I was posed the question
With the preposition of y > z < x > 1
With the preposition of y > z < x > 1
Solve for x where zx + x = y
Naturally, as maths would in simple terms dictate the answer:
x = y/z+1
Computers on the other hand would go through the convoluted length of controlling hyperbolic paraboloids as:
[memory] int / ( [+increment] [(pointer to mem)] )
x = [1 / z] * y / (1 + [(1/z)])
I only question it?
I welcome feedback, conjecture and teachings; just a neophyte lost without structure.
Here's a possible solution space which allows for nearest-neighbour deviation handling of data corroboration.
import struct
import numpy as np
import threading
def hyperbolic_parabolic_interpolation_nd_revised(all_fy_data, all_fx_data, x_interp):
"""
Performs hyperbolic-parabolic interpolation on n-dimensional data, with
sharpness dynamically adjusted by the standard deviation of nearest neighbors.
Args:
all_fy_data (list of numpy.ndarray): A list of y-data arrays.
all_fx_data (list of numpy.ndarray): A list of corresponding x-data arrays.
x_interp (numpy.ndarray): Array of x-values for interpolation.
Returns:
numpy.ndarray: Concatenated array of interpolated y-values.
"""
all_interp_y = []
num_dimensions = len(all_fy_data)
if len(all_fx_data) != num_dimensions:
raise ValueError("The number of x-data arrays must match the number of y-data arrays.")
for fx, fy in zip(all_fx_data, all_fy_data):
try:
if len(fx) != len(fy) or len(fx) < 3:
raise ValueError("X and Y data must have equal length and at least three points for this interpolation.")
interp_y = []
for x in x_interp:
# Find the three closest data points
distances = np.abs(fx - x)
closest_indices = np.argsort(distances)[:3]
x_closest = fx[closest_indices]
y_closest = fy[closest_indices]
sorted_indices = np.argsort(x_closest)
x1, x2, x3 = x_closest[sorted_indices]
y1, y2, y3 = y_closest[sorted_indices]
# Dynamically adjust sharpness based on the standard deviation of nearest neighbors
# We normalize the std dev to be a small positive number to avoid extreme sharpness values
if len(y_closest) < 2:
std_dev = 0
else:
std_dev = np.std(y_closest)
# A higher standard deviation suggests more noise/scatter, so we want to smooth the interpolation
# by reducing the sharpness. We use a reciprocal or inverse relationship.
# Adding a small epsilon to the denominator prevents division by zero.
dynamic_sharpness = 1.0 / (1.0 + std_dev + 1e-9)
# Parabolic interpolation
if np.isclose(x1, x2):
a_p = 0
b_p = (y3 - y1) / (x3 - x1) if not np.isclose(x3, x1) else 0
c_p = y1 - b_p * x1
else:
a_p = ((y3 - y1) / (x3 - x1) - (y2 - y1) / (x2 - x1)) / (x3 - x2) if not np.isclose(x3, x2) else 0
b_p = (y2 - y1) / (x2 - x1) - a_p * (x1 + x2) if not np.isclose(x2, x1) else 0
c_p = y1 - b_p * x1 - a_p * x1**2
y_parabolic = a_p * x**2 + b_p * x + c_p
# Hyperbolic interpolation (using a simple form)
if np.isclose(x2 - x1, 0) or np.isclose(x3 - x2, 0):
y_hyperbolic = y2
else:
k1 = (y2 - y1) / (x2 - x1)
k2 = (y3 - y2) / (x3 - x2)
if np.isclose(k1, k2):
y_hyperbolic = y1 + k1 * (x - x1)
else:
A = (k2 - k1) / (x3 - x1)
y_hyperbolic = y1 + k1 * (x - x1) + A * (x - x1) * (x - x2)
# Blend the two interpolations using the dynamic sharpness
# The blend factor logic remains, but now `sharpness` is `dynamic_sharpness`
blend_factor = 1 / (1 + np.exp(-dynamic_sharpness * (np.abs(x - x2) - 0.5 * (x3 - x1))))
interp_y_val = (1 - blend_factor) * y_parabolic + blend_factor * y_hyperbolic
interp_y.append(interp_y_val)
all_interp_y.extend(interp_y)
except ValueError as e:
raise ValueError(str(e))
except Exception as e:
raise Exception(f"An unexpected error occurred during interpolation for one dimension: {e}")
return np.array(all_interp_y)
def handle_client(client_socket, addr):
"""
Handles communication with a single client, receiving n-dimensional float data
and sending back hyperbolic-parabolic interpolated results.
