1048     ^ (aNumber negated) sumFromQDouble:self

  1050     ^ self + (aNumber negated)

  1412     q0 := self d0 / aQDouble d0.

  1423     q0 := aQDouble d0 / self d0.

  1413     r := self - (aQDouble * q0).

  1424     "/ Stdout showCR:('q0: %1 (a[0]=%2; b[0]=%3)\n' bindWith:q0 with:self d0 with:aQDouble d0).

  1414 

  1425     r := aQDouble - (self * q0).

  1415     q1 := r d0 / aQDouble d0.

  1426     "/ Stdout showCR:('r: %1\n' bindWith:r asDoubleArray).

  1416     r := r - (aQDouble * q1).

  1427 

  1428     q1 := r d0 / self d0.

  1429     "/ Stdout showCR:('q1: %1 (r[0]=%2; b[0]=%3)\n' bindWith:q1 with:r d0 with:aQDouble d0).

  1430     r := r - (self * q1).

  1431     "/ Stdout showCR:('r: %1\n' bindWith:r asDoubleArray).

  1418     q2 := r d0 / aQDouble d0.

  1433     q2 := r d0 / self d0.

  1419     r := r - (aQDouble * q2).

  1434     "/ Stdout showCR:('q2: %1 (r[0]=%2; b[0]=%3)\n' bindWith:q2 with:r d0 with:aQDouble d0).

  1420 

  1435     r := r - (self * q2).

  1421     q3 := r d0 / aQDouble d0.

  1436     "/ Stdout showCR:('r: %1\n' bindWith:r asDoubleArray).

  1437 

  1438     q3 := r d0 / self d0.

  1439     "/ Stdout showCR:('q3: %1 (r[0]=%2; b[0]=%3)\n' bindWith:q3 with:r d0 with:aQDouble d0).

  1495         /*

  1539 # if 0

  1512         m_renorm5(s0, s1, s2, s3, t0);

  1557 

  1513         return qd_real(s0, s1, s2, s3, t0);

  1558         __qNew_qdReal(newQD, s0, s1, s2, s3);

  1514         */

  1559         RETURN(newQD);                 

  1560 # else

  1640     "Modified: / 14-06-2017 / 11:44:53 / cg"

  1687     "Modified: / 15-06-2017 / 00:49:10 / cg"

  1787 printDigitsOn:outStream precision:precision exponentInto:expn

  1834 digitsWithPrecision:precision

  1788     |numDigits r e i d|

  1835     "generate the digits and exponent"

  1836     

  1837     |numDigits r exp i d out str|

  1793         expn value:0.

  1842         ^ { String new:precision withAll:$0 . 0 }

  1794         precision timesRepeat:[ outStream nextPut:$0 ].

  1843     ].

  1844 

  1845     out := WriteStream on:(String new:precision+5).

  1846 

  1847     "/ determine approx. exponent

  1848     exp := self d0 abs log10 floor.

  1849     exp < -300 ifTrue:[

  1850         r := r * (10.0 raisedToInteger:300).

  1851         r := r / (10.0 raisedToInteger:(exp+300)).

  1852     ] ifFalse:[

  1853         exp > 300 ifTrue:[

  1854 self halt.

  1855 "/            r := ldexpr(r, -53);

  1856 "/            r := r / qd_real(10.0) ^ exp;

  1857 "/            r := ldexp(r, 53);

  1858         ] ifFalse:[

  1859             r := r / (10.0 asQDouble raisedTo:exp).

  1860         ]

  1861     ].

  1862 

  1863     "/ Fix exponent if we are off by one

  1864     (r >= 10.0) ifTrue:[

  1865         r := r / 10.0.

  1866         exp := exp + 1.

  1867     ] ifFalse:[

  1868         (r < 1.0) ifTrue:[

  1869             r := r * 10.0.

  1870             exp := exp - 1.

  1871         ]

  1872     ].

  1873 

  1874     ((r >= 10.0) or:[ r < 1.0 ]) ifTrue:[

  1875         self error:'can''t compute exponent.'.

  1876     ].

  1877 

  1878     "/ Extract the digits

  1879     1 to:numDigits do:[:i |

  1880         d := r d0 truncated.

  1881         r := r - d.

