// Copyright 2015 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // This file implements Float-to-string conversion functions. // It is closely following the corresponding implementation // in strconv/ftoa.go, but modified and simplified for Float. package big import ( "fmt" "strconv" "strings" ) // Text converts the floating-point number x to a string according // to the given format and precision prec. The format is one of: // // 'e' -d.dddde±dd, decimal exponent, at least two (possibly 0) exponent digits // 'E' -d.ddddE±dd, decimal exponent, at least two (possibly 0) exponent digits // 'f' -ddddd.dddd, no exponent // 'g' like 'e' for large exponents, like 'f' otherwise // 'G' like 'E' for large exponents, like 'f' otherwise // 'b' -ddddddp±dd, binary exponent // 'p' -0x.dddp±dd, binary exponent, hexadecimal mantissa // // For the binary exponent formats, the mantissa is printed in normalized form: // // 'b' decimal integer mantissa using x.Prec() bits, or -0 // 'p' hexadecimal fraction with 0.5 <= 0.mantissa < 1.0, or -0 // // If format is a different character, Text returns a "%" followed by the // unrecognized format character. // // The precision prec controls the number of digits (excluding the exponent) // printed by the 'e', 'E', 'f', 'g', and 'G' formats. For 'e', 'E', and 'f' // it is the number of digits after the decimal point. For 'g' and 'G' it is // the total number of digits. A negative precision selects the smallest // number of digits necessary to identify the value x uniquely. // The prec value is ignored for the 'b' or 'p' format. // // BUG(gri) Float.Text does not accept negative precisions (issue #10991). func (x *Float) Text(format byte, prec int) string { const extra = 10 // TODO(gri) determine a good/better value here return string(x.Append(make([]byte, 0, prec+extra), format, prec)) } // String formats x like x.Text('g', 10). func (x *Float) String() string { return x.Text('g', 10) } // Append appends to buf the string form of the floating-point number x, // as generated by x.Text, and returns the extended buffer. func (x *Float) Append(buf []byte, fmt byte, prec int) []byte { // sign if x.neg { buf = append(buf, '-') } // Inf if x.form == inf { if !x.neg { buf = append(buf, '+') } return append(buf, "Inf"...) } // pick off easy formats switch fmt { case 'b': return x.fmtB(buf) case 'p': return x.fmtP(buf) } // Algorithm: // 1) convert Float to multiprecision decimal // 2) round to desired precision // 3) read digits out and format // 1) convert Float to multiprecision decimal var d decimal // == 0.0 if x.form == finite { d.init(x.mant, int(x.exp)-x.mant.bitLen()) } // 2) round to desired precision shortest := false if prec < 0 { shortest = true panic("unimplemented") // TODO(gri) complete this // roundShortest(&d, f.mant, int(f.exp)) // Precision for shortest representation mode. switch fmt { case 'e', 'E': prec = len(d.mant) - 1 case 'f': prec = max(len(d.mant)-d.exp, 0) case 'g', 'G': prec = len(d.mant) } } else { // round appropriately switch fmt { case 'e', 'E': // one digit before and number of digits after decimal point d.round(1 + prec) case 'f': // number of digits before and after decimal point d.round(d.exp + prec) case 'g', 'G': if prec == 0 { prec = 1 } d.round(prec) } } // 3) read digits out and format switch fmt { case 'e', 'E': return fmtE(buf, fmt, prec, d) case 'f': return fmtF(buf, prec, d) case 'g', 'G': // trim trailing fractional zeros in %e format eprec := prec if eprec > len(d.mant) && len(d.mant) >= d.exp { eprec = len(d.mant) } // %e is used if the exponent from the conversion // is less than -4 or greater than or equal to the precision. // If precision was the shortest possible, use eprec = 6 for // this decision. if shortest { eprec = 6 } exp := d.exp - 1 if exp < -4 || exp >= eprec { if prec > len(d.mant) { prec = len(d.mant) } return fmtE(buf, fmt+'e'-'g', prec-1, d) } if prec > d.exp { prec = len(d.mant) } return fmtF(buf, max(prec-d.exp, 0), d) } // unknown format if x.neg { buf = buf[:len(buf)-1] // sign was added prematurely - remove it again } return append(buf, '%', fmt) } // %e: d.ddddde±dd func fmtE(buf []byte, fmt byte, prec int, d decimal) []byte { // first digit ch := byte('0') if len(d.mant) > 0 { ch = d.mant[0] } buf = append(buf, ch) // .moredigits if prec > 0 { buf = append(buf, '.') i := 1 m := min(len(d.mant), prec+1) if i < m { buf = append(buf, d.mant[i:m]...) i = m } for ; i <= prec; i++ { buf = append(buf, '0') } } // e± buf = append(buf, fmt) var exp int64 if len(d.mant) > 0 { exp = int64(d.exp) - 