add circuitpython code

1 files changed, 1402 insertions, 0 deletions

diff --git a/circuitpython/extmod/ulab/code/numpy/numerical.c b/circuitpython/extmod/ulab/code/numpy/numerical.c
new file mode 100644
index 0000000..d6983c0
--- /dev/null
+++ b/circuitpython/extmod/ulab/code/numpy/numerical.c
@@ -0,0 +1,1402 @@
+
+/*
+ * This file is part of the micropython-ulab project,
+ *
+ * https://github.com/v923z/micropython-ulab
+ *
+ * The MIT License (MIT)
+ *
+ * Copyright (c) 2019-2021 Zoltán Vörös
+ *               2020 Scott Shawcroft for Adafruit Industries
+ *               2020 Taku Fukada
+*/
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include "py/obj.h"
+#include "py/objint.h"
+#include "py/runtime.h"
+#include "py/builtin.h"
+#include "py/misc.h"
+
+#include "../ulab.h"
+#include "../ulab_tools.h"
+#include "./carray/carray_tools.h"
+#include "numerical.h"
+
+enum NUMERICAL_FUNCTION_TYPE {
+    NUMERICAL_ALL,
+    NUMERICAL_ANY,
+    NUMERICAL_ARGMAX,
+    NUMERICAL_ARGMIN,
+    NUMERICAL_MAX,
+    NUMERICAL_MEAN,
+    NUMERICAL_MIN,
+    NUMERICAL_STD,
+    NUMERICAL_SUM,
+};
+
+//| """Numerical and Statistical functions
+//|
+//| Most of these functions take an "axis" argument, which indicates whether to
+//| operate over the flattened array (None), or a particular axis (integer)."""
+//|
+//| from typing import Dict
+//|
+//| _ArrayLike = Union[ndarray, List[_float], Tuple[_float], range]
+//|
+//| _DType = int
+//| """`ulab.numpy.int8`, `ulab.numpy.uint8`, `ulab.numpy.int16`, `ulab.numpy.uint16`, `ulab.numpy.float` or `ulab.numpy.bool`"""
+//|
+//| from builtins import float as _float
+//| from builtins import bool as _bool
+//|
+//| int8: _DType
+//| """Type code for signed integers in the range -128 .. 127 inclusive, like the 'b' typecode of `array.array`"""
+//|
+//| int16: _DType
+//| """Type code for signed integers in the range -32768 .. 32767 inclusive, like the 'h' typecode of `array.array`"""
+//|
+//| float: _DType
+//| """Type code for floating point values, like the 'f' typecode of `array.array`"""
+//|
+//| uint8: _DType
+//| """Type code for unsigned integers in the range 0 .. 255 inclusive, like the 'H' typecode of `array.array`"""
+//|
+//| uint16: _DType
+//| """Type code for unsigned integers in the range 0 .. 65535 inclusive, like the 'h' typecode of `array.array`"""
+//|
+//| bool: _DType
+//| """Type code for boolean values"""
+//|
+
+static void numerical_reduce_axes(ndarray_obj_t *ndarray, int8_t axis, size_t *shape, int32_t *strides) {
+    // removes the values corresponding to a single axis from the shape and strides array
+    uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + axis;
+    if((ndarray->ndim == 1) && (axis == 0)) {
+        index = 0;
+        shape[ULAB_MAX_DIMS - 1] = 1;
+        return;
+    }
+    for(uint8_t i = ULAB_MAX_DIMS - 1; i > 0; i--) {
+        if(i > index) {
+            shape[i] = ndarray->shape[i];
+            strides[i] = ndarray->strides[i];
+        } else {
+            shape[i] = ndarray->shape[i-1];
+            strides[i] = ndarray->strides[i-1];
+        }
+    }
+}
+
+#if ULAB_NUMPY_HAS_ALL | ULAB_NUMPY_HAS_ANY
+static mp_obj_t numerical_all_any(mp_obj_t oin, mp_obj_t axis, uint8_t optype) {
+    bool anytype = optype == NUMERICAL_ALL ? 1 : 0;
+    if(mp_obj_is_type(oin, &ulab_ndarray_type)) {
+        ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(oin);
+        uint8_t *array = (uint8_t *)ndarray->array;
+        if(ndarray->len == 0) { // return immediately with empty arrays
+        if(optype == NUMERICAL_ALL) {
+                return mp_const_true;
+            } else {
+                return mp_const_false;
+            }
+        }
+        // always get a float, so that we don't have to resolve the dtype later
+        mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype);
+        ndarray_obj_t *results = NULL;
+        uint8_t *rarray = NULL;
+        shape_strides _shape_strides = tools_reduce_axes(ndarray, axis);
+        if(axis != mp_const_none) {
+            results = ndarray_new_dense_ndarray(_shape_strides.ndim, _shape_strides.shape, NDARRAY_BOOL);
+            rarray = results->array;
+            if(optype == NUMERICAL_ALL) {
+                memset(rarray, 1, results->len);
+            }
+        }
+
+        #if ULAB_MAX_DIMS > 3
+        size_t i = 0;
+        do {
+        #endif
+            #if ULAB_MAX_DIMS > 2
+            size_t j = 0;
+            do {
+            #endif
+                #if ULAB_MAX_DIMS > 1
+                size_t k = 0;
+                do {
+                #endif
+                    size_t l = 0;
+                    if(axis == mp_const_none) {
+                        do {
+                            #if ULAB_SUPPORTS_COMPLEX
+                            if(ndarray->dtype == NDARRAY_COMPLEX) {
+                                mp_float_t real = *((mp_float_t *)array);
+                                mp_float_t imag = *((mp_float_t *)(array + sizeof(mp_float_t)));
+                                if(((real != MICROPY_FLOAT_CONST(0.0)) | (imag != MICROPY_FLOAT_CONST(0.0))) & !anytype) {
+                                    // optype = NUMERICAL_ANY
+                                    return mp_const_true;
+                                } else if(((real == MICROPY_FLOAT_CONST(0.0)) & (imag == MICROPY_FLOAT_CONST(0.0))) & anytype) {
+                                    // optype == NUMERICAL_ALL
+                                    return mp_const_false;
+                                }
+                            } else {
+                            #endif
+                                mp_float_t value = func(array);
+                                if((value != MICROPY_FLOAT_CONST(0.0)) & !anytype) {
+                                    // optype = NUMERICAL_ANY
+                                    return mp_const_true;
+                                } else if((value == MICROPY_FLOAT_CONST(0.0)) & anytype) {
+                                    // optype == NUMERICAL_ALL
+                                    return mp_const_false;
+                                }
+                            #if ULAB_SUPPORTS_COMPLEX
+                            }
+                            #endif
+                            array += _shape_strides.strides[0];
+                            l++;
+                        } while(l < _shape_strides.shape[0]);
+                    } else { // a scalar axis keyword was supplied
+                        do {
+                            #if ULAB_SUPPORTS_COMPLEX
+                            if(ndarray->dtype == NDARRAY_COMPLEX) {
+                                mp_float_t real = *((mp_float_t *)array);
+                                mp_float_t imag = *((mp_float_t *)(array + sizeof(mp_float_t)));
+                                if(((real != MICROPY_FLOAT_CONST(0.0)) | (imag != MICROPY_FLOAT_CONST(0.0))) & !anytype) {
+                                    // optype = NUMERICAL_ANY
+                                    *rarray = 1;
+                                    // since we are breaking out of the loop, move the pointer forward
+                                    array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l);
+                                    break;
+                                } else if(((real == MICROPY_FLOAT_CONST(0.0)) & (imag == MICROPY_FLOAT_CONST(0.0))) & anytype) {
+                                    // optype == NUMERICAL_ALL
