# Double to Borland pascal real

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This is a very small project, and probably can be done very fast. I came a long way but i can figure the last problem out. I have an old Borland pacal datafile wich uses the bp real (48 bits). I can convert it to a double (see function) but i also need to convert it back into a 48bit real (written out as bytes). It will probably take a expert to do it in 30 minutes but i cant get it done. Added some additional info for you:

----- Real48 to VBA double function

Public Function RealToDouble(Byte6Arr() As Byte) As Double

Dim dMantissa As Double

Dim i As Integer

Dim j As Long

Dim k As Long

Dim temp As Single

Dim Data As String

' BP real48 Byte example [151, 0, 0, 208, 61, 113] will give 7905000 as double result

'accumulate the mantissa

dMantissa = 1

For i = 6 To 2 Step -1

For j = IIf(i = 6, 6, 7) To 0 Step -1

k = k + 1

If (Byte6Arr(i) And (2 ^ j)) <> 0 Then

dMantissa = dMantissa + 2 ^ -k

End If

Next j

Next i

'finally, assemble all the pieces into a number

If (Byte6Arr(6) And &H80) = &H80 Then

RealToDouble = -dMantissa * 2 ^ (Byte6Arr(1) - 129)

Else

RealToDouble = dMantissa * 2 ^ (Byte6Arr(1) - 129)

End If

' round the value to the 11 digit compatible pascal48 real

RealToDouble = RoundIt(RealToDouble, 11)

End Function

----- The function Double to BP real48, this is the function you have to make

Public Function DoubleToReal(Byte8Arr() As Byte) As Byte()

Dim dMantissa As Double

Dim i As Integer

Dim j As Long

Dim k As Long

Dim Real(0 To 4) As Byte

Dim positive As Boolean

' Byte example [0, 0, 0, 0, 186, 39, 94, 65] should give 7905000 as Borland pascal real result

' determine the signbit positive or negative

If (Byte8Arr(8) And &H80) = &H80 Then

positive = False

Else

positive = True

End If

End Function

------ Some additional info on BP real48 and doubles

The Real and Double Formats

The real and double formats comprise three fields: a sign

bit, a significand field, and an exponent field. For the real

type, the fields can be visualized as arranged like this, with

the most significant bit at the left end of each field:

Field: Sign Significand(f) Exponent

Width (bits): 1 39 8

__________________________

| s | f | e |

|__ lsb_________msb_lsb_msb|

1 bit sign (s)

39 bits float (f) starting with the msb to the lsb

8 bits exponent (e) starting with msb to lsb

The value is defined as

if 0 < e <= 255 then v = (-1)^s * 2^(e-129) * (1.f).

if e=0 then V = 0

The fields of the IEEE double type are arranged like this:

Field: Sign Exponent Significand(f)

Width (bits): 1 11 52

1 11 52

__________________________

| s | e | f |

|__ msb_________lsb_msb_lsb|

if 0<e< 2047 then v = v = (-1)^s * 2^(e-1023) * (1.f).

if e=0 and f<>0 then v = (-1)^s * 2^(e-1022) * (0.f).

if e=0 and f = 0 then v = (-1)^s * 0.

if e=2047 and f=0 then v = (-1)^s * Inf.

if e=2047 and f<>0 then v is a NaN.

In a PC's memory, these values are stored with the right-most 8-

bit bytes at the lowest address (or first on a disk), so that the

real's exponent would be stored as the first byte and its sign

bit would be the most significant (leftmost) bit of the sixth

byte.

The sign bit is set when the value is less than 0.0

(negative). The exponent field (8 bits for real, 11 bits for

double) represents the integer part of the base-2 logarithm of

the value, indicating the value's absolute magnitude. The

exponent is biased by some value (129 for real, 1023 for double),

so although the binary value of the field is positive, it can

signify a negative value when the bias is subtracted from it.

The significand field (39 bits for real, 52 bits for double) is

the fractional part by which the value indicated by the exponent

is increased. Thus, for both types, the represented value is

generally

Sign Significand (Exponent - Bias)

(-1) (1 -------------------) 2

SignificandWidth

2

There are a few special cases. The value of a real is 0.0

when the exponent field is 0, i.e., when no bit in the exponent

field is set. The IEEE double has a value of 0.0 when both the

exponent field and the significand field have values of 0, but

the double's sign bit can be set to represent -0.0 as well as

0.0. When all 11 bits are set in the double's exponent field, so

that it has its highest possible value (2047), and none of the

bits in the significand field is set, so that its value is 0, the

double's value is Inf (infinity) or -Inf, depending on the sign

bit. If the double's exponent field is 2047 and its significand

is not equal to 0, the value is NaN (not a number).

