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## 33 Float Manager

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| Title - Palm OS® Programmer's API Reference Part II: System Management 33 Float Manager Float Manager Data Structures FlpCompDouble FlpDoubleBits Float Manager Functions FlpAToF FlpBase10Info FlpBufferAToF FlpBufferCorrectedAdd FlpBufferCorrectedSub FlpCorrectedAdd FlpCorrectedSub FlpFToA FlpGetExponent FlpGetSign FlpIsZero FlpNegate FlpSetNegative FlpSetPositive FlpVersion |  |  |  | This chapter provides reference material for the Float Manager API as follows: Float Manager Data Structures Float Manager Functions 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 ## FlpCompDouble 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.
    typedef union {
      double d;
      FlpDouble fd;
      UInt32 ul[2];
      FlpDoubleBits fdb;
    } FlpCompDouble
#### Field Descriptions #####
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 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.
    typedef struct {
      UInt32 sign : 1;
      Int32 exp : 11;
      UInt32 manH : 20;
      UInt32 manL;
    } FlpDoubleBits
#### Field Descriptions #####
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 ## FlpAToF #### 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]]
#### Prototype FlpDouble FlpAToF (const Char *s) #### Parameters #####
-> s | Pointer to the string to be converted.
#### Result Returns the value of the string as a floating-point number. #### Comment The mantissa of the number is limited to 32 bits. This function is close to ANSI C library compatible. ANSI requires the form: [+|-]digits[.][digits][(e|E)[+|-]digits] In order to maintain backward compatibility with the Palm OS 1.0, this function considers all of the "digits" sections to be optional. Here's a table showing the ANSI and Palm OS behavior with some sample strings:
String | ANSI | > Palm OS 1.0 | Palm OS 1.01 | Notes
--- | --- | --- | --- | ---
"+" | invalid | +0 | +0 | ANSI requires at least one digit.
".3" | invalid | 0.3 | 0.3 | ANSI requires a leading digit.
"0.3e123" | 0.3e123 | 0.3e123 | 0.3e12 | Palm OS 1.0 only allows 1 or 2 digit exponent.
"+1" | 1 | 1 | +0 | Palm OS 1.0 doesn't allow a leading '+' sign.
"1e+2" | 1e2 | 1e2 | 1 | Palm OS 1.0 doesn't allow a '+' sign in the exponent.
"0.3E3" | 0.3e3 | 0.3e3 | 0.3 | Palm OS 1.0 doesn't allow a capital 'E' to mark the exponent.
"4294967297" | 4294967297 | 4294967297 | 1 | Palm OS 1.0 uses unsigned long and wraps around.
1. Using the old Float Manager documented in Appendix C, "1.0 Float Manager."
#### Compatibility Implemented only if 2.0 New Feature Set is present. GCC users must use FlpBufferAToF instead of this function. #### See Also FlpFToA ## FlpBase10Info #### Purpose Extract detailed information on the base 10 form of a floating-point number: the base 10 mantissa, exponent, and sign. #### Prototype Err FlpBase10Info (FlpDouble a, 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.
#### Result 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 #### Purpose Convert a null-terminated ASCII string to a floating-point number. The string must be in the format: [-]x[.]yyyyyyyy[e[-]zz] #### Prototype void FlpBufferAToF (FlpDouble *result, const Char *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.
#### Result 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. GCC users must use this function instead of FlpAToF due to incompatibilities in the way GCC handles structure return values. CodeWarrior users can use either function; they are binary compatible. ## FlpBufferCorrectedAdd #### 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. #### Prototype void FlpBufferCorrectedAdd (FlpDouble *result, FlpDouble firstOperand, FlpDouble secondOperand, Int16 howAccurate) #### 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).
#### Result 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. GCC users must use this function instead of FlpCorrectedAdd due to incompatibilities in the way GCC handles structure return values. CodeWarrior users can use either function; they are binary compatible. ## FlpBufferCorrectedSub #### 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. #### Prototype void FlpBufferCorrectedSub (FlpDouble *result, FlpDouble firstOperand, FlpDouble secondOperand, Int16 howAccurate) #### 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).
#### Result 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. GCC users must use this function instead of FlpCorrectedSub due to incompatibilities in the way GCC handles structure return values. CodeWarrior users can use either function; they are binary compatible. ## FlpCorrectedAdd #### 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. #### Prototype FlpDouble FlpCorrectedAdd (FlpDouble firstOperand, FlpDouble secondOperand, Int16 howAccurate) #### 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).
#### Result 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 #### 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. #### Prototype FlpDouble FlpCorrectedSub (FlpDouble firstOperand, FlpDouble secondOperand, Int16 howAccurate) #### 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).
#### Result 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 #### Purpose Convert a floating-point number to a null-terminated ASCII string in exponential format: [-]x.yyyyyyye[-]zz #### Prototype Err FlpFToA (FlpDouble a, Char *s) #### Parameters #####
-> a | Floating-point number.
#####
<-s | Pointer to buffer to contain the ASCII string.
#### Result 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. #### Compatibility Implemented only if 2.0 New Feature Set is present. #### See Also FlpAToF ## FlpGetExponent #### Purpose Macro that returns the exponent of a 64-bit floating-point value. The returned value has the bias applied, so it ranges from -1023 to +1024. #### Prototype FlpGetExponent (x) #### Parameters #####
-> x | The value from which the exponent is to be extracted.
#### Result 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 #### Purpose Macro that returns the sign of a 64-bit floating-point value. #### Prototype FlpGetSign (x) #### Parameters #####
-> x | The value from which the sign bit is to be extracted.
#### Result 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 #### Purpose Macro that returns whether the specified 64-bit floating-point value is zero. #### Prototype FlpIsZero (x) #### Parameters #####
-> x | The value for which the sign bit is desired.
#### Result 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 #### Purpose Macro that changes the sign bit of a 64-bit floating-point number. #### Prototype FlpNegate (x) #### Parameters #####
-> x | The value in which the sign bit is to be changed.
#### Result 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 #### Purpose Macro that ensures that a 64-bit floating-point number is negative. #### Prototype FlpSetNegative (x) #### Parameters #####
-> x | The value that is to be forced negative.
#### Result 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 #### Purpose Macro that ensures that a 64-bit floating-point number is positive. #### Prototype FlpSetPositive (x) #### Parameters #####
-> x | The value that is to be forced positive.
#### Result 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 #### Purpose Returns the version number of the Float Manager. #### Prototype UInt32 FlpVersion (void) #### Parameters #####
None.
#### Result 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. |