  1882         r := r * 10.0.

  1883 

  1884         out nextPut:($0 + d).

  1885     ].

  1886 

  1887     str := out contents.

  1888     

  1889     "/ Fix out-of-range digits.

  1890     "/ huh? what is this???? 

  1891     "/ how can an "out-of-range" digit appear???

  1892     numDigits to:2 by:-1 do:[:i |

  1893         (str at:i) < $0 ifTrue:[

  1894 self halt.

  1895             str at:i-1 put:(str at:i-1) - 1.

  1896             str at:i put:(str at:i) + 10.

  1897         ] ifFalse:[

  1898             (str at:i) > $9 ifTrue:[

  1899 self halt.

  1900                 str at:i-1 put:(str at:i-1) + 1.

  1901                 str at:i put:(str at:i) - 10.

  1902             ].    

  1903         ].

  1904     ].    

  1905     

  1906     str first <= $0 ifTrue:[

  1907         self error:'non-positive leading digit'

  1908     ].

  1909 

  1910     "/ Round, handle carry 

  1911     (str at:numDigits) >= $5 ifTrue:[

  1912         str at:numDigits-1 put:(str at:numDigits-1) + 1.

  1913         i := numDigits-1.

  1914         [i > 1 and:[(str at:i) > $9]] whileTrue:[

  1915             str at:i put:(str at:i) - 10.

  1916             i := i - 1.

  1917             str at:i put:(str at:i) + 1.

  1918         ]    

  1919     ].    

  1920 

  1921     "/ If first digit is 10, shift everything.

  1922     str first > $9 ifTrue:[

  1923         exp := exp + 1.

  1924         str at:1 put:$0.

  1925         str := '1',str

  1926     ].    

  1927     ^ { (str copyTo:precision) . exp }

  1928     

  1929     "

  1930      1.2345 asQDouble digitsWithPrecision:5 -> #('12345' 0)

  1931      12.345 asQDouble digitsWithPrecision:5 -> #('12345' 1)

  1932      12345 asQDouble digitsWithPrecision:5 -> #('12345' 4)

  1933      12345.1 asQDouble digitsWithPrecision:5 -> #('12345' 4)

  1934      12345.9 asQDouble digitsWithPrecision:5 -> #('12346' 4)

  1935  

  1936      1.2345 asQDouble / 10.0 asQDouble

  1937      1.2345 asQDouble / 10.0 

  1938     "

  1939 

  1940     "Created: / 15-06-2017 / 09:10:01 / cg"

  1941 !

  1942 

  1943 digitsWithPrecision:precision exponentInto:expnHolder

  1944     "generate the digits and return exponent info"

  1945     

  1946     |numDigits r exp i d out str|

  1947 

  1948     numDigits := precision+1. "/ number of digits

  1949     r := self abs.

  1950     self d0 = 0.0 ifTrue:[

  1951         expnHolder value:0.

  1952         ^ String new:precision withAll:$0

  1953     ].

  1954 

  1955     out := WriteStream on:(String new:precision+5).

  1956 

  1957     "/ determine approx. exponent

  1958     exp := self d0 abs log10 floor.

  1959     exp < -300 ifTrue:[

  1960         r := r * (10.0 raisedToInteger:300).

  1961         r := r / (10.0 raisedToInteger:(exp+300)).

  1962     ] ifFalse:[

  1963         exp > 300 ifTrue:[

  1964 self halt.

  1965 "/            r := ldexpr(r, -53);

  1966 "/            r := r / qd_real(10.0) ^ exp;

  1967 "/            r := ldexp(r, 53);

  1968         ] ifFalse:[

  1969             r := r / (10.0 asQDouble raisedTo:exp).

  1970         ]

  1971     ].

  1972 

  1973     "/ Fix exponent if we are off by one

  1974     (r >= 10.0) ifTrue:[

  1975         r := r / 10.0.

  1976         exp := exp + 1.

  1977     ] ifFalse:[

  1978         (r < 1.0) ifTrue:[

  1979             r := r * 10.0.

  1980             exp := exp - 1.

  1981         ]

  1982     ].

  1983 

  1984     ((r >= 10.0) or:[ r < 1.0 ]) ifTrue:[

  1985         self error:'can''t compute exponent.'.

