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Annotation of coherent/a/usr/man/ALL/float, revision 1.1

1.1     ! root        1: 
        !             2: 
        !             3: float                       C Keyword                       float
        !             4: 
        !             5: 
        !             6: 
        !             7: 
        !             8: Data type
        !             9: 
        !            10: 
        !            11: Floating point  numbers are a  subset of the  real numbers.  Each
        !            12: has a built-in radix point (or ``decimal point'') that shifts, or
        !            13: ``floats'', as  the value of the number  changes.  It consists of
        !            14: the following:  one sign bit, which  indicates whether the number
        !            15: is positive or  negative; bits that encode the number's _e_x_p_o_n_e_n_t;
        !            16: and bits  that encode the  number's _f_r_a_c_t_i_o_n, or  the number upon
        !            17: which the exponent works.   In general, the magnitude of the num-
        !            18: ber  encoded depends  upon the  number of  bits in  the exponent,
        !            19: whereas  its precision  depends upon  the number  of bits  in the
        !            20: fraction.
        !            21: 
        !            22: The exponent  often uses a  bias.  This is  a value that  is sub-
        !            23: tracted from the exponent to yield  the power of two by which the
        !            24: fraction will be increased.
        !            25: 
        !            26: Floating point  numbers come in  two levels of  precision: single
        !            27: precision, called  floats; and double  precision, called doubles.
        !            28: With most microprocessors,  sizeof(float) returns four, which in-
        !            29: dicates that  it is four  chars (bytes) long,  and sizeof(double)
        !            30: returns eight.
        !            31: 
        !            32: Several  formats  are  used  to  encode floats,  including  IEEE,
        !            33: DECVAX,  and BCD  (binary coded  decimal).  COHERENT  uses DECVAX
        !            34: format throughout.
        !            35: 
        !            36: The following  describes DECVAX, IEEE, and  BCD formats, for your
        !            37: information.
        !            38: 
        !            39: ***** DECVAX Format *****
        !            40: 
        !            41: The 32 bits in a float  consist of one sign bit, an eight-bit ex-
        !            42: ponent, and  a 24-bit  fraction, as  follows.  Note that  in this
        !            43: diagram, `s' indicates  ``sign'', `e' indicates ``exponent'', and
        !            44: `f` indicates ``fraction'':
        !            45: 
        !            46: 
        !            47:         ZDDDDDDDDDDD?
        !            48:         | seee eeee | Byte 4
        !            49:         CDDDDDDDDDDD4
        !            50:         | efff ffff | Byte 3
        !            51:         CDDDDDDDDDDD4
        !            52:         | ffff ffff | Byte 2
        !            53:         CDDDDDDDDDDD4
        !            54:         | ffff ffff | Byte 1
        !            55:         @DDDDDDDDDDDY
        !            56: 
        !            57: 
        !            58: The exponent has a bias of 129.
        !            59: 
        !            60: If the sign  bit is set to one, the  number is negative; if it is
        !            61: set to zero,  then the number is positive.  If  the number is all
        !            62: 
        !            63: 
        !            64: COHERENT Lexicon                                           Page 1
        !            65: 
        !            66: 
        !            67: 
        !            68: 
        !            69: float                       C Keyword                       float
        !            70: 
        !            71: 
        !            72: 
        !            73: zeroes, then  it equals  zero; an  exponent and fraction  of zero
        !            74: plus a  sign of  one (``negative zero'')  is by definition  not a
        !            75: number.  All other forms are numeric values.
        !            76: 
        !            77: The most significant bit in the fraction is always set to one and
        !            78: is not stored.  It is usually called the ``hidden bit''.
        !            79: 
        !            80: The format  for doubles simply  adds another 32  fraction bits to
        !            81: the end of the float representation, as follows:
        !            82: 
        !            83: 
        !            84:         ZDDDDDDDDDDD?
        !            85:         | seee eeee | Byte 8
        !            86:         CDDDDDDDDDDD4
        !            87:         | efff ffff | Byte 7
        !            88:         CDDDDDDDDDDD4
        !            89:         | ffff ffff | Byte 6
        !            90:         CDDDDDDDDDDD4
        !            91:         | ffff ffff | Byte 5
        !            92:         CDDDDDDDDDDD4
        !            93:         | ffff ffff | Byte 4
        !            94:         CDDDDDDDDDDD4
        !            95:         | ffff ffff | Byte 3
        !            96:         CDDDDDDDDDDD4
        !            97:         | ffff ffff | Byte 2
        !            98:         CDDDDDDDDDDD4
        !            99:         | ffff ffff | Byte 1
        !           100:         @DDDDDDDDDDDY
        !           101: 
        !           102: 
        !           103: ***** IEEE Format *****
        !           104: 
        !           105: The IEEE  encoding of a float  is the same as  that in the DECVAX
        !           106: format.   Note, however,  that the  exponent has  a bias  of 127,
        !           107: rather than 129.
        !           108: 
        !           109: Unlike the  DECVAX format, IEEE format  assigns special values to
        !           110: several  floating  point numbers.   Note  that  in the  following
        !           111: description, a  tiny exponent  is one that  is all zeroes,  and a
        !           112: huge exponent is one that is all ones:
        !           113: 
        !           114: *  A  tiny exponent with a fraction of  zero equals zero, regard-
        !           115:    less of the setting of the sign bit.
        !           116: 
        !           117: *   A huge  exponent  with a  fraction of  zero equals  infinity,
        !           118:    regardless of the setting of the sign bit.
        !           119: 
        !           120: *  A tiny exponent with a  fraction greater than zero is a denor-
        !           121:    malized number,  i.e., a  number that  is less than  the least
        !           122:    normalized number.