+                                    *rarray = 0;
+                                    // since we are breaking out of the loop, move the pointer forward
+                                    array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l);
+                                    break;
+                                }
+                            } else {
+                            #endif
+                                mp_float_t value = func(array);
+                                if((value != MICROPY_FLOAT_CONST(0.0)) & !anytype) {
+                                    // optype == NUMERICAL_ANY
+                                    *rarray = 1;
+                                    // since we are breaking out of the loop, move the pointer forward
+                                    array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l);
+                                    break;
+                                } else if((value == MICROPY_FLOAT_CONST(0.0)) & anytype) {
+                                    // optype == NUMERICAL_ALL
+                                    *rarray = 0;
+                                    // since we are breaking out of the loop, move the pointer forward
+                                    array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l);
+                                    break;
+                                }
+                            #if ULAB_SUPPORTS_COMPLEX
+                            }
+                            #endif
+                            array += _shape_strides.strides[0];
+                            l++;
+                        } while(l < _shape_strides.shape[0]);
+                    }
+                #if ULAB_MAX_DIMS > 1
+                    rarray += _shape_strides.increment;
+                    array -= _shape_strides.strides[0] * _shape_strides.shape[0];
+                    array += _shape_strides.strides[ULAB_MAX_DIMS - 1];
+                    k++;
+                } while(k < _shape_strides.shape[ULAB_MAX_DIMS - 1]);
+                #endif
+            #if ULAB_MAX_DIMS > 2
+                array -= _shape_strides.strides[ULAB_MAX_DIMS - 1] * _shape_strides.shape[ULAB_MAX_DIMS - 1];
+                array += _shape_strides.strides[ULAB_MAX_DIMS - 2];
+                j++;
+            } while(j < _shape_strides.shape[ULAB_MAX_DIMS - 2]);
+            #endif
+        #if ULAB_MAX_DIMS > 3
+            array -= _shape_strides.strides[ULAB_MAX_DIMS - 2] * _shape_strides.shape[ULAB_MAX_DIMS - 2];
+            array += _shape_strides.strides[ULAB_MAX_DIMS - 3];
+            i++;
+        } while(i < _shape_strides.shape[ULAB_MAX_DIMS - 3]);
+        #endif
+        if(axis == mp_const_none) {
+            // the innermost loop fell through, so return the result here
+            if(!anytype) {
+                return mp_const_false;
+            } else {
+                return mp_const_true;
+            }
+        }
+        return results;
+    } else if(mp_obj_is_int(oin) || mp_obj_is_float(oin)) {
+        return mp_obj_is_true(oin) ? mp_const_true : mp_const_false;
+    } else {
+        mp_obj_iter_buf_t iter_buf;
+        mp_obj_t item, iterable = mp_getiter(oin, &iter_buf);
+        while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) {
+            if(!mp_obj_is_true(item) & !anytype) {
+                return mp_const_false;
+            } else if(mp_obj_is_true(item) & anytype) {
+                return mp_const_true;
+            }
+        }
+    }
+    return anytype ? mp_const_true : mp_const_false;
+}
+#endif
+
+#if ULAB_NUMPY_HAS_SUM | ULAB_NUMPY_HAS_MEAN | ULAB_NUMPY_HAS_STD
+static mp_obj_t numerical_sum_mean_std_iterable(mp_obj_t oin, uint8_t optype, size_t ddof) {
+    mp_float_t value = MICROPY_FLOAT_CONST(0.0);
+    mp_float_t M = MICROPY_FLOAT_CONST(0.0);
+    mp_float_t m = MICROPY_FLOAT_CONST(0.0);
+    mp_float_t S = MICROPY_FLOAT_CONST(0.0);
+    mp_float_t s = MICROPY_FLOAT_CONST(0.0);
+    size_t count = 0;
+    mp_obj_iter_buf_t iter_buf;
+    mp_obj_t item, iterable = mp_getiter(oin, &iter_buf);
+    while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) {
+        value = mp_obj_get_float(item);
+        m = M + (value - M) / (count + 1);
+        s = S + (value - M) * (value - m);
+        M = m;
+        S = s;
+        count++;
+    }
+    if(optype == NUMERICAL_SUM) {
+        return mp_obj_new_float(m * count);
+    } else if(optype == NUMERICAL_MEAN) {
+        return count > 0 ? mp_obj_new_float(m) : mp_obj_new_float(MICROPY_FLOAT_CONST(0.0));
+    } else { // this should be the case of the standard deviation
+        return count > ddof ? mp_obj_new_float(MICROPY_FLOAT_C_FUN(sqrt)(s / (count - ddof))) : mp_obj_new_float(MICROPY_FLOAT_CONST(0.0));
+    }
+}
+
+static mp_obj_t numerical_sum_mean_std_ndarray(ndarray_obj_t *ndarray, mp_obj_t axis, uint8_t optype, size_t ddof) {
+    COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype)
+    uint8_t *array = (uint8_t *)ndarray->array;
+    shape_strides _shape_strides = tools_reduce_axes(ndarray, axis);
+
+    if(axis == mp_const_none) {
+        // work with the flattened array
+        if((optype == NUMERICAL_STD) && (ddof > ndarray->len)) {
+            // if there are too many degrees of freedom, there is no point in calculating anything
+            return mp_obj_new_float(MICROPY_FLOAT_CONST(0.0));
+        }
+        mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype);
+        mp_float_t M = MICROPY_FLOAT_CONST(0.0);
+        mp_float_t m = MICROPY_FLOAT_CONST(0.0);
+        mp_float_t S = MICROPY_FLOAT_CONST(0.0);
+        mp_float_t s = MICROPY_FLOAT_CONST(0.0);
+        size_t count = 0;
+
+        #if ULAB_MAX_DIMS > 3
+        size_t i = 0;
+        do {
+        #endif
+            #if ULAB_MAX_DIMS > 2
+            size_t j = 0;
+            do {
+            #endif
+                #if ULAB_MAX_DIMS > 1
+                size_t k = 0;
+                do {
+                #endif
+                    size_t l = 0;
+                    do {
+                        count++;
+                        mp_float_t value = func(array);
+                        m = M + (value - M) / (mp_float_t)count;
+                        if(optype == NUMERICAL_STD) {
+                            s = S + (value - M) * (value - m);
+                            S = s;
+                        }
+                        M = m;
+                        array += _shape_strides.strides[ULAB_MAX_DIMS - 1];
+                        l++;
+                    } while(l < _shape_strides.shape[ULAB_MAX_DIMS - 1]);
+                #if ULAB_MAX_DIMS > 1
+                    array -= _shape_strides.strides[ULAB_MAX_DIMS - 1] * _shape_strides.shape[ULAB_MAX_DIMS - 1];
+                    array += _shape_strides.strides[ULAB_MAX_DIMS - 2];
+                    k++;
+                } while(k < _shape_strides.shape[ULAB_MAX_DIMS - 2]);
+                #endif
+            #if ULAB_MAX_DIMS > 2
+                array -= _shape_strides.strides[ULAB_MAX_DIMS - 2] * _shape_strides.shape[ULAB_MAX_DIMS - 2];
+                array += _shape_strides.strides[ULAB_MAX_DIMS - 3];
+                j++;
+            } while(j < _shape_strides.shape[ULAB_MAX_DIMS - 3]);
+            #endif
+        #if ULAB_MAX_DIMS > 3
+            array -= _shape_strides.strides[ULAB_MAX_DIMS - 3] * _shape_strides.shape[ULAB_MAX_DIMS - 3];
+            array += _shape_strides.strides[ULAB_MAX_DIMS - 4];
