浮点数：匹配多少位有效数字？

Question

In C, Given two single or double precision floating point numbers, is there an easy way to determine how many of their significant figures "match"? Ie if I have two such numbers with decimal representation 1.64298272 and 1.64298296 I would like to obtain the result 7 . If I was concerned with decimal places this would be easy but I'm not sure how to go about it if I'm interested in significant figures.

Answer 1

To do an exact compare, the value must be converted with sufficient precision. DBL_DECIMAL_DIG (typical 17) is enough for double to make unique strings as suggested by @ryyker

Form a string for both values

//         -   d   .    digits - 1        e   -  expo \0
#define N (1 + 1 + 1  + DBL_DECIMAL_DIG + 1 + 1 + 5 + 1)
char buf[N + 10];  // Some extra too to cope with strange NaN payloads
// Consider changing round mode to "round towards 0.0.  See below notes.
snprintf(buf, sizeof buf,"%+.*e", DBL_DECIMAL_DIG - 1, value);

After testing for same sign and exponent, walk leading digits.

Some sample hacked code.

if (buf1[0] != buf2[0]) return 0; // sign test
e1 = strchr(buf1, 'e');
e2 = strchr(buf1, 'e');
if (strcmp(e1,e2)) return 0; // expo test (non-finite concerns omitted here for brevity)
digit = 0;
s1 = buf1;
s2 = buf2;
while (s1 < e1 && s2 < e2) {
  if (isdigit(*s1)) {
    if (*s1 == *s1) digit++;
    else break;
  }
  s1++; s2++;
}
return digit;

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If code attempts to do this without s*printf() , the math involved to examine a binary based floating-point number and convert to decimal for compare will effectively re-do what sprintf() does already.

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Limitations:

This answers is at best a start. Consider foo(0.0, 0.0) and foo(DBL_TRUE_MIN, DBL_TRUE_MIN) here would return DBL_DECIMAL_DIG . As DBL_TRUE_MIN is about 4.940656...e-324 yet as an exact decimal has about 751 significant digits, should 751 be returned?

Research is needed also to consider edge cases .

See @Eric Postpischil good idea about first changing the rounding mode. IAC, using sprintf() is limited by a quality of implementation.

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[Update]

If a C library implements FP perIEEE-754 , then to well handle many cases, a +3 to the precision is recommended.

char buf[N + 3 + 10];
// Consider changing round mode to "round towards 0.0.  See below notes.
snprintf(buf, sizeof buf,"%+.*e", DBL_DECIMAL_DIG + 3 - 1, value);