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36    Float Manager

Palm OS® Programmer's API Reference

Palm OS® 68K SDK

     

This chapter provides reference material for the Float Manager API as follows:

The Float Manager API is declared in the header file FloatMgr.h. For more information on the Float Manager, see the section "Floating-Point" in the Palm OS Programmer's Companion, vol. I.

Float Manager Data Structures ^TOP^

FlpCompDouble Struct ^TOP^

Purpose

Float Manager functions accept and require values of type FlpDouble. The FlpCompDouble union allows you to declare values that can be interpreted either as a double or as an FlpDouble. As well, this union contains fields that provide easy access to the component parts of the double-precision floating-point number.

Prototype

typedef union {
double d;
FlpDouble fd;
UInt32 ul[2];
FlpDoubleBits fdb;
} FlpCompDouble

Fields

d
Provides access to the value as a double.
fd
Provides access to the value as a FlpDouble, which can be passed to or received from many Float Manager functions.
ul
Provides access to the value as two long integers.
fdb
Provides access to specific fields.

FlpDoubleBits Struct ^TOP^

Purpose

This structure provides direct access to the component parts of an IEEE-754 double-precision floating-point number. Use the FlpCompDouble union to convert numbers of type double to and from FlpDoubleBits.

Prototype

typedef struct {
UInt32 sign : 1;
Int32 exp : 11;
UInt32 manH : 20;
UInt32 manL;
} FlpDoubleBits

Fields

sign
The sign bit. You can also use the FlpGetSign() macro to obtain the sign bit, and the FlpNegate(), FlpSetNegative(), and FlpSetPositive() macros to set the sign bit.
exp
The bits that make up the exponent. You can also use the FlpGetExponent() macro to obtain the exponent value.
manH
The most-significant 20 bits of the mantissa.
manL
The least-significant 32 bits of the mantissa.

Float Manager Functions ^TOP^

FlpAToF Function ^TOP^

Purpose

Convert a null-terminated ASCII string to a 64-bit floating-point number. The string must have the format:

[+|-][digits][.][digits][e|E[+|-][digits]]

Declared In

FloatMgr.h

Prototype

FlpDouble FlpAToF (
   constChar*s
)

Parameters

s
Pointer to the string to be converted.

Returns

Returns the value of the string as a floating-point number.

Comments

The mantissa of the number is limited to 32 bits.

This function is close to being compatible with the ISO C library function atof. atof requires the form:

[+|-]digits[.][digits][(e|E)[+|-]digits]

In order to maintain backward compatibility with the Float Manager in Palm OS 1.0 (which could be used up to, but not including, Palm OS 4.0), this function considers all of the "digits" sections to be optional. Here's a table showing the ISO and Palm OS behavior with some sample strings:

String

ISO

>= Palm OS 4.0

< Palm OS 4.01

Notes

"+"

+0

+0

+0

".3"

0.3

0.3

0.3

"0.3e123"

0.3e123

0.3e123

0.3e12

The old Float Manager only allowed a 1 or 2 digit exponent.

"+1"

1

1

+0

The old Float Manager doesn't allow a leading '+' sign.

"1e+2"

1e2

1e2

1

The old Float Manager doesn't allow a '+' sign in the exponent.

"0.3E3"

0.3e3

0.3e3

0.3

The old Float Manager doesn't allow a capital 'E' to mark the exponent.

"4294967297"

4294967297

4294967297

1

The old Float Manager uses an unsigned long and wraps around.

1. Using the old Float Manager documented in Appendix C, "1.0 Float Manager."

Unlike atof, FlpAToF doesn't accept leading white-space characters and it doesn't accept decimal point characters other than '.'.

Compatibility

Implemented only if 2.0 New Feature Set is present. GCC users must use FlpBufferAToF() instead of this function.

See Also

FlpFToA()

FlpBase10Info Function ^TOP^

Purpose

Extract detailed information on the base 10 form of a floating-point number: the base 10 mantissa, exponent, and sign.