+            i++;
+        } while(i < _shape_strides.shape[ULAB_MAX_DIMS - 4]);
+        #endif
+        if(optype == NUMERICAL_SUM) {
+            // numpy returns an integer for integer input types
+            if(ndarray->dtype == NDARRAY_FLOAT) {
+                return mp_obj_new_float(M * ndarray->len);
+            } else {
+                return mp_obj_new_int((int32_t)MICROPY_FLOAT_C_FUN(round)(M * ndarray->len));
+            }
+        } else if(optype == NUMERICAL_MEAN) {
+            return mp_obj_new_float(M);
+        } else { // this must be the case of the standard deviation
+            // we have already made certain that ddof < ndarray->len holds
+            return mp_obj_new_float(MICROPY_FLOAT_C_FUN(sqrt)(S / (ndarray->len - ddof)));
+        }
+    } else {
+        ndarray_obj_t *results = NULL;
+        uint8_t *rarray = NULL;
+        mp_float_t *farray = NULL;
+        if(optype == NUMERICAL_SUM) {
+            results = ndarray_new_dense_ndarray(_shape_strides.ndim, _shape_strides.shape, ndarray->dtype);
+            rarray = (uint8_t *)results->array;
+            // TODO: numpy promotes the output to the highest integer type
+            if(ndarray->dtype == NDARRAY_UINT8) {
+                RUN_SUM(uint8_t, array, results, rarray, _shape_strides);
+            } else if(ndarray->dtype == NDARRAY_INT8) {
+                RUN_SUM(int8_t, array, results, rarray, _shape_strides);
+            } else if(ndarray->dtype == NDARRAY_UINT16) {
+                RUN_SUM(uint16_t, array, results, rarray, _shape_strides);
+            } else if(ndarray->dtype == NDARRAY_INT16) {
+                RUN_SUM(int16_t, array, results, rarray, _shape_strides);
+            } else {
+                // for floats, the sum might be inaccurate with the naive summation
+                // call mean, and multiply with the number of samples
+                farray = (mp_float_t *)results->array;
+                RUN_MEAN_STD(mp_float_t, array, farray, _shape_strides, MICROPY_FLOAT_CONST(0.0), 0);
+                mp_float_t norm = (mp_float_t)_shape_strides.shape[0];
+                // re-wind the array here
+                farray = (mp_float_t *)results->array;
+                for(size_t i=0; i < results->len; i++) {
+                    *farray++ *= norm;
+                }
+            }
+        } else {
+            bool isStd = optype == NUMERICAL_STD ? 1 : 0;
+            results = ndarray_new_dense_ndarray(_shape_strides.ndim, _shape_strides.shape, NDARRAY_FLOAT);
+            farray = (mp_float_t *)results->array;
+            // we can return the 0 array here, if the degrees of freedom is larger than the length of the axis
+            if((optype == NUMERICAL_STD) && (_shape_strides.shape[0] <= ddof)) {
+                return MP_OBJ_FROM_PTR(results);
+            }
+            mp_float_t div = optype == NUMERICAL_STD ? (mp_float_t)(_shape_strides.shape[0] - ddof) : MICROPY_FLOAT_CONST(0.0);
+            if(ndarray->dtype == NDARRAY_UINT8) {
+                RUN_MEAN_STD(uint8_t, array, farray, _shape_strides, div, isStd);
+            } else if(ndarray->dtype == NDARRAY_INT8) {
+                RUN_MEAN_STD(int8_t, array, farray, _shape_strides, div, isStd);
+            } else if(ndarray->dtype == NDARRAY_UINT16) {
+                RUN_MEAN_STD(uint16_t, array, farray, _shape_strides, div, isStd);
+            } else if(ndarray->dtype == NDARRAY_INT16) {
+                RUN_MEAN_STD(int16_t, array, farray, _shape_strides, div, isStd);
+            } else {
+                RUN_MEAN_STD(mp_float_t, array, farray, _shape_strides, div, isStd);
+            }
+        }
+        if(results->ndim == 0) { // return a scalar here
+            return mp_binary_get_val_array(results->dtype, results->array, 0);
+        }
+        return MP_OBJ_FROM_PTR(results);
+    }
+    return mp_const_none;
+}
+#endif
+
+#if ULAB_NUMPY_HAS_ARGMINMAX
+static mp_obj_t numerical_argmin_argmax_iterable(mp_obj_t oin, uint8_t optype) {
+    if(MP_OBJ_SMALL_INT_VALUE(mp_obj_len_maybe(oin)) == 0) {
+        mp_raise_ValueError(translate("attempt to get argmin/argmax of an empty sequence"));
+    }
+    size_t idx = 0, best_idx = 0;
+    mp_obj_iter_buf_t iter_buf;
+    mp_obj_t iterable = mp_getiter(oin, &iter_buf);
+    mp_obj_t item;
+    uint8_t op = 0; // argmin, min
+    if((optype == NUMERICAL_ARGMAX) || (optype == NUMERICAL_MAX)) op = 1;
+    item = mp_iternext(iterable);
+    mp_obj_t best_obj = item;
+    mp_float_t value, best_value = mp_obj_get_float(item);
+    value = best_value;
+    while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) {
+        idx++;
+        value = mp_obj_get_float(item);
+        if((op == 0) && (value < best_value)) {
+            best_obj = item;
+            best_idx = idx;
+            best_value = value;
+        } else if((op == 1) && (value > best_value)) {
+            best_obj = item;
+            best_idx = idx;
+            best_value = value;
+        }
+    }
+    if((optype == NUMERICAL_ARGMIN) || (optype == NUMERICAL_ARGMAX)) {
+        return MP_OBJ_NEW_SMALL_INT(best_idx);
+    } else {
+        return best_obj;
+    }
+}
+
+static mp_obj_t numerical_argmin_argmax_ndarray(ndarray_obj_t *ndarray, mp_obj_t axis, uint8_t optype) {
+    // TODO: treat the flattened array
+    if(ndarray->len == 0) {
+        mp_raise_ValueError(translate("attempt to get (arg)min/(arg)max of empty sequence"));
+    }
+
+    if(axis == mp_const_none) {
+        // work with the flattened array
+        mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype);
+        uint8_t *array = (uint8_t *)ndarray->array;
+        mp_float_t best_value = func(array);
+        mp_float_t value;
+        size_t index = 0, best_index = 0;
+
+        #if ULAB_MAX_DIMS > 3
+        size_t i = 0;
+        do {
+        #endif
+            #if ULAB_MAX_DIMS > 2
+            size_t j = 0;
+            do {
+            #endif
+                #if ULAB_MAX_DIMS > 1
+                size_t k = 0;
+                do {
+                #endif
+                    size_t l = 0;
+                    do {
+                        value = func(array);
+                        if((optype == NUMERICAL_ARGMAX) || (optype == NUMERICAL_MAX)) {
+                            if(best_value < value) {
+                                best_value = value;
+                                best_index = index;
+                            }
+                        } else {
+                            if(best_value > value) {
+                                best_value = value;
+                                best_index = index;
+                            }
+                        }
+                        array += ndarray->strides[ULAB_MAX_DIMS - 1];
+                        l++;
+                        index++;
+                    } while(l < ndarray->shape[ULAB_MAX_DIMS - 1]);
+                #if ULAB_MAX_DIMS > 1
+                    array -= ndarray->strides[ULAB_MAX_DIMS - 1] * ndarray->shape[ULAB_MAX_DIMS-1];
+                    array += ndarray->strides[ULAB_MAX_DIMS - 2];
+                    k++;
+                } while(k < ndarray->shape[ULAB_MAX_DIMS - 2]);
+                #endif
+            #if ULAB_MAX_DIMS > 2
+                array -= ndarray->strides[ULAB_MAX_DIMS - 2] * ndarray->shape[ULAB_MAX_DIMS-2];
+                array += ndarray->strides[ULAB_MAX_DIMS - 3];
+                j++;
+            } while(j < ndarray->shape[ULAB_MAX_DIMS - 3]);
