ratstr.sa


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-- Copyright (C) 2000 by K Hopper, University of Waikato, New Zealand        --
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partial class RAT_STR < $TEXT, $ANCHORED_FMT

partial class RAT_STR < $TEXT, $ANCHORED_FMT is -- This partial class provides formatting services for the class STR. -- Version 1.0 Sep 98. Copyright K Hopper, U of Waikato -- Development History -- ------------------- -- Date Who By Detail -- ---- ------ ------ -- 22 Sep 98 kh Original from FLOAT_STR private scan( cursor : STR_CURSOR ) : SAME pre ~void(cursor) post (void(result) and (initial(cursor.index) = cursor.index)) or (initial(cursor.index) < cursor.index) is -- This routine is the real number 'scanner' to obtain the real number -- value expected to be next in the indicated string - or returning with -- the string unchanged, returning void if there is a format error. start_index : CARD := cursor.index ; loc_lib : LIBCHARS := cursor.buffer.index_lib ; loc_num : INTI := INTI::build(cursor) ; if cursor.index = start_index then return void else loc_start : CARD := cursor.index ; cursor.skip_space ; if cursor.item /= loc_lib.Solidus.char then -- not a rational! cursor.set_index(start_index) ; return void end end ; cursor.skip_space ; loc_start : CARD := cursor.index ; loc_denom : INTI := INTI::build(cursor) ; if cursor.index = loc_start then cursor.set_index(start_index) ; return void else return num(loc_num).denom(loc_denom) end end ; is_rat( str : STR ) : CONVERSION_RESULTS pre true post (result = CONVERSION_RESULTS::All_Right) or (result = CONVERSION_RESULTS::Out_of_Range) or (result = CONVERSION_RESULTS::Bad_Format) or (result = CONVERSION_RESULTS::Empty) is -- This routine checks that the format of of the leading characters of -- the given string using the given repertoire and encoding corresponds to -- that required for a rational number, returning the relevant result state. if str.size = 0 then return CONVERSION_RESULTS::Empty end ; start_index : CARD := 0 ; loc_cursor : STR_CURSOR := str.cursor ; loc_res : SAME := scan(loc_cursor) ; if loc_cursor.index = start_index then return CONVERSION_RESULTS::Bad_Format else loc_cursor.set_index(start_index) ; return CONVERSION_RESULTS::All_Right end end ; build( loc_cursor : STR_CURSOR ) : SAME pre ~void(loc_cursor) post (void(result) and (initial(loc_cursor.index) = loc_cursor.index)) or (initial(loc_cursor.index) < loc_cursor.index) is -- This routine creates the real number corresponding to the textual -- representation contained in str which must have a digit both before and -- after a mandatory decimal mark! If the string indicated does not -- contain a real number as the next non-blank item in the string then zero is -- returned or if out of range then quiet_NaN is returned -- and the cursor -- has not been moved! return scan(loc_cursor) end ; create( str : STR ) : SAME pre (is_rat(str) = CONVERSION_RESULTS::All_Right) post true is -- This routine creates the real number corresponding to the textual -- representation contained in str. return build(str.cursor) end ; private float( precision, base : CARD ) : TUP{BOOL, INTI, INT, BOOL} pre (precision > 0) and (base > 1) is -- This routine returns the floating point number which is the value of -- self to the given precision and in the given base as a 4-tuple :-- -- -- Sign -- true if negative -- Mantissa -- Exponent -- Exact -- true if the value is an accurate representation of self. -- -- Where rounding is required then younding to nearest is used -- except -- when 'tie-breaking' when rounding to even (as in IEEE 754) is used. -- -- The implementation is essentially AlgorithmM described by W.D. -- Clinger in "How to Read Floating Point Numbers Accurately", Proc PLDI 1990, -- p. 92-101. if num.is_zero then return TUP{BOOL,INTI,INT,BOOL}::create(false,INTI::create(0),0,true) else beta : INTI := INTI::create(base) ; beta_n1 : INTI := beta^(precision - 1) ; beta_n : INTI := beta_n1 * beta ; sign : BOOL := num.is_neg ; numerator : INTI := num.abs ; denominator : INTI := denom ; assert denominator.is_pos ; -- approximation for exponent exponent : INT := numerator.log2 - denominator.log2 ; if base /= 2 then exponent := (exponent.flt / base.flt.log2).round.int end ; exponent := exponent - precision.int ; if exponent < 0 then numerator := numerator * beta^(-exponent) else denominator := denominator * beta^exponent end ; -- normalize mantissa (usually 0 or 1 iterations required) mantissa : INTI ; loop -- u/v * b^e = |self| mantissa := numerator / denominator ; if mantissa < beta_n1 then numerator := numerator * beta ; exponent := exponent - 1 elsif mantissa >= beta_n then denominator := denominator * beta ; exponent := exponent + 1 else break! end end ; -- Convert to float and round to nearest. rem : INTI := numerator % denominator ; divisor : INTI := denominator - rem ; if (rem > divisor) or ((rem = divisor) and mantissa.is_odd) then -- next float mantissa := mantissa + INTI::create(1) ; if mantissa = beta_n then mantissa := beta_n1 ; exponent := exponent + 1 end end ; return TUP{BOOL,INTI,INT,BOOL}::create( sign, mantissa, exponent, rem.is_zero) end end ; flt_str( precision : CARD, lib : LIBCHARS ) : STR pre precision > 0 is -- This routine returns a string representation of self as a floating -- point number using the given repertoire and encoding. raw_value : TUP{BOOL,INTI,INT,BOOL} := float(precision, 10) ; res : STR := STR::create(lib) ; if raw_value.t1 then res := res + lib.Minus_Sign.char end ; mantissa : STR := raw_value.t2.str(lib) ; digits : CARD := mantissa.size ; trailing_zeros : CARD ; loop trailing_zeros := 0.upto!(digits - 1) ; while!(mantissa[digits - 1 - trailing_zeros] = lib.digit(0).char) end ; res := res + mantissa[0] + lib.Decimal_Mark.char ; after_decimal : INT := digits.int - 1.int - trailing_zeros.int ; if after_decimal > 0.int then res := res + mantissa.substring(1,after_decimal.card) end ; exponent : INT := raw_value.t3 + digits.int - 1.int ; if exponent.is_non_zero then res := res + lib.Exponent_Mark.char + exponent.str(lib) end ; return res end ; str( lib : LIBCHARS ) : STR is -- This routine returns a string representation of self as a vulgar -- fraction (unless the value is integral) using the given repertoire and -- encoding. if is_int or is_card then return num.str else return num.str + lib.Solidus.char + denom.str end end ; str : STR is -- This routine returns a string representation of self as a vulgar -- fraction using the default repertoire and encoding. return str(LIBCHARS::default) end ; fmt( format : ANCHORED_DESCR, lib : LIBCHARS ) : STR is -- This routine returns the formatted string representation of self in -- accordance with the string format. This provides special case treatment -- where the leading component is exactly one - it reduces the value string -- to the single leading character - which is therefore expected to differ -- for the two values!. res : STR := str(lib) ; loc_fill : STR := STR::create(lib) + format.filler.char ; if format.leading = 1 then res := res.head(1) elsif res.size < format.leading then -- needs a filler res := loc_fill.repeat(format.leading - res.size) + res end ; return res + loc_fill.repeat(format.trailing) end ; fmt( format : ANCHORED_DESCR ) : STR is -- This routine returns the formatted string representation of self in -- accordance with the string format. return fmt(format,LIBCHARS::default) end ; end ; -- RAT_STR