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| 1 | +# General floating point formatting functions. |
| 2 | + |
| 3 | +# Functions: |
| 4 | +# fix(x, digits_behind) |
| 5 | +# sci(x, digits_behind) |
| 6 | + |
| 7 | +# Each takes a number or a string and a number of digits as arguments. |
| 8 | + |
| 9 | +# Parameters: |
| 10 | +# x: number to be formatted; or a string resembling a number |
| 11 | +# digits_behind: number of digits behind the decimal point |
| 12 | + |
| 13 | + |
| 14 | +import regex |
| 15 | + |
| 16 | +# Compiled regular expression to "decode" a number |
| 17 | +decoder = regex.compile( \ |
| 18 | + '^\([-+]?\)0*\([0-9]*\)\(\(\.[0-9]*\)?\)\(\([eE][-+]?[0-9]+\)?\)$') |
| 19 | +# \0 the whole thing |
| 20 | +# \1 leading sign or empty |
| 21 | +# \2 digits left of decimal point |
| 22 | +# \3 fraction (empty or begins with point) |
| 23 | +# \5 exponent part (empty or begins with 'e' or 'E') |
| 24 | + |
| 25 | +NotANumber = 'fpformat.NotANumber' |
| 26 | + |
| 27 | +# Return (sign, intpart, fraction, expo) or raise an exception: |
| 28 | +# sign is '+' or '-' |
| 29 | +# intpart is 0 or more digits beginning with a nonzero |
| 30 | +# fraction is 0 or more digits |
| 31 | +# expo is an integer |
| 32 | +def extract(s): |
| 33 | + if decoder.match(s) < 0: raise NotANumber |
| 34 | + (a1, b1), (a2, b2), (a3, b3), (a4, b4), (a5, b5) = decoder.regs[1:6] |
| 35 | + sign, intpart, fraction, exppart = \ |
| 36 | + s[a1:b1], s[a2:b2], s[a3:b3], s[a5:b5] |
| 37 | + if sign == '+': sign = '' |
| 38 | + if fraction: fraction = fraction[1:] |
| 39 | + if exppart: expo = eval(exppart[1:]) |
| 40 | + else: expo = 0 |
| 41 | + return sign, intpart, fraction, expo |
| 42 | + |
| 43 | +# Remove the exponent by changing intpart and fraction |
| 44 | +def unexpo(intpart, fraction, expo): |
| 45 | + if expo > 0: # Move the point left |
| 46 | + f = len(fraction) |
| 47 | + intpart, fraction = intpart + fraction[:expo], fraction[expo:] |
| 48 | + if expo > f: |
| 49 | + intpart = intpart + '0'*(expo-f) |
| 50 | + elif expo < 0: # Move the point right |
| 51 | + i = len(intpart) |
| 52 | + intpart, fraction = intpart[:expo], intpart[expo:] + fraction |
| 53 | + if expo < -i: |
| 54 | + fraction = '0'*(-expo-i) + fraction |
| 55 | + return intpart, fraction |
| 56 | + |
| 57 | +# Round or extend the fraction to size digs |
| 58 | +def roundfrac(intpart, fraction, digs): |
| 59 | + f = len(fraction) |
| 60 | + if f <= digs: |
| 61 | + return intpart, fraction + '0'*(digs-f) |
| 62 | + i = len(intpart) |
| 63 | + if i+digs < 0: |
| 64 | + return '0'*-digs, '' |
| 65 | + total = intpart + fraction |
| 66 | + nextdigit = total[i+digs] |
| 67 | + if nextdigit >= '5': # Hard case: increment last digit, may have carry! |
| 68 | + n = i + digs - 1 |
| 69 | + while n >= 0: |
| 70 | + if total[n] != '9': break |
| 71 | + n = n-1 |
| 72 | + else: |
| 73 | + total = '0' + total |
| 74 | + i = i+1 |
| 75 | + n = 0 |
| 76 | + total = total[:n] + chr(ord(total[n]) + 1) + '0'*(len(total)-n-1) |
| 77 | + intpart, fraction = total[:i], total[i:] |
| 78 | + if digs >= 0: |
| 79 | + return intpart, fraction[:digs] |
| 80 | + else: |
| 81 | + return intpart[:digs] + '0'*-digs, '' |
| 82 | + |
| 83 | +# Format x as [-]ddd.ddd with 'digs' digits after the point |
| 84 | +# and at least one digit before. |
| 85 | +# If digs <= 0, the point is suppressed. |
| 86 | +def fix(x, digs): |
| 87 | + if type(x) != type(''): x = `x` |
| 88 | + try: |
| 89 | + sign, intpart, fraction, expo = extract(x) |
| 90 | + except NotANumber: |
| 91 | + return x |
| 92 | + intpart, fraction = unexpo(intpart, fraction, expo) |
| 93 | + intpart, fraction = roundfrac(intpart, fraction, digs) |
| 94 | + while intpart and intpart[0] == '0': intpart = intpart[1:] |
| 95 | + if intpart == '': intpart = '0' |
| 96 | + if digs > 0: return sign + intpart + '.' + fraction |
| 97 | + else: return sign + intpart |
| 98 | + |
| 99 | +# Format x as [-]d.dddE[+-]ddd with 'digs' digits after the point |
| 100 | +# and exactly one digit before. |
| 101 | +# If digs is <= 0, one digit is kept and the point is suppressed. |
| 102 | +def sci(x, digs): |
| 103 | + if type(x) != type(''): x = `x` |
| 104 | + sign, intpart, fraction, expo = extract(x) |
| 105 | + if not intpart: |
| 106 | + while fraction and fraction[0] == '0': |
| 107 | + fraction = fraction[1:] |
| 108 | + expo = expo - 1 |
| 109 | + if fraction: |
| 110 | + intpart, fraction = fraction[0], fraction[1:] |
| 111 | + expo = expo - 1 |
| 112 | + else: |
| 113 | + intpart = '0' |
| 114 | + else: |
| 115 | + expo = expo + len(intpart) - 1 |
| 116 | + intpart, fraction = intpart[0], intpart[1:] + fraction |
| 117 | + digs = max(0, digs) |
| 118 | + intpart, fraction = roundfrac(intpart, fraction, digs) |
| 119 | + if len(intpart) > 1: |
| 120 | + intpart, fraction, expo = \ |
| 121 | + intpart[0], intpart[1:] + fraction[:-1], \ |
| 122 | + expo + len(intpart) - 1 |
| 123 | + s = sign + intpart |
| 124 | + if digs > 0: s = s + '.' + fraction |
| 125 | + e = `abs(expo)` |
| 126 | + e = '0'*(3-len(e)) + e |
| 127 | + if expo < 0: e = '-' + e |
| 128 | + else: e = '+' + e |
| 129 | + return s + 'e' + e |
| 130 | + |
| 131 | +# Interactive test run |
| 132 | +def test(): |
| 133 | + try: |
| 134 | + while 1: |
| 135 | + x, digs = input('Enter (x, digs): ') |
| 136 | + print x, fix(x, digs), sci(x, digs) |
| 137 | + except (EOFError, KeyboardInterrupt): |
| 138 | + pass |
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