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fpp.asm
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; TITLE '(C) COPYRIGHT R.T.RUSSELL 1986'
;
;Z80 FLOATING POINT PACKAGE
;(C) COPYRIGHT R.T.RUSSELL 1986
;VERSION 0.0, 26-10-1986
;VERSION 0.1, 14-12-1988 (BUG FIX)
;
;BINARY FLOATING POINT REPRESENTATION:
; 32 BIT SIGN-MAGNITUDE NORMALIZED MANTISSA
; 8 BIT EXCESS-128 SIGNED EXPONENT
; SIGN BIT REPLACES MANTISSA MSB (IMPLIED "1")
; MANTISSA=0 & EXPONENT=0 IMPLIES VALUE IS ZERO.
;
;BINARY INTEGER REPRESENTATION:
; 32 BIT 2'S-COMPLEMENT SIGNED INTEGER
; "EXPONENT" BYTE = 0 (WHEN PRESENT)
;
;NORMAL REGISTER ALLOCATION: MANTISSA - HLH'L'
; EXPONENT - C
;ALTERNATE REGISTER ALLOCATION: MANTISSA - DED'E'
; EXPONENT - B
;
;Error codes:
;
BADOP EQU 1 ;Bad operation code
DIVBY0 EQU 18 ;Division by zero
TOOBIG EQU 20 ;Too big
NGROOT EQU 21 ;Negative root
LOGRNG EQU 22 ;Log range
ACLOST EQU 23 ;Accuracy lost
EXPRNG EQU 24 ;Exp range
;
PUBLIC FPP
PUBLIC IMUL
PUBLIC IDIV
PUBLIC IBDIV
PUBLIC FMUL
PUBLIC INT
PUBLIC FDIV
PUBLIC SFLOAT
PUBLIC COPY
PUBLIC NUMTOSTR
PUBLIC SUB, FSUB, ABS
;
;Call entry and despatch code:
;
FPP: PUSH IY ;Save IY
LD IY,0
ADD IY,SP ;Save SP in IY
CALL OP ;Perform operation
CP A ;Good return (Z, NC)
EXIT: POP IY ;Restore IY
RET ;Return to caller
;
;Error exit:
;
BAD: LD A,BADOP ;"Bad operation code"
ERROR: LD SP,IY ;Restore SP from IY
OR A ;Set NZ
SCF ;Set C
JR EXIT
;
;Perform operation or function:
;
DEFC RTABLERNG = (RTABLE-DTABLE)/2
DEFC LTABLERNG = (FTABLE-DTABLE)/2
OP: CP RTABLERNG
JR NC,BAD
CP LTABLERNG
JR NC,DISPAT
EX AF,AF'
LD A,B
OR C ;Both integer?
CALL NZ,FLOATA ;No, so float both
EX AF,AF'
DISPAT: PUSH HL
LD HL,DTABLE
PUSH BC
ADD A,A ;A = op-code * 2
LD C,A
LD B,0 ;BC = op-code * 2
ADD HL,BC
LD A,(HL) ;Get low byte
INC HL
LD H,(HL) ;Get high byte
LD L,A
POP BC
EX (SP),HL
RET ;Off to routine
;
;Despatch table:
;
DTABLE: DEFW IAND ;AND (INTEGER)
DEFW IBDIV ;DIV
DEFW IEOR ;EOR
DEFW IMOD ;MOD
DEFW IOR ;OR
DEFW ILE ;<=
DEFW INE ;<>
DEFW IGE ;>=
DEFW ILT ;<
DEFW IEQ ;=
DEFW IMUL ;*
DEFW IADD ;+
DEFW IGT ;>
DEFW ISUB ;-
DEFW IPOW ;^
DEFW IDIV ;/
;
FTABLE: DEFW ABS ;ABS
DEFW ACS ;ACS
DEFW ASN ;ASN
DEFW ATN ;ATN
DEFW COS ;COS
DEFW DEG ;DEG
DEFW EXP ;EXP
DEFW INT ;INT
DEFW LN ;LN
DEFW LOG ;LOG
DEFW NOT ;NOT
DEFW RAD ;RAD
DEFW SGN ;SGN
DEFW SIN ;SIN
DEFW SQR ;SQR
DEFW TAN ;TAN
;
DEFW ZERO ;ZERO
DEFW FONE ;FONE
DEFW TRUE ;TRUE
DEFW PI ;PI
;
DEFW VAL ;VAL
DEFW NUMTOSTR ;STR$
;
DEFW SFIX ;FIX
DEFW SFLOAT ;FLOAT
;
DEFW FTEST ;TEST
DEFW FCOMP ;COMPARE
;
RTABLE: DEFW FAND ;AND (FLOATING-POINT)
DEFW FBDIV ;DIV
DEFW FEOR ;EOR
DEFW FMOD ;MOD
DEFW FOR ;OR
DEFW FLE ;<=
DEFW FNE ;<>
DEFW FGE ;>=
DEFW FLT ;<
DEFW FEQ ;=
DEFW FMUL ;*
DEFW FADD ;+
DEFW FGT ;>
DEFW FSUB ;-
DEFW FPOW ;^
DEFW FDIV ;/
;
;ARITHMETIC AND LOGICAL OPERATORS:
;All take two arguments, in HLH'L'C & DED'E'B.
