *locale_data = localeconv();

    const char *decimal_point = locale_data->decimal_point;

    if (decimal_point[0] != '.' || decimal_point[1] != 0) {

        size_t decimal_point_len = strlen(decimal_point);

        if (*buffer == '+' || *buffer == '-')

            buffer++;

        while (Py_ISDIGIT(*buffer))

            buffer++;

        if (strncmp(buffer, decimal_point, decimal_point_len) == 0) {

            *buffer = '.';

            buffer++;

            if (decimal_point_len > 1) {

                /* buffer needs to get smaller */

                size_t rest_len = strlen(buffer +

                                     (decimal_point_len - 1));

                memmove(buffer,

                    buffer + (decimal_point_len - 1),

                    rest_len);

                buffer[rest_len] = 0;

            }

        }

    }

}

/* From the C99 standard, section 7.19.6:

The exponent always contains at least two digits, and only as many more digits

as necessary to represent the exponent.

*/

#define MIN_EXPONENT_DIGITS 2

/* Ensure that any exponent, if present, is at least MIN_EXPONENT_DIGITS

   in length. */

Py_LOCAL_INLINE(void)

ensure_minimum_exponent_length(char* buffer, size_t buf_size)

{

    char *p = strpbrk(buffer, "eE");

    if (p && (*(p + 1) == '-' || *(p + 1) == '+')) {

        char *start = p + 2;

        int exponent_digit_cnt = 0;

        int leading_zero_cnt = 0;

        int in_leading_zeros = 1;

        int significant_digit_cnt;

        /* Skip over the exponent and the sign. */

        p += 2;

        /* Find the end of the exponent, keeping track of leading

           zeros. */

        while (*p && Py_ISDIGIT(*p)) {

            if (in_leading_zeros && *p == '0')

                ++leading_zero_cnt;

            if (*p != '0')

                in_leading_zeros = 0;

            ++p;

            ++exponent_digit_cnt;

        }

        significant_digit_cnt = exponent_digit_cnt - leading_zero_cnt;

        if (exponent_digit_cnt == MIN_EXPONENT_DIGITS) {

            /* If there are 2 exactly digits, we're done,

               regardless of what they contain */

        }

        else if (exponent_digit_cnt > MIN_EXPONENT_DIGITS) {

            int extra_zeros_cnt;

            /* There are more than 2 digits in the exponent.  See

               if we can delete some of the leading zeros */

            if (significant_digit_cnt < MIN_EXPONENT_DIGITS)

                significant_digit_cnt = MIN_EXPONENT_DIGITS;

            extra_zeros_cnt = exponent_digit_cnt -

                significant_digit_cnt;

            /* Delete extra_zeros_cnt worth of characters from the

               front of the exponent */

            assert(extra_zeros_cnt >= 0);

            /* Add one to significant_digit_cnt to copy the

               trailing 0 byte, thus setting the length */

            memmove(start,

                start + extra_zeros_cnt,

                significant_digit_cnt + 1);

        }

        else {

            /* If there are fewer than 2 digits, add zeros

               until there are 2, if there's enough room */

            int zeros = MIN_EXPONENT_DIGITS - exponent_digit_cnt;

            if (start + zeros + exponent_digit_cnt + 1

                  < buffer + buf_size) {

                memmove(start + zeros, start,

                    exponent_digit_cnt + 1);

                memset(start, '0', zeros);

            }

        }

    }

}

/* Remove trailing zeros after the decimal point from a numeric string; also

   remove the decimal point if all digits following it are zero.  The numeric

   string must end in '\0', and should not have any leading or trailing

   whitespace.  Assumes that the decimal point is '.'. */

Py_LOCAL_INLINE(void)

remove_trailing_zeros(char *buffer)

{

    char *old_fraction_end, *new_fraction_end, *end, *p;

    p = buffer;

    if (*p == '-' || *p == '+')

        /* Skip leading sign, if present */

        ++p;

    while (Py_ISDIGIT(*p))

        ++p;

    /* if there's no decimal point there's nothing to do */

    if (*p++ != '.')

        return;

    /* scan any digits after the point */

    while (Py_ISDIGIT(*p))

        ++p;

    old_fraction_end = p;

    /* scan up to ending '\0' */

    while (*p != '\0')

        p++;

    /* +1 to make sure that we move the null byte as well */

    end = p+1;

    /* scan back from fraction_end, looking for removable zeros */

    p = old_fraction_end;

    while (*(p-1) == '0')

        --p;

    /* and remove point if we've got that far */

    if (*(p-1) == '.')