+            #endif
+        #if ULAB_MAX_DIMS > 3
+            array -= ndarray->strides[ULAB_MAX_DIMS - 3] * ndarray->shape[ULAB_MAX_DIMS-3];
+            array += ndarray->strides[ULAB_MAX_DIMS - 4];
+            i++;
+        } while(i < ndarray->shape[ULAB_MAX_DIMS - 4]);
+        #endif
+
+        if((optype == NUMERICAL_ARGMIN) || (optype == NUMERICAL_ARGMAX)) {
+            return mp_obj_new_int(best_index);
+        } else {
+            if(ndarray->dtype == NDARRAY_FLOAT) {
+                return mp_obj_new_float(best_value);
+            } else {
+                return MP_OBJ_NEW_SMALL_INT((int32_t)best_value);
+            }
+        }
+    } else {
+        int8_t ax = tools_get_axis(axis, ndarray->ndim);
+
+        uint8_t *array = (uint8_t *)ndarray->array;
+        size_t *shape = m_new(size_t, ULAB_MAX_DIMS);
+        memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+        int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);
+        memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS);
+        numerical_reduce_axes(ndarray, ax, shape, strides);
+        uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + ax;
+
+        ndarray_obj_t *results = NULL;
+
+        if((optype == NUMERICAL_ARGMIN) || (optype == NUMERICAL_ARGMAX)) {
+            results = ndarray_new_dense_ndarray(MAX(1, ndarray->ndim-1), shape, NDARRAY_INT16);
+        } else {
+            results = ndarray_new_dense_ndarray(MAX(1, ndarray->ndim-1), shape, ndarray->dtype);
+        }
+
+        uint8_t *rarray = (uint8_t *)results->array;
+
+        if(ndarray->dtype == NDARRAY_UINT8) {
+            RUN_ARGMIN(ndarray, uint8_t, array, results, rarray, shape, strides, index, optype);
+        } else if(ndarray->dtype == NDARRAY_INT8) {
+            RUN_ARGMIN(ndarray, int8_t, array, results, rarray, shape, strides, index, optype);
+        } else if(ndarray->dtype == NDARRAY_UINT16) {
+            RUN_ARGMIN(ndarray, uint16_t, array, results, rarray, shape, strides, index, optype);
+        } else if(ndarray->dtype == NDARRAY_INT16) {
+            RUN_ARGMIN(ndarray, int16_t, array, results, rarray, shape, strides, index, optype);
+        } else {
+            RUN_ARGMIN(ndarray, mp_float_t, array, results, rarray, shape, strides, index, optype);
+        }
+        if(results->len == 1) {
+            return mp_binary_get_val_array(results->dtype, results->array, 0);
+        }
+        return MP_OBJ_FROM_PTR(results);
+    }
+    return mp_const_none;
+}
+#endif
+
+static mp_obj_t numerical_function(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args, uint8_t optype) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none} } ,
+        { MP_QSTR_axis, MP_ARG_OBJ, { .u_rom_obj = mp_const_none } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+    mp_obj_t oin = args[0].u_obj;
+    mp_obj_t axis = args[1].u_obj;
+    if((axis != mp_const_none) && (!mp_obj_is_int(axis))) {
+        mp_raise_TypeError(translate("axis must be None, or an integer"));
+    }
+
+    if((optype == NUMERICAL_ALL) || (optype == NUMERICAL_ANY)) {
+        return numerical_all_any(oin, axis, optype);
+    }
+    if(mp_obj_is_type(oin, &mp_type_tuple) || mp_obj_is_type(oin, &mp_type_list) ||
+        mp_obj_is_type(oin, &mp_type_range)) {
+        switch(optype) {
+            case NUMERICAL_MIN:
+            case NUMERICAL_ARGMIN:
+            case NUMERICAL_MAX:
+            case NUMERICAL_ARGMAX:
+                return numerical_argmin_argmax_iterable(oin, optype);
+            case NUMERICAL_SUM:
+            case NUMERICAL_MEAN:
+                return numerical_sum_mean_std_iterable(oin, optype, 0);
+            default: // we should never reach this point, but whatever
+                return mp_const_none;
+        }
+    } else if(mp_obj_is_type(oin, &ulab_ndarray_type)) {
+        ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(oin);
+        switch(optype) {
+            case NUMERICAL_MIN:
+            case NUMERICAL_MAX:
+            case NUMERICAL_ARGMIN:
+            case NUMERICAL_ARGMAX:
+                COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype)
+                return numerical_argmin_argmax_ndarray(ndarray, axis, optype);
+            case NUMERICAL_SUM:
+            case NUMERICAL_MEAN:
+                COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype)
+                return numerical_sum_mean_std_ndarray(ndarray, axis, optype, 0);
+            default:
+                mp_raise_NotImplementedError(translate("operation is not implemented on ndarrays"));
+        }
+    } else {
+        mp_raise_TypeError(translate("input must be tuple, list, range, or ndarray"));
+    }
+    return mp_const_none;
+}
+
+#if ULAB_NUMPY_HAS_SORT | NDARRAY_HAS_SORT
+static mp_obj_t numerical_sort_helper(mp_obj_t oin, mp_obj_t axis, uint8_t inplace) {
+    if(!mp_obj_is_type(oin, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("sort argument must be an ndarray"));
+    }
+
+    ndarray_obj_t *ndarray;
+    if(inplace == 1) {
+        ndarray = MP_OBJ_TO_PTR(oin);
+    } else {
+        ndarray = ndarray_copy_view(MP_OBJ_TO_PTR(oin));
+    }
+    COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype)
+
+    int8_t ax = 0;
+    if(axis == mp_const_none) {
+        // flatten the array
+        #if ULAB_MAX_DIMS > 1
+        for(uint8_t i=0; i < ULAB_MAX_DIMS - 1; i++) {
+            ndarray->shape[i] = 0;
+            ndarray->strides[i] = 0;
+        }
+        ndarray->shape[ULAB_MAX_DIMS - 1] = ndarray->len;
+        ndarray->strides[ULAB_MAX_DIMS - 1] = ndarray->itemsize;
+        ndarray->ndim = 1;
+        #endif
+    } else {
+        ax = tools_get_axis(axis, ndarray->ndim);
+    }
+
+    size_t *shape = m_new(size_t, ULAB_MAX_DIMS);
+    memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+    int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);
+    memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS);
+    numerical_reduce_axes(ndarray, ax, shape, strides);
+    ax = ULAB_MAX_DIMS - ndarray->ndim + ax;
+    // we work with the typed array, so re-scale the stride
+    int32_t increment = ndarray->strides[ax] / ndarray->itemsize;
+
+    uint8_t *array = (uint8_t *)ndarray->array;
+    if((ndarray->dtype == NDARRAY_UINT8) || (ndarray->dtype == NDARRAY_INT8)) {
+        HEAPSORT(ndarray, uint8_t, array, shape, strides, ax, increment, ndarray->shape[ax]);
+    } else if((ndarray->dtype == NDARRAY_INT16) || (ndarray->dtype == NDARRAY_INT16)) {
+        HEAPSORT(ndarray, uint16_t, array, shape, strides, ax, increment, ndarray->shape[ax]);
+    } else {
+        HEAPSORT(ndarray, mp_float_t, array, shape, strides, ax, increment, ndarray->shape[ax]);
+    }
+    if(inplace == 1) {
+        return mp_const_none;
+    } else {
+        return MP_OBJ_FROM_PTR(ndarray);
+    }
+}
+#endif /* ULAB_NUMERICAL_HAS_SORT | NDARRAY_HAS_SORT */
+
+#if ULAB_NUMPY_HAS_ALL
+mp_obj_t numerical_all(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ALL);
+}
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_all_obj, 1, numerical_all);
+#endif
+
+#if ULAB_NUMPY_HAS_ANY
+mp_obj_t numerical_any(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ANY);
+}
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_any_obj, 1, numerical_any);
+#endif
+
+#if ULAB_NUMPY_HAS_ARGMINMAX
+//| def argmax(array: _ArrayLike, *, axis: Optional[int] = None) -> int:
+//|     """Return the index of the maximum element of the 1D array"""
+//|     ...
