cull-thresholds.c

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/*
 
MIT License
 
Copyright (c) 2026 PCSX-Redux authors
 
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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*/
 
// Cull-threshold probes. Naming:
//   CT_<prim>_OK_<dim>     -- primitive rendered as expected
//   CT_<prim>_DROP_<dim>   -- primitive culled, anchor reads sentinel
//   CT_<prim>_DROPMECH_*   -- silent-drop verification
 
CESTER_BODY(
 
// Probe-anchor pixel for all tests: (5, 3). The 32x32 sentinel-fill
// region is plenty large for this anchor.
#define ANCHOR_X 5
#define ANCHOR_Y 3
 
// ---- Flat untextured triangle (GP0 0x20) ---------------------------------
 
static void drawTriOk(void) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* In-limit: dx max = 100, dy max = 20. Anchor (5, 3) covered. */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, 100, 0, 0, 20);
    rasterFlushPrimitive();
}
 
static void drawTriEdgeDx(int16_t dx) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* dx = v2.x - v1.x = dx. v1-v3 dx = 0. Worst-edge dx = `dx`. */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, (int16_t)dx, 0, 0, 20);
    rasterFlushPrimitive();
}
 
static void drawTriEdgeDy(int16_t dy) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* dy = v3.y - v1.y = dy. Worst-edge dy = `dy`. */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, 20, 0, 0, (int16_t)dy);
    rasterFlushPrimitive();
}
 
// ---- Gouraud triangle (GP0 0x30) -----------------------------------------
 
static void drawGTriOk(void) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    rasterGouraudTri(RASTER_CMD_RED, 0, 0,
                     RASTER_CMD_RED, 100, 0,
                     RASTER_CMD_RED, 0, 20);
    rasterFlushPrimitive();
}
 
static void drawGTriEdgeDx(int16_t dx) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    rasterGouraudTri(RASTER_CMD_RED, 0, 0,
                     RASTER_CMD_RED, dx, 0,
                     RASTER_CMD_RED, 0, 20);
    rasterFlushPrimitive();
}
 
// ---- Flat textured triangle (GP0 0x24) -----------------------------------
 
static void drawTexTriOk(void) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    setTexpage(TEX15_TX, TEX15_TY, 2);
    setTextureWindow(0, 0, 0, 0);
    rasterTexTri(TEX_MOD_NEUTRAL,
                 0, 0,    0, 0,
                 100, 0,  15, 0,
                 0, 20,   0, 15,
                 CLUT15_FIELD, TEX15_TPAGE);
    rasterFlushPrimitive();
}
 
static void drawTexTriEdgeDx(int16_t dx) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    setTexpage(TEX15_TX, TEX15_TY, 2);
    setTextureWindow(0, 0, 0, 0);
    rasterTexTri(TEX_MOD_NEUTRAL,
                 0, 0,    0, 0,
                 dx, 0,   15, 0,
                 0, 20,   0, 15,
                 CLUT15_FIELD, TEX15_TPAGE);
    rasterFlushPrimitive();
}
 
// ---- Flat untextured quad (GP0 0x28) -------------------------------------
 
static void drawQuadOk(void) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    rasterFlatQuad(RASTER_CMD_GREEN, 0, 0, 100, 0, 0, 20, 100, 20);
    rasterFlushPrimitive();
}
 
static void drawQuadEdgeDx(int16_t dx) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* Largest edge dx = `dx`. */
    rasterFlatQuad(RASTER_CMD_GREEN, 0, 0, dx, 0, 0, 20, dx, 20);
    rasterFlushPrimitive();
}
 
static void drawQuadEdgeDy(int16_t dy) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    rasterFlatQuad(RASTER_CMD_GREEN, 0, 0, 20, 0, 0, dy, 20, dy);
    rasterFlushPrimitive();
}
 
