@DATABASE Libraries_Manual @NODE MAIN "Amiga® RKM Libraries: 35 Math Libraries" @INDEX Libraries/Lib_Index/MAIN @TOC Libraries_Manual/Add This chapter describes the structure and calling sequences required to access the Motorola Fast Floating Point (FFP), the IEEE single-precision math libraries and the IEEE double-precision math libraries via the Amiga-supplied interfaces. In its present state, the FFP library consists of three separate entities: the basic math library, the transcendental math library, and C and assembly-language interfaces to the basic math library plus FFP conversion functions. The IEEE single-precision, introduced in Release 2, and the double-precision libraries each presently consists of two entities: the basic math library and the transcendental math library. Open Each Library Separately. ----------------------------- Each @{"Task" link Libraries/Lib_21/21-1} using an IEEE math library must open the library itself. Library base pointers to these libraries may not be shared. Libraries can be context sensitive and may use the Task structure to keep track of the current context. Sharing of library bases by Tasks may seem to work in some systems. This is true for any of the IEEE math libraries. Depending on the compiler used, it is not always necessary to explicitly call the library functions for basic floating point operations as adding, subtracting, dividing, etc. Consult the manual supplied with the compiler for information regarding the compiler options for floating point functions. @{" Math Libraries and Functions " link 35-1} @{" FFP Floating Point Data Format " link 35-2} @{" FFP Basic Mathematics Library " link 35-3} @{" FFP Transcendental Mathematics Library " link 35-4} @{" FFP Mathematics Conversion Library " link 35-5} @{" IEEE Single-Precision Data Format " link 35-6} @{" IEEE Single-Precision Basic Math Library " link 35-7} @{" IEEE Single-Precision Transcendental Math Library " link 35-8} @{" IEEE Double-Precision Data Format " link 35-9} @{" IEEE Double-Precision Basic Math Library " link 35-10} @{" IEEE Double-Precision Transcendental Math Library " link 35-11} @{" Function Reference " link 35-12} @{" Compile and Link Commands for SAS C 5.10 " link 35-13} @ENDNODE @NODE 35-1 "35 Math Libraries / Math Libraries and Functions" There are six math libraries providing functions ranging from adding two floating point numbers to calculating a hyperbolic cosine. They are: mathffp.library the basic function library mathtrans.library the FFP transcendental math library mathieeesingbas.library the IEEE single-precision library mathieesingtrans.library the IEEE single-precision transcendental library mathieeedoubbas.library the IEEE double-precision library mathieesingtrans.library the IEEE double-precision transcendental library @ENDNODE @NODE 35-2 "35 Math Libraries / FFP Floating Point Data Format" FFP floating-point variables are defined within C by the float or FLOAT directive. In assembly language they are simply defined by a DC.L/DS.L statement. All FFP floating-point variables are defined as 32-bit entities (longwords) with the following format: _____________________________________________ | | | MMMMMMMM MMMMMMMM MMMMMMMM EEEEEEE | | 31 23 15 7 | |_____________________________________________| The mantissa is considered to be a binary fixed-point fraction; except for 0, it is always normalized (the mantissa is shifted over and the exponent adjusted, so that the mantissa has a 1 bit in its highest position). Thus, it represents a value of less than 1 but greater than or equal to 1/2. The sign bit is reset (0) for a positive value and set (1) for a negative value. The exponent is the power of two needed to correctly position the mantissa to reflect the number's true arithmetic value. It is held in excess-64 notation, which means that the two's-complement values are adjusted upward by 64, thus changing $40 (-64) through $3F (+63) to $00 through $7F. This facilitates comparisons among floating-point values. The value of 0 is defined as all 32 bits being 0s. The sign, exponent, and mantissa are entirely cleared. Thus, 0s are always treated as positive. The range allowed by this format is as follows: DECIMAL: 9.22337177 * 10^18 > +VALUE > 5.42101070 * 10^-20 -9.22337177 * 10^18 < -VALUE < -2.71050535 * 10^-20 BINARY (HEXADECIMAL): .FFFFFF * 2^63 > +VALUE > .800000 * 2^-63 -.FFFFFF * 2^63 < -VALUE < -.800000 * 2^-64 Remember that you cannot perform any arithmetic on these variables without using the fast floating-point libraries. The formats of the variables are incompatible with the arithmetic format of C-generated code; hence, all floating-point operations are performed through function calls. @ENDNODE @NODE 35-3 "35 Math Libraries / FFP Basic Mathematics Library" The FFP basic math library contains entries for the basic mathematics functions such as add, subtract and divide. It resides in ROM and is opened by calling @{"OpenLibrary()" link Libraries/Lib_17/17-5 15} with "mathffp.library" as the argument. #include #include #include struct Library *MathBase; VOID main() { if (MathBase = OpenLibrary("mathffp.library", 0)) { . . . CloseLibrary(MathBase); } else printf("Can't open mathffp.library\\n"); } The global variable MathBase is used internally for all future library references. @{" FFP Basic Functions " link 35-3-1} @ENDNODE @NODE 35-3-1 "35 / FFP Basic Mathematics Library / FFP Basic Functions" @{"SPAbs()" link AutoDocs/mathffp/SPAbs()} FLOAT SPAbs( FLOAT parm ); Take absolute value of FFP variable. @{"SPAdd()" link AutoDocs/mathffp/SPAdd()} FLOAT SPAdd( FLOAT leftParm, FLOAT rightParm); Add two FFP variables. @{"SPCeil()" link AutoDocs/mathffp/SPCeil()} FLOAT SPCeil( FLOAT parm );  Computer largest integer less than or equal to variable. @{"SPCmp()" link AutoDocs/mathffp/SPCmp()} LONG SPCmp( FLOAT leftParm, FLOAT rightParm); Compare two FFP variables. @{"SPDiv()" link AutoDocs/mathffp/SPDiv()} FLOAT SPDiv( FLOAT leftParm, FLOAT rightParm); Divide two FFP variables. @{"SPFix()" link AutoDocs/mathffp/SPFix()} LONG SPFix( FLOAT parm ); Convert FFP variable to integer. @{"SPFloor()" link AutoDocs/mathffp/SPFloor()} FLOAT SPFloor( FLOAT parm ); Compute least integer greater than or equal to variable. @{"SPFlt()" link AutoDocs/mathffp/SPFlt()} FLOAT SPFlt( long integer ); Convert integer variable to FFP. @{"SPMul()" link AutoDocs/mathffp/SPMul()} FLOAT SPMul( FLOAT leftParm, FLOAT rightParm); Multiply two FFP variables. @{"SPNeg()" link AutoDocs/mathffp/SPNeg()} FLOAT SPNeg( FLOAT parm ); Take two's complement of FFP variable. @{"SPSub()" link AutoDocs/mathffp/SPSub()} FLOAT SPSub( FLOAT leftParm, FLOAT rightParm); Subtract two FFP variables. @{"SPTst()" link AutoDocs/mathffp/SPTst()} LONG SPTst( FLOAT parm ); Test an FFP variable against zero. Be sure to include the proper data type definitions shown below. #include #include #include struct Library *MathBase; VOID main() { FLOAT f1, f2, f3; LONG i1; if (MathBase = OpenLibrary("mathffp.library", 0)) { i1 = SPFix(f1); /* Call SPFix entry */ f1 = SPFlt(i1); /* Call SPFlt entry */ if (SPCmp(f1,f2)) {}; /* Call SPCmp entry */ if (!