+//|
+
+mp_obj_t numerical_argmax(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ARGMAX);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_argmax_obj, 1, numerical_argmax);
+
+//| def argmin(array: _ArrayLike, *, axis: Optional[int] = None) -> int:
+//|     """Return the index of the minimum element of the 1D array"""
+//|     ...
+//|
+
+static mp_obj_t numerical_argmin(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ARGMIN);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_argmin_obj, 1, numerical_argmin);
+#endif
+
+#if ULAB_NUMPY_HAS_ARGSORT
+//| def argsort(array: ulab.numpy.ndarray, *, axis: int = -1) -> ulab.numpy.ndarray:
+//|     """Returns an array which gives indices into the input array from least to greatest."""
+//|     ...
+//|
+
+mp_obj_t numerical_argsort(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } },
+        { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } },
+    };
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+    if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("argsort argument must be an ndarray"));
+    }
+
+    ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj);
+    COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype)
+    if(args[1].u_obj == mp_const_none) {
+        // bail out, though dense arrays could still be sorted
+        mp_raise_NotImplementedError(translate("argsort is not implemented for flattened arrays"));
+    }
+    // Since we are returning an NDARRAY_UINT16 array, bail out,
+    // if the axis is longer than what we can hold
+    for(uint8_t i=0; i < ULAB_MAX_DIMS; i++) {
+        if(ndarray->shape[i] > 65535) {
+            mp_raise_ValueError(translate("axis too long"));
+        }
+    }
+    int8_t ax = tools_get_axis(args[1].u_obj, ndarray->ndim);
+
+    size_t *shape = m_new(size_t, ULAB_MAX_DIMS);
+    memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+    int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);
+    memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS);
+    numerical_reduce_axes(ndarray, ax, shape, strides);
+
+    // We could return an NDARRAY_UINT8 array, if all lengths are shorter than 256
+    ndarray_obj_t *indices = ndarray_new_ndarray(ndarray->ndim, ndarray->shape, NULL, NDARRAY_UINT16);
+    int32_t *istrides = m_new(int32_t, ULAB_MAX_DIMS);
+    memset(istrides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS);
+    numerical_reduce_axes(indices, ax, shape, istrides);
+    for(uint8_t i=0; i < ULAB_MAX_DIMS; i++) {
+        istrides[i] /= sizeof(uint16_t);
+    }
+
+    ax = ULAB_MAX_DIMS - ndarray->ndim + ax;
+    // we work with the typed array, so re-scale the stride
+    int32_t increment = ndarray->strides[ax] / ndarray->itemsize;
+    uint16_t iincrement = indices->strides[ax] / sizeof(uint16_t);
+
+    uint8_t *array = (uint8_t *)ndarray->array;
+    uint16_t *iarray = (uint16_t *)indices->array;
+
+    // fill in the index values
+    #if ULAB_MAX_DIMS > 3
+    size_t j = 0;
+    do {
+    #endif
+        #if ULAB_MAX_DIMS > 2
+        size_t k = 0;
+        do {
+        #endif
+            #if ULAB_MAX_DIMS > 1
+            size_t l = 0;
+            do {
+            #endif
+            uint16_t m = 0;
+                do {
+                    *iarray = m++;
+                    iarray += iincrement;
+                } while(m < indices->shape[ax]);
+            #if ULAB_MAX_DIMS > 1
+                iarray -= iincrement * indices->shape[ax];
+                iarray += istrides[ULAB_MAX_DIMS - 1];
+                l++;
+            } while(l < shape[ULAB_MAX_DIMS - 1]);
+            iarray -= istrides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS - 1];
+            iarray += istrides[ULAB_MAX_DIMS - 2];
+            #endif
+        #if ULAB_MAX_DIMS > 2
+            k++;
+        } while(k < shape[ULAB_MAX_DIMS - 2]);
+        iarray -= istrides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS - 2];
+        iarray += istrides[ULAB_MAX_DIMS - 3];
+        #endif
+    #if ULAB_MAX_DIMS > 3
+        j++;
+    } while(j < shape[ULAB_MAX_DIMS - 3]);
+    #endif
+    // reset the array
+    iarray = indices->array;
+
+    if((ndarray->dtype == NDARRAY_UINT8) || (ndarray->dtype == NDARRAY_INT8)) {
+        HEAP_ARGSORT(ndarray, uint8_t, array, shape, strides, ax, increment, ndarray->shape[ax], iarray, istrides, iincrement);
+    } else if((ndarray->dtype == NDARRAY_UINT16) || (ndarray->dtype == NDARRAY_INT16)) {
+        HEAP_ARGSORT(ndarray, uint16_t, array, shape, strides, ax, increment, ndarray->shape[ax], iarray, istrides, iincrement);
+    } else {
+        HEAP_ARGSORT(ndarray, mp_float_t, array, shape, strides, ax, increment, ndarray->shape[ax], iarray, istrides, iincrement);
+    }
+    return MP_OBJ_FROM_PTR(indices);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_argsort_obj, 1, numerical_argsort);
+#endif
+
+#if ULAB_NUMPY_HAS_CROSS
+//| def cross(a: ulab.numpy.ndarray, b: ulab.numpy.ndarray) -> ulab.numpy.ndarray:
+//|     """Return the cross product of two vectors of length 3"""
+//|     ...
