Merge branch 'master' into TAN

STATUS.md

@@ -253,10 +253,10 @@ Floating point mathematical routines - not official, but well known and broadly
 | `$E097`   | `rnd_FAC1`             | DONE     |                                                    |
 | `$E09A`   | `rnd_A`                | DONE     |                                                    |
 | `$E0BE`   | `rnd_generate`         | DONE     |                                                    |
-| `$E264`   | `cos_FAC1`             | PARTIAL  | needs `sin_FAC1`                                   |
+| `$E264`   | `cos_FAC1`             | PARTIAL  | not fully tested yet                               |
-| `$E26B`   | `sin_FAC1`             | NOT DONE | some work already started                          |
+| `$E26B`   | `sin_FAC1`             | PARTIAL  | not fully tested yet                               |
 | `$E2B4`   | `tan_FAC1`             | PARTIAL  | not fully tested yet                               |
-| `$E30E`   | `atn_FAC1`             | NOT DONE |                                                    |
+| `$E30E`   | `atn_FAC1`             | PARTIAL  | not fully tested yet                               |
 
 <br />
 

src/basic/,stubs_math/e26b.sin_FAC1.s

@@ -1,29 +0,0 @@
-;; #LAYOUT# STD *       #TAKE
-;; #LAYOUT# *   BASIC_0 #TAKE
-;; #LAYOUT# *   *       #IGNORE
-
-;
-; Math package - sine of FAC1 in radians
-;
-; See also:
-; - [CM64] Computes Mapping the Commodore 64 - page 210 - XXX address does not match
-; - https://www.c64-wiki.com/wiki/Floating_point_arithmetic
-; - https://codebase64.org/doku.php?id=base:kernal_floating_point_mathematics
-;
-
-; XXX provide implementation
-
-sin_FAC1:
-
-	+STUB_IMPLEMENTATION
-
-poly_sin:
-
-	!byte $05                          ; series length - 1
-
-	+PUT_CONST_POLY_SIN_1
-	+PUT_CONST_POLY_SIN_2
-	+PUT_CONST_POLY_SIN_3
-	+PUT_CONST_POLY_SIN_4
-	+PUT_CONST_POLY_SIN_5
-	+PUT_CONST_POLY_SIN_6

src/basic/math/FCOMP.s

@@ -12,7 +12,7 @@
 ;
 ; Output:
 ; - .A - $00 for equal, $01 for FAC1 > RAM, $FF for FAC1 < RAM
-; - flags N/Z, depending on whether FAC1 is 0, positive, or negative
+; - flags N/Z, Z=1 if equal, N=1 if FAC1 < RAM, Z=0, N=0 if FAC1 > RAM
 ;
 ; Notes:
 ; - uses vector at $24, leaves FAC1 and FAC2 unchanged (Codebase64)
@@ -28,9 +28,6 @@ FCOMP:
     sta INDEX+2
     sty INDEX+3
 
-    jsr sgn_FAC1_A          ; Set N/Z flag for FAC1 and store on stack
-    php
-
     ldy #$01
     lda (INDEX+2),Y
     eor FAC1_sign           ; Check if signs are different
@@ -69,7 +66,6 @@ FCOMP:
 
 FCOMP_equal:
     lda #$00
-    plp
     rts
 
 
@@ -78,7 +74,6 @@ FCOMP_less_than:
     bpl FCOMP_FF
 FCOMP_01:
     lda #$01
-    plp
     rts
     
