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Text File | 1988-11-02 | 15.9 KB | 389 lines

\ SFLOAT3 Third part of Software Floating-Point Package. \ \ (c) Copyright 1988 by Robert L. Smith \ 2300 St Francis Dr. \ Palo Alto, CA 94303 \ (415)856-9321 \ \ Permission is granted to use this package or its derivatives for \ private use. For permission to use it in programs or packages \ sold for profit, please contact the author. \ 1GEXPTAB \ HIDDEN Table of (1 - e**(k/16)) for k <= 0 Table of (e**(k/16) - 1) for k >= 0 GEXPTAB ( -- addr ) \ HIDDEN Points to center of 1GEXPTAB. Y**2 \ HIDDEN Label for code subroutine for squaring the argument in (BX,CX). FRACT* \ HIDDEN Label for code subroutine to multiply two 32 bit floating point fractions. GEXP1- \ HIDDEN Auxiliary function for exp(x) -1. GEXP1 ( F: r1 -- r2 ) \ HIDDEN Auxilliary function for exp(x) for small arguments x < 2^-4 FNORMALIZE ( F: ur1 -- r2 ) Normalize the unnormalized floating point number at the top of the stack. >INTFRACT ( F: r1 -- r2 ; -- int ) Convert a floating point number into an integer and a real number fractional part. Note that r2 may not be normalized. FLOOR ( F: r -- ; -- n ) Convert the floating point number to the largest integer less than or equal to the floating point number. CEILING ( F: r -- ; -- n ) Convert the floating point number to the smallest integer not less than the floating point number. GEXPTAB@ ( F: -- r ; n -- ) \ HIDDEN Fetch a floating point number from the EXPTAB indexed by the integer at the top of the stack. AUX- ( F: r1 -- r2 ; n -- ) \ HIDDEN Auxilliary tables for calculating the exponential function. Auxiliary function used with FEXP AUX+ ( F: r1 -- r2 ; n -- ) \ HIDDEN Auxiliary function used with FEXP GEXP0 ( F: r1 -- r2 ; -- n ) \ HIDDEN Auxiliary function used with FEXP GEXPLN2 ( F: r1 -- r2 ; -- n ) \ HIDDEN Auxiliary function used with FEXP FEXP ( F: r1 -- r2 ) Floating point exponential function e^x FALN ( F: r1 -- r2 ) \ FVG Required Alternative name for the exponential function. This is the name specified in the FVG Standard Floating Point Extension. F** ( F: r1 +r2 -- r3 ) \ FVG Required Leave the value of r1 raised to the power +r2. Note that +r2 must be non-negative, even if it converts exactly to an integer. FALOG ( F: r1 -- r2 ) \ FVG Required Take the inverse log of r1, i.e., raise 10 to the power of r1. F2** ( F: -- r ; n -- ) \ HIDDEN Return a floating point value of 2 raised to the specified power. F2**N-1 ( F: -- r ; n -- ) \ HIDDEN Return a floating point number of 1 less than 2 raised to the specified power. FEXP-1 ( F: r1 -- r2 ) \ ( e**x - 1 ) \ HIDDEN (e^x) - 1. FSINH1 ( F: r1 -- r2 ) \ HIDDEN Hyperbolic sin of a positive argument. FSINH ( F: r1 -- r2 ) \ FVG Optional Hyberbolic sin function. FCOSH ( F: r1 -- r2 ) \ FVG Optional Hyperbolic cosine function. FTANH1 ( F: r1 -- r2 ) \ HIDDEN Hyperbolic tangent function of a positive argument. FTANH ( F: r1 -- r2 ) \ FVG Optional Hyperbolic tangent function. F1.0E10 ( F: -- r ) Return a floating point constant of 10^10 . F0.5 ( F: -- r ) Return a floating point constant of value 0.5 . T# ( t1 -- t2 ) Convert the least significant digit of the triple number t1 to an ASCII character and put it in the numeric output buffer. The remaining value of the number replaces t1 on the stack. TDUP0= ( t -- t flag ) Push a flag of -1 on the stack if the triple number t is zero. Otherwise push a value of 0. The triple number is left unchanged. FPARTS ( F: r -- ; t sign exp ) Convert a floating point number to a triple precision integer, the sign of the number, and a power of ten. (E.) ( F: r -- ; -- addr cnt ) Convert a floating point number to an address and count suitable to be typed. The output is in exponential format. E. ( F: r -- ) \ FVG Required Print a floating point number in exponential (power of ten) format. E.R ( F: r -- ; n1 n2 ) \ FVG Optional Display the floating point number r on the currently selected output device in exponential form with n1 digits to the right of the decimal point, right justified in a field of width n2. F#PLACES ( -- n ) \ FVG Optional A constant leaving the maximum number of significant digits when a real number is converted to its decimal ASCII equivalent for display. PLACES ( n -- ) \ FVG Required Set the default number of digits that will be printed to the right of the decimal point by the F. operator. The argument will be limited