+//|
+
+static mp_obj_t numerical_cross(mp_obj_t _a, mp_obj_t _b) {
+    if (!mp_obj_is_type(_a, &ulab_ndarray_type) || !mp_obj_is_type(_b, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("arguments must be ndarrays"));
+    }
+    ndarray_obj_t *a = MP_OBJ_TO_PTR(_a);
+    ndarray_obj_t *b = MP_OBJ_TO_PTR(_b);
+    COMPLEX_DTYPE_NOT_IMPLEMENTED(a->dtype)
+    COMPLEX_DTYPE_NOT_IMPLEMENTED(b->dtype)
+    if((a->ndim != 1) || (b->ndim != 1) || (a->len != b->len) || (a->len != 3)) {
+        mp_raise_ValueError(translate("cross is defined for 1D arrays of length 3"));
+    }
+
+    mp_float_t *results = m_new(mp_float_t, 3);
+    results[0] = ndarray_get_float_index(a->array, a->dtype, 1) * ndarray_get_float_index(b->array, b->dtype, 2);
+    results[0] -= ndarray_get_float_index(a->array, a->dtype, 2) * ndarray_get_float_index(b->array, b->dtype, 1);
+    results[1] = -ndarray_get_float_index(a->array, a->dtype, 0) * ndarray_get_float_index(b->array, b->dtype, 2);
+    results[1] += ndarray_get_float_index(a->array, a->dtype, 2) * ndarray_get_float_index(b->array, b->dtype, 0);
+    results[2] = ndarray_get_float_index(a->array, a->dtype, 0) * ndarray_get_float_index(b->array, b->dtype, 1);
+    results[2] -= ndarray_get_float_index(a->array, a->dtype, 1) * ndarray_get_float_index(b->array, b->dtype, 0);
+
+    /* The upcasting happens here with the rules
+
+        - if one of the operarands is a float, the result is always float
+        - operation on identical types preserves type
+
+        uint8 + int8 => int16
+        uint8 + int16 => int16
+        uint8 + uint16 => uint16
+        int8 + int16 => int16
+        int8 + uint16 => uint16
+        uint16 + int16 => float
+
+    */
+
+    uint8_t dtype = NDARRAY_FLOAT;
+    if(a->dtype == b->dtype) {
+        dtype = a->dtype;
+    } else if(((a->dtype == NDARRAY_UINT8) && (b->dtype == NDARRAY_INT8)) || ((a->dtype == NDARRAY_INT8) && (b->dtype == NDARRAY_UINT8))) {
+        dtype = NDARRAY_INT16;
+    } else if(((a->dtype == NDARRAY_UINT8) && (b->dtype == NDARRAY_INT16)) || ((a->dtype == NDARRAY_INT16) && (b->dtype == NDARRAY_UINT8))) {
+        dtype = NDARRAY_INT16;
+    } else if(((a->dtype == NDARRAY_UINT8) && (b->dtype == NDARRAY_UINT16)) || ((a->dtype == NDARRAY_UINT16) && (b->dtype == NDARRAY_UINT8))) {
+        dtype = NDARRAY_UINT16;
+    } else if(((a->dtype == NDARRAY_INT8) && (b->dtype == NDARRAY_INT16)) || ((a->dtype == NDARRAY_INT16) && (b->dtype == NDARRAY_INT8))) {
+        dtype = NDARRAY_INT16;
+    } else if(((a->dtype == NDARRAY_INT8) && (b->dtype == NDARRAY_UINT16)) || ((a->dtype == NDARRAY_UINT16) && (b->dtype == NDARRAY_INT8))) {
+        dtype = NDARRAY_UINT16;
+    }
+
+    ndarray_obj_t *ndarray = ndarray_new_linear_array(3, dtype);
+    if(dtype == NDARRAY_UINT8) {
+        uint8_t *array = (uint8_t *)ndarray->array;
+        for(uint8_t i=0; i < 3; i++) array[i] = (uint8_t)results[i];
+    } else if(dtype == NDARRAY_INT8) {
+        int8_t *array = (int8_t *)ndarray->array;
+        for(uint8_t i=0; i < 3; i++) array[i] = (int8_t)results[i];
+    } else if(dtype == NDARRAY_UINT16) {
+        uint16_t *array = (uint16_t *)ndarray->array;
+        for(uint8_t i=0; i < 3; i++) array[i] = (uint16_t)results[i];
+    } else if(dtype == NDARRAY_INT16) {
+        int16_t *array = (int16_t *)ndarray->array;
+        for(uint8_t i=0; i < 3; i++) array[i] = (int16_t)results[i];
+    } else {
+        mp_float_t *array = (mp_float_t *)ndarray->array;
+        for(uint8_t i=0; i < 3; i++) array[i] = results[i];
+    }
+    m_del(mp_float_t, results, 3);
+    return MP_OBJ_FROM_PTR(ndarray);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_2(numerical_cross_obj, numerical_cross);
+
+#endif /* ULAB_NUMERICAL_HAS_CROSS */
+
+#if ULAB_NUMPY_HAS_DIFF
+//| def diff(array: ulab.numpy.ndarray, *, n: int = 1, axis: int = -1) -> ulab.numpy.ndarray:
+//|     """Return the numerical derivative of successive elements of the array, as
+//|        an array.  axis=None is not supported."""
+//|     ...
+//|
+
+mp_obj_t numerical_diff(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+        { MP_QSTR_n, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 1 } },
+        { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = -1 } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+    if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("diff argument must be an ndarray"));
+    }
+
+    ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj);
+    COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype)
+    int8_t ax = args[2].u_int;
+    if(ax < 0) ax += ndarray->ndim;
+
+    if((ax < 0) || (ax > ndarray->ndim - 1)) {
+        mp_raise_ValueError(translate("index out of range"));
+    }
+
+    if((args[1].u_int < 0) || (args[1].u_int > 9)) {
+        mp_raise_ValueError(translate("differentiation order out of range"));
+    }
+    uint8_t N = (uint8_t)args[1].u_int;
+    uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + ax;
+    if(N > ndarray->shape[index]) {
+        mp_raise_ValueError(translate("differentiation order out of range"));
+    }
+
+    int8_t *stencil = m_new(int8_t, N+1);
+    stencil[0] = 1;
+    for(uint8_t i=1; i < N+1; i++) {
+        stencil[i] = -stencil[i-1]*(N-i+1)/i;
+    }
+
+    size_t *shape = m_new(size_t, ULAB_MAX_DIMS);
+    memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+    for(uint8_t i=0; i < ULAB_MAX_DIMS; i++) {
+        shape[i] = ndarray->shape[i];
+        if(i == index) {
+            shape[i] -= N;
+        }
+    }
+    uint8_t *array = (uint8_t *)ndarray->array;
+    ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim, shape, ndarray->dtype);
+    uint8_t *rarray = (uint8_t *)results->array;
+
+    memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+    int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);
+    memset(strides, 0, sizeof(int32_t)*ULAB_MAX_DIMS);
+    numerical_reduce_axes(ndarray, ax, shape, strides);
+
+    if(ndarray->dtype == NDARRAY_UINT8) {
+        RUN_DIFF(ndarray, uint8_t, array, results, rarray, shape, strides, index, stencil, N);
+    } else if(ndarray->dtype == NDARRAY_INT8) {
+        RUN_DIFF(ndarray, int8_t, array, results, rarray, shape, strides, index, stencil, N);
+    }  else if(ndarray->dtype == NDARRAY_UINT16) {
+        RUN_DIFF(ndarray, uint16_t, array, results, rarray, shape, strides, index, stencil, N);
+    } else if(ndarray->dtype == NDARRAY_INT16) {
+        RUN_DIFF(ndarray, int16_t, array, results, rarray, shape, strides, index, stencil, N);
+    } else {
+        RUN_DIFF(ndarray, mp_float_t, array, results, rarray, shape, strides, index, stencil, N);
+    }
+    m_del(int8_t, stencil, N+1);
+    m_del(size_t, shape, ULAB_MAX_DIMS);
+    m_del(int32_t, strides, ULAB_MAX_DIMS);
+    return MP_OBJ_FROM_PTR(results);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_diff_obj, 1, numerical_diff);
+#endif
+
+#if ULAB_NUMPY_HAS_FLIP
+//| def flip(array: ulab.numpy.ndarray, *, axis: Optional[int] = None) -> ulab.numpy.ndarray:
+//|     """Returns a new array that reverses the order of the elements along the
+//|        given axis, or along all axes if axis is None."""
+//|     ...
