From a post in news:comp.lang.tcl :
Floating point values are usually transferred in IEEE format. I have written the following code to read an IEEE float value for the case that your machine doesn't use IEEE natively.
proc IEEE2float {data byteorder} {
if {$byteorder == 0} {
set code [binary scan $data cccc se1 e2f1 f2 f3]
} else {
set code [binary scan $data cccc f3 f2 e2f1 se1]
}
set se1 [expr {($se1 + 0x100) % 0x100}]
set e2f1 [expr {($e2f1 + 0x100) % 0x100}]
set f2 [expr {($f2 + 0x100) % 0x100}]
set f3 [expr {($f3 + 0x100) % 0x100}]
set sign [expr {$se1 >> 7}]
set exponent [expr {(($se1 & 0x7f) << 1 | ($e2f1 >> 7))}]
set f1 [expr {$e2f1 & 0x7f}]
set fraction [expr {double($f1)*0.0078125 + \
double($f2)*3.0517578125e-05 + \
double($f3)*1.19209289550781e-07}]
set res [expr {($sign ? -1. : 1.) * \
pow(2.,double($exponent-127)) * \
(1. + $fraction)}]
return $res
}It expects a binary buffer containing an IEEE number and the byte order the number is in (0 for big-endian and 1 for little-endian).
3fa22435 yields 1.2667299509 (big-endian) or 6.1330860035e-07 (little).
+ Frank Pilhofer [email protected] + | http://www.uni-frankfurt.de/~fp/
1750A to Float Conversion
To go along with converting to IEEE floating point here are two Tcl procedures to convert to and from a MIL-STD-1750A 32-bit floating number. The procedure 1750afloat take a integer value (1750a) and returns the floating point representation. The procedure float1750a take a floating point number and returns the integer representation of the 1750a value
if {0} {
1750A floating point numbers are representd as a fractional
mantissa times 2 rasied to the power of the exponent.
The 32-bit format is:
MSB LSB
smmm mmmm mmmm mmmm mmmm mmmm seee eeee
0 31
}
proc 1750afloat {input_word} {
if {![string is integer $input_word]} {
return "invalid input: \"$input_word\" not a integer"
}
set mantissa [expr $input_word >> 8]
set exponent [expr ($input_word & 0xff)]
if {[expr $exponent & 0x80] != 0} {
set exponent [expr int($exponent - 256)]
}
set realnum [expr $mantissa * pow(2, $exponent - 23)]
return $realnum
}
proc float1750a {realnum} {
if {![string is double $realnum]} {
return "invalid input: \"$realnum\" not a double"
}
if {$realnum == 0} {
set output_word 0
} else {
set exponent [expr int(ceil(log(abs($realnum)) / log(2.)))]
set mantissa [expr round($realnum / pow(2, $exponent - 23))]
#boundary condition check and repair at 0x800000
if {$mantissa == 8388608} {
set mantissa [expr $mantissa / 2]
incr exponent
}
set output_word [expr ($mantissa << 8) | ($exponent & 0xff)]
}
return $output_word
}# examples per MIL-STD-1750A section 4.1.5
format %X [float1750a [expr .9999999 * pow(2,127)]] ;#7FFFFF7F format %X [float1750a [expr .5 * pow(2,127)]] ;#4000007F format %X [float1750a [expr .625 * pow(2,4)]] ;#50000004 format %X [float1750a [expr .5 * pow(2,1)]] ;#40000001 format %X [float1750a [expr .5 * pow(2,0)]] ;#40000000 format %X [float1750a [expr .5 * pow(2,-1)]] ;#400000FF format %X [float1750a [expr .5 * pow(2,-128)]] ;#40000080 format %X [float1750a [expr .0 * pow(2,0)]] ;#0 format %X [float1750a [expr -1.0 * pow(2,0)]] ;#80000000 format %X [float1750a [expr -.5000001 * pow(2,-128)]] ;#BFFFFF80 format %X [float1750a [expr -.7500001 * pow(2,4)]] ;#9FFFFF04
# wrap test of the procedures
1750afloat [float1750a 1.222332] ;#1.22233200073