fix(plot): 修复复审问题（2 P2 + 1 P3）

- P2 复杂表达式绕过异常回退：解析与渲染共同纳入局部异常回退；
  AST 深度/节点数上限拦截 RecursionError
- P2 极端有限范围生成 nan SVG：校验坐标跨度有限且 >0，回退安全范围；
  _polyline 拒绝非有限像素坐标
- P3 更新接口契约文档：function-plot 静态 SVG 已实现

Co-Authored-By: Claude Code <noreply@anthropic.com>

backend/app/export/exporters/html.py

@@ -203,16 +203,17 @@ class HtmlExporter:
         return f"函数图像：{diag.message}{loc}"
 
     def _render_function_plot(self, node: DocumentNode, warnings: list[str]) -> str:
-        # 解析 fenced 源码：有合法 plot 且无 error → 内嵌静态 SVG；否则回退占位并转诊断
-        parsed = parse_source(node.text)
-        for diag in parsed.diagnostics:
-            warnings.append(self._format_plot_diagnostic(diag))
-        if parsed.plot is None:
-            return f'<pre class="function-plot">{html.escape(node.text)}</pre>'
+        # 解析与渲染共同纳入局部异常回退：单个图像失败只回退占位 + warning，
+        # 绝不阻断整篇导出（含复杂表达式触发的 RecursionError 等异常）。
         try:
+            parsed = parse_source(node.text)
+            for diag in parsed.diagnostics:
+                warnings.append(self._format_plot_diagnostic(diag))
+            if parsed.plot is None:
+                return f'<pre class="function-plot">{html.escape(node.text)}</pre>'
             rendered = render_svg(parsed.plot)
-        except Exception as exc:  # 渲染异常回退占位，绝不阻断整篇导出
-            warnings.append(f"函数图像：渲染失败，已回退占位（{exc}）")
+        except Exception as exc:
+            warnings.append(f"函数图像：解析或渲染失败，已回退占位（{exc}）")
             return f'<pre class="function-plot">{html.escape(node.text)}</pre>'
         warnings.extend(rendered.warnings)
         return f'<figure class="function-plot">{rendered.content}</figure>'

backend/app/plot/parser.py

@@ -47,6 +47,11 @@ _ALLOWED_UNARY = (ast.UAdd, ast.USub)
 _DIRECTIVE_KEYS = frozenset({"domain", "range", "xlabel", "ylabel", "grid"})
 _NUMBER_RE = re.compile(r"^(\d+\.?\d*|\.\d+)([eE][+-]?\d+)?$")
 
+# 表达式复杂度上限：深层嵌套或海量节点在递归校验/求值时会触发 RecursionError，
+# 用白名单校验提前拦截，保证失败走正常诊断路径而不是异常逃逸出导出链路。
+_MAX_AST_DEPTH = 200
+_MAX_AST_NODES = 1000
+
 
 class PlotParseError(Exception):
     """表达式解析/校验失败，携带可定位诊断。"""
@@ -136,8 +141,19 @@ def _preprocess(expr: str) -> str:
     return _insert_implicit_multiplication(expr.replace("^", "**"))
 