(SPTst(f1))) {}; /* Call SPTst entry */ f1 = SPAbs(f2); /* Call SPAbs entry */ f1 = SPNeg(f2); /* Call SPNeg entry */ f1 = SPAdd(f2, f3); /* Call SPAdd entry */ f1 = SPSub(f2, f3); /* Call SPSub entry */ f1 = SPMul(f2, f3); /* Call SPMul entry */ f1 = SPDiv(f2, f3); /* Call SPDiv entry */ f1 = SPCeil(f2); /* Call SPCeil entry */ f1 = SPFloor(f2); /* Call SPFloor entry */ CloseLibrary(MathBase); } else printf("Can't open mathffp.library\\n"); } The assembly language interface to the FFP basic math routines is shown below, including some details about how the system flags are affected by each operation. The access mechanism is: MOVEA.L _MathBase,A6 JSR _LVOSPFix(A6) __________________________________________________________________ | | | FFP Basic Assembly Functions | | | | Function Input Output Condition Codes | |__________________________________________________________________| | | | | | | _LVOSPAbs | D0=FFP arg | D0=FFP absolute | N=0 | | | | value | Z=1 if result | | | | | is zero | | | | | V=0 | | | | | C=undefined | | | | | X=undefined | |-------------|-------------|--------------------|-----------------| | _LVOSPAdd | D1=FFP arg1 | D0=FFP addition | N=1 if result | | | D0=FFP arg2 | of arg1 + arg2 | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if result | | | | | overflowed | | | | | C=undefined | | | | | Z=undefined | |-------------|-------------|--------------------|-----------------| | _LVOSPCeil | D0=FFP arg | D0=least integer | N=1 if result | | | | >=arg | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=undefined | | | | | C=undefined | | | | | Z=undefined | |-------------|-------------|--------------------|-----------------| | _LVOSPCmp | D1=FFP arg1 | D0=+1 if arg1>arg2 | N=0 | | | D0=FFP arg2 | D0=-1 if arg1arg1 | | | | | GE=arg2>=arg1 | | | | | EQ=arg2=arg1 | | | | | NE=arg2<>arg1 | | | | | LT=arg20.0 | N=1 if result | | | | D0=-1 if arg<0.0 | is negative | | | | D0=0 if arg=0.0 | Z=1 if result | | | | | is zero | | | | | V=0 | | | | | C=undefined | | | | | X=undefined | | | Note: This | | EQ=arg=0.0 | | | routine | | NE=arg<>0.0 | | | trashes the | | PL=arg>=0.0 | | | arg in D1. | | MI=arg<0.0 | |_____________|_____________|____________________|_________________| @ENDNODE @NODE 35-4 "35 Math Libraries / FFP Transcendental Mathematics Library" The FFP transcendental math library contains entries for the transcendental math functions sine, cosine, and square root. It resides on disk and is opened by calling @{"OpenLibrary()" link Libraries/Lib_17/17-5 15} with "mathtrans.library" as the argument. #include #include #include #include struct Library *MathTransBase; VOID main() { if (MathTransBase = OpenLibrary("mathtrans.library",0)) { . . . CloseLibrary(MathTransBase); } else printf("Can't open mathtrans.library\\n"); } The global variable MathTransBase is used internally for all future library references. Note that the transcendental math library is dependent upon the basic math library, which it will open if it is not open already. If you want to use the basic math functions in conjunction with the transcendental math functions however, you have to specifically open the basic math library yourself. @{" FFP Transcendental Functions " link 35-4-1} @ENDNODE @NODE 35-4-1 "35 / Transcendental Mathematics Library / FFP Transcendental Functions" @{"SPAsin()" link AutoDocs/mathtrans/SPAsin()} FLOAT SPAsin( FLOAT parm ); Return arccosine of FFP variable. @{"SPAcos()" link AutoDocs/mathtrans/SPAcos()} FLOAT SPAcos( FLOAT parm ); Return arctangent of FFP variable. @{"SPAtan()" link AutoDocs/mathtrans/SPAtan()} FLOAT SPAtan( FLOAT parm ); Return arcsine of FFP variable. @{"SPSin()" link AutoDocs/mathtrans/SPSin()} FLOAT SPSin( FLOAT parm ); Return sine of FFP variable. This function accepts an FFP radian argument and returns the trigonometric sine value. For extremely large arguments where little or no precision would result, the computation is aborted and the "V" condition code is set. A direct return to the caller is made. @{"SPCos()" link AutoDocs/mathtrans/SPCos()} FLOAT SPCos( FLOAT parm ); Return cosine of FFP variable. This function accepts an FFP radian argument and returns the trigonometric cosine value. For extremely large arguments where little or no precision would result, the computation is aborted and the "V" condition code is set. A direct return to the caller is made. @{"SPTan()" link AutoDocs/mathtrans/SPTan()} FLOAT SPTan( FLOAT parm ); Return tangent of FFP variable. This function accepts an FFP radian argument and returns the trigonometric tangent value. For extremely large arguments where little or no precision would result, the computation is aborted and the "V" condition code is set. A direct return to the caller is made. @{"SPSincos()" link AutoDocs/mathtrans/SPSincos()} FLOAT SPSincos( FLOAT *cosResult, FLOAT parm); Return sine and cosine of FFP variable. This function accepts an FFP radian argument and returns the trigonometric sine as its result and the trigonometric cosine in the first parameter. If both the sine and cosine are required for a single radian value, this function will result in almost twice the execution speed of calling the SPSin() and SPCos() functions independently. For extremely large arguments where little or no precision would result, the computation is aborted and the "V" condition code is set. A direct return to the caller is made. @{"SPSinh()" link AutoDocs/mathtrans/SPSinh()} FLOAT SPSinh( FLOAT parm ); Return hyperbolic sine of FFP variable. @{"SPCosh()" link AutoDocs/mathtrans/SPCosh()} FLOAT SPCosh( FLOAT parm ); Return hyperbolic cosine of FFP variable. @{"SPTanh()" link AutoDocs/mathtrans/SPTanh()} FLOAT SPTanh( FLOAT parm ); Return hyperbolic tangent of FFP variable. @{"SPExp()" link AutoDocs/mathtrans/SPExp()} FLOAT SPExp( FLOAT parm ); Return e to the FFP variable power. This function accepts an FFP argument and returns the result representing the value of e (2.71828...) raised to that power. @{"SPLog()" link AutoDocs/mathtrans/SPLog()} FLOAT SPLog( FLOAT parm ); Return natural log (base e) of FFP variable. @{"SPLog10()" link AutoDocs/mathtrans/SPLog10()} FLOAT SPLog10( FLOAT parm ); Return log (base 10) of FFP variable. @{"SPPow()" link AutoDocs/mathtrans/SPPow()} FLOAT SPPow( FLOAT power, FLOAT arg ); Return FFP arg2 to FFP arg1. @{"SPSqrt()" link AutoDocs/mathtrans/SPSqrt()} FLOAT SPSqrt( FLOAT parm ); Return square root of FFP variable. @{"SPTieee()" link AutoDocs/mathtrans/SPTieee()} FLOAT SPTieee( FLOAT parm ); Convert FFP variable to IEEE format @{"SPFieee()" link AutoDocs/mathtrans/SPFieee()} FLOAT SPFieee( FLOAT parm ); Convert IEEE variable to FFP format. Be sure to include proper data type definitions, as shown in the example below. @{" mathtrans.c " link lib_examples/mathtrans.c/MAIN} The Amiga assembly language interface to the FFP transcendental math routines is shown below, including some details about how the system flags are affected by the operation. This interface resides in the library file amiga.lib and must be linked with the user code. Note that the access mechanism from assembly language is: MOVEA.L _MathTransBase,A6 JSR _LVOSPAsin(A6) _______________________________________________________________________ | | | FFP Transcendental Assembly Functions | | | | Function Input Output Condition Codes | |_______________________________________________________________________| | | | | | | _LVOSPAsin | D0=FFP arg | D0=FFP arcsine | N=0 | | | | radian | Z=1 if result | | | | | is zero | | | | | V=0 | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPAcos | D0=FFP arg | D0=FFP arccosine | N=0 | | | | radian | Z=1 if result | | | | | is zero | | | | | V=1 if overflow | | | | | occurred | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPAtan | D0=FFP arg | D0=FFP arctangent | N=0 | | | | radian | Z=1 if result | | | | | is zero | | | | | V=0 | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPSin | D0=FFP arg | D0=FFP sine | N=1 if result | | | in radians | | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if result | | | | | is meaningless | | | | | (input magnitude | | | | | too large) | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPCos | D0=FFP arg | D0=FFP cosine | N=1 if result | | | in radians | | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if result | | | | | is meaningless | | | | | (input magnitude | | | | | too large) | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPTan | D0=FFP arg | D0=FFP tangent | N=1 if result | | | in radians | | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if result | | | | | is meaningless | | | | | (input magnitude | | | | | too large) | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPSincos | D0=FFP arg | D0=FFP sine | N=1 if result | | | in radians | (D1)=FFP cosine | is negative | | | D1=Address | | Z=1 if result | | | to store | | is zero | | | cosine result | | V=1 if result | | | | | is meaningless | | | | | (input magnitude | | | | | too large) | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPSinh | D0=FFP arg | D0=FFP hyperbolic | N=1 if result | | | in radians | sine | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if overflow | | | | | occurred | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPCosh | D0=FFP arg | D0=FFP hyperbolic | N=1 if result | | | in radians | cosine | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if overflow | | | | | occurred | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPTanh | D0=FFP arg | D0=FFP hyperbolic | N=1 if result | | | in radians | tangent | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if overflow | | | | | occurred | | | | | C=undefined | | | | | X=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPExp | D0=FFP arg | D0=FFP exponential | N=0 | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if overflow | | | | | occurred | | | | | C=undefined | | | | | Z=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPLog | D0=FFP arg | D0=FFP natural | N=1 if result | | | | logarithm | is negative | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if arg is | | | | | negative or zero | | | | | C=undefined | | | | | Z=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPLog10 | D0=FFP arg | D0=FFP logarithm | N=1 if result | | | | (base 10) | is negative | | | | |Z=1 if result | | | | | is zero | | | | |V=1 if arg is | | | | | negative or zero | | | | | C=undefined | | | | | Z=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPPow | D0=FFP | D0=FFP result of | N=0 | | | exponent value | arg taken to | Z=1 if result | | | D1=FFP | exp power | is zero | | | arg value | | V=1 if result | | | | | overflowed | | | | | or arg < 0 | | | | | C=undefined | | | | | Z=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPSqrt | D0=FFP arg | D0=FFP square root | N=0 | | | | | Z=1 if result | | | | | is zero | | | | | V=1 if arg was | | | | | negative | | | | | C=undefined | | | | | Z=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPTieee | D0=FFP | D0=IEEE | N=1 if result | | | format arg | floating-point | is negative | | | | format | Z=1 if result | | | | | is zero | | | | | V=undefined | | | | | C=undefined | | | | | Z=undefined | |--------------|----------------|--------------------|------------------| | _LVOSPFieee | D0=IEEE | D0=FFP format | N=undefined | | | floating-point | | Z=1 if result | | | format arg | | is zero | | | | | V=1 if result | | | | | overflowed | | | | | C=undefined | | | | | Z=undefined | |______________|________________|____________________|__________________| @ENDNODE @NODE 35-5 "35 Math Libraries / FFP Mathematics Conversion Library" The FFP mathematics conversion library provides functions to convert ASCII strings to their FFP equivalents and vice versa. It is accessed by linking code into the executable file being created. The name of the file to include in the library description of the link command line is amiga.lib. When this is included, direct calls are made to the conversion functions. Only a C interface exists for the conversion functions; there is no assembly language interface. The basic math library is required in order to access these functions. #include #include #include struct Library *MathBase; VOID main() { if (MathBase = OpenLibrary("mathffp.library", 33)) { . . . CloseLibrary(MathBase); } else printf("Can't open mathffp.library\\n"); } @{" Math Support Functions " link 35-5-1} @ENDNODE @NODE 35-5-1 "35 / FFP Mathematics Conversion Library / Math Support Functions" @{"afp()" link AutoDocs/amiga_lib/afp()} FLOAT afp( BYTE *string ); Convert ASCII string into FFP equivalent. @{"arnd()" link AutoDocs/amiga_lib/arnd()} VOID arnd( LONG place, LONG exp, BYTE *string); Round ASCII representation of FFP number. @{"dbf()" link AutoDocs/amiga_lib/dbf()} FLOAT dbf( ULONG exp, ULONG mant); Convert FFP dual-binary number to FFP equivalent. @{"fpa()" link AutoDocs/amiga_lib/fpa()} LONG fpa( FLOAT fnum, BYTE *string); Convert FFP variable into ASCII equivalent. Be sure to include proper data type definitions, as shown in the example below. Print statements have been included to help clarify the format of the math conversion function calls. @{" mathffp.c " link lib_examples/mathffp.c/MAIN} @ENDNODE @NODE 35-6 "35 Math Libraries / IEEE Single-Precision Data Format" The IEEE single-precision variables are defined as 32-bit entities with the following format: ______________________________________________ | | | SEEEEEEE MMMMMMMM MMMMMMMM MMMMMMMM | | 31 23 15 7 | |______________________________________________| Hidden Bit In The Mantissa. --------------------------- There is a "hidden" bit in the mantissa part of the IEEE numbers. Since all numbers are normalized, the integer (high) bit of the mantissa is dropped off. The IEEE single-precision range is 1.3E-38 (1.4E-45 de-normalized) to 3.4E+38. The exponent is the power of two needed to correctly position the mantissa to reflect the number's true arithmetic value. If both the exponent and the mantissa have zero in every position, the value is zero. If only the exponent has zero in every position, the value is an unnormal (extremely small). If all bits of the exponent are set to 1 the value is either a positive or negative infinity or a Not a Number (NaN). NaN is sometimes used to indicate an uninitialized variable. @ENDNODE @NODE 35-7 "35 Math Libraries / IEEE Single-Precision Basic Math Library" The ROM-based IEEE single-precision basic math library was introduced in V36. This library contains entries for the basic IEEE single-precision mathematics functions, such as add, subtract, and divide. (Note, registered developers can license a disk-based version of this library from @{"CATS" link Libraries/Lib_1/1-5}, for usage with V33). The library is opened by making calling @{"OpenLibrary()" link Libraries/Lib_17/17-5 15} with "mathieeesingbas.library" as the argument. Do not share the library base pointer between tasks -- @{"see note" link MAIN 12} at beginning of chapter for details. #include #include #include struct Library *MathIeeeSingBasBase; VOID main() { /* do not share base pointer between tasks. */ if (MathIeeeSingBasBase = OpenLibrary("mathieeesingbas.library", 37)) { . . . CloseLibrary(MathIeeeSingBasBase); } else printf("Can't open mathieeesingbas.library\\n"); } The global variable MathIeeeSingBasBase is used internally for all future library references. If an 680X0/68881/68882 processor combination is available, it will be used by the IEEE single-precision basic library instead of the software emulation. Also, if an autoconfigured math resource is available, that will be used. Typically this is a 68881 designed as a 16 bit I/O port, but it could be another device as well. @{" SP IEEE Basic Functions (V36 or Greater) " link 35-7-1} @ENDNODE @NODE 35-7-1 "35 / SP Basic Math Library / SP IEEE Basic Functions (V36 or Greater)" @{"IEEESPAbs()" link AutoDocs/mathieeesingbas/IEEESPAbs()} FLOAT ( FLOAT parm ); Take absolute value of IEEE single-precision variable. @{"IEEESPAdd()" link AutoDocs/mathieeesingbas/IEEESPAdd()} FLOAT IEEESPAdd( FLOAT leftParm, FLOAT rightParm); Add two IEEE single-precision variables. @{"IEEESPCeil()" link AutoDocs/mathieeesingbas/IEEESPCeil()} FLOAT IEEESPCeil( FLOAT parm ); Compute least integer greater than or equal to variable. @{"IEEESPCmp()" link AutoDocs/mathieeesingbas/IEEESPCmp()} LONG IEEESPCmp( FLOAT leftParm, FLOAT rightParm ); Compare two IEEE single-precision variables. @{"IEEESPDiv()" link AutoDocs/mathieeesingbas/IEEESPDiv()} FLOAT IEEESPDiv( FLOAT dividend, FLOAT divisor ); Divide two IEEE single-precision variables. @{"IEEESPFix()" link AutoDocs/mathieeesingbas/IEEESPFix()} LONG IEEESPFix( FLOAT parm ); Convert IEEE single-precision variable to integer. @{"IEEESPFloor()" link