 FCOMP_greater_than:
@@ -86,5 +81,4 @@ FCOMP_greater_than:
     bpl FCOMP_01
 FCOMP_FF:
     lda #$FF
-    plp
     rts

src/basic/math/e26b.sin_FAC1.s

@@ -0,0 +1,55 @@
+;; #LAYOUT# STD *       #TAKE
+;; #LAYOUT# *   BASIC_0 #TAKE
+;; #LAYOUT# *   *       #IGNORE
+
+;
+; Math package - sine of FAC1 in radians
+;
+; See also:
+; - [CM64] Computes Mapping the Commodore 64 - page 210 - XXX address does not match
+; - https://www.c64-wiki.com/wiki/Floating_point_arithmetic
+; - https://codebase64.org/doku.php?id=base:kernal_floating_point_mathematics
+; - https://www.c64-wiki.com/wiki/SIN
+
+
+
+sin_FAC1:
+
+    jsr mov_FAC1_FAC2               ; FAC1 <- X / (2*pi)     (X2)
+    ldy #>const_DOUBLE_PI
+    lda #<const_DOUBLE_PI
+    jsr mov_MEM_FAC1
+    jsr div_FAC2_FAC1
+
+    jsr mov_FAC1_FAC2               ; FAC2 <- X2
+    jsr int_FAC1                    ; FAC1 <- INT(X2)
+    jsr sub_FAC2_FAC1               ; FAC1 <- X2 - INT(X2)   (F)
+
+    ldy #>const_QUARTER
+    lda #<const_QUARTER
+    jsr FCOMP
+    bmi sin_next                    ; FAC1 < 0.25
+
+    ldy #>sin_three_quarters
+    lda #<sin_three_quarters
+    jsr FCOMP
+    bmi sin_q23                     ; FAC1 < 0.75
+
+    jsr mov_FAC1_FAC2               ; FAC1 <- FAC1 - 1.0
+    ldy #>const_ONE
+    lda #<const_ONE
+    jsr mov_MEM_FAC1
+    jsr sub_FAC2_FAC1
+    +bra sin_next
+
+sin_q23:
+    ldy #>const_HALF
+    lda #<const_HALF
+    jsr sub_MEM_FAC1                ; FAC1 <- 0.5 - FAC1
+
+    ; FALLTHROUGH
+    
+sin_next:
+    ldy #>poly_sin
+    lda #<poly_sin
+    jmp poly1_FAC1

src/basic/math/e30e.atn_FAC1.s

@@ -0,0 +1,57 @@
+;; #LAYOUT# STD *       #TAKE
+;; #LAYOUT# *   BASIC_0 #TAKE
+;; #LAYOUT# *   *       #IGNORE
+
+;
+; Math package - arc tangent of FAC1
+;
+; See also:
+; - [CM64] Computes Mapping the Commodore 64 - page 211
+; - https://www.c64-wiki.com/wiki/Floating_point_arithmetic
+; - https://codebase64.org/doku.php?id=base:kernal_floating_point_mathematics
+; - https://www.c64-wiki.com/wiki/ATN
+
+; Algorithm:
+; 1. Save sign of x
+; 2. Calculate AX = |x|   (we can use that arctan(-x) = -arctan(x)
+; 3. If AX > 1 set AX = 1/AX  (we can use that arctan(x) = pi/2 - arctan(1/x) )
+; 4. Use polynomial to approximate arctan(AX) now since 0 <= AX <= 1
+; 5. Adjust sign of result and offset with pi/2 if needed as per above
+
+
+atn_FAC1:
+    lda FAC1_sign               ; Save sign of FAC1 on the stack
+    pha
+    lda #$00                    ; FAC1 = abs(FAC1)
+    sta FAC1_sign
+    sta TEMPF1                  ; AX not scaled
+
+    lda #<const_ONE
+    ldy #>const_ONE
+    jsr FCOMP
+    bmi atn_skipscale
+
+    lda #<const_ONE
+    ldy #>const_ONE
+    jsr div_MEM_FAC1
+    inc TEMPF1                  ; AX scaled
+
+atn_skipscale:
+    lda #<poly_atn
+    ldy #>poly_atn
+    jsr poly1_FAC1
+
+    lda TEMPF1
+    beq atn_skipoffset
+
+    lda #<const_HALF_PI
+    ldy #>const_HALF_PI
+    jsr sub_MEM_FAC1
+
+atn_skipoffset:
+    pla
+    bpl atn_out
+    jmp toggle_sign_FAC1
+    
+atn_out:
+    rts

src/basic/math/poly_atn.s

@@ -1,22 +1,10 @@
 ;; #LAYOUT# STD *       #TAKE
-;; #LAYOUT# *   BASIC_0 #TAKE
+;; #LAYOUT# X16 BASIC_0 #TAKE-OFFSET 2000
+;; #LAYOUT# *  BASIC_0  #TAKE
 ;; #LAYOUT# *   *       #IGNORE
 