 
-def _check_node(node: ast.AST) -> None:
-    """白名单校验：任何越界节点都抛 FUNCTION_PLOT_EXPRESSION_UNSAFE。"""
+def _check_node(node: ast.AST, depth: int = 0, counter: list[int] | None = None) -> None:
+    """白名单校验：任何越界节点都抛 FUNCTION_PLOT_EXPRESSION_UNSAFE。
+
+    同时限制 AST 深度与节点总数，避免超长/超深表达式在递归校验或求值时触发
+    RecursionError 而绕过解析失败路径。
+    """
+    if counter is None:
+        counter = [0]
+    if depth > _MAX_AST_DEPTH:
+        _unsafe(f"表达式嵌套过深（超过 {_MAX_AST_DEPTH} 层）")
+    counter[0] += 1
+    if counter[0] > _MAX_AST_NODES:
+        _unsafe(f"表达式过于复杂（节点数超过 {_MAX_AST_NODES}）")
     if isinstance(node, ast.Constant):
         if isinstance(node.value, bool) or not isinstance(node.value, (int, float)):
             _unsafe(f"不支持的常量 {node.value!r}")
@@ -149,13 +165,13 @@ def _check_node(node: ast.AST) -> None:
     if isinstance(node, ast.BinOp):
         if not isinstance(node.op, _ALLOWED_BINOPS):
             _unsafe(f"不支持的运算符 {type(node.op).__name__}")
-        _check_node(node.left)
-        _check_node(node.right)
+        _check_node(node.left, depth + 1, counter)
+        _check_node(node.right, depth + 1, counter)
         return
     if isinstance(node, ast.UnaryOp):
         if not isinstance(node.op, _ALLOWED_UNARY):
             _unsafe(f"不支持的运算符 {type(node.op).__name__}")
-        _check_node(node.operand)
+        _check_node(node.operand, depth + 1, counter)
         return
     if isinstance(node, ast.Call):
         if not isinstance(node.func, ast.Name) or node.func.id not in _FUNCTIONS:
@@ -166,7 +182,7 @@ def _check_node(node: ast.AST) -> None:
         if len(node.args) != 1:
             _unsafe(f"{node.func.id} 需要 1 个参数，实际 {len(node.args)} 个")
         for arg in node.args:
-            _check_node(arg)
+            _check_node(arg, depth + 1, counter)
         return
     _unsafe(f"不支持的语法 {type(node).__name__}")
 
@@ -184,6 +200,15 @@ def parse_expression(expr: str) -> ast.Expression:
                 message=f"表达式语法错误：{exc.msg}",
             )
         ) from exc
+    except RecursionError as exc:
+        # 极深嵌套可能在 ast.parse 阶段就触发 RecursionError，转为可定位诊断
+        raise PlotParseError(
+            PlotDiagnostic(
+                severity="error",
+                code="FUNCTION_PLOT_PARSE_FAILED",
+                message="表达式嵌套过深，无法解析",
+            )
+        ) from exc
     _check_node(tree.body)
     return tree
 

backend/app/plot/render.py

@@ -26,6 +26,16 @@ def _safe_color(color: str | None, fallback: str) -> str:
     return color.strip() if color and _COLOR_RE.match(color.strip()) else fallback
 
 
+def _valid_span(lo: float, hi: float) -> bool:
+    """范围跨度有效：端点有限、跨度有限且大于零。
+
+    端点相减可能溢出为 ``inf``（如 ``-1e308`` 到 ``1e308``），需单独校验跨度，
+    否则后续坐标换算会生成含 ``nan`` 的 SVG。
+    """
+    span = hi - lo
+    return math.isfinite(lo) and math.isfinite(hi) and math.isfinite(span) and span > 0
+
+
 def _fmt_num(v: float) -> str:
     if v == 0:
         return "0"
@@ -116,6 +126,12 @@ def _polyline(
             continue
         px = sx(x)
         py = sy(y)
+        # 映射后的坐标必须有限：显式 range 下极端 y 值可能让像素坐标溢出为 inf
+        if not (math.isfinite(px) and math.isfinite(py)):
+            if points:
+                segments.append(f'<polyline points="{" ".join(points)}" fill="none" stroke="{color}"/>')
+                points = []
+            continue
         points.append(f"{px:.2f},{py:.2f}")
     if points:
         segments.append(f'<polyline points="{" ".join(points)}" fill="none" stroke="{color}"/>')
@@ -186,7 +202,7 @@ def render_svg(plot: FunctionPlot) -> StaticRenderResult:
     """把已解析的 FunctionPlot 渲染为内嵌 SVG。"""
     warnings: list[str] = []
     xmin, xmax = plot.domain
-    if not (math.isfinite(xmin) and math.isfinite(xmax)) or xmin >= xmax:
+    if not _valid_span(xmin, xmax):
         warnings.append("domain 无效，回退到 [-10, 10]")
         xmin, xmax = -10.0, 10.0
 
@@ -200,10 +216,10 @@ def render_svg(plot: FunctionPlot) -> StaticRenderResult:
             continue
         fns.append((expr, tree))
 