        !           123: 
        !           124: *   A huge  exponent with  a  fraction greater  than zero  is, by
        !           125:    definition, not a number.   These values can be used to handle
        !           126:    special conditions.
        !           127: 
        !           128: 
        !           129: 
        !           130: COHERENT Lexicon                                           Page 2
        !           131: 
        !           132: 
        !           133: 
        !           134: 
        !           135: float                       C Keyword                       float
        !           136: 
        !           137: 
        !           138: 
        !           139: An IEEE double, unlike DECVAX format, increases the number of ex-
        !           140: ponent bits.  It consists of  a sign bit, an 11-bit exponent, and
        !           141: a 53-bit fraction, as follows:
        !           142: 
        !           143: 
        !           144:         ZDDDDDDDDDDD?
        !           145:         | seee eeee | Byte 8
        !           146:         CDDDDDDDDDDD4
        !           147:         | eeee ffff | Byte 7
        !           148:         CDDDDDDDDDDD4
        !           149:         | ffff ffff | Byte 6
        !           150:         CDDDDDDDDDDD4
        !           151:         | ffff ffff | Byte 5
        !           152:         CDDDDDDDDDDD4
        !           153:         | ffff ffff | Byte 4
        !           154:         CDDDDDDDDDDD4
        !           155:         | ffff ffff | Byte 3
        !           156:         CDDDDDDDDDDD4
        !           157:         | ffff ffff | Byte 2
        !           158:         CDDDDDDDDDDD4
        !           159:         | ffff ffff | Byte 1
        !           160:         @DDDDDDDDDDDY
        !           161: 
        !           162: 
        !           163: The exponent has a bias of  1,023.  The rules of encoding are the
        !           164: same as for floats.
        !           165: 
        !           166: ***** BCD Format *****
        !           167: 
        !           168: The BCD  format (``binary  coded decimal'', also  called ``packed
        !           169: decimal'') is  used to eliminate  rounding errors that  alter the
        !           170: worth of  an account by a  fraction of a cent.   It consists of a
        !           171: sign, an exponent, and a chain of four-bit numbers, each of which
        !           172: is defined to hold the values zero through nine.
        !           173: 
        !           174: A BCD float has a sign bit, seven bits of exponent, and six four-
        !           175: bit digits.  In the following diagrams, `d' indicates ``digit'':
        !           176: 
        !           177: 
        !           178:         ZDDDDDDDDDDD?
        !           179:         | seee eeee | Byte 4
        !           180:         CDDDDDDDDDDD4
        !           181:         | dddd dddd | Byte 3
        !           182:         CDDDDDDDDDDD4
        !           183:         | dddd dddd | Byte 2
        !           184:         CDDDDDDDDDDD4
        !           185:         | dddd dddd | Byte 1
        !           186:         @DDDDDDDDDDDY
        !           187: 
        !           188: 
        !           189: A BCD double has a sign bit, 11 bits of exponent, and 13 four-bit
        !           190: digits, as follows:
        !           191: 
        !           192: 
        !           193: 
        !           194: 
        !           195: 
        !           196: COHERENT Lexicon                                           Page 3
        !           197: 
        !           198: 
        !           199: 
        !           200: 
        !           201: float                       C Keyword                       float
        !           202: 
        !           203: 
        !           204: 
        !           205:         ZDDDDDDDDDDD?
        !           206:         | seee eeee | Byte 8
        !           207:         CDDDDDDDDDDD4
        !           208:         | eeee dddd | Byte 7
        !           209:         CDDDDDDDDDDD4
        !           210:         | dddd dddd | Byte 6
        !           211:         CDDDDDDDDDDD4
        !           212:         | dddd dddd | Byte 5
        !           213:         CDDDDDDDDDDD4
        !           214:         | dddd dddd | Byte 4
        !           215:         CDDDDDDDDDDD4
        !           216:         | dddd dddd | Byte 3
        !           217:         CDDDDDDDDDDD4
        !           218:         | dddd dddd | Byte 2
        !           219:         CDDDDDDDDDDD4
        !           220:         | dddd dddd | Byte 1
        !           221:         @DDDDDDDDDDDY
        !           222: 
        !           223: 
        !           224: Passing the hexadecimal numbers A through F in a digit yields un-
        !           225: predictable results.
        !           226: 
        !           227: The following rules apply when handling BCD numbers:
        !           228: 
        !           229: *  A tiny exponent with a fraction of zero equals zero.
        !           230: 
        !           231: *  A tiny exponent with a fraction of non-zero indicates a denor-
        !           232:    malized number.
        !           233: 
        !           234: *  A huge exponent with a fraction of zero indicates infinity.
        !           235: 
        !           236: *  A huge exponent with a fraction of non-zero is, by definition,
        !           237:    not a number; these non-numbers are used to indicate errors.
        !           238: 
        !           239: ***** See Also *****
        !           240: 
        !           241: C keywords, data formats, double
        !           242: _T_h_e _A_r_t _o_f _C_o_m_p_u_t_e_r _P_r_o_g_r_a_m_m_i_n_g, vol. 2, page 180_f_f
        !           243: 
        !           244: 
        !           245: 
        !           246: 
        !           247: 
        !           248: 
        !           249: 
        !           250: 
        !           251: 
        !           252: 
        !           253: 
        !           254: 
        !           255: 
        !           256: 
        !           257: 
        !           258: 
        !           259: 
        !           260: 
        !           261: 
        !           262: COHERENT Lexicon                                           Page 4
        !           263: 
        !           264: 

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