tests/lapi: add math tests

The patch adds a tests for Lua math standard unctions. Also, the
patch introduces a helper `lua_current_version_ge_than()` for
convenient versions comparisons and a helper `approx_equal()` for
convenient numbers comparisons.

Rules from trigonometric identities [1] has been used as
invariants for trigonometric functions.

1. https://en.wikipedia.org/wiki/List_of_trigonometric_identities

Author: ligurio

tests/lapi/lib.lua

@@ -7,12 +7,31 @@ Test helpers.
 
 -- The function determines a Lua version.
 local function lua_version()
+    local major, minor = _VERSION:match("([%d]+)%.(%d+)")
+    local version = {
+        major = tonumber(major),
+        minor = tonumber(minor),
+    }
     local is_luajit, _ = pcall(require, "jit")
-    if is_luajit then
-        return "LuaJIT"
+    local lua_name = is_luajit and "LuaJIT" or "PUC Rio Lua"
+    return lua_name, version
+end
+
+local function version_ge(version1, version2)
+    if version1.major ~= version2.major then
+        return version1.major > version2.major
+    else
+        return version1.minor >= version2.minor
     end
+end
 
-    return _VERSION
+local function lua_current_version_ge_than(major, minor)
+    local _, current_version = lua_version()
+    return version_ge(current_version, { major = major, minor = minor })
+end
+
+local function lua_current_version_lt_than(major, minor)
+    return not lua_current_version_ge_than(major, minor)
 end
 
 -- By default `lua_Integer` is ptrdiff_t in Lua 5.1 and Lua 5.2
@@ -56,9 +75,22 @@ local function bitwise_op(op_name)
     end
 end
 
+local function math_pow(x, y)
+    return x ^ y
+end
+
+local function approx_equal(a, b, epsilon)
+    local abs = math.abs
+    return abs(a - b) <= ((abs(a) < abs(b) and abs(b) or abs(a)) * epsilon)
+end
+
 return {
-    lua_version = lua_version,
+    approx_equal = approx_equal,
     bitwise_op = bitwise_op,
+    lua_version = lua_version,
+    lua_current_version_ge_than = lua_current_version_ge_than,
+    lua_current_version_lt_than = lua_current_version_lt_than,
+    math_pow = math_pow,
     MAX_INT64 = MAX_INT64,
     MIN_INT64 = MIN_INT64,
     MAX_INT = MAX_INT,

tests/lapi/math_abs_test.lua

@@ -0,0 +1,33 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Misleading assertion in asm_fload() for mips,
+https://github.com/LuaJIT/LuaJIT/issues/1043
+
+Synopsis: math.abs(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local n = fdp:consume_number(test_lib.MIN_INT, test_lib.MAX_INT)
+    local abs = n
+    if abs < 0 then
+        abs = -abs
+    end
+    assert(math.abs(n) == abs)
+end
+
+local args = {
+    artifact_prefix = "math_abs_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_acos_test.lua

@@ -0,0 +1,33 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Synopsis: math.acos(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local x = fdp:consume_number(-1, 1)
+    local y = math.acos(x)
+    assert(y >= 0)
+    assert(y <= math.pi)
+    local epsilon = 1^-10
+    if x ~= 0 then
+        assert(test_lib.approx_equal(y, math.pi - math.acos(-x), epsilon))
+        assert(test_lib.approx_equal(math.cos(y), x, epsilon))
+    end
+end
+
+local args = {
+    artifact_prefix = "math_acos_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_asin_test.lua

@@ -0,0 +1,31 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Synopsis: math.asin(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local x = fdp:consume_number(-1, 1)
+    local y = math.asin(x)
+    assert(type(y) == "number")
+    assert(y >= -math.pi / 2)
+    assert(y <=  math.pi / 2)
+    local epsilon = 1^-10
+    assert(test_lib.approx_equal(math.sin(y), x, epsilon))
+end
+
+local args = {
+    artifact_prefix = "math_asin_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_atan_test.lua