// ---- Flat textured quad (GP0 0x2C) ---------------------------------------
 
static void drawTexQuadOk(void) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    setTexpage(TEX15_TX, TEX15_TY, 2);
    setTextureWindow(0, 0, 0, 0);
    rasterFlatTexQuad(TEX_MOD_NEUTRAL,
                      0, 0,    0, 0,
                      100, 0,  15, 0,
                      0, 20,   0, 15,
                      100, 20, 15, 15,
                      CLUT15_FIELD, TEX15_TPAGE);
    rasterFlushPrimitive();
}
 
static void drawTexQuadEdgeDx(int16_t dx) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    setTexpage(TEX15_TX, TEX15_TY, 2);
    setTextureWindow(0, 0, 0, 0);
    rasterFlatTexQuad(TEX_MOD_NEUTRAL,
                      0, 0,    0, 0,
                      dx, 0,   15, 0,
                      0, 20,   0, 15,
                      dx, 20,  15, 15,
                      CLUT15_FIELD, TEX15_TPAGE);
    rasterFlushPrimitive();
}
 
// ---- Line (GP0 0x40) -----------------------------------------------------
 
static void drawLineEdgeDx(int16_t dx) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* Line at y=ANCHOR_Y crossing x=ANCHOR_X if dx is large enough.
       Line endpoint at (dx, 3) - if line drops, anchor is sentinel. */
    rasterFlatLine(RASTER_CMD_BLUE, 0, 3, dx, 3);
    rasterFlushPrimitive();
}
 
// ---- Variable-size rect (GP0 0x60) ---------------------------------------
 
static void drawRectSize(int16_t w, int16_t h) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    rasterFlatRect(RASTER_CMD_WHITE, 0, 0, w, h);
    rasterFlushPrimitive();
}
 
// ---- Drop-mechanism probe ------------------------------------------------
//
// Submit an oversized triangle (suspected to drop) followed by a
// known-good small triangle at a clearly different anchor (10, 10).
// If hardware silently drops the first and proceeds with the second,
// pixel (10, 10) reads RASTER_VRAM_GREEN. If the drop corrupts the
// command stream, pixel (10, 10) reads sentinel.
 
static void drawDropMechProbe(void) {
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* Oversized tri (dx=2047 - way over limit). */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, 2047, 0, 0, 20);
    /* Small good tri whose interior includes (10, 10). */
    rasterFlatTri(RASTER_CMD_GREEN, 8, 8, 14, 8, 8, 14);
    rasterFlushPrimitive();
}
 
)  // CESTER_BODY
 
// ============================================================================
// Baseline + threshold tests per primitive type
// ============================================================================
 
// ---- Triangle (GP0 0x20) ----
 
CESTER_TEST(ct_tri_baseline, gpu_raster_phase14,
    drawTriOk();
    ASSERT_PIXEL_EQ(RASTER_VRAM_RED, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dx_1023_ok, gpu_raster_phase14,
    drawTriEdgeDx(1023);
    /* In-limit per psx-spx. Should render. */
    ASSERT_PIXEL_EQ(CT_TRI_DX_1023, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dx_1024_drop, gpu_raster_phase14,
    drawTriEdgeDx(1024);
    /* Suspected drop boundary. */
    ASSERT_PIXEL_EQ(CT_TRI_DX_1024, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dx_1025_drop, gpu_raster_phase14,
    drawTriEdgeDx(1025);
    ASSERT_PIXEL_EQ(CT_TRI_DX_1025, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dx_2047_drop, gpu_raster_phase14,
    drawTriEdgeDx(2047);
    /* Way over limit. */
    ASSERT_PIXEL_EQ(CT_TRI_DX_2047, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dy_511_ok, gpu_raster_phase14,
    drawTriEdgeDy(511);
    ASSERT_PIXEL_EQ(CT_TRI_DY_511, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dy_512_drop, gpu_raster_phase14,
    drawTriEdgeDy(512);
    ASSERT_PIXEL_EQ(CT_TRI_DY_512, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dy_513_drop, gpu_raster_phase14,
    drawTriEdgeDy(513);
    ASSERT_PIXEL_EQ(CT_TRI_DY_513, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_tri_dy_1023_drop, gpu_raster_phase14,
    drawTriEdgeDy(1023);
    ASSERT_PIXEL_EQ(CT_TRI_DY_1023, ANCHOR_X, ANCHOR_Y);
)
 