        --p;

    new_fraction_end = p;

    memmove(new_fraction_end, old_fraction_end, end-old_fraction_end);

}

/* Ensure that buffer has a decimal point in it.  The decimal point will not

   be in the current locale, it will always be '.'. Don't add a decimal point

   if an exponent is present.  Also, convert to exponential notation where

   adding a '.0' would produce too many significant digits (see issue 5864).

   Returns a pointer to the fixed buffer, or NULL on failure.

*/

Py_LOCAL_INLINE(char *)

ensure_decimal_point(char* buffer, size_t buf_size, int precision)

{

    int digit_count, insert_count = 0, convert_to_exp = 0;

    const char *chars_to_insert;

    char *digits_start;

    /* search for the first non-digit character */

    char *p = buffer;

    if (*p == '-' || *p == '+')

        /* Skip leading sign, if present.  I think this could only

           ever be '-', but it can't hurt to check for both. */

        ++p;

    digits_start = p;

    while (*p && Py_ISDIGIT(*p))

        ++p;

    digit_count = Py_SAFE_DOWNCAST(p - digits_start, Py_ssize_t, int);

    if (*p == '.') {

        if (Py_ISDIGIT(*(p+1))) {

            /* Nothing to do, we already have a decimal

               point and a digit after it */

        }

        else {

            /* We have a decimal point, but no following

               digit.  Insert a zero after the decimal. */

            /* can't ever get here via PyOS_double_to_string */

            assert(precision == -1);

            ++p;

            chars_to_insert = "0";

            insert_count = 1;

        }

    }

    else if (!(*p == 'e' || *p == 'E')) {

        /* Don't add ".0" if we have an exponent. */

        if (digit_count == precision) {

            /* issue 5864: don't add a trailing .0 in the case

               where the '%g'-formatted result already has as many

               significant digits as were requested.  Switch to

               exponential notation instead. */

            convert_to_exp = 1;

            /* no exponent, no point, and we shouldn't land here

               for infs and nans, so we must be at the end of the

               string. */

            assert(*p == '\0');

        }

        else {

            assert(precision == -1 || digit_count < precision);

            chars_to_insert = ".0";

            insert_count = 2;

        }

    }

    if (insert_count) {

        size_t buf_len = strlen(buffer);

        if (buf_len + insert_count + 1 >= buf_size) {

            /* If there is not enough room in the buffer

               for the additional text, just skip it.  It's

               not worth generating an error over. */

        }

        else {

            memmove(p + insert_count, p,

                buffer + strlen(buffer) - p + 1);

            memcpy(p, chars_to_insert, insert_count);

        }

    }

    if (convert_to_exp) {

        int written;

        size_t buf_avail;

        p = digits_start;

        /* insert decimal point */

        assert(digit_count >= 1);

        memmove(p+2, p+1, digit_count); /* safe, but overwrites nul */

        p[1] = '.';

        p += digit_count+1;

        assert(p <= buf_size+buffer);

        buf_avail = buf_size+buffer-p;

        if (buf_avail == 0)

            return NULL;

        /* Add exponent.  It's okay to use lower case 'e': we only

           arrive here as a result of using the empty format code or

           repr/str builtins and those never want an upper case 'E' */

        written = PyOS_snprintf(p, buf_avail, "e%+.02d", digit_count-1);

        if (!(0 <= written &&

              written < Py_SAFE_DOWNCAST(buf_avail, size_t, int)))

            /* output truncated, or something else bad happened */

            return NULL;

        remove_trailing_zeros(buffer);

    }

    return buffer;

}

/* see FORMATBUFLEN in unicodeobject.c */

#define FLOAT_FORMATBUFLEN 120

/**

 * _PyOS_ascii_formatd:

 * @buffer: A buffer to place the resulting string in

 * @buf_size: The length of the buffer.

 * @format: The printf()-style format to use for the

 *          code to use for converting.

 * @d: The #gdouble to convert

 * @precision: The precision to use when formatting.

 *

 * Converts a #gdouble to a string, using the '.' as

 * decimal point. To format the number you pass in

 * a printf()-style format string. Allowed conversion

 * specifiers are 'e', 'E', 'f', 'F', 'g', 'G', and 'Z'.

 *

 * 'Z' is the same as 'g', except it always has a decimal and

 *     at least one digit after the decimal.

 *

 * Return value: The pointer to the buffer with the converted string.

 * On failure returns NULL but does not set any Python exception.