  1986     ].

  1987 

  1988     "/ Extract the digits

  1989     1 to:numDigits do:[:i |

  1990         d := r d0 truncated.

  1991         r := r - d.

  1992         r := r * 10.0.

  1993 

  1994         out nextPut:($0 + d).

  1995     ].

  1996 

  1997     str := out contents.

  1998     

  1999     "/ Fix out-of-range digits.

  2000     "/ huh? what is this???? 

  2001     "/ how can an "out-of-range" digit appear???

  2002     i := numDigits.

  2003     [i > 1] whileTrue:[

  2004         (str at:i) < $0 ifTrue:[

  2005             self halt.

  2006             str at:i-1 put:(str at:i-1) - 1.

  2007             str at:i put:(str at:i) + 10.

  2008         ] ifFalse:[

  2009             (str at:i) > $9 ifTrue:[

  2010                 self halt.

  2011                 str at:i-1 put:(str at:i-1) + 1.

  2012                 str at:i put:(str at:i) - 10.

  2013             ].    

  2014         ].

  2015         i := i - 1.

  2016     ].    

  2017     

  2018     (str at:1) <= $0 ifTrue:[

  2019         self error:'non-positive leading digit'

  2020     ].

  2021 

  2022     "/ Round, handle carry 

  2023     (str at:numDigits) >= $5 ifTrue:[

  2024         str at:numDigits-1 put:(str at:numDigits-1) + 1.

  2025         i := numDigits-1.

  2026         [i > 1 and:[(str at:i) > $9]] whileTrue:[

  2027             str at:i put:(str at:i) - 10.

  2028             i := i - 1.

  2029             str at:i put:(str at:i) + 1.

  2030         ]    

  2031     ].    

  2032 

  2033     "/ If first digit is 10, shift everything.

  2034     (str at:1) > $9 ifTrue:[

  2035         exp := exp + 1.

  2036         str at:1 put:$0.

  2037         str := '1',str

  2038     ].    

  2039     expnHolder value:exp.

  2040     ^ (str copyTo:precision).

  2041     

  2042     "

  2043      1.2345 asQDouble digitsWithPrecision:5 exponentInto:[:e | Transcript showCR:e] -> '12345' / 0

  2044      12.345 asQDouble digitsWithPrecision:5 exponentInto:[:e | Transcript showCR:e] -> '12345' / 1

  2045      12345 asQDouble digitsWithPrecision:5 exponentInto:[:e | Transcript showCR:e]

  2046      12345.1 asQDouble digitsWithPrecision:5 exponentInto:[:e | Transcript showCR:e]

  2047      12345.9 asQDouble digitsWithPrecision:5 exponentInto:[:e | Transcript showCR:e]

  2048  

  2049      1.2345 asQDouble / 10.0 asQDouble

  2050      1.2345 asQDouble / 10.0 

  2051     "

  2052 

  2053     "Created: / 15-06-2017 / 09:05:42 / cg"

  2054 !

  2055 

  2056 printOn:aStream

  2057     "return a printed representation of the receiver"

  2058 

  2059     self d1 = 0.0 ifTrue:[

  2060         self d0 printOn:aStream.

  1797 

  2063     self

  1798     "/ determine approx. exponent

  2064         printOn:aStream precision:0 width:0 

  1799     e := self d0 abs log10 floor.

  2065         fixed:false showPositive:false uppercase:false fillChar:(Character space)

  1800     self halt.

  2066 

  1801     e < -300 ifTrue:[

  2067     "

  1802         r := r * (10.0 raisedToInteger:300).

  2068      (QDouble fromFloat:1.2345) printOn:Transcript

  1803         r := r / (10.0 raisedToInteger:(e+300)).

  2069      ((QDouble fromFloat:1.2345) / 10.0) printOn:Transcript

  2070     "

  2071 

  2072     "Created: / 15-06-2017 / 01:51:36 / cg"

  2073     "Modified (comment): / 15-06-2017 / 08:50:25 / cg"

  2074 !

  2075 

  2076 printOn:aStream precision:precision width:width 

  2077     fixed:fixed showPositive:showPositive uppercase:uppercase fillChar:fillChar

  2078 

  2079     "return a printed representation of the receiver.