// ---- Gouraud triangle (GP0 0x30) ----
 
CESTER_TEST(ct_gtri_baseline, gpu_raster_phase14,
    drawGTriOk();
    ASSERT_PIXEL_EQ(RASTER_VRAM_RED, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_gtri_dx_1023_ok, gpu_raster_phase14,
    drawGTriEdgeDx(1023);
    ASSERT_PIXEL_EQ(CT_GTRI_DX_1023, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_gtri_dx_1024_drop, gpu_raster_phase14,
    drawGTriEdgeDx(1024);
    ASSERT_PIXEL_EQ(CT_GTRI_DX_1024, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_gtri_dx_2047_drop, gpu_raster_phase14,
    drawGTriEdgeDx(2047);
    ASSERT_PIXEL_EQ(CT_GTRI_DX_2047, ANCHOR_X, ANCHOR_Y);
)
 
// ---- Textured triangle (GP0 0x24) ----
 
CESTER_TEST(ct_textri_baseline, gpu_raster_phase14,
    drawTexTriOk();
    /* Anchor (5, 3) samples texel u=15*5/100=0 (UV interpolation,
       roughly). Just verify it's NOT sentinel. */
    int16_t v = (int16_t)rasterReadPixel(ANCHOR_X, ANCHOR_Y);
    ramsyscall_printf("OBS x=%d y=%d val=0x%04x expect=NOT-SENTINEL\n",
                      ANCHOR_X, ANCHOR_Y, (unsigned)v);
    cester_assert_uint_ne((unsigned)RASTER_SENTINEL, (unsigned)v);
)
 
CESTER_TEST(ct_textri_dx_1023_ok, gpu_raster_phase14,
    drawTexTriEdgeDx(1023);
    int16_t v = (int16_t)rasterReadPixel(ANCHOR_X, ANCHOR_Y);
    ramsyscall_printf("OBS x=%d y=%d val=0x%04x expect=CT_TEXTRI_DX_1023\n",
                      ANCHOR_X, ANCHOR_Y, (unsigned)v);
    cester_assert_uint_eq((unsigned)CT_TEXTRI_DX_1023, (unsigned)v);
)
 
CESTER_TEST(ct_textri_dx_1024_drop, gpu_raster_phase14,
    drawTexTriEdgeDx(1024);
    ASSERT_PIXEL_EQ(CT_TEXTRI_DX_1024, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_textri_dx_2047_drop, gpu_raster_phase14,
    drawTexTriEdgeDx(2047);
    ASSERT_PIXEL_EQ(CT_TEXTRI_DX_2047, ANCHOR_X, ANCHOR_Y);
)
 
// ---- Quad (GP0 0x28) ----
 
CESTER_TEST(ct_quad_baseline, gpu_raster_phase14,
    drawQuadOk();
    ASSERT_PIXEL_EQ(RASTER_VRAM_GREEN, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_quad_dx_1023_ok, gpu_raster_phase14,
    drawQuadEdgeDx(1023);
    ASSERT_PIXEL_EQ(CT_QUAD_DX_1023, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_quad_dx_1024_drop, gpu_raster_phase14,
    drawQuadEdgeDx(1024);
    ASSERT_PIXEL_EQ(CT_QUAD_DX_1024, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_quad_dx_2047_drop, gpu_raster_phase14,
    drawQuadEdgeDx(2047);
    ASSERT_PIXEL_EQ(CT_QUAD_DX_2047, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_quad_dy_511_ok, gpu_raster_phase14,
    drawQuadEdgeDy(511);
    ASSERT_PIXEL_EQ(CT_QUAD_DY_511, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_quad_dy_512_drop, gpu_raster_phase14,
    drawQuadEdgeDy(512);
    ASSERT_PIXEL_EQ(CT_QUAD_DY_512, ANCHOR_X, ANCHOR_Y);
)
 
// ---- Textured quad (GP0 0x2C) ----
 
CESTER_TEST(ct_texquad_baseline, gpu_raster_phase14,
    drawTexQuadOk();
    int16_t v = (int16_t)rasterReadPixel(ANCHOR_X, ANCHOR_Y);
    ramsyscall_printf("OBS x=%d y=%d val=0x%04x expect=NOT-SENTINEL\n",
                      ANCHOR_X, ANCHOR_Y, (unsigned)v);
    cester_assert_uint_ne((unsigned)RASTER_SENTINEL, (unsigned)v);
)
 