 **/

static char *

_PyOS_ascii_formatd(char       *buffer,

                   size_t      buf_size,

                   const char *format,

                   double      d,

                   int         precision)

{

    char format_char;

    size_t format_len = strlen(format);

    /* Issue 2264: code 'Z' requires copying the format.  'Z' is 'g', but

       also with at least one character past the decimal. */

    char tmp_format[FLOAT_FORMATBUFLEN];

    /* The last character in the format string must be the format char */

    format_char = format[format_len - 1];

    if (format[0] != '%')

        return NULL;

    /* I'm not sure why this test is here.  It's ensuring that the format

       string after the first character doesn't have a single quote, a

       lowercase l, or a percent. This is the reverse of the commented-out

       test about 10 lines ago. */

    if (strpbrk(format + 1, "'l%"))

        return NULL;

    /* Also curious about this function is that it accepts format strings

       like "%xg", which are invalid for floats.  In general, the

       interface to this function is not very good, but changing it is

       difficult because it's a public API. */

    if (!(format_char == 'e' || format_char == 'E' ||

          format_char == 'f' || format_char == 'F' ||

          format_char == 'g' || format_char == 'G' ||

          format_char == 'Z'))

        return NULL;

    /* Map 'Z' format_char to 'g', by copying the format string and

       replacing the final char with a 'g' */

    if (format_char == 'Z') {

        if (format_len + 1 >= sizeof(tmp_format)) {

            /* The format won't fit in our copy.  Error out.  In

               practice, this will never happen and will be

               detected by returning NULL */

            return NULL;

        }

        strcpy(tmp_format, format);

        tmp_format[format_len - 1] = 'g';

        format = tmp_format;

    }

    /* Have PyOS_snprintf do the hard work */

    PyOS_snprintf(buffer, buf_size, format, d);

    /* Do various fixups on the return string */

    /* Get the current locale, and find the decimal point string.

       Convert that string back to a dot. */

    change_decimal_from_locale_to_dot(buffer);

    /* If an exponent exists, ensure that the exponent is at least

       MIN_EXPONENT_DIGITS digits, providing the buffer is large enough

       for the extra zeros.  Also, if there are more than

       MIN_EXPONENT_DIGITS, remove as many zeros as possible until we get

       back to MIN_EXPONENT_DIGITS */

    ensure_minimum_exponent_length(buffer, buf_size);

    /* If format_char is 'Z', make sure we have at least one character

       after the decimal point (and make sure we have a decimal point);

       also switch to exponential notation in some edge cases where the

       extra character would produce more significant digits that we

       really want. */

    if (format_char == 'Z')

        buffer = ensure_decimal_point(buffer, buf_size, precision);

    return buffer;

}

/* The fallback code to use if _Py_dg_dtoa is not available. */

char * PyOS_double_to_string(double val,

                                         char format_code,

                                         int precision,

                                         int flags,

                                         int *type)

{

    char format[32];

    Py_ssize_t bufsize;

    char *buf;

    int t, exp;

    int upper = 0;

    /* Validate format_code, and map upper and lower case */

    switch (format_code) {

    case 'e':          /* exponent */

    case 'f':          /* fixed */

    case 'g':          /* general */

        break;

    case 'E':

        upper = 1;

        format_code = 'e';

        break;

    case 'F':

        upper = 1;

        format_code = 'f';

        break;

    case 'G':

        upper = 1;

        format_code = 'g';

        break;

    case 'r':          /* repr format */

        /* Supplied precision is unused, must be 0. */

        if (precision != 0) {

            PyErr_BadInternalCall();

            return NULL;

        }

        /* The repr() precision (17 significant decimal digits) is the

           minimal number that is guaranteed to have enough precision

           so that if the number is read back in the exact same binary

           value is recreated.  This is true for IEEE floating point

           by design, and also happens to work for all other modern

           hardware. */

        precision = 17;

        format_code = 'g';

        break;

    default:

        PyErr_BadInternalCall();

        return NULL;

    }

    /* Here's a quick-and-dirty calculation to figure out how big a buffer

       we need.  In general, for a finite float we need:

         1 byte for each digit of the decimal significand, and

         1 for a possible sign

         1 for a possible decimal point

         2 for a possible [eE][+-]

         1 for each digit of the exponent;  if we allow 19 digits

           total then we're safe up to exponents of 2**63.