;Output in HLH'L'C
;All registers except IX, IY destroyed.
; (N.B. FPOW destroys IX).
;
;FAND - Floating-point AND.
;IAND - Integer AND.
;
FAND: CALL FIX2
IAND: LD A,H
AND D
LD H,A
LD A,L
AND E
LD L,A
EXX
LD A,H
AND D
LD H,A
LD A,L
AND E
LD L,A
EXX
RET
;
;FEOR - Floating-point exclusive-OR.
;IEOR - Integer exclusive-OR.
;
FEOR: CALL FIX2
IEOR: LD A,H
XOR D
LD H,A
LD A,L
XOR E
LD L,A
EXX
LD A,H
XOR D
LD H,A
LD A,L
XOR E
LD L,A
EXX
RET
;
;FOR - Floating-point OR.
;IOR - Integer OR.
;
FOR: CALL FIX2
IOR: LD A,H
OR D
LD H,A
LD A,L
OR E
LD L,A
EXX
LD A,H
OR D
LD H,A
LD A,L
OR E
LD L,A
EXX
RET
;
;FMOD - Floating-point remainder.
;IMOD - Integer remainder.
;
FMOD: CALL FIX2
IMOD: LD A,H
XOR D ;DIV RESULT SIGN
BIT 7,H
EX AF,AF'
BIT 7,H
CALL NZ,NEGATE ;MAKE ARGUMENTS +VE
CALL SWAP
BIT 7,H
CALL NZ,NEGATE
LD B,H
LD C,L
LD HL,0
EXX
LD B,H
LD C,L
LD HL,0
LD A,-33
CALL DIVA ;DIVIDE
EXX
LD C,0 ;INTEGER MARKER
EX AF,AF'
RET Z
JP NEGATE
;
;BDIV - Integer division.
;
FBDIV: CALL FIX2
IBDIV: CALL IMOD
OR A
CALL SWAP
LD C,0
RET P
JP NEGATE
;
;ISUB - Integer subtraction.
;FSUB - Floating point subtraction with rounding.
;
ISUB: CALL SUB
RET PO
CALL ADD
CALL FLOAT2
FSUB: LD A,D
XOR 80H ;CHANGE SIGN THEN ADD
LD D,A
JR FADD
;
;Reverse subtract.
;
RSUB: LD A,H
XOR 80H
LD H,A
JR FADD
;
;IADD - Integer addition.
;FADD - Floating point addition with rounding.
