py/modmath: Add math.factorial, optimised and non-opt implementations.

This commit adds the math.factorial function in two variants:
- squared difference, which is faster than the naive version, relatively
  compact, and non-recursive;
- a mildly optimised recursive version, faster than the above one.

There are some more optimisations that could be done, but they tend to take
more code, and more storage space.  The recursive version seems like a
sensible compromise.

The new function is disabled by default, and uses the non-optimised version
by default if it is enabled.  The options are MICROPY_PY_MATH_FACTORIAL
and MICROPY_OPT_MATH_FACTORIAL.

1 files changed, 68 insertions, 1 deletions

diff --git a/py/modmath.c b/py/modmath.c
index 6072c780a..d106f240c 100644
--- a/py/modmath.c
+++ b/py/modmath.c
@@ -169,7 +169,7 @@ MATH_FUN_1(gamma, tgamma)
 // lgamma(x): return the natural logarithm of the gamma function of x
 MATH_FUN_1(lgamma, lgamma)
 #endif
-//TODO: factorial, fsum
+//TODO: fsum
 
 // Function that takes a variable number of arguments
 
@@ -232,6 +232,70 @@ STATIC mp_obj_t mp_math_degrees(mp_obj_t x_obj) {
 }
 STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_degrees_obj, mp_math_degrees);
 
+#if MICROPY_PY_MATH_FACTORIAL
+
+#if MICROPY_OPT_MATH_FACTORIAL
+
+// factorial(x): slightly efficient recursive implementation
+STATIC mp_obj_t mp_math_factorial_inner(mp_uint_t start, mp_uint_t end) {
+    if (start == end) {
+        return mp_obj_new_int(start);
+    } else if (end - start == 1) {
+        return mp_binary_op(MP_BINARY_OP_MULTIPLY, MP_OBJ_NEW_SMALL_INT(start), MP_OBJ_NEW_SMALL_INT(end));
+    } else if (end - start == 2) {
+        mp_obj_t left = MP_OBJ_NEW_SMALL_INT(start);
+        mp_obj_t middle = MP_OBJ_NEW_SMALL_INT(start + 1);
+        mp_obj_t right = MP_OBJ_NEW_SMALL_INT(end);
+        mp_obj_t tmp = mp_binary_op(MP_BINARY_OP_MULTIPLY, left, middle);
+        return mp_binary_op(MP_BINARY_OP_MULTIPLY, tmp, right);
+    } else {
+        mp_uint_t middle = start + ((end - start) >> 1);
+        mp_obj_t left = mp_math_factorial_inner(start, middle);
+        mp_obj_t right = mp_math_factorial_inner(middle + 1, end);
+        return mp_binary_op(MP_BINARY_OP_MULTIPLY, left, right);
+    }
+}
+STATIC mp_obj_t mp_math_factorial(mp_obj_t x_obj) {
+    mp_int_t max = mp_obj_get_int(x_obj);
+    if (max < 0) {
+        mp_raise_msg(&mp_type_ValueError, "negative factorial");
+    } else if (max == 0) {
+        return MP_OBJ_NEW_SMALL_INT(1);
+    }
+    return mp_math_factorial_inner(1, max);
+}
+
+#else
+
+// factorial(x): squared difference implementation
+// based on http://www.luschny.de/math/factorial/index.html
+STATIC mp_obj_t mp_math_factorial(mp_obj_t x_obj) {
+    mp_int_t max = mp_obj_get_int(x_obj);
+    if (max < 0) {
+        mp_raise_msg(&mp_type_ValueError, "negative factorial");
+    } else if (max <= 1) {
+        return MP_OBJ_NEW_SMALL_INT(1);
+    }
+    mp_int_t h = max >> 1;
+    mp_int_t q = h * h;
+    mp_int_t r = q << 1;
+    if (max & 1) {
+        r *= max;
+    }
+    mp_obj_t prod = MP_OBJ_NEW_SMALL_INT(r);
+    for (mp_int_t num = 1; num < max - 2; num += 2) {
+        q -= num;
+        prod = mp_binary_op(MP_BINARY_OP_MULTIPLY, prod, MP_OBJ_NEW_SMALL_INT(q));
+    }
+    return prod;
+}
+
+#endif
+
+STATIC MP_DEFINE_CONST_FUN_OBJ_1(mp_math_factorial_obj, mp_math_factorial);
+
+#endif
+
 STATIC const mp_rom_map_elem_t mp_module_math_globals_table[] = {
     { MP_ROM_QSTR(MP_QSTR___name__), MP_ROM_QSTR(MP_QSTR_math) },
     { MP_ROM_QSTR(MP_QSTR_e), mp_const_float_e },
@@ -274,6 +338,9 @@ STATIC const mp_rom_map_elem_t mp_module_math_globals_table[] = {
     { MP_ROM_QSTR(MP_QSTR_trunc), MP_ROM_PTR(&mp_math_trunc_obj) },
     { MP_ROM_QSTR(MP_QSTR_radians), MP_ROM_PTR(&mp_math_radians_obj) },
     { MP_ROM_QSTR(MP_QSTR_degrees), MP_ROM_PTR(&mp_math_degrees_obj) },
+    #if MICROPY_PY_MATH_FACTORIAL
+    { MP_ROM_QSTR(MP_QSTR_factorial), MP_ROM_PTR(&mp_math_factorial_obj) },
+    #endif
     #if MICROPY_PY_MATH_SPECIAL_FUNCTIONS
     { MP_ROM_QSTR(MP_QSTR_erf), MP_ROM_PTR(&mp_math_erf_obj) },
     { MP_ROM_QSTR(MP_QSTR_erfc), MP_ROM_PTR(&mp_math_erfc_obj) },