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22.3.3 FORMAT Floating-Point Printers

22.3.3.1 Tilde F: Fixed-Format Floating-Point

The next arg is printed as a float.

The full form is ~w,d,k,overflowchar,padcharF. The parameter w is the width of the field to be printed; d is the number of digits to print after the decimal point; k is a scale factor that defaults to 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; this represents the magnitude of the value of arg times 10^k, rounded to d fractional digits. 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 6.375 using the format ~4,2F may correctly produce either 6.37 or 6.38. Leading zeros are not permitted, except that a single zero digit is output before the decimal point if the printed value is less than one, and this single zero digit is not output at all if w=d+1.

If it is impossible to print the value in the required format in a field of width w, 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 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 and exactly d characters will follow the decimal point. For example, the directive ~,2F will print exactly two digits after the decimal point and as many as necessary before the decimal point.

If the parameter d is omitted, then there is no constraint on the number of digits to appear after the decimal point. 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 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 permitted by the width constraint.

If both w and d are omitted, then the effect is to print the value using ordinary free-format output; prin1 uses this format for any number whose magnitude is either zero or between 10^-3 (inclusive) and 10^7 (exclusive).

If w is omitted, then if the magnitude of arg is so large (or, if d is also omitted, so small) that more than 100 digits would have to be printed, then an implementation is free, at its discretion, to print the number using exponential notation instead, as if by the directive ~E (with all parameters to ~E defaulted, not taking their values from the ~F directive).

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 not supplied 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.

If arg is a complex number or some non-numeric object, then it is printed using the format directive ~wD, thereby printing it in decimal radix and a minimum field width of w.

~F binds *print-escape* to false and *print-readably* to false.

22.3.3.2 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 dk+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 10^7. 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.

If arg is a complex number or some non-numeric object, then it is printed using the format directive ~wD, thereby printing it in decimal radix and a minimum field width of w.

~E binds *print-escape* to false and *print-readably* to false.

22.3.3.3 Tilde G: General Floating-Point

The next arg is printed as a float in either fixed-format or exponential notation as appropriate.

The full form is ~w,d,e,k,overflowchar,padchar,exponentcharG. The format in which to print arg depends on the magnitude (absolute value) of the arg. Let n be an integer such that 10^n-1 ≤ |arg| < 10^n. Let ee equal e+2, or 4 if e is omitted. Let ww equal wee, or nil if w is omitted. If d is omitted, first let q be the number of digits needed to print arg with no loss of information and without leading or trailing zeros; then let d equal (max q (min n 7)). Let dd equal dn.

If 0 ≤ ddd, then arg is printed as if by the format directives

~ww,dd,,overflowchar,padcharF~ee@T

Note that the scale factor k is not passed to the ~F directive. For all other values of dd, arg is printed as if by the format directive

~w,d,e,k,overflowchar,padchar,exponentcharE

In either case, an @ modifier is supplied to the ~F or ~E directive if and only if one was supplied to the ~G directive.

~G binds *print-escape* to false and *print-readably* to false.

22.3.3.4 Tilde Dollarsign: Monetary Floating-Point

The next arg is printed as a float in fixed-format notation.

The full form is ~d,n,w,padchar$. The parameter d is the number of digits to print after the decimal point (default value 2); n is the minimum number of digits to print before the decimal point (default value 1); w is the minimum total width of the field to be printed (default value 0).

First padding and the sign are output. 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. If the : modifier is used, the sign appears before any padding, and otherwise after the padding. If w is supplied and the number of other characters to be output is less than w, then copies of padchar (which defaults to a space) are output to make the total field width equal w. Then n digits are printed for the integer part of arg, with leading zeros if necessary; then a decimal point; then d digits of fraction, properly rounded.

If the magnitude of arg is so large that more than m digits would have to be printed, where m is the larger of w and 100, then an implementation is free, at its discretion, to print the number using exponential notation instead, as if by the directive ~w,q,,,,padcharE, where w and padchar are present or omitted according to whether they were present or omitted in the ~$ directive, and where q=d+n− 1, where d and n are the (possibly default) values given to the ~$ directive.

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 arg is a complex number or some non-numeric object, then it is printed using the format directive ~wD, thereby printing it in decimal radix and a minimum field width of w.

~$ binds *print-escape* to false and *print-readably* to false.