AutoDocs/mathieeesingbas/IEEESPFloor()} FLOAT IEEESPFloor( FLOAT parm ); Compute largest integer less than or equal to variable. @{"IEEESPFlt()" link AutoDocs/mathieeesingbas/IEEESPFlt()} FLOAT IEEESPFlt( long integer ); Convert integer variable to IEEE single-precision. @{"IEEESPMul()" link AutoDocs/mathieeesingbas/IEEESPMul()} FLOAT IEEESPMul( FLOAT leftParm, FLOAT rightParm ); Multiply two IEEE single-precision variables. @{"IEEESPNeg()" link AutoDocs/mathieeesingbas/IEEESPNeg()} FLOAT IEEESPNeg( FLOAT parm ); Take two's complement of IEEE single-precision variable. @{"IEEESPSub()" link AutoDocs/mathieeesingbas/IEEESPSub()} FLOAT IEEESPSub( FLOAT leftParm, FLOAT rightParm ); Subtract two IEEE single-precision variables. @{"IEEESPTst()" link AutoDocs/mathieeesingbas/IEEESPTst()} LONG IEEESPTst( FLOAT parm ); Test an IEEE single-precision variable against zero. Be sure to include proper data type definitions, as shown in the example below. @{" mathieeesingbas.c " link lib_examples/mathieeesingbas.c/MAIN} The Amiga assembly language interface to the IEEE single-precision basic math routines is shown below, including some details about how the system flags are affected by each operation. Note that the access mechanism from assembly language is as shown below: MOVEA.L _MathIeeeSingBasBase,A6 JSR _LVOIEEESPFix(A6) _________________________________________________________________________ | | | SP IEEE Basic Assembly Functions | | | | Function Input Output Condition Codes| |_________________________________________________________________________| | | | | | | _LVOIEEESPFix | D0=IEEE arg | D0=Integer | N=undefined | | | double-precision | (two's complement) | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPFlt | D0=Integer arg | D0=IEEE | N=undefined | | | (two's | single-precision | Z=undefined | | | complement) | | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPCmp | D0=IEEE arg1 | D0=+1 if arg1>arg2 | N=1 if result | | | single-precision | D0=-1 if arg1arg1 | | | | | GE=arg2>=arg1 | | | | | EQ=arg2=arg1 | | | | | NE=arg2<>arg1 | | | | | LT=arg20.0 | N=1 if result | | | single-precision | D0=-1 if arg<0.0 | is negative | | | | D0=0 if arg=0.0 | Z=1 if result | | | | | is zero | | | | | V=0 | | | | | C=undefined | | | | | X=undefined | | | | | EQ=arg=0.0 | | | | | NE=arg<>0.0 | | | | | PL=arg>=0.0 | | | | | MI=arg<0.0 | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPAbs | D0=IEEE arg | D0=IEEE | N=undefined | | | single-precision | single-precision | Z=undefined | | | | absolute value | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPNeg | D0=IEEE arg | D0=IEEE | N=undefined | | | single-precision | single-precision | Z=undefined | | | | negated | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPAdd | D0=IEEE arg1 | D0=IEEE | N=undefined | | | single-precision | single-precision | Z=undefined | | | D1=IEEE arg2 | addition of | V=undefined | | | single-precision | arg1+arg2 | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPSub | D0=IEEE arg1 | D0=IEEE | N=undefined | | | single-precision | single-precision | Z=undefined | | | D1=IEEE arg2 | subtraction of | V=undefined | | | single-precision | arg1-arg2 | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPMul | D0=IEEE arg1 | D0=IEEE | N=undefined | | | single-precision | single-precision | Z=undefined | | | D1=IEEE arg2 | multiplication of | V=undefined | | | single-precision | arg1*arg2 | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPDiv | D0=IEEE arg1 | D0=IEEE | N=undefined | | | single-precision | single-precision | Z=undefined | | | D1=IEEE arg2 | division of | V=undefined | | | single-precision | arg1/arg2 | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPCeil | D0=IEEE variable | D0=least integer | N=undefined | | | single-precision | >= variable | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEESPFloor | D0=IEEE variable | D0=largest integer | N=undefined | | | single-precision | <= arg | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |_________________|__________________|____________________|_______________| @ENDNODE @NODE 35-8 "35 Math Libraries / IEEE Single-Precision Transcendental Math Library" The IEEE single-precision transcendental math library was introduced in V36. It contains entries for transcendental math functions such as sine, cosine, and square root. This library resides on disk and is opened by calling @{"OpenLibrary()" link Libraries/Lib_17/17-5 15} with "mathieeesingtrans.library" as the argument. Do not share the library base pointer between tasks -- @{"see note" link MAIN 12} at beginning of chapter. #include #include struct Library *MathIeeeSingTransBase; #include VOID main() { if (MathIeeeSingTransBase = OpenLibrary("mathieeesingtrans.library",37)) { . . . CloseLibrary(MathIeeeSingTransBase); } else printf("Can't open mathieeesingtrans.library\\n"); } The global variable MathIeeeSingTransBase is used internally for all future library references. The IEEE single-precision transcendental math library is dependent upon the IEEE single-precision basic math library, which it will open if it is not open already. If you want to use the IEEE single-precision basic math functions in conjunction with the transcendental math functions however, you have to specifically open the basic math library yourself. Just as the IEEE single-precision basic math library, the IEEE single-precision transcendental math library will take advantage of a 680X0/68881 combination or another math resource, if present. @{" SP IEEE Transcendental Functions (V36 Or Greater) " link 35-8-1} @ENDNODE @NODE 35-8-1 "35 / / SP IEEE Transcendental Functions (V36 Or Greater)" @{"IEEESPAsin()" link AutoDocs/mathieeesingtrans/IEEESPAsin()} FLOAT IEEESPAsin( FLOAT parm ); Return arcsine of IEEE single-precision variable. @{"IEEESPAcos()" link AutoDocs/mathieeesingtrans/IEEESPAcos()} FLOAT IEEESPAcos( FLOAT parm ); Return arccosine of IEEE single-precision variable. @{"IEEESPAtan()" link AutoDocs/mathieeesingtrans/IEEESPAtan()} FLOAT IEEESPAtan( FLOAT parm ); Return arctangent of IEEE single-precision variable. @{"IEEESPSin()" link AutoDocs/mathieeesingtrans/IEEESPSin()} FLOAT IEEESPSin( FLOAT parm ); Return sine of IEEE single-precision variable. This function accepts an IEEE radian argument and returns the trigonometric sine value. @{"IEEESPCos()" link AutoDocs/mathieeesingtrans/IEEESPCos()} FLOAT IEEESPCos( FLOAT parm ); Return cosine of IEEE single-precision variable. This function accepts an IEEE radian argument and returns the trigonometric cosine value. @{"IEEESPTan()" link AutoDocs/mathieeesingtrans/IEEESPTan()} FLOAT IEEESPTan( FLOAT parm ); Return tangent of IEEE single-precision variable. This function accepts an IEEE radian argument and returns the trigonometric tangent value. @{"IEEESPSincos()" link AutoDocs/mathieeesingtrans/IEEESPSincos()} FLOAT IEEESPSincos( FLOAT *cosptr, FLOAT parm ); Return sine and cosine of IEEE single-precision variable. This function accepts an IEEE radian argument and returns the trigonometric sine as its result and the cosine in the first parameter. @{"IEEESPSinh()" link AutoDocs/mathieeesingtrans/IEEESPSinh()} FLOAT IEEESPSinh( FLOAT parm ); Return hyperbolic sine of IEEE single-precision variable. @{"IEEESPCosh()" link AutoDocs/mathieeesingtrans/IEEESPCosh()} FLOAT IEEESPCosh( FLOAT parm ); Return hyperbolic cosine of IEEE single-precision variable. @{"IEEESPTanh()" link AutoDocs/mathieeesingtrans/IEEESPTanh()} FLOAT IEEESPTanh( FLOAT parm ); Return hyperbolic tangent of IEEE single-precision variable. @{"IEEESPExp()" link AutoDocs/mathieeesingtrans/IEEESPExp()} FLOAT IEEESPExp( FLOAT parm ); Return e to the IEEE variable power. This function accept an IEEE single-precision argument and returns the result representing the value of e (2.712828...) raised to that power. @{"IEEESPFieee()" link AutoDocs/mathieeesingtrans/IEEESPFieee()} FLOAT IEEESPFieee( FLOAT parm ); Convert IEEE single-precision