add atn_FAC1

STATUS.md

@@ -256,7 +256,7 @@ Floating point mathematical routines - not official, but well known and broadly
 | `$E264`   | `cos_FAC1`             | PARTIAL  | needs `sin_FAC1`                                   |
 | `$E26B`   | `sin_FAC1`             | NOT DONE | some work already started                          |
 | `$E2B4`   | `tan_FAC1`             | NOT DONE |                                                    |
-| `$E30E`   | `atn_FAC1`             | NOT DONE |                                                    |
+| `$E30E`   | `atn_FAC1`             | PARTIAL  | not fully tested yet                               |
 
 <br />
 

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

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/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