Expects a leading byte (always 2 for this refactored version),
followed by the number of data dimensions, then for each dimension:
the number of floats in the x array, the x array, the number of floats in the y array, the y array.
Finally, it expects the number of interpolation x values and the interpolation x values.
"""
print(f"Handling client: {addr}")
try:
# Receive operation code (expecting 2 for hyperbolic-parabolic)
operation_code_bytes = client_socket.recv(1)
if not operation_code_bytes:
print(f"Client {addr} disconnected unexpectedly (no operation code).")
return
operation_code = struct.unpack('!B', operation_code_bytes)[0]
if operation_code != 2:
error_message = f"Invalid operation code for hyperbolic-parabolic interpolation: {operation_code}".encode('utf-8')
client_socket.sendall(struct.pack('!I', len(error_message)))
client_socket.sendall(error_message)
print(f"Client {addr} sent an invalid operation code: {operation_code}")
return
# Receive the number of data dimensions
num_dimensions_bytes = client_socket.recv(4)
if not num_dimensions_bytes:
print(f"Client {addr} disconnected unexpectedly (no number of dimensions).")
return
num_dimensions = struct.unpack('!I', num_dimensions_bytes)[0]
all_fx_data = []
all_fy_data = []
for dim in range(num_dimensions):
# Receive the number of floats in the x array for this dimension
num_fx_bytes = client_socket.recv(4)
if not num_fx_bytes:
print(f"Client {addr} disconnected unexpectedly (no length for x data in dimension {dim+1}).")
return
num_fx = struct.unpack('!I', num_fx_bytes)[0]
# Receive the x float data for this dimension
fx_bytes = b''
expected_fx_bytes = num_fx * 4
while len(fx_bytes) < expected_fx_bytes:
chunk = client_socket.recv(4096)
if not chunk:
print(f"Client {addr} disconnected unexpectedly (incomplete x data in dimension {dim+1}).")
return
fx_bytes += chunk
fx_data = np.array(struct.unpack(f'!{num_fx}f', fx_bytes))
all_fx_data.append(fx_data)
# Receive the number of floats in the y array for this dimension
num_fy_bytes = client_socket.recv(4)
if not num_fy_bytes:
print(f"Client {addr} disconnected unexpectedly (no length for y data in dimension {dim+1}).")
return
num_fy = struct.unpack('!I', num_fy_bytes)[0]
# Receive the y float data for this dimension
fy_bytes = b''
expected_fy_bytes = num_fy * 4
while len(fy_bytes) < expected_fy_bytes:
chunk = client_socket.recv(4096)
if not chunk:
print(f"Client {addr} disconnected unexpectedly (incomplete y data in dimension {dim+1}).")
return
fy_bytes += chunk
fy_data = np.array(struct.unpack(f'!{num_fy}f', fy_bytes))
all_fy_data.append(fy_data)
# Receive the number of interpolation x values
interp_x_count_bytes = client_socket.recv(4)
if not interp_x_count_bytes:
print(f"Client {addr} disconnected unexpectedly (no length for interpolation x).")
return
interp_x_count = struct.unpack('!I', interp_x_count_bytes)[0]
# Receive the interpolation x values
interp_x_bytes = b''
expected_interp_x_bytes = interp_x_count * 4
while len(interp_x_bytes) < expected_interp_x_bytes:
chunk = client_socket.recv(4096)
if not chunk:
print(f"Client {addr} disconnected unexpectedly (incomplete interpolation x).")
