`nvl2` result type depends on the type of its first argument

[neilconway]

Describe the bug

The result of nvl2(x, a, b) should depend only on a and b; x is only checked for NULL. The type of x currently changes the result type, and some combinations fail:

• Decimal results are widened to a larger precision and scale, or turned into strings.
• Timestamp results fail to plan when x is an integer, and fail during optimization when x is a string literal.

The equivalent CASE WHEN x IS NOT NULL THEN a ELSE b END works in every case.

To Reproduce

CREATE TABLE t AS SELECT
  1 AS i, 1.5 AS f, 'a' AS s,
  CAST(1.23 AS DECIMAL(5,2)) AS d1, CAST(4.56 AS DECIMAL(5,2)) AS d2,
  TIMESTAMP '2024-01-01 10:00:00' AS ts1, TIMESTAMP '2024-01-02 10:00:00' AS ts2;

SELECT arrow_typeof(CASE WHEN i IS NOT NULL THEN d1 ELSE d2 END) AS case_type FROM t;
-- Decimal128(5, 2)

SELECT nvl2(i, d1, d2) AS v, arrow_typeof(nvl2(i, d1, d2)) AS v_type FROM t;
-- 1.23 | Decimal128(22, 2)

SELECT nvl2(f, d1, d2) AS v, arrow_typeof(nvl2(f, d1, d2)) AS v_type FROM t;
-- 1.230000000000000 | Decimal128(30, 15)

SELECT nvl2(s, d1, d2) AS v, arrow_typeof(nvl2(s, d1, d2)) AS v_type FROM t;
-- 1.23 | Utf8

SELECT nvl2(i, ts1, ts2) AS v FROM t;
-- Error during planning: Execution error: Function 'nvl2' user-defined coercion failed with: Internal error: Coercion from Int64 to Timestamp(ns) failed..

SELECT nvl2('a', ts1, ts2) AS v FROM t;
-- Optimizer rule 'simplify_expressions' failed
-- caused by
-- Failed to cast field 'lit' from Utf8 to Timestamp(ns)
-- caused by
-- Arrow error: Parser error: Error parsing timestamp from 'a': timestamp must contain at least 10 characters

Expected behavior

nvl2 returns the same results as the equivalent CASE expression:

• The three decimal queries return 1.23 as Decimal128(5, 2).
• The two timestamp queries return 2024-01-01T10:00:00.

Additional context

Reproduced on main at commit 2b1fcae, in both release and debug builds.

This bug report was generated by Claude.

[CuteChuanChuan]

take