  2080      This is a parametrized entry, which can be used by printf-like functions"

  2081 

  2082     |sgn count delta exp|

  2083 

  2084     self d1 = 0.0 ifTrue:[

  2085         self d0 printOn:aStream.

  2086         ^ self.

  2087     ].

  2088 

  2089     count := 0.

  2090     sgn := true.

  2091     exp := 0.

  2092     

  2093     self isInfinite ifTrue:[

  2094         self < 0 ifTrue:[

  2095             aStream nextPut:$-.

  2096             count := 1.

  2097         ] ifFalse:[

  2098             showPositive ifTrue:[

  2099                 aStream nextPut:$+.

  2100                 count := 1.

  2101             ] ifFalse:[

  2102                 sgn := false.

  2103             ].    

  2104         ].

  2105         uppercase ifTrue:[

  2106             aStream nextPutAll:'INF'

  2107         ] ifFalse:[

  2108             aStream nextPutAll:'inf'

  2109         ].

  2110         count := count + 3.

  1805         e > 300 ifTrue:[

  2112         self isNaN ifTrue:[

  1806         ] ifFalse:[

  2113             uppercase ifTrue:[

  2114                 aStream nextPutAll:'NAN'

  2115             ] ifFalse:[

  2116                 aStream nextPutAll:'nan'

  2117             ].

  2118             count := count + 3.

  2119         ] ifFalse:[        

  2120             self < 0 ifTrue:[

  2121                 aStream nextPut:$-.

  2122                 count := count + 1.

  2123             ] ifFalse:[

  2124                 showPositive ifTrue:[

  2125                     aStream nextPut:$+.

  2126                     count := count + 1.

  2127                 ] ifFalse:[

  2128                     sgn := false.

  2129                 ].    

  2130             ].

  2131             self = 0.0 ifTrue:[

  2132                 aStream nextPut:$0.

  2133                 count := count + 1.

  2134                 precision > 0 ifTrue:[

  2135                     aStream nextPut:$..

  2136                     count := count + 1.

  2137                     precision timesRepeat:[ aStream nextPut:$0 ].

  2138                     count := count + precision.

  2139                 ].    

  2140                 self halt.

  2141             ] ifFalse:[

  2142                 |off d d_width_extra|

  2143                 

  2144                 "/ non-zero case

  2145                 off := fixed 

  2146                         ifTrue:[ 1 + self abs log10 floor ]

  2147                         ifFalse:[1].

  2148                 d := precision + off.

  2149                 d_width_extra := d.

  2150                 fixed ifTrue:[

  2151                     d_width_extra := 120 max:d.

  2152                 ].    

  2153                 "/ highly special case - fixed mode, precision is zero, abs(*this) < 1.0

  2154                 "/ without this trap a number like 0.9 printed fixed with 0 precision prints as 0

  2155                 "/ should be rounded to 1.

  2156                 (fixed and:[ (precision == 0) and:[ (self abs < 1.0) ]]) ifTrue:[

  2157                     (self abs >= 0.5) ifTrue:[

  2158                         aStream nextPut:$1

  2159                     ] ifFalse:[

  2160                         aStream nextPut:$0

  2161                     ].

  2162                     ^ self

  2163                 ].

  2164                 

  2165                 "/ handle near zero to working precision (but not exactly zero)

  2166                 (fixed and:[ d <= 0 ]) ifTrue:[

  2167                     aStream nextPut:$0.

  2168                     (precision > 0) ifTrue:[

  2169                         aStream nextPut:$. .

  2170                         aStream next:precision put:$0.

  2171                     ]

  2172                 ] ifFalse:[

  2173                     "/ default

  2174 

  2175                     |t j|

  2176 

  2177                     fixed ifTrue:[

  2178                         t := String streamContents:[:s |

  2179                                 self 

  2180                                     printDigitsOn:s 

  2181                                     precision:d_width_extra 

  2182                                     exponentInto:[:e | exp := e]

  2183                              ].    

  2184                     ] ifFalse:[

  2185                         t := String streamContents:[:s |

  2186                                 self 

  2187                                     printDigitsOn:s 

  2188                                     precision:d 

  2189                                     exponentInto:[:e | exp := e]

  2190                              ].    