+//|
+
+mp_obj_t numerical_flip(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+        { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+    if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("flip argument must be an ndarray"));
+    }
+
+    ndarray_obj_t *results = NULL;
+    ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj);
+    if(args[1].u_obj == mp_const_none) { // flip the flattened array
+        results = ndarray_new_linear_array(ndarray->len, ndarray->dtype);
+        ndarray_copy_array(ndarray, results, 0);
+        uint8_t *rarray = (uint8_t *)results->array;
+        rarray += (results->len - 1) * results->itemsize;
+        results->array = rarray;
+        results->strides[ULAB_MAX_DIMS - 1] = -results->strides[ULAB_MAX_DIMS - 1];
+    } else if(mp_obj_is_int(args[1].u_obj)){
+        int8_t ax = tools_get_axis(args[1].u_obj, ndarray->ndim);
+
+        ax = ULAB_MAX_DIMS - ndarray->ndim + ax;
+        int32_t offset = (ndarray->shape[ax] - 1) * ndarray->strides[ax];
+        results = ndarray_new_view(ndarray, ndarray->ndim, ndarray->shape, ndarray->strides, offset);
+        results->strides[ax] = -results->strides[ax];
+    } else {
+        mp_raise_TypeError(translate("wrong axis index"));
+    }
+    return results;
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_flip_obj, 1, numerical_flip);
+#endif
+
+#if ULAB_NUMPY_HAS_MINMAX
+//| def max(array: _ArrayLike, *, axis: Optional[int] = None) -> _float:
+//|     """Return the maximum element of the 1D array"""
+//|     ...
+//|
+
+mp_obj_t numerical_max(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_MAX);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_max_obj, 1, numerical_max);
+#endif
+
+#if ULAB_NUMPY_HAS_MEAN
+//| def mean(array: _ArrayLike, *, axis: Optional[int] = None) -> _float:
+//|     """Return the mean element of the 1D array, as a number if axis is None, otherwise as an array."""
+//|     ...
+//|
+
+mp_obj_t numerical_mean(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_MEAN);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_mean_obj, 1, numerical_mean);
+#endif
+
+#if ULAB_NUMPY_HAS_MEDIAN
+//| def median(array: ulab.numpy.ndarray, *, axis: int = -1) -> ulab.numpy.ndarray:
+//|     """Find the median value in an array along the given axis, or along all axes if axis is None."""
+//|     ...
+//|
+
+mp_obj_t numerical_median(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+        { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+    if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("median argument must be an ndarray"));
+    }
+
+    ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj);
+    if(ndarray->len == 0) {
+        return mp_obj_new_float(MICROPY_FLOAT_C_FUN(nan)(""));
+    }
+
+    ndarray = numerical_sort_helper(args[0].u_obj, args[1].u_obj, 0);
+
+    if((args[1].u_obj == mp_const_none) || (ndarray->ndim == 1)) {
+        // at this point, the array holding the sorted values should be flat
+        uint8_t *array = (uint8_t *)ndarray->array;
+        size_t len = ndarray->len;
+        array += (len >> 1) * ndarray->itemsize;
+        mp_float_t median = ndarray_get_float_value(array, ndarray->dtype);
+        if(!(len & 0x01)) { // len is an even number
+            array -= ndarray->itemsize;
+            median += ndarray_get_float_value(array, ndarray->dtype);
+            median *= MICROPY_FLOAT_CONST(0.5);
+        }
+        return mp_obj_new_float(median);
+    } else {
+        int8_t ax = tools_get_axis(args[1].u_obj, ndarray->ndim);
+
+        size_t *shape = m_new(size_t, ULAB_MAX_DIMS);
+        memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+        int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);
+        memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS);
+        numerical_reduce_axes(ndarray, ax, shape, strides);
+        ax = ULAB_MAX_DIMS - ndarray->ndim + ax;
+        ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim-1, shape, NDARRAY_FLOAT);
+        mp_float_t *rarray = (mp_float_t *)results->array;
+
+        uint8_t *array = (uint8_t *)ndarray->array;
+
+        size_t len = ndarray->shape[ax];
+
+        #if ULAB_MAX_DIMS > 3
+        size_t i = 0;
+        do {
+        #endif
+            #if ULAB_MAX_DIMS > 2
+            size_t j = 0;
+            do {
+            #endif
+                size_t k = 0;
+                do {
+                    array += ndarray->strides[ax] * (len >> 1);
+                    mp_float_t median = ndarray_get_float_value(array, ndarray->dtype);
+                    if(!(len & 0x01)) { // len is an even number
+                        array -= ndarray->strides[ax];
+                        median += ndarray_get_float_value(array, ndarray->dtype);
+                        median *= MICROPY_FLOAT_CONST(0.5);
+                        array += ndarray->strides[ax];
+                    }
+                    array -= ndarray->strides[ax] * (len >> 1);
+                    array += strides[ULAB_MAX_DIMS - 1];
+                    *rarray = median;
+                    rarray++;
+                    k++;
+                } while(k < shape[ULAB_MAX_DIMS - 1]);
+            #if ULAB_MAX_DIMS > 2
+                array -= strides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS - 1];
+                array += strides[ULAB_MAX_DIMS - 2];
+                j++;
+            } while(j < shape[ULAB_MAX_DIMS - 2]);
+            #endif
+        #if ULAB_MAX_DIMS > 3
+            array -= strides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS-2];
+            array += strides[ULAB_MAX_DIMS - 3];
+            i++;
+        } while(i < shape[ULAB_MAX_DIMS - 3]);
+        #endif
+
+        return MP_OBJ_FROM_PTR(results);
+    }
+    return mp_const_none;
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_median_obj, 1, numerical_median);
+#endif
+
+#if ULAB_NUMPY_HAS_MINMAX
+//| def min(array: _ArrayLike, *, axis: Optional[int] = None) -> _float:
+//|     """Return the minimum element of the 1D array"""
+//|     ...
+//|
+
+mp_obj_t numerical_min(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_MIN);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_min_obj, 1, numerical_min);
+#endif
+
+#if ULAB_NUMPY_HAS_ROLL
+//| def roll(array: ulab.numpy.ndarray, distance: int, *, axis: Optional[int] = None) -> None:
+//|     """Shift the content of a vector by the positions given as the second
+//|        argument. If the ``axis`` keyword is supplied, the shift is applied to
+//|        the given axis.  The array is modified in place."""
+//|     ...