;
IADD: CALL ADD
RET PO
CALL SUB
CALL FLOAT2
FADD: DEC B
INC B
RET Z ;ARG 2 ZERO
DEC C
INC C
JP Z,SWAP ;ARG 1 ZERO
EXX
LD BC,0 ;INITIALISE
EXX
LD A,H
XOR D ;XOR SIGNS
PUSH AF
LD A,B
CP C ;COMPARE EXPONENTS
CALL C,SWAP ;MAKE DED'E'B LARGEST
LD A,B
SET 7,H ;IMPLIED 1
CALL NZ,FIX ;ALIGN
POP AF
LD A,D ;SIGN OF LARGER
SET 7,D ;IMPLIED 1
JP M,FADD3 ;SIGNS DIFFERENT
CALL ADD ;HLH'L'=HLH'L'+DED'E'
CALL C,DIV2 ;NORMALISE
SET 7,H
JR FADD4
;
FADD3: CALL SUB ;HLH'L'=HLH'L'-DED'E'
CALL C,NEG ;NEGATE HLH'L'B'C'
CALL FLO48
CPL ;CHANGE RESULT SIGN
FADD4: EXX
EX DE,HL
LD HL,8000H
OR A ;CLEAR CARRY
SBC HL,BC
EX DE,HL
EXX
CALL Z,ODD ;ROUND UNBIASSED
CALL C,ADD1 ;ROUND UP
CALL C,INCC
RES 7,H
DEC C
INC C
JP Z,ZERO
OR A ;RESULT SIGNQ
RET P ;POSITIVE
SET 7,H ;NEGATIVE
RET
;
;IDIV - Integer division.
;FDIV - Floating point division with rounding.
;
IDIV: CALL FLOAT2
FDIV: DEC B ;TEST FOR ZERO
INC B
LD A,DIVBY0
JP Z,ERROR ;"Division by zero"
DEC C ;TEST FOR ZERO
INC C
RET Z
LD A,H
XOR D ;CALC. RESULT SIGN
EX AF,AF' ;SAVE SIGN
SET 7,D ;REPLACE IMPLIED 1's
SET 7,H
PUSH BC ;SAVE EXPONENTS
LD B,D ;LOAD REGISTERS
LD C,E
LD DE,0
EXX
LD B,D
LD C,E
LD DE,0
LD A,-32 ;LOOP COUNTER
CALL DIVA ;DIVIDE
EXX
BIT 7,D
EXX
CALL Z,DIVB ;NORMALISE & INC A
EX DE,HL
EXX
SRL B ;DIVISOR/2
RR C
OR A ;CLEAR CARRY
SBC HL,BC ;REMAINDER-DIVISOR/2
CCF
EX DE,HL ;RESULT IN HLH'L'
CALL Z,ODD ;ROUND UNBIASSED
CALL C,ADD1 ;ROUND UP
POP BC ;RESTORE EXPONENTS
CALL C,INCC
RRA ;LSB OF A TO CARRY
LD A,C ;COMPUTE NEW EXPONENT
SBC A,B
CCF
JP CHKOVF
;
;IMUL - Integer multiplication.
;
IMUL: LD A,H
XOR D
EX AF,AF' ;SAVE RESULT SIGN
BIT 7,H
CALL NZ,NEGATE
CALL SWAP
BIT 7,H
CALL NZ,NEGATE
LD B,H
LD C,L
LD HL,0
EXX
LD B,H
LD C,L
LD HL,0
LD A,-33
CALL MULA ;MULTIPLY
EXX
LD C,191 ;PRESET EXPONENT
CALL TEST ;TEST RANGE
JR NZ,IMUL1 ;TOO BIG
BIT 7,D
JR NZ,IMUL1
CALL SWAP
LD C,D ;INTEGER MARKER
EX AF,AF'
RET P
JP NEGATE
;
IMUL1: DEC C
EXX
SLA E
RL D
EXX
RL E
RL D
EXX
ADC HL,HL
EXX
ADC HL,HL
JP P,IMUL1 ;NORMALISE
EX AF,AF'
RET M
RES 7,H ;POSITIVE
RET
;
;FMUL - Floating point multiplication with rounding.