  2191                     ].

  2192 

  2193                     fixed ifTrue:[

  2194                         "/ fix the string if it's been computed incorrectly

  2195                         "/ round here in the decimal string if required

  2196                         t := self round_string_qd:t at:(d + 1) offsetInto:[:o | off := o].

  2197 

  2198                         (off > 0) ifTrue:[

  2199                             aStream next:off putAll:t startingAt:0.

  2200                             (precision > 0) ifTrue:[

  2201                                 aStream nextPut:$. .

  2202                                 aStream next:precision putAll:t startingAt:off+1.

  2203                             ]

  2204                         ] ifFalse:[

  2205                             aStream nextPutAll:'0.'.

  2206                             (off < 0) ifTrue:[

  2207                                 aStream next:off negated put:$0.

  2208                             ].

  2209                             aStream next:d putAll:t startingAt:0.

  2210                         ]

  2211                     ] ifFalse:[

  2212                         aStream nextPut:(t at:1).

  2213                         (precision > 0) ifTrue:[

  2214                             aStream nextPut:$. .

  2215                         ].

  2216                         aStream next:precision putAll:t startingAt:2.

  2217                     ]

  2218                 ].

  2219             ].

  1809     

  2222 

  1810     

  2223     "/ trap for improper offset with large values

  1811     "

  2224     "/ without this trap, output of values of the for 10^j - 1 fail for j > 28

  1812      1.2345 asQDouble printDigitsOn:Transcript precision:5 exponentInto:[:e |]

  2225     "/ and are output with the point in the wrong place, leading to a dramatically off value

  1813     "

  2226 

  1814 

  2227 "/    (fixed and:[ (precision > 0) ]) ifTrue:[

  1815     "Created: / 13-06-2017 / 17:28:08 / cg"

  2228 "/        "/ make sure that the value isn't dramatically larger

  2229 "/        from_string = atof(s.c_str());

  2230 "/

  2231 "/        // if this ratio is large, then we've got problems

  2232 "/        if( fabs( from_string / this->x[0] ) > 3.0 ){

  2233 "/

  2234 "/                int point_position;

  2235 "/                char temp;

  2236 "/

  2237 "/                // loop on the string, find the point, move it up one

  2238 "/                // don't act on the first character

  2239 "/                for(i=1; i < s.length(); i++){

  2240 "/                        if(s[i] == '.'){

  2241 "/                                s[i] = s[i-1] ;

  2242 "/                                s[i-1] = '.' ;

  2243 "/                                break;

  2244 "/                        }

  2245 "/                }

  2246 "/

  2247 "/                from_string = atof(s.c_str());

  2248 "/                // if this ratio is large, then the string has not been fixed

  2249 "/                if( fabs( from_string / this->x[0] ) > 3.0 ){

  2250 "/                        dd_real::error("Re-rounding unsuccessful in large number fixed point trap.") ;

  2251 "/                }

  2252 "/        }

  2253 "/    }

  2254 "/

  2255 "/    if (!!fixed) {

  2256 "/      /* Fill in exponent part */

  2257 "/      s += uppercase ? 'E' : 'e';

  2258 "/      append_expn(s, e);

  2259 "/    }

  2260 "/  }

  2261 

  2262     "/ fill in the blanks

  2263     (delta := width-count) > 0 ifTrue:[

  2264         self halt.

  2265 "/    if (fmt & ios_base::internal) {

  2266 "/      if (sgn)

  2267 "/        s.insert(static_cast<string::size_type>(1), delta, fill);

  2268 "/      else

  2269 "/        s.insert(static_cast<string::size_type>(0), delta, fill);

  2270 "/    } else if (fmt & ios_base::left) {

  2271 "/      s.append(delta, fill);

  2272 "/    } else {

  2273 "/      s.insert(static_cast<string::size_type>(0), delta, fill);

  2274 "/    }

  2275 "/  }

  2276     ].

  2277 

  2278     "Created: / 15-06-2017 / 02:37:31 / cg"

  1821     self d1 = 0.0 ifTrue:[

  2284     ^ String streamContents:[:s | self printOn:s]

  1822         ^ self d0 printString

  1823     ].

  1824     ^ self d0 printString , '...'