number to IEEE single-precision number. The only purpose of this function is to provide consistency with the double-precision math IEEE library. @{"IEEESPLog()" link AutoDocs/mathieeesingtrans/IEEESPLog()} FLOAT IEEESPLog( FLOAT parm ); Return natural log (base e of IEEE single-precision variable. @{"IEEESPLog10()" link AutoDocs/mathieeesingtrans/IEEESPLog10()} FLOAT IEEESPLog10( FLOAT parm ); Return log (base 10) of IEEE single-precision variable. @{"IEEESPPow()" link AutoDocs/mathieeesingtrans/IEEESPPow()} FLOAT IEEESPPow( FLOAT exp, FLOAT arg ); Return IEEE single-precision arg2 to IEEE single-precision arg1. @{"IEEESPSqrt()" link AutoDocs/mathieeesingtrans/IEEESPSqrt()} FLOAT IEEESPSqrt( FLOAT parm ); Return square root of IEEE single-precision variable. @{"IEEESPTieee()" link AutoDocs/mathieeesingtrans/IEEESPTieee()} FLOAT IEEESPTieee( FLOAT parm ); Convert IEEE single-precision number to IEEE single-precision number. The only purpose of this function is to provide consistency with the double-precision math IEEE library. Be sure to include the proper data type definitions as shown below. @{" mathieeesingtrans.c " link lib_examples/mathieeesingtrans.c/MAIN} The section below describes the Amiga assembly interface to the IEEE single-precision transcendental math library. The access mechanism from assembly language is: MOVEA.L _MathIeeeSingTransBase,A6 JSR _LVOIEEESPAsin(A6) _________________________________________________________________________ | | | SP IEEE Transcendental Assembly Functions | | | | Function Input Output Condition Codes | |_________________________________________________________________________| | | | | | | _LVOIEEESPAsin | D0=IEEE arg | D0=IEEE arcsine | N=undefined | | | | radian | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPAcos | D0=IEEE arg | D0=IEEE arccosine | N=undefined | | | single-precision | radian | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPAtan | D0=IEEE arg | D0=IEEE arctangent | N=undefined | | | single-precision | radian | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPSin | D0=IEEE arg | D0=IEEE sine | N=undefined | | | in radians | | Z=undefined | | | single-precision | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPCos | D0=IEEE arg | D0=IEEE cosine | N=undefined | | | in radians | | Z=undefined | | | single-precision | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPTan | D0=IEEE arg | D0=IEEE tangent | N=undefined | | | in radians | | Z=undefined | | | single-precision | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPSincos | A0=Addr to store | D0=IEEE sine | N=undefined | | | cosine result | (A0)=IEEE cosine | Z=undefined | | | D0=IEEE arg | | V=undefined | | | in radians | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPSinh | D0=IEEE arg | D0=IEEE hyperbolic | N=undefined | | | in radians | sine | Z=undefined | | | single-precision | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPCosh | D0=IEEE arg | D0=IEEE hyperbolic | N=undefined | | | in radians | cosine | Z=undefined | | | single-precision | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPTanh | D0=IEEE arg | D0=IEEE hyperbolic | N=undefined | | | in radians | tangent | Z=undefined | | | single-precision | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPExp | D0=IEEE arg | D0=IEEE exponential | N=undefined | | | single-precision | | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPLog | D0=IEEE arg | D0=IEEE natural | N=undefined | | | single-precision | logarithm | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPLog10 | D0=IEEE arg | D0=IEEE logarithm | N=undefined | | | single-precision | (base 10) | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|------------------|---------------------|-------------| | _LVOIEEESPPow | D0=IEEE | D0=IEEE result of | N=undefined | | | exponent value | arg taken to | Z=undefined | | | single-precision | exp power | V=undefined | | | D1=IEEE | | C=undefined | | | arg value | | X=undefined | | | single-precision | | | |------------------|------------------|---------------------|-------------| | _LVOIEEESPSqrt | D0=IEEE arg | D0=IEEE square root | N=undefined | | | single-precision | | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |__________________|__________________|_____________________|_____________| @ENDNODE @NODE 35-9 "35 Math Libraries / IEEE Double-Precision Data Format" The IEEE double-precision variables are defined as 64-bit entities with the following format: ______________________________________________ | | | SEEEEEEE EEEEEIMM MMMMMMMM MMMMMMMM | | 63 55 47 39 | |______________________________________________| ______________________________________________ | | | MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM | | 31 23 15 7 | |______________________________________________| Hidden Bit In The Mantissa. --------------------------- There is a "hidden" bit in the mantissa part of the IEEE numbers. Since all numbers are normalized, the integer (high) bit of the mantissa is dropped off. The IEEE double-precision range is 2.2E-308 (4.9E-324 de-normalized) to 1.8E+307. The exponent is the power of two needed to correctly position the mantissa to reflect the number's true arithmetic value. If both the exponent and the mantissa have zero in every position, the value is zero. If only the exponent has zero in every position, the value is an unnormal (extremely small). If all bits of the exponent are set to 1 the value is either a positive or negative infinity or a Not a Number (NaN). NaN is sometimes used to indicate an uninitialized variable. @ENDNODE @NODE 35-10 "35 Math Libraries / IEEE Double-Precision Basic Math Library" The IEEE double-precision basic math library contains entries for the basic IEEE mathematics functions, such as add, subtract, and divide. This library resides on disk and is opened by calling @{"OpenLibrary()" link Libraries/Lib_17/17-5 15} with "mathieeedoubbas.library" as the argument. Do not share the library base pointer between tasks -- @{"see note" link MAIN 12} at beginning of chapter for details. #include #include #include struct Library *MathIeeeDoubBasBase; VOID main() { /* do not share base pointer between tasks. */ if (MathIeeeDoubBasBase = OpenLibrary("mathieeedoubbas.library", 34)) { . . . CloseLibrary(MathIeeeDoubBasBase); } else printf("Can't open mathieeedoubbas.library\\n"); } The global variable MathIeeeDoubBasBase is used internally for all future library references. If an 680X0/68881/68882 processor combination is available, it will be used by the IEEE basic library instead of the software emulation. Also, if an autoconfigured math resource is available, that will be used. Typically this is a 68881 designed as a 16 bit I/O port, but it could be another device as well. @{" DP IEEE Basic Functions " link 35-10-1} @ENDNODE @NODE 35-10-1 "35 /IEEE Double-Precision Basic Math Library / DP IEEE Basic Functions" @{"IEEEDPAbs()" link AutoDocs/mathieeedoubbas/IEEEDPAbs()} DOUBLE IEEEDPAbs( DOUBLE parm ); Take absolute value of IEEE double-precision variable. @{"IEEEDPAdd()" link AutoDocs/mathieeedoubbas/IEEEDPAdd()} DOUBLE IEEEDPAdd( DOUBLE leftParm, DOUBLE rightParm ); Add two IEEE double-precision variables. @{"IEEEDPCeil()" link AutoDocs/mathieeedoubbas/IEEEDPCeil()} DOUBLE IEEEDPCeil( DOUBLE parm ); Compute least integer greater than or equal to variable. @{"IEEEDPCmp()" link AutoDocs/mathieeedoubbas/IEEEDPCmp()} LONG IEEEDPCmp( DOUBLE leftParm, DOUBLE rightParm ); Compare two IEEE double-precision variables. @{"IEEEDPDiv()" link AutoDocs/mathieeedoubbas/IEEEDPDiv()} DOUBLE IEEEDPDiv( DOUBLE dividend, DOUBLE divisor ); Divide two IEEE double-precision variables. @{"IEEEDPFix()" link AutoDocs/mathieeedoubbas/IEEEDPFix()} LONG IEEEDPFix( DOUBLE parm ); Convert IEEE double-precision variable to integer. @{"IEEEDPFloor()" link AutoDocs/mathieeedoubbas/IEEEDPFloor()} DOUBLE IEEEDPFloor( DOUBLE parm ); Compute largest integer less than or equal to