Declared In

FloatMgr.h

Prototype

Err FlpBase10Info (
   FlpDoublea,
   UInt32*mantissaP,
   Int16*exponentP,
   Int16*signP
)

Parameters

a
The floating-point number.
mantissaP
The base 10 mantissa.
exponentP
The base 10 exponent.
signP
The sign: 1 if the number is negative, 0 otherwise.

Returns

Returns 0 if no error, or flpErrOutOfRange if the supplied floating-point number is either not a number (NaN) or is infinite.

Comments

The mantissa is normalized so it contains at least 8 significant digits when printed as an integer value.

Compatibility

Implemented only if 2.0 New Feature Set is present.

See Also

FlpGetExponent(), FlpGetSign()

FlpBufferAToF Function ^TOP^

Purpose

Convert a null-terminated ASCII string to a floating-point number. The string must be in the format: [-]x[.]yyyyyyyy[e[-]zz]

Declared In

FloatMgr.h

Prototype

void FlpBufferAToF (
   FlpDouble*result,
   constChar*s
)

Parameters

result
Pointer to the structure into which the return value is placed.
s
Pointer to the null-terminated ASCII string to be converted.

Returns

Returns the value of the string as a floating-point number.

Comments

See FlpAToF() for a complete description of this function.

Compatibility

Implemented only if 2.0 New Feature Set is present. Because the Palm OS ABI was not well-specified in this area, GCC by default implemented structure return differently from the compiler used to build the ROM. As a result, GCC users must use this function instead of FlpAToF(). CodeWarrior users can use either function; they are binary compatible.

FlpBufferCorrectedAdd Function ^TOP^

Purpose

Adds two floating-point numbers and corrects for least-significant-bit errors when the result should be zero but is instead very close to zero.

Declared In

FloatMgr.h

Prototype

void FlpBufferCorrectedAdd (
   FlpDouble*result,
   FlpDoublefirstOperand,
   FlpDoublesecondOperand,
   Int16howAccurate
)

Parameters

result
Pointer to the structure into which the return value is placed.
firstOperand
The first of the two numbers to be added.
secondOperand
The second of the two numbers to be added.
howAccurate
The smallest difference in exponents that won't force the result to zero. The value returned from this function is forced to zero if the difference between exponents in the smaller of the two operands and the result exceeds this value. Supply a value of zero for this parameter to obtain the default level of accuracy (which is equivalent to a howAccurate value of 48).

Returns

Returns the calculated result.

Comments

See FlpCorrectedAdd() for a complete description of this function.

Compatibility

Implemented only if 2.0 New Feature Set is present. Because the Palm OS ABI was not well-specified in this area, GCC by default implemented structure return differently from the compiler used to build the ROM. As a result, GCC users must use this function instead of FlpCorrectedAdd(). CodeWarrior users can use either function; they are binary compatible.

FlpBufferCorrectedSub Function ^TOP^

Purpose

Subtracts two floating-point numbers and corrects for least-significant-bit errors when the result should be zero but is instead very close to zero.

Declared In

FloatMgr.h

Prototype

void FlpBufferCorrectedSub (
   FlpDouble*result,
   FlpDoublefirstOperand,
   FlpDoublesecondOperand,
   Int16howAccurate
)

Parameters

result
Pointer to the structure into which the return value is placed.
firstOperand
The value from which secondOperand is to be subtracted.
secondOperand
The value to subtract from firstOperand.
howAccurate
The smallest difference in exponents that won't force the result to zero. The value returned from this function is forced to zero if the difference between exponents in the smaller of the two operands and the result exceeds this value. Supply a value of zero for this parameter to obtain the default level of accuracy (which is equivalent to a howAccurate value of 48).

Returns

Returns the calculated result.

Comments

See FlpCorrectedSub() for a complete description of this function.