The real's format permits an absolute range of approximately

2.9e-39 to [url removed, login to view] (decimal) and a precision of 11-12 significant

decimal digits. The double's wider format offers an absolute

range of approximately 5.0e-324 to [url removed, login to view] and a precision of 15-

16 significant digits. (The tiniest values represented by

doubles sacrifice precision for their very low magnitude.)

Conversion Functions

Conversion between a real and a double mainly involves

transferring the bit fields from the source to the target.

Because there is no high-level access to the bits in a double,

and C has no real type, both double and real must be treated as

arrays, the elements of which can be manipulated individually at

the bit level. Instead of treating doubles and reals as arrays

of bytes, it is more efficient to treat them as arrays of 16-bit

unsigned ints. A typedef statement in BPREAL.C declares the

"real" type as an array of 3 unsigned ints, and a "doublearray"

union so that doubles can be handled as arrays of 4 unsigned

ints.

The bits contained in each of the arrays' elements are

listed below. For each element, its contents are listed from

left to right (most significant bit to least significant), and

bit 1 of each field is the field's most significant bit:

real[2] Sign 1, Significand 1-15

real[1] Significand 16-31

real[0] Significand 32-39, Exponent 1-8

doublearray.a[3] Sign 1, Exponent 1-11, Significand 1-4

doublearray.a[2] Significand 5-20

doublearray.a[1] Significand 21-36

doublearray.a[0] Significand 37-52

Conversion from real to double is straightforward, because

any value that can be represented by a real can be represented by

a double. The real_to_double function first checks whether the

exponent is 0. If so, it returns the double 0.0. Otherwise, it

adds 894 to the exponent because the double's exponent bias

(1023) is 894 greater than the real's bias (129), and it places

the exponent in the correct location in the double (element 3,

shifted 4 bits to the left). It then moves the sign bit and the

39-bit significand to their proper locations.

Conversion from double to real is trickier, because the IEEE

type has greater range and precision and more special cases than

the real. Since error-free conversion is not assured, the

double_to_real function returns an error code of an enumerated

type called prconverr (for Pascal Real Conversion Error). The

error codes range in increasing seriousness from prOK, which

means no error, to prNaN, which means that the double value was

NaN (not a number), which cannot be represented by a real.

The double_to_real function first checks whether the double

value is 0.0 or -0.0, either of which is converted to a real

representation of 0.0 before returning prOK.

Next, the function checks whether all the bits in the

double's exponent are set. If they are, the double's value is

either Inf or NaN (or one of their negations). If the value is

Inf, the real's exponent and significand fields are filled so as

to represent the largest value possible, the sign bit is

transferred, and the code prInf is returned. If the value is

NaN, a real value of 0.0 and a code of prNaN are returned.

After these tests, the significand is rounded. The real's

39-bit significand does not allow as much precision as the

double's 52-bit significand. To keep as much precision as

possible, the 40th bit of the double's significand is tested. If

the 40th bit is set, the significand's 39th bit is incremented.

If all of the first 40 bits of the double's significand are set,

bits 1 to 39 are cleared and the exponent is incremented. The

exponent field is guaranteed not to be filled, so incrementing

the exponent will succeed, because the function has already

tested the exponent for its maximum value in checking whether the

double's value was Inf or NaN.

After rounding, the function places the value of the

double's exponent in a variable and checks whether it fits within

the range of valid real exponents. Real exponents range from 1

to 255 biased, or -128 to 126. To fit in this range, the

double's biased exponent must range from 895 to 1149. If the

double's exponent is less then 895, a real value of 0.0 and a

code of prPosUnderflow or prNegUnderflow (depending on the

double's sign) are returned. If the double's exponent is greater

than 1149, the real is set to its maximum value, the double's

sign bit is transferred to the real, and a code of prOverflow is

returned.

After these checks, the function is assured of a valid

conversion. The exponent is re-biased for the real range, and it

is transferred to the real along with the sign bit and the first

39 bits of the double's significand (which may have been

rounded). A code of prOK is then returned.