@@ -0,0 +1,30 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Synopsis: math.atan(y [, x])
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local x = fdp:consume_number(test_lib.MIN_INT, test_lib.MAX_INT)
+    local y = math.atan(x)
+    assert(type(y) == "number")
+    assert(y >= -math.pi / 2)
+    assert(y <=  math.pi / 2)
+    assert(math.atan(-x) == -y)
+end
+
+local args = {
+    artifact_prefix = "math_atan_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_ceil_test.lua

@@ -0,0 +1,39 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+vm_mips.dasc assumes 32-bit FPU register model,
+https://github.com/LuaJIT/LuaJIT/issues/1040
+
+math.ceil fails to return -0 for -1 < x < -0.5,
+https://github.com/LuaJIT/LuaJIT/issues/859
+
+ARM64 - corrupted local variable on trace exit / snapshot replay,
+https://github.com/LuaJIT/LuaJIT/issues/579
+
+x86/x64: Fix math.ceil(-0.9) result sign,
+https://github.com/LuaJIT/LuaJIT/issues/859
+
+Synopsis: math.ceil(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local x = fdp:consume_number(test_lib.MIN_INT, test_lib.MAX_INT)
+    local res = math.ceil(x)
+    assert(type(res) == "number")
+end
+
+local args = {
+    artifact_prefix = "math_ceil_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_cos_test.lua

@@ -0,0 +1,38 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Synopsis: math.cos(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local x = fdp:consume_number(test_lib.MIN_INT, test_lib.MAX_INT)
+    local cos_x = math.cos(x)
+    assert(type(cos_x) == "number")
+    assert(cos_x >= -1 and cos_x <= 1)
+    local epsilon = 1^-10
+
+    local n = fdp:consume_number(0, 100)
+    -- Calculate the functions of the form `cos(i*pi - x), where
+    -- i = 1, 3, 5, etc. These functions are equivalent, given the
+    -- trigonometric identity.
+    for i = 1, n do
+        assert(test_lib.approx_equal(
+            math.abs(math.cos(i * math.pi - x)), math.abs(cos_x), epsilon))
+    end
+end
+
+local args = {
+    artifact_prefix = "math_cos_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_deg_test.lua

@@ -0,0 +1,27 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Synopsis: math.deg(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local a = fdp:consume_number(test_lib.MIN_INT, test_lib.MAX_INT)
+    local res = math.deg(a)
+    assert(type(res) == "number")
+end
+
+local args = {
+    artifact_prefix = "math_deg_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_exp_test.lua

@@ -0,0 +1,27 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Synopsis: math.exp(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local a = fdp:consume_number(test_lib.MIN_INT, test_lib.MAX_INT)
+    local res = math.exp(a)
+    assert(type(res) == "number")
+end
+
+local args = {
+    artifact_prefix = "math_exp_",
+}
+luzer.Fuzz(TestOneInput, nil, args)

tests/lapi/math_floor_test.lua

@@ -0,0 +1,27 @@
+--[[
+SPDX-License-Identifier: ISC
+Copyright (c) 2023-2025, Sergey Bronnikov.
+
+18 – The Mathematical Library
+https://www.lua.org/pil/18.html
+
+6.7 – Mathematical Functions
+https://www.lua.org/manual/5.3/manual.html#6.7
+
+Synopsis: math.floor(x)
+]]
+
+local luzer = require("luzer")
+local test_lib = require("lib")
+
+local function TestOneInput(buf)
+    local fdp = luzer.FuzzedDataProvider(buf)
+    local a = fdp:consume_number(test_lib.MIN_INT, test_lib.MAX_INT)
+    local res = math.floor(a)
+    assert(type(res) == "number")
+end
+
+local args = {
+    artifact_prefix = "math_floor_",
+}
+luzer.Fuzz(TestOneInput, nil, args)