ANSI Common Lisp 22 Printer 22.3 Formatted Output 22.3.3 FORMAT Floating-Point Printers
22.214.171.124 Tilde E: Exponential Floating-Point
The next arg is printed as a float in exponential notation.
The full form is ~w,d,e,k,overflowchar,padchar,exponentcharE. The parameter w is the width of the field to be printed; d is the number of digits to print after the decimal point; e is the number of digits to use when printing the exponent; k is a scale factor that defaults to one (not zero).
Exactly w characters will be output. First, leading copies of the character padchar (which defaults to a space) are printed, if necessary, to pad the field on the left. If the arg is negative, then a minus sign is printed; if the arg is not negative, then a plus sign is printed if and only if the @ modifier was supplied. Then a sequence of digits containing a single embedded decimal point is printed. The form of this sequence of digits depends on the scale factor k. If k is zero, then d digits are printed after the decimal point, and a single zero digit appears before the decimal point if the total field width will permit it. If k is positive, then it must be strictly less than d+2; k significant digits are printed before the decimal point, and d-k+1 digits are printed after the decimal point. If k is negative, then it must be strictly greater than - d; a single zero digit appears before the decimal point if the total field width will permit it, and after the decimal point are printed first - k zeros and then d+k significant digits. The printed fraction must be properly rounded. When rounding up and rounding down would produce printed values equidistant from the scaled value of arg, then the implementation is free to use either one. For example, printing the argument 637.5 using the format ~8,2E may correctly produce either 6.37E+2 or 6.38E+2.
Following the digit sequence, the exponent is printed. First the character parameter exponentchar is printed; if this parameter is omitted, then the exponent marker that prin1 would use is printed, as determined from the type of the float and the current value of *read-default-float-format*. Next, either a plus sign or a minus sign is printed, followed by e digits representing the power of ten by which the printed fraction must be multiplied to properly represent the rounded value of arg.
If it is impossible to print the value in the required format in a field of width w, possibly because k is too large or too small or because the exponent cannot be printed in e character positions, then one of two actions is taken. If the parameter overflowchar is supplied, then w copies of that parameter are printed instead of the scaled value of arg. If the overflowchar parameter is omitted, then the scaled value is printed using more than w characters, as many more as may be needed; if the problem is that d is too small for the supplied k or that e is too small, then a larger value is used for d or e as may be needed.
If the w parameter is omitted, then the field is of variable width. In effect a value is chosen for w in such a way that no leading pad characters need to be printed.
If the parameter d is omitted, then there is no constraint on the number of digits to appear. A value is chosen for d in such a way that as many digits as possible may be printed subject to the width constraint imposed by the parameter w, the constraint of the scale factor k, and the constraint that no trailing zero digits may appear in the fraction, except that if the fraction to be printed is zero then a single zero digit should appear after the decimal point.
If the parameter e is omitted, then the exponent is printed using the smallest number of digits necessary to represent its value.
If all of w, d, and e are omitted, then the effect is to print the value using ordinary free-format exponential-notation output; prin1 uses a similar format for any non-zero number whose magnitude is less than 10-3 or greater than or equal to 107. The only difference is that the ~E directive always prints a plus or minus sign in front of the exponent, while prin1 omits the plus sign if the exponent is non-negative.
If arg is a rational number, then it is coerced to be a single float and then printed. Alternatively, an implementation is permitted to process a rational number by any other method that has essentially the same behavior but avoids loss of precision or overflow because of the coercion. If w and d are unsupplied and the number has no exact decimal representation, for example 1/3, some precision cutoff must be chosen by the implementation since only a finite number of digits may be printed.