Compatibility

Implemented only if 2.0 New Feature Set is present. Because the Palm OS ABI was not well-specified in this area, GCC by default implemented structure return differently from the compiler used to build the ROM. As a result, GCC users must use this function instead of FlpCorrectedSub(). CodeWarrior users can use either function; they are binary compatible.

FlpCorrectedAdd Function ^TOP^

Purpose

Adds two floating-point numbers and corrects for least-significant-bit errors when the result should be zero but is instead very close to zero.

Declared In

FloatMgr.h

Prototype

FlpDouble FlpCorrectedAdd (
   FlpDoublefirstOperand,
   FlpDoublesecondOperand,
   Int16howAccurate
)

Parameters

firstOperand
The first of the two numbers to be added.
secondOperand
The second of the two numbers to be added.
howAccurate
The smallest difference in exponents that won't force the result to zero. The value returned from FlpCorrectedAdd is forced to zero if, when the exponent of the result of the addition is subtracted from the exponent of the smaller of the two operands, the difference exceeds the value specified for howAccurate. Supply a value of zero for this parameter to obtain the default level of accuracy (which is equivalent to a howAccurate value of 48).

Returns

Returns the calculated result.

Comments

Adding or subtracting a large number and a small number produces a result similar in magnitude to the larger number. Adding or subtracting two numbers that are similar in magnitude can, depending on their signs, produce a result with a very small exponent (that is, a negative exponent that is large in magnitude). If the difference between the result's exponent and that of the operands is close to the number of significant bits expressible by the mantissa, it is quite possible that the result should in fact be zero.

There also exist cases where it may be useful to retain accuracy in the low-order bits of the mantissa. For instance: 99999999 + 0.00000001 - 99999999. However, unless the fractional part is an exact (negative) power of two, it is doubtful that what few bits of mantissa that are available will be enough to properly represent the fractional value. In this example, the 99999999 requires 26 bits, leaving 26 bits for the .00000001; this guarantees inaccuracy after the subtraction.

The problem arises from the difficulty in representing decimal fractions such as 0.1 in binary. After about three successive additions or subtractions, errors begin to appear in the least significant bits of the mantissa. If the value represented by the most significant bits of the mantissa is then subtracted away, the least significant bit error is normalized and becomes the actual result—when in fact the result should be zero.

This problem is only an issue for addition and subtraction.

Compatibility

Implemented only if 2.0 New Feature Set is present. GCC users must use FlpBufferCorrectedAdd() instead of this function.

See Also

FlpCorrectedSub()

FlpCorrectedSub Function ^TOP^

Purpose

Subtracts two floating-point numbers and corrects for least-significant-bit errors when the result should be zero but is instead very close to zero.

Declared In

FloatMgr.h

Prototype

FlpDouble FlpCorrectedSub (
   FlpDoublefirstOperand,
   FlpDoublesecondOperand,
   Int16howAccurate
)

Parameters

firstOperand
The value from which secondOperand is to be subtracted.
secondOperand
The value to subtract from firstOperand.
howAccurate
The smallest difference in exponents that won't force the result to zero.The value returned from FlpCorrectedSub is forced to zero if, when the exponent of the result of the subtraction is subtracted from the exponent of the smaller of the two operands, the difference exceeds the value specified for howAccurate. Supply a value of zero for this parameter to obtain the default level of accuracy (which is equivalent to a howAccurate value of 48).

Returns

Returns the calculated result.

Comments

See the comments for FlpCorrectedAdd().

Compatibility

Implemented only if 2.0 New Feature Set is present. GCC users must use FlpBufferCorrectedSub() instead of this function.

FlpFToA Function ^TOP^

Purpose

Convert a floating-point number to a null-terminated ASCII string in exponential format: [-]x.yyyyyyye[-]zz

Declared In

FloatMgr.h

Prototype

Err FlpFToA (
   FlpDoublea,
   Char*s
)

Parameters

a
Floating-point number.
s
Pointer to buffer to contain the ASCII string.