variable. @{"IEEEDPFlt()" link AutoDocs/mathieeedoubbas/IEEEDPFlt()} DOUBLE IEEEDPFlt( long integer ); Convert integer variable to IEEE double-precision. @{"IEEEDPMul()" link AutoDocs/mathieeedoubbas/IEEEDPMul()} DOUBLE IEEEDPMul( DOUBLE factor1, DOUBLE factor2 ); Multiply two IEEE double-precision variables. @{"IEEEDPNeg()" link AutoDocs/mathieeedoubbas/IEEEDPNeg()} DOUBLE IEEEDPNeg( DOUBLE parm ); Take two's complement of IEEE double-precision variable. @{"IEEEDPSub()" link AutoDocs/mathieeedoubbas/IEEEDPSub()} DOUBLE IEEEDPSub( DOUBLE leftParm, DOUBLE rightParm ); Subtract two IEEE double-precision variables. @{"IEEEDPTst()" link AutoDocs/mathieeedoubbas/IEEEDPTst()} LONG IEEEDPTst( DOUBLE parm ); Test an IEEE double-precision variable against zero. Be sure to include proper data type definitions, as shown in the example below. @{" mathieeedoubbas.c " link lib_examples/mathieeedoubbas.c/MAIN} The Amiga assembly language interface to the IEEE double-precision floating-point basic math routines is shown below, including some details about how the system flags are affected by each operation. The access mechanism from assembly language is: MOVEA.L _MathIeeeDoubBasBase,A6 JSR _LVOIEEEDPFix(A6) _________________________________________________________________________ | | | DP IEEE Basic Assembly Functions | | | | Function Input Output Condition Codes | |_________________________________________________________________________| | | | | | | _LVOIEEEDPFix | D0/D1=IEEE arg | D0=Integer | N=undefined | | | double-precision | (two's complement) | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPFl | D0=Integer arg | D0/D1=IEEE | N=undefined | | | (two's | double-precision | Z=undefined | | | complement) | | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPCmp | D0/D1=IEEE arg1 | D0=+1 if arg1>arg2 | N=1 if result | | | double-precision | D0=-1 if arg1arg1 | | | | | GE=arg2>=arg1 | | | | | EQ=arg2=arg1 | | | | | NE=arg2<>arg1 | | | | | LT=arg20.0 | N=1 if result | | | double-precision | D0=-1 if arg<0.0 | is negative | | | | D0=0 if arg=0.0 | Z=1 if result | | | | | is zero | | | | | V=0 | | | | | C=undefined | | | | | X=undefined | | | | | EQ=arg=0.0 | | | | | NE=arg<>0.0 | | | | | PL=arg>=0.0 | | | | | MI=arg<0.0 | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPAbs | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | double-precision | double-precision | Z=undefined | | | | absolute value | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPNeg | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | double-precision | double-precision | Z=undefined | | | | negated | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPAdd | D0/D1=IEEE arg1 | D0/D1=IEEE | N=undefined | | | double-precision | double-precision | Z=undefined | | | | addition of | V=undefined | | | D2/D3=IEEE arg2 | arg1+arg2 | C=undefined | | | double-precision | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPSub | D0/D1=IEEE arg1 | D0/D1=IEEE | N=undefined | | | double-precision | double-precision | Z=undefined | | | | subtraction of | V=undefined | | | D2/D3=IEEE arg2 | arg1-arg2 | C=undefined | | | double-precision | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPMul | D0/D1=IEEE arg1 | D0/D1=IEEE | N=undefined | | | double-precision | double-precision | Z=undefined | | | | multiplication of | V=undefined | | | D2/D3=IEEE arg2 | arg1*arg2 | C=undefined | | | double-precision | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPDiv | D0/D1=IEEE arg1 | D0/D1=IEEE | N=undefined | | | double-precision | double-precision | Z=undefined | | | | division of | V=undefined | | | D2/D3=IEEE arg2 | arg1/arg2 | C=undefined | | | double-precision | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPCeil | D0/D1=IEEE arg | D0/D1=least | N=undefined | | | double-precision | integer | Z=undefined | | | | >= arg | V=undefined | | | | | C=undefined | | | | | X=undefined | |-----------------|------------------|--------------------|---------------| | _LVOIEEEDPFloor | D0/D1=IEEE arg | D0/D1=largest | N=undefined | | | double-precision | integer | Z=undefined | | | | <= arg | V=undefined | | | | | C=undefined | | | | | X=undefined | |_________________|__________________|____________________|_______________| @ENDNODE @NODE 35-11 "35 Math Libraries / IEEE Double-Precision Transcendental Math Library" The IEEE double-precision transcendental math library contains entries for the transcendental math functions such as sine, cosine, and square root. The library resides on disk and is opened by calling @{"OpenLibrary()" link Libraries/Lib_17/17-5 15} with "mathieeedoubtrans.library" as the argument. Do not share the library base pointer between tasks -- @{"see note" link MAIN 12} at beginning of chapter for details. #include #include #include struct Library *MathIeeeDoubTransBase; VOID main() { if (MathIeeeDoubTransBase = OpenLibrary("mathieeedoubtrans.library",34)) { . . . CloseLibrary(MathIeeeDoubTransBase); } else printf("Can't open mathieeedoubtrans.library\\n"); } The global variable MathIeeeDoubTransBase is used internally for all future library references. The IEEE double-precision transcendental math library is dependent upon the IEEE double-precision basic math library, which it will open if it is not open already. If you want to use the IEEE double-precision basic math functions in conjunction with the transcendental math functions however, you have to specifically open the basic math library yourself. Just as the IEEE double-precision basic math library, the IEEE double-precision transcendental math library will take advantage of a 680X0/68881 combination or another math resource, if present. @{" DP IEEE Transcendental Functions " link 35-11-1} @ENDNODE @NODE 35-11-1 "35 / / DP IEEE Transcendental Functions" @{"IEEEDPAsin()" link AutoDocs/mathieeedoubtrans/IEEEDPAsin()} DOUBLE IEEEDPAsin( DOUBLE parm ); Return arcsine of IEEE variable. @{"IEEEDPAcos()" link AutoDocs/mathieeedoubtrans/IEEEDPAcos()} DOUBLE IEEEDPAcos( DOUBLE parm ); Return arccosine of IEEE variable. @{"IEEEDPAtan()" link AutoDocs/mathieeedoubtrans/IEEEDPAtan()} DOUBLE IEEEDPAtan( DOUBLE parm ); Return arctangent of IEEE variable. @{"IEEEDPSin()" link AutoDocs/mathieeedoubtrans/IEEEDPSin()} DOUBLE IEEEDPSin( DOUBLE parm ); Return sine of IEEE variable. This function accepts an IEEE radian argument and returns the trigonometric sine value. @{"IEEEDPCos()" link AutoDocs/mathieeedoubtrans/IEEEDPCos()} DOUBLE IEEEDPCos( DOUBLE parm ); Return cosine of IEEE variable. This function accepts an IEEE radian argument and returns the trigonometric cosine value. @{"IEEEDPTan()" link AutoDocs/mathieeedoubtrans/IEEEDPTan()} DOUBLE IEEEDPTan( DOUBLE parm ); Return tangent of IEEE variable. This function accepts an IEEE radian argument and returns the trigonometric tangent value. @{"IEEEDPSincos()" link AutoDocs/mathieeedoubtrans/IEEEDPSincos()} DOUBLE IEEEDPSincos( DOUBLE *pf2, DOUBLE parm ); Return sine and cosine of IEEE variable. This function accepts an IEEE radian argument and returns the trigonometric sine as its result and the trigonometric cosine in the first parameter. @{"IEEEDPSinh()" link AutoDocs/mathieeedoubtrans/IEEEDPSinh()} DOUBLE IEEEDPSinh( DOUBLE parm ); Return hyperbolic sine of IEEE variable. @{"IEEEDPCosh()" link AutoDocs/mathieeedoubtrans/IEEEDPCosh()} DOUBLE IEEEDPCosh( DOUBLE parm ); Return hyperbolic cosine of IEEE variable. @{"IEEEDPTanh()" link AutoDocs/mathieeedoubtrans/IEEEDPTanh()} DOUBLE IEEEDPTanh( DOUBLE parm ); Return hyperbolic tangent of IEEE variable. @{"IEEEDPExp()" link AutoDocs/mathieeedoubtrans/IEEEDPExp()} DOUBLE IEEEDPExp( DOUBLE parm ); Return e to the IEEE variable power. This function accept an IEEE argument and returns the result representing the value of e (2.712828...) raised to that power. @{"IEEEDPFieee()" link AutoDocs/mathieeedoubtrans/IEEEDPFieee()} DOUBLE IEEEDPFieee( FLOAT single ); Convert IEEE single-precision number to IEEE double-precision