         1 for the trailing nul byte

       This gives a total of 24 + the number of digits in the significand,

       and the number of digits in the significand is:

         for 'g' format: at most precision, except possibly

           when precision == 0, when it's 1.

         for 'e' format: precision+1

         for 'f' format: precision digits after the point, at least 1

           before.  To figure out how many digits appear before the point

           we have to examine the size of the number.  If fabs(val) < 1.0

           then there will be only one digit before the point.  If

           fabs(val) >= 1.0, then there are at most

         1+floor(log10(ceiling(fabs(val))))

           digits before the point (where the 'ceiling' allows for the

           possibility that the rounding rounds the integer part of val

           up).  A safe upper bound for the above quantity is

           1+floor(exp/3), where exp is the unique integer such that 0.5

           <= fabs(val)/2**exp < 1.0.  This exp can be obtained from

           frexp.

       So we allow room for precision+1 digits for all formats, plus an

       extra floor(exp/3) digits for 'f' format.

    */

    if (isnan(val) || isinf(val))

        /* 3 for 'inf'/'nan', 1 for sign, 1 for '\0' */

        bufsize = 5;

    else {

        bufsize = 25 + precision;

        if (format_code == 'f' && fabs(val) >= 1.0) {

            frexp(val, &exp);

            bufsize += exp/3;

        }

    }

    buf = PyMem_Malloc(bufsize);

    if (buf == NULL) {

        PyErr_NoMemory();

        return NULL;

    }

    /* Handle nan and inf. */

    if (isnan(val)) {

        strcpy(buf, "nan");

        t = Py_DTST_NAN;

    } else if (isinf(val)) {

        if (copysign(1., val) == 1.)

            strcpy(buf, "inf");

        else

            strcpy(buf, "-inf");

        t = Py_DTST_INFINITE;

    } else {

        t = Py_DTST_FINITE;

        if (flags & Py_DTSF_ADD_DOT_0)

            format_code = 'Z';

        PyOS_snprintf(format, sizeof(format), "%%%s.%i%c",

                      (flags & Py_DTSF_ALT ? "#" : ""), precision,

                      format_code);

        _PyOS_ascii_formatd(buf, bufsize, format, val, precision);

        if (flags & Py_DTSF_NO_NEG_0 && buf[0] == '-') {

            char *buf2 = buf + 1;

            while (*buf2 == '0' || *buf2 == '.') {

                ++buf2;

            }

            if (*buf2 == 0 || *buf2 == 'e') {

                size_t len = buf2 - buf + strlen(buf2);

                assert(buf[len] == 0);

                memmove(buf, buf+1, len);

            }

        }

    }

    /* Add sign when requested.  It's convenient (esp. when formatting

     complex numbers) to include a sign even for inf and nan. */

    if (flags & Py_DTSF_SIGN && buf[0] != '-') {

        size_t len = strlen(buf);

        /* the bufsize calculations above should ensure that we've got

           space to add a sign */

        assert((size_t)bufsize >= len+2);

        memmove(buf+1, buf, len+1);

        buf[0] = '+';

    }

    if (upper) {

        /* Convert to upper case. */

        char *p1;

        for (p1 = buf; *p1; p1++)

            *p1 = Py_TOUPPER(*p1);

    }

    if (type)

        *type = t;

    return buf;

}

#else  // _PY_SHORT_FLOAT_REPR == 1

/* _Py_dg_dtoa is available. */

/* I'm using a lookup table here so that I don't have to invent a non-locale

   specific way to convert to uppercase */

#define OFS_INF 0

#define OFS_NAN 1

#define OFS_E 2

/* The lengths of these are known to the code below, so don't change them */

static const char * const lc_float_strings[] = {

    "inf",

    "nan",

    "e",

};

static const char * const uc_float_strings[] = {

    "INF",

    "NAN",

    "E",

};

/* Convert a double d to a string, and return a PyMem_Malloc'd block of

   memory contain the resulting string.

   Arguments:

     d is the double to be converted

     format_code is one of 'e', 'f', 'g', 'r'.  'e', 'f' and 'g'

       correspond to '%e', '%f' and '%g';  'r' corresponds to repr.

     mode is one of '0', '2' or '3', and is completely determined by

       format_code: 'e' and 'g' use mode 2; 'f' mode 3, 'r' mode 0.

     precision is the desired precision

     always_add_sign is nonzero if a '+' sign should be included for positive

       numbers

     add_dot_0_if_integer is nonzero if integers in non-exponential form

       should have ".0" added.  Only applies to format codes 'r' and 'g'.

     use_alt_formatting is nonzero if alternative formatting should be

       used.  Only applies to format codes 'e', 'f' and 'g'.  For code 'g',

       at most one of use_alt_formatting and add_dot_0_if_integer should

       be nonzero.

     type, if non-NULL, will be set to one of these constants to identify

       the type of the 'd' argument:

     Py_DTST_FINITE

     Py_DTST_INFINITE

     Py_DTST_NAN

   Returns a PyMem_Malloc'd block of memory containing the resulting string,

    or NULL on error. If NULL is returned, the Python error has been set.

