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Copy pathfpmath.asm
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517 lines (506 loc) · 13.6 KB
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;
; Floating-point mathematic routines for CP1610 processor
;
; by Oscar Toledo G.
; https://nanochess.org/
;
; Creation date: Sep/20/2025. Added fpsin and fpcos.
; Revision date: Oct/05/2025. Corrected bug in both fpsin and fpcos. Added fptan, fpln,
; fpexp, fpsqrt, fparctan, and fppow.
;
; These routines are based on the mathematic routines
; I made for my Pascal compiler for transputer.
; https://nanochess.org/pascal.html
;
; sin function
;
; r0,r1 = Floating-point value
;
fpsin: PROC
PSHR R5
MVII #$45f3,R2
MVII #$183E,R3
CALL fpmul
PSHR R0
PSHR R1
MVII #$0000,R2
MVII #$003F,R3
CALL fpadd
CALL fpdivby2
CALL fpdivby2
CALL fpfloor
CALL fpmulby2
CALL fpmulby2
MOVR R0,R2
MOVR R1,R3
PULR R1
PULR R0
CALL fpsub
PSHR R0
PSHR R1
MVII #$0000,R2
MVII #$003F,R3
CALL fpcomp
PULR R1
PULR R0
BNC @@1
MOVR R0,R2
MOVR R1,R3
MVII #$0000,R0
MVII #$0040,R1
CALL fpsub
@@1:
PSHR R0
PSHR R1
MOVR R0,R2
MOVR R1,R3
CALL fpmul
CALL fpmulby2
MVII #$0000,R2
MVII #$003F,R3
CALL fpsub
PSHR R0
PSHR R1
MVII #$CC9C,R2
MVII #$C4A7,R3
CALL fpmul
MVII #$3E15,R2
MVII #$F62E,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$1E5F,R2
MVII #$DEB4,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$2a9f,R2
MVII #$b439,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$23b0,R2
MVII #$34bd,R3
CALL fpadd
PULR R3
PULR R2
CALL fpmul
MVII #$4464,R2
MVII #$bc3f,R3
CALL fpadd
PULR R3
PULR R2
CALL fpmul
PULR PC
ENDP
;
; cos function
;
; r0,r1 = floating-point value
;
fpcos: PROC
PSHR R5
MVII #$921F,R2
MVII #$9E3F,R3
CALL fpadd
PULR R5
B fpsin
ENDP
;
; tan function
;
; r0,r1 = floating-point value
;
fptan: PROC
PSHR R5
PSHR R0
PSHR R1
CALL fpcos
PULR R3
PULR R2
PSHR R0
PSHR R1
MOVR R2,R0
MOVR R3,R1
CALL fpsin
PULR R3
PULR R2
CALL fpdiv
PULR PC
ENDP
;
; sqrt function
;
; r0,r1 = floating-point value
;
fpsqrt: PROC
PSHR R5
CALL fpln ; ln
CALL fpdivby2 ; * 0.5
CALL fpexp ; exp
PULR PC
ENDP
;
; pow function
;
; r0,r1 = number.
; r2,r3 = power.
;
fppow: PROC
PSHR R5
PSHR R2
PSHR R3
CALL fpln ; ln
PULR R3
PULR R2
CALL fpmul
CALL fpexp ; exp
PULR PC
ENDP
;
; ln function
;
fpln: PROC
PSHR R5
MOVR R1,R2
ANDI #$80,R2
BEQ @@1
CLRR R0
CLRR R1
PULR PC
@@1:
MOVR R1,R2
ANDI #$7F,R2
BEQ @@0
SUBI #FPEXP_BIAS-1,R2
PSHR R2
ANDI #$FF00,R1
ADDI #$003E,R1 ; Now number is in the range 0.5-0.99
PSHR R0
PSHR R1
MVII #$6a09,R2
MVII #$e63e,R3
CALL fpsub
PULR R3
PULR R2
PSHR R0
PSHR R1
MVII #$6a09,R0
MVII #$e63e,R1
CALL fpadd
MOVR R0,R2
MOVR R1,R3
PULR R1
PULR R0
CALL fpdiv
PSHR R0
PSHR R1
MOVR R0,R2
MOVR R1,R3
CALL fpmul
MVII #$2387,R2
MVII #$583D,R3
PSHR R0
PSHR R1
CALL fpmul
MVII #$476F,R2
MVII #$3C3D,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$A61B,R2
MVII #$4C3D,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$2776,R2
MVII #$C03E,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$EC70,R2
MVII #$9C3E,R3
CALL fpadd
PULR R3
PULR R2
CALL fpmul
MVII #$7154,R2
MVII #$7640,R3
CALL fpadd
PULR R3
PULR R2
CALL fpmul
MVII #$0000,R2
MVII #$00BE,R3
CALL fpadd
@@test:
PULR R4
PSHR R0
PSHR R1
MOVR R4,R0
CALL fpfromint
PULR R3
PULR R2
CALL fpadd ; Add exponent.