-;
+; Polynomial for the atn function
-; Math package - arc tangent of FAC1
-;
-; See also:
-; - [CM64] Computes Mapping the Commodore 64 - page 211
-; - https://www.c64-wiki.com/wiki/Floating_point_arithmetic
-; - https://codebase64.org/doku.php?id=base:kernal_floating_point_mathematics
-;
 
-; XXX provide implementation
-
-atn_FAC1:
-
-	+STUB_IMPLEMENTATION
-	
 poly_atn:
 
     !byte $0B                          ; series length - 1

src/basic/math/poly_sin.s

@@ -0,0 +1,23 @@
+;; #LAYOUT# STD *       #TAKE
+;; #LAYOUT# X16 BASIC_0 #TAKE-OFFSET 2000
+;; #LAYOUT# *  BASIC_0  #TAKE
+;; #LAYOUT# *   *       #IGNORE
+
+; Polynomial for the sine function
+
+
+poly_sin:
+
+	!byte $05                          ; series length - 1
+
+	+PUT_CONST_POLY_SIN_1
+	+PUT_CONST_POLY_SIN_2
+	+PUT_CONST_POLY_SIN_3
+	+PUT_CONST_POLY_SIN_4
+	+PUT_CONST_POLY_SIN_5
+	+PUT_CONST_POLY_SIN_6
+
+	
+; Constant 0.75 needed for sine calculation
+sin_three_quarters:
+    !byte $80, $40, $00, $00, $00

strings/07A9E0A0E22050B86810034CB4BF60

@@ -0,0 +1,3 @@
+$07 + LDA #$E0 + LDY #$E2 + JSR $B850 + PLA + BPL $03 + JMP $BFB4 + RTS
+
+Load address of known constant into YA + call well known floating point function + branch on top of stack and call other well known floating point function.

strings/0B76B383BDD3791EF4A6F57B83FCB0107C0C1F67CA7CDE53CBC17D1464704C7DB7EA517A7D6330887E7E9244993A7E4CCC91C77FAAAAAA138100000000

@@ -0,0 +1 @@
+12 floating point numbers making upp the approximation polynomial for the ATN function. This polynomial is described in "Computer Approximations" by John Fraser Hart et al. (ISBN 0-88275-642-7) according to https://www.c64-wiki.com/wiki/POLY1

strings/85248425A0

@@ -0,0 +1,3 @@
+STA $24 + STY $25 + LDY fragment
+
+Store YA to well known vector address in the zero page

strings/A0B9200FBB

@@ -0,0 +1,3 @@
+LDY #$B9 + JSR $BB0F
+
+Partially set input and call well known floating point function

strings/A0E22050B8

@@ -0,0 +1,3 @@
+LDY #$E2 + JSR $B850
+
+Partial load of input + call to known floating point function

strings/A9E0A0E220

@@ -0,0 +1,3 @@
+LDA #$E0 + LDY #$E2 + JSR fragment
+
+Load address of known constant and call some function

strings/B9200FBB

@@ -0,0 +1,3 @@
+$B9 + JSR $BB0F
+
+Fragment + call to well known floating point function

strings/BCA0B920

@@ -0,0 +1,3 @@
+$BC + LDY #$B9 + JMP
+
+Fragments

strings/DAA2A56648

@@ -0,0 +1,3 @@
+$DA + $A2 + LDA $66 + PHA
+
+Fragment + push FAC1 sign on stack