;
FMUL: DEC B ;TEST FOR ZERO
INC B
JP Z,ZERO
DEC C ;TEST FOR ZERO
INC C
RET Z
LD A,H
XOR D ;CALC. RESULT SIGN
EX AF,AF'
SET 7,D ;REPLACE IMPLIED 1's
SET 7,H
PUSH BC ;SAVE EXPONENTS
LD B,H ;LOAD REGISTERS
LD C,L
LD HL,0
EXX
LD B,H
LD C,L
LD HL,0
LD A,-32 ;LOOP COUNTER
CALL MULA ;MULTIPLY
CALL C,MULB ;NORMALISE & INC A
EXX
PUSH HL
LD HL,8000H
OR A ;CLEAR CARRY
SBC HL,DE
POP HL
CALL Z,ODD ;ROUND UNBIASSED
CALL C,ADD1 ;ROUND UP
POP BC ;RESTORE EXPONENTS
CALL C,INCC
RRA ;LSB OF A TO CARRY
LD A,C ;COMPUTE NEW EXPONENT
ADC A,B
CHKOVF: JR C,CHKO1
JP P,ZERO ;UNDERFLOW
JR CHKO2
CHKO1: JP M,OFLOW ;OVERFLOW
CHKO2: ADD A,80H
LD C,A
JP Z,ZERO
EX AF,AF' ;RESTORE SIGN BIT
RES 7,H
RET P
SET 7,H
RET
;
;IPOW - Integer involution.
;
IPOW: CALL SWAP
BIT 7,H
PUSH AF ;SAVE SIGN
CALL NZ,NEGATE
IPOW0: LD C,B
LD B,32 ;LOOP COUNTER
IPOW1: CALL X2
JR C,IPOW2
DJNZ IPOW1
POP AF
EXX
INC L ;RESULT=1
EXX
LD C,H
RET
;
IPOW2: POP AF
PUSH BC
EX DE,HL
PUSH HL
EXX
EX DE,HL
PUSH HL
EXX
LD IX,0
ADD IX,SP
JR Z,IPOW4
PUSH BC
EXX
PUSH DE
EXX
PUSH DE
CALL SFLOAT
CALL RECIP
LD (IX+4),C
EXX
LD (IX+0),L
LD (IX+1),H
EXX
LD (IX+2),L
LD (IX+3),H
JR IPOW5
;
IPOW3: PUSH BC
EXX
SLA E
RL D
PUSH DE
EXX
RL E
RL D
PUSH DE
LD A,'*' & 0FH
PUSH AF
CALL COPY
CALL OP ;SQUARE
POP AF
CALL DLOAD5
CALL C,OP ;MULTIPLY BY X
IPOW5: POP DE
EXX
POP DE
EXX
LD A,C
POP BC
LD C,A
IPOW4: DJNZ IPOW3
POP AF
POP AF
POP AF
RET
;
FPOW0: POP AF
POP AF
POP AF
JR IPOW0
;
;FPOW - Floating-point involution.
;
FPOW: BIT 7,D
PUSH AF
CALL SWAP
CALL PUSH5
DEC C
INC C
JR Z,FPOW0
LD A,158
CP C
JR C,FPOW1
INC A
CALL FIX
EX AF,AF'
JP P,FPOW0
FPOW1: CALL SWAP
CALL LN0
CALL POP5
POP AF
CALL FMUL
JP EXP0
;
;Integer and floating-point compare.
;Result is TRUE (-1) or FALSE (0).
;
FLT: CALL FCP
JR ILT1
ILT: CALL ICP
ILT1: RET NC
JR TRUE
;
FGT: CALL FCP
JR IGT1
IGT: CALL ICP
IGT1: RET Z
RET C
JR TRUE
;
FGE: CALL FCP
JR IGE1
IGE: CALL ICP
IGE1: RET C
JR TRUE
;
FLE: CALL FCP
JR ILE1
ILE: CALL ICP
ILE1: JR Z,TRUE
RET NC
JR TRUE
;
FNE: CALL FCP
JR INE1
INE: CALL ICP
INE1: RET Z
JR TRUE
;
FEQ: CALL FCP
JR IEQ1
IEQ: CALL ICP
IEQ1: RET NZ
TRUE: LD HL,-1
EXX
LD HL,-1
EXX
XOR A
LD C,A
RET
;
;FUNCTIONS:
;
;Result returned in HLH'L'C (floating point)
;Result returned in HLH'L' (C=0) (integer)
;All registers except IY destroyed.