-    # 纵轴范围：显式 range 有效则用之；无效（退化/非有限）丢弃并自动采样重算
+    # 纵轴范围：显式 range 有效则用之；无效（退化/非有限/跨度溢出）丢弃并自动采样重算
     if plot.range is not None:
         lo, hi = float(plot.range[0]), float(plot.range[1])
-        if math.isfinite(lo) and math.isfinite(hi) and lo < hi:
+        if _valid_span(lo, hi):
             ymin, ymax = lo, hi
         else:
             warnings.append("range 无效，改用自动范围")
@@ -211,6 +227,11 @@ def render_svg(plot: FunctionPlot) -> StaticRenderResult:
     else:
         ymin, ymax = _compute_range(fns, xmin, xmax)
 
+    # 最终防线：自动范围在极端样本下也可能溢出，坐标映射前必须保证跨度有限且大于零
+    if not _valid_span(ymin, ymax):
+        warnings.append("y 范围跨度无法表示，回退到 [-10, 10]")
+        ymin, ymax = -10.0, 10.0
+
     def sx(x: float) -> float:
         return _MARGIN + (x - xmin) / (xmax - xmin) * (_WIDTH - 2 * _MARGIN)
 

backend/tests/test_plot.py

@@ -192,3 +192,58 @@ def test_html_exporter_function_plot_render_error_falls_back(monkeypatch) -> Non
     html = result.content.decode("utf-8")
     assert '<pre class="function-plot">' in html
     assert any("渲染失败" in w for w in result.warnings)
+
+
+# --------------------------------------------------------------------------- #
+# 审阅回归：复杂表达式 / 极端数值范围
+# --------------------------------------------------------------------------- #
+def test_parse_expression_rejects_excessive_depth() -> None:
+    # P2：超长加法链的 AST 深度超限，应拒绝为 PlotParseError 而非触发 RecursionError
+    expr = "+".join(["1"] * 300)
+    with pytest.raises(PlotParseError) as exc:
+        parse_expression(expr)
+    assert exc.value.diagnostic.code == "FUNCTION_PLOT_EXPRESSION_UNSAFE"
+
+
+def test_parse_expression_rejects_excessive_nodes() -> None:
+    # P2：浅层但节点超限的表达式（满二叉树）应被节点数上限拦截
+    def balanced(depth: int) -> str:
+        if depth == 0:
+            return "x"
+        return f"({balanced(depth - 1)}+{balanced(depth - 1)})"
+
+    expr = balanced(10)  # ~2047 个节点，深度仅 ~10
+    with pytest.raises(PlotParseError) as exc:
+        parse_expression(expr)
+    assert exc.value.diagnostic.code == "FUNCTION_PLOT_EXPRESSION_UNSAFE"
+
+
+def test_html_exporter_function_plot_deep_expression_falls_back() -> None:
+    # P2：复杂表达式解析失败应回退占位，不阻断整篇导出
+    expr = "+".join(["1"] * 300)
+    md = f"```function-plot\ny = {expr}\n```"
+    result = asyncio.run(HtmlExporter().export(parse_document(md), ExportOptions()))
+    html = result.content.decode("utf-8")
+    assert '<pre class="function-plot">' in html
+    assert "<svg" not in html
+    assert any("函数图像" in w for w in result.warnings)
+
+
+def test_render_svg_extreme_domain_no_nan() -> None:
+    # P2：有限但跨度溢出的 domain 应回退安全范围，SVG 不得含 nan/inf
+    plot = parse_source("domain: -1e308, 1e308\nrange: -1, 1\ny = 0").plot
+    rendered = render_svg(plot)
+    assert "<svg" in rendered.content
+    assert "nan" not in rendered.content
+    assert "inf" not in rendered.content
+    assert any("domain" in w for w in rendered.warnings)
+
+
+def test_render_svg_extreme_range_no_nan() -> None:
+    # P2：有限但跨度溢出的 range 应回退自动范围，SVG 不得含 nan/inf
+    plot = parse_source("domain: -1, 1\nrange: -1e308, 1e308\ny = x").plot
+    rendered = render_svg(plot)
+    assert "<svg" in rendered.content
+    assert "nan" not in rendered.content
+    assert "inf" not in rendered.content
+    assert any("range" in w for w in rendered.warnings)