to the range 0 to 10. Default value is 10. (F.FRACT) ( F: r -- #pl ) \ HIDDEN An auxilliary function for F. and F.R to convert the digits to the right of the decimal point in a form suitable for display. (F.INT1) ( F: r -- ; sign -- addr cnt ) \ HIDDEN An auxilliary function for F.R . HOLDBL ( n -- ) \ HIDDEN An auxilliary function to a spaces to the output string for F.R . (F.INT2) \ HIDDEN An auxilliary function for use with F.R (F.INTR) \ HIDDEN Another auxilliary function for F.R (F.1) ( F: r1 -- r2 r3 ; #pl -- sign flag ) An auxilliary function for use with F. and F.R for printing the fractional part of a floating point number. F. ( F: r -- ) \ FVG Required Display the floating point number on the currently selected output device in fixed-point form; i.e., the location of the decimal point is adjusted so that no exponent need be displayed. The number of digits to the right of the decimal point specified by the most recent execution of the word PLACES are printed to the right of the decimal point. A trailing blank follows. For example, 4 PLACES 1.2345E02 F. will display as 123.4500b (where the "b" denotes an ASCII blank). If the number of digits to the left of the decimal point is greater than 14, the error routine is called. F.R ( F: r -- ; n1 n2 ) \ FVG Optional Display r on the currently selected output device in fixed point form with n1 digits to the right of the decimal place, right justified in a field of width n2. If the number cannot be represented within the given field width, the error routine is called and the value is printed in exponent form. For example, 1.2345e2 4 12 F.R will display as bbbb123.4500 (where each "b" character denotes an ASCII blank). ?FSTACK ( F: -- ) Check the floating point stack for overflow or underflow. Display an error message if appropriate. .FS ( F: -- ) Display the number of items on the floating point stack, and display the top four numbers in exponent form. If the stack is less than 4 deep, display the actual number present. The floating point stack is left unchanged by this operation. UNPACK ( F: r -- ; -- d n ) \ FVG Optional Convert a floating point number to a double precision integer amd a power of 10. FASINH ( F: r1 -- r2 ) \ FVG Optional Inverse hyperbolic sin function. FACOSH ( F: r1 -- r2 ) \ FVG Optional Inverse hyperbolic cosine function. FATANH ( F: r1 -- r2 ) \ FVG Optional Inverse hyperbolic tangent function. UMT* ( ut1 n -- ut2 ) Multiply a triple number by a single. TS+ ( ut1 n -- ut2 ) Add a single precision number to a triple. TCONVERT ( ut1 adr1 -- ut2 adr2 ) Similiar to CONVERT. Fetches convertable digits from the specified address and converts the digits according to BASE until a non-digit is encountered. addr2 points to the unconvertable character. TFLOAT ( F: -- r ; ut -- ) Float a triple precision unsigned number. VARIABLE FPT 0 FPT ! FLTS ( -- addr ) A variable containing a flag. If the flag is non-zero, numbers which have an imbedded decimal point or comma are treated as floating point values. Otherwise, the numbers are treated as double numbers. FLOATS ( -- ) Set the flag FLTS . Allows floating point numbers to be input using imbedded decimal points and optional exponent fields. For example: FLOATS 1.234 -5.4 will produce two floating point numbers. Note, however, that a single precision integer, such as 7 , will remain a single precision integer, and a double number with a terminating decimal point, such as 1234. , will remain a double number. DOUBLES ( -- ) Clear the FLTS flag so that the usual rules for double numbers applies. PACK ( F: -- r ; d n -- ) \ FVG Optional Convert a double integer and a power of 10 to a floating point number. -NUMBER ( adr1 -- adr2 flag ) Fetch next charcter from string at adr1. If character is an ASCII - (minus) sign, return the incremented address and a flag of -1. If the character is not an ASCII "-", don't increment the address, and return a flag of 0. 