;
;ABS - Absolute value
;Result is numeric, variable type.
;
ABS: BIT 7,H
RET Z ;POSITIVE/ZERO
DEC C
INC C
JP Z,NEGATE ;INTEGER
RES 7,H
RET
;
;NOT - Complement integer.
;Result is integer numeric.
;
NOT: CALL SFIX
LD A,H
CPL
LD H,A
LD A,L
CPL
LD L,A
EXX
LD A,H
CPL
LD H,A
LD A,L
CPL
LD L,A
EXX
XOR A ;NUMERIC MARKER
RET
;
;PI - Return PI (3.141592654)
;Result is floating-point numeric.
;
PI: LD HL,490FH
EXX
LD HL,0DAA2H
EXX
LD C,81H
XOR A ;NUMERIC MARKER
RET
;
;DEG - Convert radians to degrees
;Result is floating-point numeric.
;
DEG: CALL FPI180
CALL FMUL
XOR A
RET
;
;RAD - Convert degrees to radians
;Result is floating-point numeric.
;
RAD: CALL FPI180
CALL FDIV
XOR A
RET
;
;180/PI
;
FPI180: CALL SFLOAT
LD DE,652EH
EXX
LD DE,0E0D3H
EXX
LD B,85H
RET
;
;SGN - Return -1, 0 or +1
;Result is integer numeric.
;
SGN: CALL TEST
OR C
RET Z ;ZERO
BIT 7,H
JP NZ,TRUE ;-1
CALL ZERO
JP ADD1 ;1
;
;VAL - Return numeric value of string.
;Input: ASCII string at IX
;Result is variable type numeric.
;
VAL: CALL SIGNQ
PUSH AF
CALL CON
POP AF
CP '-'
LD A,0 ;NUMERIC MARKER
RET NZ
DEC C
INC C
JP Z,NEGATE ;ZERO/INTEGER
LD A,H
XOR 80H ;CHANGE SIGN (FP)
LD H,A
XOR A
RET
;
;INT - Floor function
;Result is integer numeric.
;
INT: DEC C
INC C
RET Z ;ZERO/INTEGER
LD A,159
LD B,H ;B7=SIGN BIT
CALL FIX
EX AF,AF'
AND B
CALL M,ADD1 ;NEGATIVE NON-INTEGER
LD A,B
OR A
CALL M,NEGATE
XOR A
LD C,A
RET
;
;SQR - square root
;Result is floating-point numeric.
;
SQR: CALL SFLOAT
SQR0: BIT 7,H
LD A,NGROOT
JP NZ,ERROR ;"-ve root"
DEC C
INC C
RET Z ;ZERO
SET 7,H ;IMPLIED 1
BIT 0,C
CALL Z,DIV2 ;MAKE EXPONENT ODD
LD A,C
SUB 80H
SRA A ;HALVE EXPONENT
ADD A,80H
LD C,A
PUSH BC ;SAVE EXPONENT
EX DE,HL
LD HL,0
LD B,H
LD C,L
EXX
EX DE,HL
LD HL,0
LD B,H
LD C,L
LD A,-31
CALL SQRA ;ROOT
EXX
BIT 7,B
EXX
CALL Z,SQRA ;NORMALISE & INC A
CALL SQRB
OR A ;CLEAR CARRY
CALL DIVB
RR E ;LSB TO CARRY
LD H,B
LD L,C
EXX
LD H,B
LD L,C
CALL C,ADD1 ;ROUND UP
POP BC ;RESTORE EXPONENT
CALL C,INCC
RRA
SBC A,A
ADD A,C
LD C,A
RES 7,H ;POSITIVE
XOR A
RET
;
;TAN - Tangent function
;Result is floating-point numeric.
;
TAN: CALL SFLOAT
CALL PUSH5
CALL COS0
CALL POP5
CALL PUSH5
CALL SWAP
CALL SIN0
CALL POP5
CALL FDIV
XOR A ;NUMERIC MARKER
RET
;
;COS - Cosine function
;Result is floating-point numeric.
