spec: math completeness — trig, quotient, gcd/lcm, radix number<->string

Phase 15 implementation:
- spec/primitives.sx: stdlib.math module — sin/cos/tan/asin/acos/atan/exp/log/expt/quotient/gcd/lcm/number->string/string->number (13 primitives)
- JS platform: stdlib.math module; strict string->number parsing (rejects partial matches like "fg" in base 16)
- OCaml: expt, quotient, gcd, lcm, number->string (radix), string->number (radix); atan updated to accept optional 2nd arg (atan2 form)
- spec/tests/test-math.sx: 44 tests — trig/inverse trig, expt, quotient semantics, gcd/lcm, radix formatting/parsing, tower integration
- JS: 2311/4801 (+2 net); OCaml: 4547/5629 (+1 net); zero regressions in math area

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

spec/primitives.sx

@@ -948,4 +948,90 @@
   :returns "boolean"
   :doc "True if a char is immediately available on the port.")
 
+(define-module :stdlib.math)
+
+(define-primitive
+  "sin"
+  :params ((x :as number))
+  :returns "float"
+  :doc "Sine of x (radians).")
+
+(define-primitive
+  "cos"
+  :params ((x :as number))
+  :returns "float"
+  :doc "Cosine of x (radians).")
+
+(define-primitive
+  "tan"
+  :params ((x :as number))
+  :returns "float"
+  :doc "Tangent of x (radians).")
+
+(define-primitive
+  "asin"
+  :params ((x :as number))
+  :returns "float"
+  :doc "Arc sine of x; result in radians.")
+
+(define-primitive
+  "acos"
+  :params ((x :as number))
+  :returns "float"
+  :doc "Arc cosine of x; result in radians.")
+
+(define-primitive
+  "atan"
+  :params ((x :as number) &rest (y :as number))
+  :returns "float"
+  :doc "Arc tangent. (atan x) → radians in (-π/2, π/2). (atan y x) → atan2(y, x).")
+
+(define-primitive
+  "exp"
+  :params ((x :as number))
+  :returns "float"
+  :doc "e raised to the power x.")
+
+(define-primitive
+  "log"
+  :params ((x :as number))
+  :returns "float"
+  :doc "Natural logarithm of x.")
+
+(define-primitive
+  "expt"
+  :params ((base :as number) (exp :as number))
+  :returns "number"
+  :doc "base raised to the power exp. Alias: pow.")
+
+(define-primitive
+  "quotient"
+  :params ((a :as number) (b :as number))
+  :returns "integer"
+  :doc "Integer quotient: truncate(a / b) toward zero. Sign follows dividend.")
+
+(define-primitive
+  "gcd"
+  :params ((a :as number) (b :as number))
+  :returns "integer"
+  :doc "Greatest common divisor of a and b.")
+
+(define-primitive
+  "lcm"
+  :params ((a :as number) (b :as number))
+  :returns "integer"
+  :doc "Least common multiple of a and b.")
+
+(define-primitive
+  "number->string"
+  :params ((n :as number) &rest (radix :as number))
+  :returns "string"
+  :doc "Convert number n to string. Optional radix (default 10). E.g. (number->string 255 16) → \"ff\".")
+
+(define-primitive
+  "string->number"
+  :params ((s :as string) &rest (radix :as number))
+  :returns "any"
+  :doc "Parse string s as a number. Optional radix (default 10). Returns nil on failure.")
+
 (define-module :stdlib.hash-table)

spec/tests/test-math.sx

@@ -0,0 +1,131 @@
+
+(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")))