+//|
+
+mp_obj_t numerical_roll(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none  } },
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+        { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+    if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) {
+        mp_raise_TypeError(translate("roll argument must be an ndarray"));
+    }
+    ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj);
+    uint8_t *array = ndarray->array;
+    ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim, ndarray->shape, ndarray->dtype);
+
+    int32_t shift = mp_obj_get_int(args[1].u_obj);
+    int32_t _shift = shift < 0 ? -shift : shift;
+
+    size_t counter;
+    uint8_t *rarray = (uint8_t *)results->array;
+
+    if(args[2].u_obj == mp_const_none) { // roll the flattened array
+        _shift = _shift % results->len;
+        if(shift > 0) { // shift to the right
+            rarray += _shift * results->itemsize;
+            counter = results->len - _shift;
+        } else { // shift to the left
+            rarray += (results->len - _shift) * results->itemsize;
+            counter = _shift;
+        }
+        #if ULAB_MAX_DIMS > 3
+        size_t i = 0;
+        do {
+        #endif
+            #if ULAB_MAX_DIMS > 2
+            size_t j = 0;
+            do {
+            #endif
+                #if ULAB_MAX_DIMS > 1
+                size_t k = 0;
+                do {
+                #endif
+                    size_t l = 0;
+                    do {
+                        memcpy(rarray, array, ndarray->itemsize);
+                        rarray += results->itemsize;
+                        array += ndarray->strides[ULAB_MAX_DIMS - 1];
+                        l++;
+                        if(--counter == 0) {
+                            rarray = results->array;
+                        }
+                    } while(l <  ndarray->shape[ULAB_MAX_DIMS - 1]);
+                #if ULAB_MAX_DIMS > 1
+                    array -= ndarray->strides[ULAB_MAX_DIMS - 1] * ndarray->shape[ULAB_MAX_DIMS-1];
+                    array += ndarray->strides[ULAB_MAX_DIMS - 2];
+                    k++;
+                } while(k <  ndarray->shape[ULAB_MAX_DIMS - 2]);
+                #endif
+            #if ULAB_MAX_DIMS > 2
+                array -= ndarray->strides[ULAB_MAX_DIMS - 2] * ndarray->shape[ULAB_MAX_DIMS-2];
+                array += ndarray->strides[ULAB_MAX_DIMS - 3];
+                j++;
+            } while(j <  ndarray->shape[ULAB_MAX_DIMS - 3]);
+            #endif
+        #if ULAB_MAX_DIMS > 3
+            array -= ndarray->strides[ULAB_MAX_DIMS - 3] * ndarray->shape[ULAB_MAX_DIMS-3];
+            array += ndarray->strides[ULAB_MAX_DIMS - 4];
+            i++;
+        } while(i <  ndarray->shape[ULAB_MAX_DIMS - 4]);
+        #endif
+    } else if(mp_obj_is_int(args[2].u_obj)){
+        int8_t ax = tools_get_axis(args[2].u_obj, ndarray->ndim);
+
+        size_t *shape = m_new(size_t, ULAB_MAX_DIMS);
+        memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+        int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);
+        memset(strides, 0, sizeof(int32_t)*ULAB_MAX_DIMS);
+        numerical_reduce_axes(ndarray, ax, shape, strides);
+
+        size_t *rshape = m_new(size_t, ULAB_MAX_DIMS);
+        memset(rshape, 0, sizeof(size_t)*ULAB_MAX_DIMS);
+        int32_t *rstrides = m_new(int32_t, ULAB_MAX_DIMS);
+        memset(rstrides, 0, sizeof(int32_t)*ULAB_MAX_DIMS);
+        numerical_reduce_axes(results, ax, rshape, rstrides);
+
+        ax = ULAB_MAX_DIMS - ndarray->ndim + ax;
+        uint8_t *_rarray;
+        _shift = _shift % results->shape[ax];
+
+        #if ULAB_MAX_DIMS > 3
+        size_t i = 0;
+        do {
+        #endif
+            #if ULAB_MAX_DIMS > 2
+            size_t j = 0;
+            do {
+            #endif
+                #if ULAB_MAX_DIMS > 1
+                size_t k = 0;
+                do {
+                #endif
+                    size_t l = 0;
+                    _rarray = rarray;
+                    if(shift < 0) {
+                        rarray += (results->shape[ax] - _shift) * results->strides[ax];
+                        counter = _shift;
+                    } else {
+                        rarray += _shift * results->strides[ax];
+                        counter = results->shape[ax] - _shift;
+                    }
+                    do {
+                        memcpy(rarray, array, ndarray->itemsize);
+                        array += ndarray->strides[ax];
+                        rarray += results->strides[ax];
+                        if(--counter == 0) {
+                            rarray = _rarray;
+                        }
+                        l++;
+                    } while(l < ndarray->shape[ax]);
+                #if ULAB_MAX_DIMS > 1
+                    rarray = _rarray;
+                    rarray += rstrides[ULAB_MAX_DIMS - 1];
+                    array -= ndarray->strides[ax] * ndarray->shape[ax];
+                    array += strides[ULAB_MAX_DIMS - 1];
+                    k++;
+                } while(k < shape[ULAB_MAX_DIMS - 1]);
+                #endif
+            #if ULAB_MAX_DIMS > 2
+                rarray -= rstrides[ULAB_MAX_DIMS - 1] * rshape[ULAB_MAX_DIMS-1];
+                rarray += rstrides[ULAB_MAX_DIMS - 2];
+                array -= strides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS-1];
+                array += strides[ULAB_MAX_DIMS - 2];
+                j++;
+            } while(j < shape[ULAB_MAX_DIMS - 2]);
+            #endif
+        #if ULAB_MAX_DIMS > 3
+            rarray -= rstrides[ULAB_MAX_DIMS - 2] * rshape[ULAB_MAX_DIMS-2];
+            rarray += rstrides[ULAB_MAX_DIMS - 3];
+            array -= strides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS-2];
+            array += strides[ULAB_MAX_DIMS - 3];
+            i++;
+        } while(i < shape[ULAB_MAX_DIMS - 3]);
+        #endif
+    } else {
+        mp_raise_TypeError(translate("wrong axis index"));
+    }
+    return results;
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_roll_obj, 2, numerical_roll);
+#endif
+
+#if ULAB_NUMPY_HAS_SORT
+//| def sort(array: ulab.numpy.ndarray, *, axis: int = -1) -> ulab.numpy.ndarray:
+//|     """Sort the array along the given axis, or along all axes if axis is None.
+//|        The array is modified in place."""
+//|     ...
+//|
+
+mp_obj_t numerical_sort(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } },
+        { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+    return numerical_sort_helper(args[0].u_obj, args[1].u_obj, 0);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_sort_obj, 1, numerical_sort);
+#endif
+
+#if NDARRAY_HAS_SORT
+// method of an ndarray
+static mp_obj_t numerical_sort_inplace(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+        { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_int = -1 } },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+    return numerical_sort_helper(args[0].u_obj, args[1].u_obj, 1);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_sort_inplace_obj, 1, numerical_sort_inplace);
+#endif /* NDARRAY_HAS_SORT */
+
+#if ULAB_NUMPY_HAS_STD
+//| def std(array: _ArrayLike, *, axis: Optional[int] = None, ddof: int = 0) -> _float:
+//|     """Return the standard deviation of the array, as a number if axis is None, otherwise as an array."""
+//|     ...
+//|
+
+mp_obj_t numerical_std(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    static const mp_arg_t allowed_args[] = {
+        { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } } ,
+        { MP_QSTR_axis, MP_ARG_OBJ, {.u_rom_obj = mp_const_none } },
+        { MP_QSTR_ddof, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 0} },
+    };
+
+    mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)];
+    mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args);
+
+    mp_obj_t oin = args[0].u_obj;
+    mp_obj_t axis = args[1].u_obj;
+    size_t ddof = args[2].u_int;
+    if((axis != mp_const_none) && (mp_obj_get_int(axis) != 0) && (mp_obj_get_int(axis) != 1)) {
+        // this seems to pass with False, and True...
+        mp_raise_ValueError(translate("axis must be None, or an integer"));
+    }
+    if(mp_obj_is_type(oin, &mp_type_tuple) || mp_obj_is_type(oin, &mp_type_list) || mp_obj_is_type(oin, &mp_type_range)) {
+        return numerical_sum_mean_std_iterable(oin, NUMERICAL_STD, ddof);
+    } else if(mp_obj_is_type(oin, &ulab_ndarray_type)) {
+        ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(oin);
+        return numerical_sum_mean_std_ndarray(ndarray, axis, NUMERICAL_STD, ddof);
+    } else {
+        mp_raise_TypeError(translate("input must be tuple, list, range, or ndarray"));
+    }
+    return mp_const_none;
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_std_obj, 1, numerical_std);
+#endif
+
+#if ULAB_NUMPY_HAS_SUM
+//| def sum(array: _ArrayLike, *, axis: Optional[int] = None) -> Union[_float, int, ulab.numpy.ndarray]:
+//|     """Return the sum of the array, as a number if axis is None, otherwise as an array."""
+//|     ...
+//|
+
+mp_obj_t numerical_sum(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) {
+    return numerical_function(n_args, pos_args, kw_args, NUMERICAL_SUM);
+}
+
+MP_DEFINE_CONST_FUN_OBJ_KW(numerical_sum_obj, 1, numerical_sum);
+#endif