CESTER_TEST(ct_texquad_dx_1023_ok, gpu_raster_phase14,
    drawTexQuadEdgeDx(1023);
    int16_t v = (int16_t)rasterReadPixel(ANCHOR_X, ANCHOR_Y);
    ramsyscall_printf("OBS x=%d y=%d val=0x%04x expect=CT_TEXQUAD_DX_1023\n",
                      ANCHOR_X, ANCHOR_Y, (unsigned)v);
    cester_assert_uint_eq((unsigned)CT_TEXQUAD_DX_1023, (unsigned)v);
)
 
CESTER_TEST(ct_texquad_dx_1024_drop, gpu_raster_phase14,
    drawTexQuadEdgeDx(1024);
    ASSERT_PIXEL_EQ(CT_TEXQUAD_DX_1024, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_texquad_dx_2047_drop, gpu_raster_phase14,
    drawTexQuadEdgeDx(2047);
    ASSERT_PIXEL_EQ(CT_TEXQUAD_DX_2047, ANCHOR_X, ANCHOR_Y);
)
 
// ---- Line (GP0 0x40) ----
//
// Lines don't really have "edges" in the polygon sense; the cull
// concept is about the endpoint delta. Per psx-spx GPU registers the
// line endpoint delta is limited to ±1023 horizontally / ±511
// vertically; oversized lines are dropped.
 
CESTER_TEST(ct_line_dx_100_baseline, gpu_raster_phase14,
    drawLineEdgeDx(100);
    /* Line should render through (5, 3). */
    ASSERT_PIXEL_EQ(RASTER_VRAM_BLUE, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_line_dx_1023_ok, gpu_raster_phase14,
    drawLineEdgeDx(1023);
    ASSERT_PIXEL_EQ(CT_LINE_DX_1023, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_line_dx_1024_drop, gpu_raster_phase14,
    drawLineEdgeDx(1024);
    ASSERT_PIXEL_EQ(CT_LINE_DX_1024, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_line_dx_2047_drop, gpu_raster_phase14,
    drawLineEdgeDx(2047);
    ASSERT_PIXEL_EQ(CT_LINE_DX_2047, ANCHOR_X, ANCHOR_Y);
)
 
// ---- Variable-size rect (GP0 0x60) ----
//
// Rectangles have their own "size" command word. psx-spx documents
// the rectangle width as masked to ((W-1) & 0x3FF) + 1 = max 1024.
// So w=1024 wraps to 0 (no draw); w=1025 wraps to 1; etc. Verify.
 
CESTER_TEST(ct_rect_w16_baseline, gpu_raster_phase14,
    drawRectSize(16, 16);
    ASSERT_PIXEL_EQ(RASTER_VRAM_WHITE, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_rect_w1023, gpu_raster_phase14,
    drawRectSize(1023, 16);
    /* Hardware should fill - 1023 within mask range. */
    ASSERT_PIXEL_EQ(CT_RECT_W_1023, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_rect_w1024, gpu_raster_phase14,
    drawRectSize(1024, 16);
    /* psx-spx: ((1024-1)&0x3FF)+1 = 1024. Renders. */
    ASSERT_PIXEL_EQ(CT_RECT_W_1024, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_rect_w1025, gpu_raster_phase14,
    drawRectSize(1025, 16);
    /* ((1025-1)&0x3FF)+1 = 1. Renders only 1 pixel wide; anchor
       (5, 3) is outside that single-column rect -> sentinel. */
    ASSERT_PIXEL_EQ(CT_RECT_W_1025, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_rect_h511, gpu_raster_phase14,
    drawRectSize(16, 511);
    ASSERT_PIXEL_EQ(CT_RECT_H_511, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_rect_h512, gpu_raster_phase14,
    drawRectSize(16, 512);
    /* ((512-1)&0x1FF)+1 = 512. Renders. */
    ASSERT_PIXEL_EQ(CT_RECT_H_512, ANCHOR_X, ANCHOR_Y);
)
 
CESTER_TEST(ct_rect_h513, gpu_raster_phase14,
    drawRectSize(16, 513);
    /* ((513-1)&0x1FF)+1 = 1. Wraps to height 1; anchor (5, 3) is
       outside the single-row rect -> sentinel. */
    ASSERT_PIXEL_EQ(CT_RECT_H_513, ANCHOR_X, ANCHOR_Y);
)
 