number. @{"IEEEDPLog()" link AutoDocs/mathieeedoubtrans/IEEEDPLog()} DOUBLE IEEEDPLog( DOUBLE parm ); Return natural log (base e of IEEE variable. @{"IEEEDPLog10()" link AutoDocs/mathieeedoubtrans/IEEEDPLog10()} DOUBLE IEEEDPLog10( DOUBLE parm ); Return log (base 10) of IEEE variable. @{"IEEEDPPow()" link AutoDocs/mathieeedoubtrans/IEEEDPPow()} DOUBLE IEEEDPPow( DOUBLE exp, DOUBLE arg ); Return IEEE arg2 to IEEE arg1. @{"IEEEDPSqrt()" link AutoDocs/mathieeedoubtrans/IEEEDPSqrt()} DOUBLE IEEEDPSqrt( DOUBLE parm ); Return square root of IEEE variable. @{"IEEEDPTieee()" link AutoDocs/mathieeedoubtrans/IEEEDPTieee()} FLOAT IEEEDPTieee( DOUBLE parm ); Convert IEEE double-precision number to IEEE single-precision number. Be sure to include proper data type definitions as shown below. @{" mathieeedoubtrans.c " link lib_examples/mathieeedoubtrans.c/MAIN} The section below describes the Amiga assembly interface to the IEEE double-precision transcendental math library. The access mechanism from assembly language is: MOVEA.L _MathIeeeDoubTransBase,A6 JSR _LVOIEEEDPAsin(A6) _______________________________________________________________________ | | | DP IEEE Transcendental Assembly Functions | | | | Function Input Output Condition Codes | |_______________________________________________________________________| | | | | | | _LVOIEEEDPAsin | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | | arcsine radian | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPAcos | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | | arccosine radian | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPAtan | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | | arctangent radian | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPSin | D0/D1=IEEE arg | D0/D1=IEEE sine | N=undefined | | | in radians | | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPCos | D0/D1=IEEE arg | D0/D1=IEEE cosine | N=undefined | | | in radians | | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPTan | D0/D1=IEEE arg | D0/D1=IEEE tangent | N=undefined | | | in radians | | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPSincos | A0=Address to | D0/D1=IEEE sine | N=undefined | | | store cosine | (A0)=IEEE cosine | Z=undefined | | | result | | V=undefined | | | D0/D1=IEEE arg | | C=undefined | | | in radians | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPSin | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | in radians | hyperbolic sine | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPCosh | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | in radians | hyperbolic cosine | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPTanh | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | in radians | hyperbolic tangent | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPExp | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | | exponential | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPLog | D0/D1=IEEE arg | D0/D1=IEEE natural | N=undefined | | | | logarithm | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPLog10 | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | | logarithm | Z=undefined | | | | (base 10) | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPPow | D0/D1=IEEE exp | D0/D1=IEEE | N=undefined | | | D2/D3=IEEE arg | of arg taken to | Z=undefined | | | | exp power | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPSqrt | D0/D1=IEEE arg | D0/D1=IEEE | N=undefined | | | | square root | Z=undefined | | | | | V=undefined | | | | | C=undefined | | | | | X=undefined | |------------------|----------------|---------------------|-------------| | _LVOIEEEDPTieee | D0/D1=IEEE arg | D0=single-precision | N=undefined | | | | IEEE floating-point | Z=undefined | | | | format | V=undefined | | | | | C=undefined | | | | | X=undefined | |__________________|________________|_____________________|_____________| @ENDNODE @NODE 35-12 "35 Math Libraries / Function Reference" Here's a brief summary of the functions covered in this chapter. Refer to the Amiga ROM Kernel Reference Manual: Includes and Autodocs for additional information. _______________________________________________________________________ | | | FFP Basic Functions | |=======================================================================| | @{"SPAbs()" link AutoDocs/mathffp/SPAbs()} Take absolute value of FFP variable | | @{"SPAdd()" link AutoDocs/mathffp/SPAdd()} Add two FFP variables | | @{"SPCeil()" link AutoDocs/mathffp/SPCeil()} Compute least integer greater than or equal to variable. | | @{"SPCmp()" link AutoDocs/mathffp/SPCmp()} Compare two FFP variables | | @{"SPDiv()" link AutoDocs/mathffp/SPDiv()} Divide two FFP variables | | @{"SPFix()" link AutoDocs/mathffp/SPFix()} Convert FFP variable to integer | | @{"SPFloor()" link AutoDocs/mathffp/SPFloor()} Computer largest integer less than or equal to variable. | | @{"SPFlt()" link AutoDocs/mathffp/SPFlt()} Convert integer variable to FFP | | @{"SPMul()" link AutoDocs/mathffp/SPMul()} Multiply two FFP variables | | @{"SPNeg()" link AutoDocs/mathffp/SPNeg()} Take two's complement of FFP variable | | @{"SPSub()" link AutoDocs/mathffp/SPSub()} Subtract two FFP variables | | @{"SPTst()" link AutoDocs/mathffp/SPTst()} Test an FFP variable against zero | |_______________________________________________________________________| _______________________________________________________________________ | | | FFP Transcendental Functions | |=======================================================================| | @{"SPAcos()" link AutoDocs/mathtrans/SPAcos()} Return arccosine of FFP variable. | | @{"SPAsin()" link AutoDocs/mathtrans/SPAsin()} Return arcsine of FFP variable. | | @{"SPAtan()" link AutoDocs/mathtrans/SPAtan()} Return arctangent of FFP variable. | | @{"SPCos()" link AutoDocs/mathtrans/SPCos()} Return cosine of FFP variable. | | @{"SPCosh()" link AutoDocs/mathtrans/SPCosh()} Return hyperbolic cosine of FFP variable. | | @{"SPExp()" link AutoDocs/mathtrans/SPExp()} Return e to the FFP variable power. | | @{"SPFieee()" link AutoDocs/mathtrans/SPFieee()} Convert IEEE variable to FFP format. | | @{"SPLog()" link AutoDocs/mathtrans/SPLog()} Return natural log (base e) of FFP variable. | | @{"SPLog10()" link AutoDocs/mathtrans/SPLog10()} Return log (base 10) of FFP variable. | | @{"SPPow()" link AutoDocs/mathtrans/SPPow()} Return FFP arg2 to FFP arg1. | | @{"SPSin()" link AutoDocs/mathtrans/SPSin()} Return sine of FFP variable. | | @{"SPSincos()" link AutoDocs/mathtrans/SPSincos()} Return sine and cosine of FFP variable. | | @{"SPSinh()" link AutoDocs/mathtrans/SPSinh()} Return hyperbolic sine of FFP variable. | | @{"SPSqrt()" link AutoDocs/mathtrans/SPSqrt()} Return square root of FFP variable. | | @{"SPTan()" link AutoDocs/mathtrans/SPTan()} Return tangent of FFP variable. | | @{"SPTanh()" link AutoDocs/mathtrans/SPTanh()} Return hyperbolic tangent of FFP variable. | | @{"SPTieee()" link AutoDocs/mathtrans/SPTieee()} Convert FFP variable to IEEE format | |_______________________________________________________________________| _______________________________________________________________________ | | | Math Support Functions | |=======================================================================| | @{"afp()" link AutoDocs/amiga_lib/afp()} Convert ASCII string into FFP equivalent. | | @{"fpa()" link AutoDocs/amiga_lib/fpa()} Convert FFP variable into ASCII equivalent. | | @{"arnd()" link AutoDocs/amiga_lib/arnd()} Round ASCII representation of FFP number. | | @{"dbf()" link AutoDocs/amiga_lib/dbf()} Convert FFP dual-binary number to FFP equivalent. | |_______________________________________________________________________| _______________________________________________________________________ | | | SP IEEE Basic Functions (V36) | |=======================================================================| | @{"IEEESPAbs()" link AutoDocs/mathieeesingbas/IEEESPAbs()} Take absolute value of IEEE