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.

ports/unix/mpconfigport_coverage.h

@@ -32,6 +32,7 @@
 
 #include <mpconfigport.h>
 
+#define MICROPY_OPT_MATH_FACTORIAL     (1)
 #define MICROPY_FLOAT_HIGH_QUALITY_HASH (1)
 #define MICROPY_ENABLE_SCHEDULER       (1)
 #define MICROPY_READER_VFS             (1)
@@ -41,6 +42,7 @@
 #define MICROPY_PY_BUILTINS_HELP       (1)
 #define MICROPY_PY_BUILTINS_HELP_MODULES (1)
 #define MICROPY_PY_SYS_GETSIZEOF       (1)
+#define MICROPY_PY_MATH_FACTORIAL      (1)
 #define MICROPY_PY_URANDOM_EXTRA_FUNCS (1)
 #define MICROPY_PY_IO_BUFFEREDWRITER (1)
 #define MICROPY_PY_IO_RESOURCE_STREAM (1)

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) },

py/mpconfig.h

@@ -407,6 +407,12 @@
 #define MICROPY_OPT_MPZ_BITWISE (0)
 #endif
 
+
+// Whether math.factorial is large, fast and recursive (1) or small and slow (0).
+#ifndef MICROPY_OPT_MATH_FACTORIAL
+#define MICROPY_OPT_MATH_FACTORIAL (0)
+#endif
+
 /*****************************************************************************/
 /* Python internal features                                                  */
 
@@ -988,6 +994,11 @@ typedef double mp_float_t;
 #define MICROPY_PY_MATH_SPECIAL_FUNCTIONS (0)
 #endif
 
+// Whether to provide math.factorial function
+#ifndef MICROPY_PY_MATH_FACTORIAL
+#define MICROPY_PY_MATH_FACTORIAL (0)
+#endif
+
 // Whether to provide "cmath" module
 #ifndef MICROPY_PY_CMATH
 #define MICROPY_PY_CMATH (0)

tests/float/math_factorial_intbig.py

@@ -0,0 +1,14 @@
+try:
+    import math
+    math.factorial
+except (ImportError, AttributeError):
+    print('SKIP')
+    raise SystemExit
+
+
+for fun in (math.factorial,):
+    for x in range(-1, 30):
+        try:
+            print('%d' % fun(x))
+        except ValueError as e:
+            print('ValueError')