MVII #$62E4,R2 ; 1 / 1.442695
MVII #$313E,R3 ; precision is important here.
CALL fpmul
@@0:
PULR PC
ENDP
;
; exp function
;
fpexp: PROC
PSHR R5
MVII #$7154,R2 ; 1.442695
MVII #$753F,R3 ; precision is important here.
CALL fpmul
PSHR R0
PSHR R1
CALL fp2int
MOVR R0,R4
CALL fpfromint
MOVR R0,R2
MOVR R1,R3
PULR R1
PULR R0
PSHR R4
CALL fpsub
PSHR R0
PSHR R1
MVII #$2AAC,R2
MVII #$8A28,R3
CALL fpmul
MVII #$4F25,R2
MVII #$402B,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$0127,R2
MVII #$dc2f,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$42f1,R2
MVII #$4e32,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$5d89,R2
MVII #$0435,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$3b2a,R2
MVII #$b038,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$c6b0,R2
MVII #$8c3a,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$ebfb,R2
MVII #$de3c,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$62e4,R2
MVII #$2e3e,R3
CALL fpadd
PULR R3
PULR R2
CALL fpmul
MVII #$0000,R2
MVII #$003F,R3
CALL fpadd
PULR R4
ADDR R4,R1
PULR PC
ENDP
;
; arctan function
;
fparctan: PROC
PSHR R5
MOVR R1,R2
ANDI #$80,R2
PSHR R2
ANDI #$FF7F,R1 ; Make it positive (fpabs)
PSHR R0
PSHR R1
MVII #$0000,R2
MVII #$003F,R3
CALL fpcomp
PULR R1
PULR R0
BEQ @@1
BNC @@1
MVII #1,R2
PSHR R2
MOVR R0,R2
MOVR R1,R3
MVII #$0000,R0
MVII #$003F,R1
CALL fpdiv
B @@2
@@1: CLRR R2
PSHR R2
@@2:
PSHR R0
PSHR R1
MOVR R0,R2
MOVR R1,R3
CALL fpmul
PSHR R0
PSHR R1
MVII #$C5FD,R2
MVII #$7433,R3
CALL fpmul
MVII #$ADB1,R2
MVII #$9CB6,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$7DA2,R2
MVII #$FA38,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$AF88,R2
MVII #$46B9,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$682E,R2
MVII #$143A,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$EF03,R2
MVII #$46BA,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$335C,R2
MVII #$C23B,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$72C1,R2
MVII #$1EBB,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$C6E4,R2
MVII #$243B,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$248F,R2
MVII #$F6BC,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$9999,R2
MVII #$7E3C,R3
CALL fpadd
PULR R3
PULR R2
PSHR R2
PSHR R3
CALL fpmul
MVII #$5555,R2
MVII #$54BD,R3
CALL fpadd
PULR R3
PULR R2
CALL fpmul
MVII #$FFFF,R2
MVII #$FE3E,R3
CALL fpadd
PULR R3
PULR R2
CALL fpmul
PULR R4
TSTR R4
BEQ @@3
MOVR R0,R2
MOVR R1,R3
MVII #$921F,R0
MVII #$B43F,R1
CALL fpsub
@@3: PULR R4
TSTR R4
BEQ @@4
XORI #$0080,R1
@@4: PULR PC
ENDP