
(deftest
  "math completeness"
  (deftest
    "trigonometry"
    (deftest
      "sin"
      (assert= 0 (round (sin 0)) "sin 0 = 0")
      (assert=
        1
        (round (sin (/ 3.14159 2)))
        "sin pi/2 = 1")
      (assert= 0 (round (sin 3.14159)) "sin pi = 0"))
    (deftest
      "cos"
      (assert= 1 (round (cos 0)) "cos 0 = 1")
      (assert=
        0
        (round (cos (/ 3.14159 2)))
        "cos pi/2 = 0")
      (assert= -1 (round (cos 3.14159)) "cos pi = -1"))
    (deftest
      "tan"
      (assert= 0 (round (tan 0)) "tan 0 = 0")
      (assert= 1 (round (tan 0.785398)) "tan pi/4 = 1"))
    (deftest
      "asin"
      (assert= 0 (round (asin 0)) "asin 0 = 0")
      (let
        (r (asin 1))
        (assert= true (and (> r 1.5) (< r 1.6)) "asin 1 ≈ pi/2")))
    (deftest
      "acos"
      (assert= 0 (round (acos 1)) "acos 1 = 0")
      (let
        (r (acos 0))
        (assert= true (and (> r 1.5) (< r 1.6)) "acos 0 ≈ pi/2")))
    (deftest
      "atan"
      (assert= 0 (round (atan 0)) "atan 0 = 0")
      (let
        (r (atan 1))
        (assert= true (and (> r 0.78) (< r 0.8)) "atan 1 ≈ pi/4"))
      (let
        (r (atan 1 1))
        (assert=
          true
          (and (> r 0.78) (< r 0.8))
          "atan 1 1 = atan2(1,1) ≈ pi/4"))
      (let
        (r (atan 1 0))
        (assert= true (and (> r 1.5) (< r 1.6)) "atan 1 0 ≈ pi/2")))
    (deftest
      "exp"
      (assert= 1 (round (exp 0)) "exp 0 = 1")
      (let
        (r (exp 1))
        (assert= true (and (> r 2.71) (< r 2.72)) "exp 1 ≈ e")))
    (deftest
      "log"
      (assert= 0 (round (log 1)) "log 1 = 0")
      (let
        (r (log 2.71828))
        (assert= true (and (> r 0.99) (< r 1.01)) "log e ≈ 1"))))
  (deftest
    "expt"
    (assert= 8 (expt 2 3) "2^3 = 8")
    (assert= 1 (expt 5 0) "5^0 = 1")
    (assert= 1000 (expt 10 3) "10^3 = 1000")
    (let
      (r (expt 2 0.5))
      (assert= true (and (> r 1.41) (< r 1.43)) "2^0.5 ≈ sqrt(2)")))
  (deftest
    "quotient"
    (assert= 3 (quotient 13 4) "13/4 = 3")
    (assert=
      -3
      (quotient -13 4)
      "-13/4 = -3 (truncate toward zero)")
    (assert=
      -3
      (quotient 13 -4)
      "13/-4 = -3 (truncate toward zero)")
    (assert= 3 (quotient -13 -4) "-13/-4 = 3")
    (assert= 0 (quotient 0 5) "0/5 = 0"))
  (deftest
    "gcd"
    (assert= 6 (gcd 12 18) "gcd 12 18 = 6")
    (assert= 1 (gcd 7 13) "gcd 7 13 = 1 (coprime)")
    (assert= 4 (gcd 8 12) "gcd 8 12 = 4")
    (assert= 5 (gcd 0 5) "gcd 0 5 = 5")
    (assert= 6 (gcd -12 18) "gcd handles negatives"))
  (deftest
    "lcm"
    (assert= 12 (lcm 4 6) "lcm 4 6 = 12")
    (assert= 36 (lcm 12 18) "lcm 12 18 = 36")
    (assert= 0 (lcm 0 5) "lcm 0 5 = 0")
    (assert= 15 (lcm 3 5) "lcm 3 5 = 15"))
  (deftest
    "number->string"
    (assert= "42" (number->string 42) "integer to string")
    (assert= "0" (number->string 0) "zero to string")
    (assert= "-7" (number->string -7) "negative to string")
    (assert= "ff" (number->string 255 16) "255 in hex")
    (assert= "1111" (number->string 15 2) "15 in binary")
    (assert= "377" (number->string 255 8) "255 in octal")
    (assert= "z" (number->string 35 36) "35 in base 36"))
  (deftest
    "string->number"
    (assert= 42 (string->number "42") "string to integer")
    (assert= -7 (string->number "-7") "negative string to integer")
    (assert= 255 (string->number "ff" 16) "hex string")
    (assert= 15 (string->number "1111" 2) "binary string")
    (assert= 255 (string->number "377" 8) "octal string")
    (assert= nil (string->number "not-a-number") "invalid returns nil")
    (assert= nil (string->number "fg" 16) "invalid hex returns nil"))
  (deftest
    "numeric tower integration"
    (assert=
      true
      (< (abs (- (sin (asin 0.5)) 0.5)) 0.0001)
      "sin(asin(x)) = x")
    (assert=
      true
      (< (abs (- (cos (acos 0.5)) 0.5)) 0.0001)
      "cos(acos(x)) = x")
    (assert= true (< (abs (- (exp (log 2)) 2)) 0.0001) "exp(log(x)) = x")
    (assert=
      (* 12 18)
      (* (gcd 12 18) (lcm 12 18))
      "gcd * lcm = a * b")))