1 // -1 because first digit was printed before '.' } if exp < 0 { ch = '-' exp = -exp } else { ch = '+' } buf = append(buf, ch) // dd...d if exp < 10 { buf = append(buf, '0') // at least 2 exponent digits } return strconv.AppendInt(buf, exp, 10) } // %f: ddddddd.ddddd func fmtF(buf []byte, prec int, d decimal) []byte { // integer, padded with zeros as needed if d.exp > 0 { m := min(len(d.mant), d.exp) buf = append(buf, d.mant[:m]...) for ; m < d.exp; m++ { buf = append(buf, '0') } } else { buf = append(buf, '0') } // fraction if prec > 0 { buf = append(buf, '.') for i := 0; i < prec; i++ { ch := byte('0') if j := d.exp + i; 0 <= j && j < len(d.mant) { ch = d.mant[j] } buf = append(buf, ch) } } return buf } // fmtB appends the string of x in the format mantissa "p" exponent // with a decimal mantissa and a binary exponent, or 0" if x is zero, // and returns the extended buffer. // The mantissa is normalized such that is uses x.Prec() bits in binary // representation. // The sign of x is ignored, and x must not be an Inf. func (x *Float) fmtB(buf []byte) []byte { if x.form == zero { return append(buf, '0') } if debugFloat && x.form != finite { panic("non-finite float") } // x != 0 // adjust mantissa to use exactly x.prec bits m := x.mant switch w := uint32(len(x.mant)) * _W; { case w < x.prec: m = nat(nil).shl(m, uint(x.prec-w)) case w > x.prec: m = nat(nil).shr(m, uint(w-x.prec)) } buf = append(buf, m.decimalString()...) buf = append(buf, 'p') e := int64(x.exp) - int64(x.prec) if e >= 0 { buf = append(buf, '+') } return strconv.AppendInt(buf, e, 10) } // fmtP appends the string of x in the format 0x." mantissa "p" exponent // with a hexadecimal mantissa and a binary exponent, or 0" if x is zero, // ad returns the extended buffer. // The mantissa is normalized such that 0.5 <= 0.mantissa < 1.0. // The sign of x is ignored, and x must not be an Inf. func (x *Float) fmtP(buf []byte) []byte { if x.form == zero { return append(buf, '0') } if debugFloat && x.form != finite { panic("non-finite float") } // x != 0 // remove trailing 0 words early // (no need to convert to hex 0's and trim later) m := x.mant i := 0 for i < len(m) && m[i] == 0 { i++ } m = m[i:] buf = append(buf, "0x."...) buf = append(buf, strings.TrimRight(m.hexString(), "0")...) buf = append(buf, 'p') if x.exp >= 0 { buf = append(buf, '+') } return strconv.AppendInt(buf, int64(x.exp), 10) } func min(x, y int) int { if x < y { return x } return y } // Format implements fmt.Formatter. It accepts all the regular // formats for floating-point numbers ('e', 'E', 'f', 'F', 'g', // 'G') as well as 'b', 'p', and 'v'. See (*Float).Text for the // interpretation of 'b' and 'p'. The 'v' format is handled like // 'g'. // Format also supports specification of the minimum precision // in digits, the output field width, as well as the format verbs // '+' and ' ' for sign control, '0' for space or zero padding, // and '-' for left or right justification. See the fmt package // for details. // // BUG(gri) A missing precision for the 'g' format, or a negative // (via '*') precision is not yet supported. Instead the // default precision (6) is used in that case (issue #10991). func (x *Float) Format(s fmt.State, format rune) { prec, hasPrec := s.Precision() if !hasPrec { prec = 6 // default precision for 'e', 'f' } switch format { case 'e', 'E', 'f', 'b', 'p': // nothing to do case 'F': // (*Float).Text doesn't support 'F'; handle like 'f' format = 'f' case 'v': // handle like 'g' format = 'g' fallthrough case 'g', 'G': if !hasPrec { // TODO(gri) uncomment once (*Float).Text handles prec < 0 // prec = -1 // default precision for 'g', 'G' } default: fmt.Fprintf(s, "%%!%c(*big.Float=%s)", format, x.String()) return } var buf []byte buf = x.Append(buf, byte(format), prec) if len(buf) == 0 { buf = []byte("?") // should never happen, but don't crash } // len(buf) > 0 var sign string switch { case buf[0] == '-': sign = "-" buf = buf[1:] case buf[0] == '+': // +Inf sign = "+" if s.Flag(' ') { sign = " " } buf = buf[1:] case s.Flag('+'): sign = "+" case s.Flag(' '): sign = " " } var padding int if width, hasWidth := s.Width(); hasWidth && width > len(sign)+len(buf) { padding = width - len(sign) - len(buf) } switch { case s.Flag('0') && !x.IsInf(): // 0-padding on left writeMultiple(s, sign, 1) writeMultiple(s, "0", padding) s.Write(buf) case s.Flag('-'): // padding on right writeMultiple(s, sign, 1) s.Write(buf) writeMultiple(s, " ", padding) default: // padding on left writeMultiple(s, " ", padding) writeMultiple(s, sign, 1) s.Write(buf) } }