1FNUMBER ( F: -- r ; ut adr -- -1 ) \ or ( ut adr -- 0 ) if not convertable. Attempt to convert the string specified by adr to a floating point number. If the result is successful, return the number and a -1 flag on the stack. If the attempt fails, return a zero on the stack. Note that ut is an unsigned triple precision number. (FNUMBER?) ( F: -- r ; adr -- -1) \ (adr -- d 1 ) \ ( adr -- 0 ) Attempt to convert the string at adr into either a floating point number or a double precision number, and return a flag. If the conversion process failed, return a flag of 0. If the string was converted into a floating point number, return the number and a flag of -1. If the string was converted into a double integer, return the value and a flag of 1. The value of FLTS (set by FLOATS or cleared by DOUBLES ) determines if a numeric string with an imbedded decimal point is a floating point number or a double number. FNUMBER ( F: -- r ; adr -- -1 ) \ ( adr -- d 1 ) Convert the string at the specified address into a real or integer number, with a flag of -1 or 1, respectively. If the number cannot be converted, print an error message. F# ( F: -- r ) Convert the string following F# into a floating point number. This includes numbers with or without decimal points. Thus F# 34 yields the equivalent of 34X0 . If SFLOAT is loaded, even if in NOFLOATING mode, F# still converts the following number and pushes it onto the floating point stack. #? ( number --- d 1 ) \ ( F: -- r ; number --- -1 ) If possible, convert the following word in the input stream into a number. If the string converts to a floating point number, the flag is set to -1 . If the string converts to an integer, the flag is set to 1. If the string cannot be converted, a standard error message is sent. (FLIT) ( F: -- r ) An in-line function to pick up an in-line literal (three words) and push onto the floating point stack. FLITERAL ( F: -- r ) Create an in-line literal. FINTERP ( -- ) A version of INTERPRET which recognizes floating point numbers. (F]) ( -- ) A version of the compiler, ] , which recognizes floating point number. DEFER OLD-INTERP \ HIDDEN A deferred word to hold the previous Interpreter. DEFER OLD-] \ HIDDEN A deferred word to hold the previous Compiler. OLD-?STACK \ HIDDEN A deferred word to hold the previous function which checks the stack. FLOATING ( -- ) Replace the current interpreter and compiler with the Floating Point version. This mostly affects the ability to enter floating point numbers. NOFLOATING ( -- ) Restore the previous interpreter and compiler. AUXTAN ( F: r1 -- ur2 ) \ ur2 is tan(x) - x , |x| < 2**-4 \ HIDDEN Auxilary tangent function. TANTAB ( -- addr ) \ HIDDEN Table of tan(i/16) for i = 0 to 12. GTAN0 ( F: r1 -- r2 r3 ) \ HIDDEN The tangent is the ratio of r2 to r3. GTAN1 ( F: r1 -- r2 r3 ; flag ) \ HIDDEN Return the tangent of r1 as a ratio of numbers r2 and r3. The flag is non-zero if r1 is sufficiently large that the quadrant cannot be determined. GTAN2 ( F: r1 -- r2 r3 ; -- flag1 flag2 ) \ HIDDEN Return the tangent of r1 as a ratio of numbers r2 and r3. Flag1 is non-zero if r1 is sufficiently large that the quadrant cannot be determined. Flag2 is non-zero if r3 = 0. FTAN ( F: r1 -- r2 ) \ FVG Required The input is a floating point number in radians. The output is is the tangent of the number. An error condition exists for sufficiently large input values. FSIN ( F: r1 -- r2 ) \ FVG Required Returns the sine of the input number in radians. Input and output values are floating point numbers. An error condition exists for sufficiently large input values. FCOS ( F: r1 -- r2 ) \ FVG Required Returns the cosine of the floating point argument in radians. An error condition exists for sufficiently large input arguments. AUXATAN ( F: r1 -- ur2 ) \ HIDDEN Auxilliary arctangent function for small positive numbers in the range 0 <= r1 < 2^-4 . ATANTAB ( -- addr ) \ HIDDEN A table of arctan (k/16), for k = 0 to 16. GATAN1 ( F: r1 -- r2 ) \ HIDDEN Auxilliary arctangent function for 0 <= r1 <= 1.0 GATAN2 ( F: r1 -- r2 ) \ HIDDEN Auxilliary arctangent function for positive arguments. FATAN ( F: r1 -- r2 ) \ FVG Required Returns a floating point value equal to the arctangent of the input argument. The result is expressed in radians. FASIN ( F: r1 -- r2 ) \ FVG Required Returns a floating point value equal to the arcsine of the input argument. The result is expressed in radians. If the input argument exceeds 1.0 in value, an error condition results. FACOS ( F: r1 -- r2 ) \ FVG Required Returns a floating point value equal to the arccosine of the input argument. The result is expressed in radians. If the input argument exceeds 1.0 in value, an error condition results. FTRIG0 ( F: r1 -- r2 ) Returns a floating point value equal to the square root of the absolute value of (1.0 - (r1^2)). This is a useful auxilliary function suggested in APL.