mandelbrot: correct wrong formula (i² == -1!)

Author: hansfbaier

formula.txt

@@ -4,10 +4,10 @@ concrete:
 x_next + i*y_next = (x + i*y)^2 + cx + i*cy
 
 distribute square:
-x_next + i*y_next = x*x + i*2*xy + y*y + cx + i*cy
+x_next + i*y_next = x*x + i*2*xy - y*y + cx + i*cy
 
 separate real/imaginary:
-x_next = x*x + y*y + cx
+x_next = x*x - y*y + cx
 y_next = 2*x*y + cy
 
 pipeline
@@ -17,12 +17,13 @@ stage 1:
 2xy_stage1 = 2*x*y
 
 stage 2:
-   xx_plus_yy = xx_stage_1 + yy_stage1
+   xx_plus_yy  = xx_stage_1 + yy_stage1
+   xx_minus_yy = xx_stage_1 - yy_stage1
    2xy_stage2 = 2xy_stage1
 
 stage 3:
-    x_next = xx_plus_yy + cx
-    y_next = 2xy_stage2 + cy
+    x_next = xx_minus_yy + cx
+    y_next = 2xy_stage2  + cy
 
 stage 4:
     x = x_next

fractalmanager_basic_test.gtkw

@@ -1,15 +1,15 @@
 [*]
 [*] GTKWave Analyzer v3.3.111 (w)1999-2020 BSI
-[*] Tue Oct 12 21:54:23 2021
+[*] Tue Oct 12 23:08:00 2021
 [*]
-[dumpfile] "test_FractalManagerTest_test_basic.vcd"
-[dumpfile_mtime] "Sat Oct  9 06:13:22 2021"
-[dumpfile_size] 40250
-[savefile] "fractalmanager_basic_test.gtkw"
-[timestart] 281600
+[dumpfile] "/devel/HDL/src/deca-mandelbrot/test_FractalManagerTest_test_basic.vcd"
+[dumpfile_mtime] "Tue Oct 12 23:01:21 2021"
+[dumpfile_size] 850573
+[savefile] "/devel/HDL/src/deca-mandelbrot/fractalmanager_basic_test.gtkw"
+[timestart] 0
 [size] 3828 2090
 [pos] -1 -1
-*-15.404525 21425000 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
+*-21.404526 455600 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 [treeopen] top.
 [sst_width] 357
 [signals_width] 450
@@ -131,13 +131,18 @@ top.current_y[63:0]
 -Core0
 @28
 top.core_0.fsm_state
-@25
+@24
 top.core_0.iterations_out[31:0]
 @40000420
 [fpshift_count] 56
 top.core_0.cx_in[63:0]
 [fpshift_count] 56
 top.core_0.cy_in[63:0]
+@24
+top.pixelx_0[63:0]
+@25
+top.pixely_0[63:0]
+@40000420
 [fpshift_count] 56
 top.core_0.x[63:0]
 [fpshift_count] 56
@@ -156,6 +161,10 @@ top.core_1.iterations_out[31:0]
 top.core_1.cx_in[63:0]
 [fpshift_count] 56
 top.core_1.cy_in[63:0]
+@22
+top.pixelx_1[63:0]
+top.pixely_1[63:0]
+@40000420
 [fpshift_count] 56
 top.core_1.x[63:0]
 [fpshift_count] 56

mandelbrot.py

@@ -48,6 +48,7 @@ def elaborate(self, platform: Platform) -> Module:
 
         # pipeline stage 2
         xx_plus_yy    = Signal(signed(bitwidth))
+        xx_minus_yy   = Signal(signed(bitwidth))
         two_xy_stage2 = Signal(signed(bitwidth))
 
         # pipeline stage 3
@@ -96,12 +97,13 @@ def elaborate(self, platform: Platform) -> Module:
                 # stage 2
                 two_xy_stage2 .eq(two_xy_stage1),
                 xx_plus_yy    .eq(xx + yy),
+                xx_minus_yy   .eq(xx - yy),
             ]
 
         with m.If(stage_enable[2]):
             m.d.sync += [
                 # stage 3
-                x             .eq(xx_plus_yy    + self.cx_in),
+                x             .eq(xx_minus_yy   + self.cx_in),
                 y             .eq(two_xy_stage2 + self.cy_in),
                 escape        .eq(xx_plus_yy > four),
                 iteration     .eq(iteration + 1),
@@ -163,7 +165,7 @@ def iterate_mandel(self, scale, dut, start_x, start_y, check=True):
         done = 0
         yield from self.advance_cycles(3)
         while done == 0:
-            x = ((x * x) >> scale) + start_x
+            x = ((x * x) >> scale) - ((y * y) >> scale) + start_x
             y = ((x * y) >> (scale - 1)) + start_y
             dut_x = (yield dut.x)
             dut_y = (yield dut.y)

mandelbrot_basic_test.gtkw

@@ -1,6 +1,6 @@
 [*]
 [*] GTKWave Analyzer v3.3.111 (w)1999-2020 BSI
-[*] Sat Oct  9 05:49:48 2021
+[*] Wed Oct 13 00:52:29 2021
 [*]
 [dumpfile] "test_MandelbrotTest_test_basic.vcd"
 [dumpfile_mtime] "Sat Oct  9 01:11:25 2021"
@@ -19,6 +19,8 @@
 top.clk
 @40000420
 [fpshift_count] 56
+top.four[63:0]
+[fpshift_count] 56
 top.cx_in[63:0]
 [fpshift_count] 56
 top.cy_in[63:0]
@@ -30,10 +32,8 @@ top.fsm_state
 top.busy_out
 [color] 3
 top.result_ready_out
-@29
 [color] 3
 top.result_read_in
-@28
 [color] 3
 top.result_read
 [color] 3