Returns

Returns 0 if no error, or flpErrOutOfRange if the supplied value is infinite or is not a number. In this case, the buffer is set to the string "INF", "-INF", or "NaN" as appropriate.

Comments

If the supplied floating-point number is zero, the returned string doesn't use the exponential format but is simply "0".

Compatibility

Implemented only if 2.0 New Feature Set is present.

See Also

FlpAToF()

FlpGetExponent Macro ^TOP^

Purpose

Returns the exponent of a 64-bit floating-point value. The returned value has the bias applied, so it ranges from -1023 to +1024.

Declared In

FloatMgr.h

Prototype

#define FlpGetExponent (
   x
)

Parameters

x
The value from which the exponent is to be extracted.

Returns

Returns a UInt32 containing the exponent of the specified value.

Compatibility

Implemented only if 2.0 New Feature Set is present.

See Also

FlpBase10Info(), FlpGetSign()

FlpGetSign Macro ^TOP^

Purpose

Returns the sign of a 64-bit floating-point value.

Declared In

FloatMgr.h

Prototype

#define FlpGetSign (
   x
)

Parameters

x
The value from which the sign bit is to be extracted.

Returns

Returns a UInt32 with a nonzero value if the specified value is negative, and with a zero value if it is positive.

Compatibility

Implemented only if 2.0 New Feature Set is present.

See Also

FlpBase10Info(), FlpGetExponent(), FlpNegate(), FlpSetNegative(), FlpSetPositive()

FlpIsZero Macro ^TOP^

Purpose

Returns whether the specified 64-bit floating-point value is zero.

Declared In

FloatMgr.h

Prototype

#define FlpIsZero (
   x
)

Parameters

x
The value for which the sign bit is desired.

Returns

Returns a UInt32 with a nonzero value if the specified value is zero, and with a zero value if the specified value is other than zero.

Compatibility

Implemented only if 2.0 New Feature Set is present.

FlpNegate Macro ^TOP^

Purpose

Changes the sign bit of a 64-bit floating-point number.

Declared In

FloatMgr.h

Prototype

#define FlpNegate (
   x
)

Parameters

x
The value in which the sign bit is to be changed.

Returns

Returns a 64-bit floating-point value which is the negative of the value specified by x.

Compatibility

Implemented only if 2.0 New Feature Set is present.

See Also

FlpGetSign(), FlpSetNegative(), FlpSetPositive()

FlpSetNegative Macro ^TOP^

Purpose

Ensures that a 64-bit floating-point number is negative.

Declared In

FloatMgr.h

Prototype

#define FlpSetNegative (
   x
)

Parameters

x
The value that is to be forced negative.

Returns

If the supplied 64-bit floating-point value is negative, that value is returned unchanged. If the supplied value is positive, the negative of that value is returned.

Compatibility

Implemented only if 2.0 New Feature Set is present.

See Also

FlpGetSign(), FlpNegate(), FlpSetPositive()

FlpSetPositive Macro ^TOP^

Purpose

Ensures that a 64-bit floating-point number is positive.

Declared In

FloatMgr.h

Prototype

#define FlpSetPositive (
   x
)

Parameters

x
The value that is to be forced positive.

Returns

If the supplied 64-bit floating-point value is positive, that value is returned unchanged. If the supplied value is negative, its absolute value is returned.

Compatibility

Implemented only if 2.0 New Feature Set is present.

See Also

FlpGetSign(), FlpNegate(), FlpSetNegative()

FlpVersion Function ^TOP^

Purpose

Returns the version number of the Float Manager.

Declared In

FloatMgr.h

Prototype

UInt32 FlpVersion (
   void
)

Parameters

None.

Returns

Returns the version number of the Float Manager. The current version is represented by the constant flpVersion, which is defined in FloatMgr.h.

Compatibility

Implemented only if 2.0 New Feature Set is present.