// ---- Drop-mechanism probe ----
 
CESTER_TEST(ct_drop_mech_second_renders, gpu_raster_phase14,
    drawDropMechProbe();
    /* If the oversized first tri was silently dropped, the second
       tri rendered and pixel (10, 10) is green. If the drop
       corrupted the command stream, (10, 10) reads sentinel. */
    ASSERT_PIXEL_EQ(RASTER_VRAM_GREEN, 10, 10);
)
 
CESTER_TEST(ct_drop_mech_oversized_not_rendered, gpu_raster_phase14,
    drawDropMechProbe();
    /* The first oversized tri at (0, 0)-(2047, 0)-(0, 20) was
       dropped. Anchor (5, 3) - inside that tri's intended bounds
       but outside the second tri's bounds - should be sentinel. */
    ASSERT_PIXEL_UNTOUCHED(ANCHOR_X, ANCHOR_Y);
)
 
// ---- Per-vertex absolute coordinate test ----
//
// Triangle with one vertex at a high absolute X but small edge dx
// between the other two vertices. Per-edge rule predicts render;
// per-vertex-abs rule predicts drop.
 
CESTER_TEST(ct_tri_vertex_abs_just_low_edges, gpu_raster_phase14,
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* v1 = (0, 0), v2 = (1024, 0), v3 = (1024, 20). Edges:
       v1-v2 dx=1024 (over limit if dx>1023).
       v2-v3 dx=0.
       v1-v3 dx=1024 (over limit).
       So this test triangle has TWO edges over - it's a control
       confirming over-limit cull, not strictly a per-vertex-abs
       isolation. */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, 1024, 0, 1024, 20);
    rasterFlushPrimitive();
    ASSERT_PIXEL_EQ(CT_TRI_VERTEX_ABS_OVER, ANCHOR_X, ANCHOR_Y);
)
 
/* Pre-truncation per-vertex absolute coord probes. The GP0 vertex
   format stores x/y as int16 but the rasterizer interprets only the
   low 11 bits as signed. We can test whether hardware enforces an
   independent per-vertex absolute-coord rule BEFORE the 11-bit
   truncation by sending the same effective post-truncation triangle
   in two ways: one with all coords in the 11-bit range, one with a
   vertex coord that has bits set above bit 10 but produces the same
   low-11-bit result. If both render identically, no pre-truncation
   rule. If the probe drops (sentinel at anchor), there IS one.
   Baseline geometry: (0,0)-(20,0)-(0,20). Anchor (5,3) is inside
   the post-truncation triangle in both cases. */
CESTER_TEST(ct_tri_pretrunc_baseline, gpu_raster_phase14,
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* All low-11-bit vertices; should render at anchor. */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, 20, 0, 0, 20);
    rasterFlushPrimitive();
    ASSERT_PIXEL_EQ(RASTER_VRAM_RED, ANCHOR_X, ANCHOR_Y);
)
CESTER_TEST(ct_tri_pretrunc_bit11, gpu_raster_phase14,
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* Same effective triangle - v2.x = 2068 = 0x814 truncates to
       low 11 bits = 0x14 = 20. If hardware truncates first then
       checks per-edge, this renders identically to the baseline.
       If a pre-truncation per-vertex absolute rule fires on |x| >
       1023, the polygon drops and anchor is sentinel. */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, 2068, 0, 0, 20);
    rasterFlushPrimitive();
    ASSERT_PIXEL_EQ(CT_TRI_PRETRUNC_BIT11, ANCHOR_X, ANCHOR_Y);
)
CESTER_TEST(ct_tri_pretrunc_bit15, gpu_raster_phase14,
    rasterReset();
    rasterClearTestRegion(0, 0, 32, 32);
    /* v2.x = -32748 = 0x8014 in 16-bit two's complement. Low 11
       bits = 0x014 = 20. Maximum bit-pattern divergence from the
       11-bit truncated value: every high bit set. If any per-vertex
       rule fires above 11-bit range, this drops. */
    rasterFlatTri(RASTER_CMD_RED, 0, 0, (int16_t)0x8014, 0, 0, 20);
    rasterFlushPrimitive();
    ASSERT_PIXEL_EQ(CT_TRI_PRETRUNC_BIT15, ANCHOR_X, ANCHOR_Y);
)