;
COS: CALL SFLOAT
COS0: CALL SCALE
INC E
INC E
LD A,E
JR SIN1
;
;SIN - Sine function
;Result is floating-point numeric.
;
SIN: CALL SFLOAT
SIN0: PUSH HL ;H7=SIGN
CALL SCALE
POP AF
RLCA
RLCA
RLCA
AND 4
XOR E
SIN1: PUSH AF ;OCTANT
RES 7,H
RRA
CALL PIBY4
CALL C,RSUB ;X=(PI/4)-X
POP AF
PUSH AF
AND 3
JP PO,SIN2 ;USE COSINE APPROX.
CALL PUSH5 ;SAVE X
CALL SQUARE ;PUSH X*X
CALL POLY
DEFW 0A8B7H ;a(8)
DEFW 3611H
DEFB 6DH
DEFW 0DE26H ;a(6)
DEFW 0D005H
DEFB 73H
DEFW 80C0H ;a(4)
DEFW 888H
DEFB 79H
DEFW 0AA9DH ;a(2)
DEFW 0AAAAH
DEFB 7DH
DEFW 0 ;a(0)
DEFW 0
DEFB 80H
CALL POP5
CALL POP5
CALL FMUL
JP SIN3
;
SIN2: CALL SQUARE ;PUSH X*X
CALL POLY
DEFW 0D571H ;b(8)
DEFW 4C78H
DEFB 70H
DEFW 94AFH ;b(6)
DEFW 0B603H
DEFB 76H
DEFW 9CC8H ;b(4)
DEFW 2AAAH
DEFB 7BH
DEFW 0FFDDH ;b(2)
DEFW 0FFFFH
DEFB 7EH
DEFW 0 ;b(0)
DEFW 0
DEFB 80H
CALL POP5
SIN3: POP AF
AND 4
RET Z
DEC C
INC C
RET Z ;ZERO
SET 7,H ;MAKE NEGATIVE
RET
;
;Floating-point one:
;
FONE: LD HL,0
EXX
LD HL,0
EXX
LD C,80H
RET
;
DONE: LD DE,0
EXX
LD DE,0
EXX
LD B,80H
RET
;
PIBY4: LD DE,490FH
EXX
LD DE,0DAA2H
EXX
LD B,7FH
RET
;
;EXP - Exponential function
;Result is floating-point numeric.
;
EXP: CALL SFLOAT
EXP0: CALL LN2 ;LN(2)
EXX
DEC E
LD BC,0D1CFH ;0.6931471805599453
EXX
PUSH HL ;H7=SIGN
CALL MOD48 ;"MODULUS"
POP AF
BIT 7,E
JR Z,EXP1
RLA
JP C,ZERO
LD A,EXPRNG
JP ERROR ;"Exp range"
;
EXP1: AND 80H
OR E
PUSH AF ;INTEGER PART
RES 7,H
CALL PUSH5 ;PUSH X*LN(2)
CALL POLY
DEFW 4072H ;a(7)
DEFW 942EH
DEFB 73H
DEFW 6F65H ;a(6)
DEFW 2E4FH
DEFB 76H
DEFW 6D37H ;a(5)
DEFW 8802H
DEFB 79H
DEFW 0E512H ;a(4)
DEFW 2AA0H
DEFB 7BH
DEFW 4F14H ;a(3)
DEFW 0AAAAH
DEFB 7DH
DEFW 0FD56H ;a(2)
DEFW 7FFFH
DEFB 7EH
DEFW 0FFFEH ;a(1)
DEFW 0FFFFH
DEFB 7FH
DEFW 0 ;a(0)
DEFW 0
DEFB 80H
CALL POP5
POP AF
PUSH AF
CALL P,RECIP ;X=1/X
POP AF
JP P,EXP4
AND 7FH
NEG
EXP4: ADD A,80H
ADD A,C
JR C,EXP2
JP P,ZERO ;UNDERFLOW
JR EXP3
EXP2: JP M,OFLOW ;OVERFLOW
EXP3: ADD A,80H
JP Z,ZERO
LD C,A
XOR A ;NUMERIC MARKER
RET
;
RECIP: CALL DONE