single-precision variable. | | @{"IEEESPAdd()" link AutoDocs/mathieeesingbas/IEEESPAdd()} Add two IEEE single-precision variables. | | @{"IEEESPCeil()" link AutoDocs/mathieeesingbas/IEEESPCeil()} Compute least integer greater than or equal to | | variable. | | @{"IEEESPCmp()" link AutoDocs/mathieeesingbas/IEEESPCmp()} Compare two IEEE single-precision variables. | | @{"IEEESPDiv()" link AutoDocs/mathieeesingbas/IEEESPDiv()} Divide two IEEE single-precision variables. | | @{"IEEESPFix()" link AutoDocs/mathieeesingbas/IEEESPFix()} Convert IEEE single-precision variable to integer. | | @{"IEEESPFloor()" link AutoDocs/mathieeesingbas/IEEESPFloor()} Compute largest integer less than or equal to | | variable. | | @{"IEEESPFlt()" link AutoDocs/mathieeesingbas/IEEESPFlt()} Convert integer variable to IEEE single-precision. | | @{"IEEESPMul()" link AutoDocs/mathieeesingbas/IEEESPMul()} Multiply two IEEE single-precision variables. | | @{"IEEESPNeg()" link AutoDocs/mathieeesingbas/IEEESPNeg()} Take two's complement of IEEE single-precision | | variable. | | @{"IEEESPSub()" link AutoDocs/mathieeesingbas/IEEESPSub()} Subtract two IEEE single-precision variables. | | @{"IEEESPTst()" link AutoDocs/mathieeesingbas/IEEESPTst()} Test an IEEE single-precision variable against zero. | |_______________________________________________________________________| _______________________________________________________________________ | | | SP IEEE Transcendental Functions (V36) | |=======================================================================| | @{"IEEESPACos()" link AutoDocs/mathieeesingtrans/IEEESPACos()} Return arccosine of IEEE single-precision variable. | | @{"IEEESPASin()" link AutoDocs/mathieeesingtrans/IEEESPASin()} Return arcsine of IEEE single-precision variable. | | @{"IEEESPAtan()" link AutoDocs/mathieeesingtrans/IEEESPAtan()} Return arctangent of IEEE single-precision variable. | | @{"IEEESPCos()" link AutoDocs/mathieeesingtrans/IEEESPCos()} Return cosine of IEEE single-precision variable. | | @{"IEEESPCosh()" link AutoDocs/mathieeesingtrans/IEEESPCosh()} Return hyperbolic cosine of IEEE single-precision | | variable. | | @{"IEEESPExp()" link AutoDocs/mathieeesingtrans/IEEESPExp()} Return e to the IEEE variable power. | | @{"IEEESPLog()" link AutoDocs/mathieeesingtrans/IEEESPLog()} Return natural log (base e of IEEE single-precision | | variable. | | @{"IEEESPLog10()" link AutoDocs/mathieeesingtrans/IEEESPLog10()} Return log (base 10) of IEEE single-precision | | variable. | | @{"IEEESPPow()" link AutoDocs/mathieeesingtrans/IEEESPPow()} Return power of IEEE single-precision variable. | | @{"IEEESPSin()" link AutoDocs/mathieeesingtrans/IEEESPSin()} Return sine of IEEE single-precision variable. | | @{"IEEESPSincos()" link AutoDocs/mathieeesingtrans/IEEESPSincos()} Return sine and cosine of IEEE single-precision | | variable. | | @{"IEEESPSinh()" link AutoDocs/mathieeesingtrans/IEEESPSinh()} Return hyperbolic sine of IEEE single-precision | | variable. | | @{"IEEESPSqrt()" link AutoDocs/mathieeesingtrans/IEEESPSqrt()} Return square root of IEEE single-precision variable. | | @{"IEEESPTan()" link AutoDocs/mathieeesingtrans/IEEESPTan()} Return tangent of IEEE single-precision variable. | | @{"IEEESPTanh()" link AutoDocs/mathieeesingtrans/IEEESPTanh()} Return hyperbolic tangent of IEEE single-precision | | variable. | |_______________________________________________________________________| _______________________________________________________________________ | | | DP IEEE Basic Functions | |=======================================================================| | @{"IEEEDPAbs()" link AutoDocs/mathieeedoubbas/IEEEDPAbs()} Take absolute value of IEEE double-precision variable. | | @{"IEEEDPAdd()" link AutoDocs/mathieeedoubbas/IEEEDPAdd()} Add two IEEE double-precision variables. | | @{"IEEEDPCeil()" link AutoDocs/mathieeedoubbas/IEEEDPCeil()} Compute least integer greater than or equal to | | variable. | | @{"IEEEDPCmp()" link AutoDocs/mathieeedoubbas/IEEEDPCmp()} Compare two IEEE double-precision variables. | | @{"IEEEDPDiv()" link AutoDocs/mathieeedoubbas/IEEEDPDiv()} Divide two IEEE double-precision variables. | | @{"IEEEDPFix()" link AutoDocs/mathieeedoubbas/IEEEDPFix()} Convert IEEE double-precision variable to integer. | | @{"IEEEDPFloor()" link AutoDocs/mathieeedoubbas/IEEEDPFloor()} Compute largest integer less than or equal to | | variable. | | @{"IEEEDPFlt()" link AutoDocs/mathieeedoubbas/IEEEDPFlt()} Convert integer variable to IEEE double-precision. | | @{"IEEEDPMul()" link AutoDocs/mathieeedoubbas/IEEEDPMul()} Multiply two IEEE double-precision variables. | | @{"IEEEDPNeg()" link AutoDocs/mathieeedoubbas/IEEEDPNeg()} Take two's complement of IEEE double-precision | | variable. | | @{"IEEEDPSub()" link AutoDocs/mathieeedoubbas/IEEEDPSub()} Subtract two IEEE single-precision variables. | | @{"IEEEDPTst()" link AutoDocs/mathieeedoubbas/IEEEDPTst()} Test an IEEE double-precision variable against zero. | |_______________________________________________________________________| _______________________________________________________________________ | | | DP IEEE Transcendental Functions | |=======================================================================| | @{"IEEEDPACos()" link AutoDocs/mathieeedoubtrans/IEEEDPACos()} Return arccosine of IEEE double-precision variable. | | @{"IEEEDPASin()" link AutoDocs/mathieeedoubtrans/IEEEDPASin()} Return arcsine of IEEE double-precision variable. | | @{"IEEEDPAtan()" link AutoDocs/mathieeedoubtrans/IEEEDPAtan()} Return arctangent of IEEE double-precision variable. | | @{"IEEEDPCos()" link AutoDocs/mathieeedoubtrans/IEEEDPCos()} Return cosine of IEEE double-precision variable. | | @{"IEEEDPCosh()" link AutoDocs/mathieeedoubtrans/IEEEDPCosh()} Return hyperbolic cosine of IEEE double-precision | | variable. | | @{"IEEEDPExp()" link AutoDocs/mathieeedoubtrans/IEEEDPExp()} Return e to the IEEE variable power. | | @{"IEEEDPFieee()" link AutoDocs/mathieeedoubtrans/IEEEDPFieee()} Convert IEEE single-precision number to IEEE | | double-precision number. | | @{"IEEEDPLog()" link AutoDocs/mathieeedoubtrans/IEEEDPLog()} Return natural log (base e of IEEE double-precision | | variable. | | @{"IEEEDPLog10()" link AutoDocs/mathieeedoubtrans/IEEEDPLog10()} Return log (base 10) of IEEE double-precision | | variable. | | @{"IEEEDPPow()" link AutoDocs/mathieeedoubtrans/IEEEDPPow()} Return power of IEEE double-precision variable. | | @{"IEEEDPSin()" link AutoDocs/mathieeedoubtrans/IEEEDPSin()} Return sine of IEEE double-precision variable. | | @{"IEEEDPSincos()" link AutoDocs/mathieeedoubtrans/IEEEDPSincos()} Return sine and cosine of IEEE double-precision | | variable. | | @{"IEEEDPSinh()" link AutoDocs/mathieeedoubtrans/IEEEDPSinh()} Return hyperbolic sine of IEEE double-precision | | variable. | | @{"IEEEDPSqrt()" link AutoDocs/mathieeedoubtrans/IEEEDPSqrt()} Return square root of IEEE double-precision variable. | | @{"IEEEDPTan()" link AutoDocs/mathieeedoubtrans/IEEEDPTan()} Return tangent of IEEE double-precision variable. | | @{"IEEEDPTanh()" link AutoDocs/mathieeedoubtrans/IEEEDPTanh()} Return hyperbolic tangent of IEEE double-precision | | variable. | | @{"IEEEDPTieee()" link AutoDocs/mathieeedoubtrans/IEEEDPTieee()} Convert IEEE double-precision number to IEEE | | single-precision number. | |_______________________________________________________________________| @ENDNODE @NODE 35-13 "35 Math Libraries / Compile and Link Commands for SAS C 5.10" FFP Basic, Transcendental and Math Support functions ---------------------------------------------------- lc -b1 -cfistq -ff -v -y .c blink lib:c.o + .o TO LIB lib:lcmffp.lib + lib:lc.lib + lib:amiga.lib IEEE Single-Precision and Double-Precision Basic and Transcendental Functions ------------------------------------------------------------------- lc -b1 -cfistq -fi -v -y .c blink lib:c.o + .o TO LIB lib:lcmieee.lib + lib:lc.lib + lib:amiga.lib @ENDNODE