 */

static char *

format_float_short(double d, char format_code,

                   int mode, int precision,

                   int always_add_sign, int add_dot_0_if_integer,

                   int use_alt_formatting, int no_negative_zero,

                   const char * const *float_strings, int *type)

{

    char *buf = NULL;

    char *p = NULL;

    Py_ssize_t bufsize = 0;

    char *digits, *digits_end;

    int decpt_as_int, sign, exp_len, exp = 0, use_exp = 0;

    Py_ssize_t decpt, digits_len, vdigits_start, vdigits_end;

    _Py_SET_53BIT_PRECISION_HEADER;

    /* _Py_dg_dtoa returns a digit string (no decimal point or exponent).

       Must be matched by a call to _Py_dg_freedtoa. */

    _Py_SET_53BIT_PRECISION_START;

    digits = _Py_dg_dtoa(d, mode, precision, &decpt_as_int, &sign,

                         &digits_end);

    _Py_SET_53BIT_PRECISION_END;

    decpt = (Py_ssize_t)decpt_as_int;

    if (digits == NULL) {

        /* The only failure mode is no memory. */

        PyErr_NoMemory();

        goto exit;

    }

    assert(digits_end != NULL && digits_end >= digits);

    digits_len = digits_end - digits;

    if (no_negative_zero && sign == 1 &&

            (digits_len == 0 || (digits_len == 1 && digits[0] == '0'))) {

        sign = 0;

    }

    if (digits_len && !Py_ISDIGIT(digits[0])) {

        /* Infinities and nans here; adapt Gay's output,

           so convert Infinity to inf and NaN to nan, and

           ignore sign of nan. Then return. */

        /* ignore the actual sign of a nan */

        if (digits[0] == 'n' || digits[0] == 'N')

            sign = 0;

        /* We only need 5 bytes to hold the result "+inf\0" . */

        bufsize = 5; /* Used later in an assert. */

        buf = (char *)PyMem_Malloc(bufsize);

        if (buf == NULL) {

            PyErr_NoMemory();

            goto exit;

        }

        p = buf;

        if (sign == 1) {

            *p++ = '-';

        }

        else if (always_add_sign) {

            *p++ = '+';

        }

        if (digits[0] == 'i' || digits[0] == 'I') {

            strncpy(p, float_strings[OFS_INF], 3);

            p += 3;

            if (type)

                *type = Py_DTST_INFINITE;

        }

        else if (digits[0] == 'n' || digits[0] == 'N') {

            strncpy(p, float_strings[OFS_NAN], 3);

            p += 3;

            if (type)

                *type = Py_DTST_NAN;

        }

        else {

            /* shouldn't get here: Gay's code should always return

               something starting with a digit, an 'I',  or 'N' */

            Py_UNREACHABLE();

        }

        goto exit;

    }

    /* The result must be finite (not inf or nan). */

    if (type)

        *type = Py_DTST_FINITE;

    /* We got digits back, format them.  We may need to pad 'digits'

       either on the left or right (or both) with extra zeros, so in

       general the resulting string has the form

         [<sign>]<zeros><digits><zeros>[<exponent>]

       where either of the <zeros> pieces could be empty, and there's a

       decimal point that could appear either in <digits> or in the

       leading or trailing <zeros>.

       Imagine an infinite 'virtual' string vdigits, consisting of the

       string 'digits' (starting at index 0) padded on both the left and

       right with infinite strings of zeros.  We want to output a slice

         vdigits[vdigits_start : vdigits_end]

       of this virtual string.  Thus if vdigits_start < 0 then we'll end

       up producing some leading zeros; if vdigits_end > digits_len there

       will be trailing zeros in the output.  The next section of code

       determines whether to use an exponent or not, figures out the

       position 'decpt' of the decimal point, and computes 'vdigits_start'

       and 'vdigits_end'. */

    vdigits_end = digits_len;

    switch (format_code) {

    case 'e':

        use_exp = 1;

        vdigits_end = precision;

        break;

    case 'f':

        vdigits_end = decpt + precision;

        break;

    case 'g':

        if (decpt <= -4 || decpt >

            (add_dot_0_if_integer ? precision-1 : precision))