REAL Input: The F and E Descriptors

The Fw.d, Ew.d, ESw.d, ENw.d, Ew.dEe, ESw.dEe and ENw.dEe descriptors are used for REAL input; however, they all have the same effect as Fw.d. Therefore, we shall only discuss Fw.d. The general form of the Fw.d descriptor is as follows:

rFw.d

The meaning of r, w and m are:

F is for REAL
w is the width of field, which indicates that a real number should be read in from the next w positions.
d is the number of digits in the fractional part. There are two possibilities:
1. If the number in the w contains a decimal point, d is ignored and the value read is the number described in the w positions.
2. If the number in the w positions does not have a decimal point, then the right most d positions are considered to be the fractional point. More precisely, a decimal point is inserted between the d and the d+1 positions from the right.
Please note that spaces may be ignored or treated as zeros. Therefore, adding a decimal point in your input is a wise choice.
For example, suppose we have the following:
```
REAL :: u, v, w

READ(*,"(F5.2,F5.2,F5.2)")  u, v, w
```
and the input is
```
         1    1
....5....0....5
1 2 3 4.5 1 9.4
```
Let us assume that spaces are ignored. u takes the first five positions which contains 1, a space, 2, a space and 3. Since F5.2 is used to read this number (i.e., 123) which does not have a decimal point, a decimal point is inserted between 1 and 2. Hence, u receives 1.23. Variable v takes the next five positions, which contains a space, 4.5 and another space. Since this value contains a decimal point, it is read as is and v receives 4.5. Variable w takes the last five positions, which contain 1, a space, and 9.4. This gives 19.4 and therefore w receives 19.4.
Suppose spaces are treated as zeros. The first five positions are 1, space, 2, space and 3, which is equivalent to 10203. Therefore, u receives 102.03. Similarly, variables v and w receive 4.5 and 109.4, respectively.
The number in the w positions can contain a E followed by the value of the exponent.
The w positions must contain a legal real number with an optional sign and/or an E followed by an exponent. The exponent, if any, must be an integer.
A real number without a decimal point in the w positions consists of an optional sign, followed by a sequence of digits. In this case, the place of the decimal point is determined by the value of d.
A real number with a decimal point starts with an optional sign, followed by zero or more digits (the integral part), followed by a decimal point, followed by zero or more digits (the fractional part). Thus, -.345, 0.345, +123 are all correct input real numbers. Note that the integral part or the fractional part must have one digit. As a result, -. is not a correct input real number.
A real number with an exponent starts with a real number, with or without a decimal point, followed by E, followed by an optional sign, followed by an integer. Thus, 12345E-9 and 12.345E-23 are correct real numbers. If the input real number contains an exponent, then d applies to the number itself. For example, if we have
```
REAL :: u

READ(*,"(F10.4)")  u
```
and the input is
```
         1
....5....0
12345E20 
```
then u takes the first ten positions. If spaces are ignored, the exponent is 20 and 12345 is read in with 4 digits in the fractional part. Therefore, the actual value read in is 1.2345×10²⁰. If spaces are treated as zeros, the value read in becomes 1.2345×10²⁰⁰⁰. For most computers, this value could be too larger to be stored in memory.
No other symbols can be used; otherwise, the READ statement that uses this format will report an error and stop. If all w positions are spaces, the value is treated as a zero.
Converting an input real number to a number in computer memory cannot be exact, because the input number is in base-10 representation and most computers use base-2 or base-16 internal representation for real numbers.
r is the repetition indicator, which gives the number of times the edit descriptor should be repeated. For example, 3F5.3 is equivalent to F5.3, F5.3, F5.3.

Examples

Suppose we have the following input and the system ignores spaces.

         1    1    2
....5....0....5....0
12 3.4  56E 78.  90

What are the values in each variable after reading in the above input?
```
REAL :: a, b, c, d

READ(*,"(F3.0, F4.1, F6.2, F7.3)")  a, b, c, d
```
Suppose spaces are ignored. Variable a takes the first three positions, which contains 1, 2 and a space. After removing spaces, we have 12 and since F3.0 states no digits for the fractional part, the value read in is 12.0. Variable b takes the next four positions, which contain 3, a decimal point, a 4 and a space. After removing all spaces, we have 3.4. Since there is a decimal point, the value will be read in as is. Thus, b receives 3.4. Variable c takes the next six positions, which contain a space, 5, 6, E, a space and 7. After removing all spaces, we have 56E7. Thus, the exponent is 7 and 56 is read with F6.2 (i.e., two digits after the decimal point). Therefore, variable c receives 0.56×10⁷. Variable d takes the next seven positions, which contain a 8, a decimal point, two spaces, 9, 0 and a space. After removing all spaces, we have 8.90. Since it contains a decimal point, the value will be read in as is and d receives 8.9
If the system treats spaces as zeros, a, b, c and d receive 120, 3.4, 0.56×10⁷, and 8.009, respectively.
What are the values in each variable after reading in the above input?
```
REAL :: a, b, c, d

READ(*,"(F6.1, F3.2, F5.0, F6.1)")  a, b, c, d
```
Variable a takes the first 6 positions, which contain 1, 2, a space, 3, a decimal point and 4. Thus, a receives 123.4. Variable b takes the next three positions, which contain two spaces and 5. Thus, b receives 0.05. Variable c takes the next five positions, which contains 6, E, a space, 7 and 8. Hence, c receives 6×10⁷⁸. Finally, d takes the next six positions, which contains a decimal point, two spaces, 9, 0 and a space. Hence, d receives 0.9.
If the system treats spaces as zeros, a, b, c and d receive 1203.4, 0.05, 6×10⁷⁸ and 0.009, respectively.