return
interp_x_bytes += chunk
interp_x_data = np.array(struct.unpack(f'!{interp_x_count}f', interp_x_bytes))
# Perform hyperbolic-parabolic interpolation with the revised function
# Note: The sharpness parameter is no longer needed here.
result = hyperbolic_parabolic_interpolation_nd_revised(all_fy_data, all_fx_data, interp_x_data)
# Send the float result back to the client
result_bytes = struct.pack(f'!{len(result)}f', *result)
result_length = len(result_bytes)
client_socket.sendall(struct.pack('!I', result_length))
client_socket.sendall(result_bytes)
except ValueError as e:
print(f"ValueError on server from {addr}: {e}")
error_message = str(e).encode('utf-8')
client_socket.sendall(struct.pack('!I', len(error_message)))
client_socket.sendall(error_message)
except ConnectionResetError:
print(f"Client {addr} forcibly closed the connection.")
except Exception as e:
print(f"An unexpected error occurred in handle_client for {addr}: {e}")
finally:
client_socket.close()
print(f"Connection with client {addr} closed.")
def start_server(host, port):
"""
Starts a server to listen for incoming n-dimensional float data streams for
hyperbolic-parabolic interpolation.
Handles each client connection in a separate thread.
"""
server_socket = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
server_socket.bind((host, port))
server_socket.listen(5)
print(f"Server listening on {host}:{port}")
try:
while True:
client_socket, addr = server_socket.accept()
print(f"Accepted connection from {addr}")
client_thread = threading.Thread(target=handle_client, args=(client_socket, addr))
client_thread.start()
except KeyboardInterrupt:
print("\nServer shutting down...")
finally:
server_socket.close()
print("Server socket closed.")
if __name__ == "__main__":
SERVER_HOST = '127.0.0.1'
SERVER_PORT = 12345
start_server(SERVER_HOST, SERVER_PORT)
Assembly client:
section .data
msg_handling db "Handling client: ", 0
msg_disconnected_op_code db "Client %d.%d.%d.%d disconnected unexpectedly (no operation code).", 0
msg_invalid_op_code db "Invalid operation code for hyperbolic-parabolic interpolation: %u", 0
msg_disconnected_num_dim db "Client %d.%d.%d.%d disconnected unexpectedly (no number of dimensions).", 0
msg_disconnected_x_len db "Client %d.%d.%d.%d disconnected unexpectedly (no length for x data in dimension %u).", 0
msg_disconnected_incomplete_x db "Client %d.%d.%d.%d disconnected unexpectedly (incomplete x data in dimension %u).", 0
msg_disconnected_y_len db "Client %d.%d.%d.%d disconnected unexpectedly (no length for y data in dimension %u).", 0
msg_disconnected_incomplete_y db "Client %d.%d.%d.%d disconnected unexpectedly (incomplete y data in dimension %u).", 0
msg_disconnected_interp_x_len db "Client %d.%d.%d.%d disconnected unexpectedly (no length for interpolation x).", 0
msg_disconnected_incomplete_interp_x db "Client %d.%d.%d.%d disconnected unexpectedly (incomplete interpolation x).", 0
msg_value_error db "ValueError on server from %d.%d.%d.%d: %s", 0
msg_connection_reset db "Client %d.%d.%d.%d forcibly closed the connection.", 0
msg_unexpected_error db "An unexpected error occurred in handle_client for %d.%d.%d.%d: %s", 0
msg_connection_closed db "Connection with client %d.%d.%d.%d closed.", 0
op_code_expected dw 2 ; Expecting operation code 2
float_size dw 4
chunk_size dw 4096
struct_unpack_fmt_b db "!B", 0
struct_unpack_fmt_i db "!I", 0
struct_unpack_fmt_f db "!%uf", 0 ; Placeholder for number of floats
struct_pack_fmt_i db "!I", 0
struct_pack_fmt_f db "!%uf", 0 ; Placeholder for number of floats
section .bss
client_address resd 4 ; To store client IP address
num_dimensions_received resd 1
num_fx_received resd 1
num_fy_received resd 1
num_interp_x_received resd 1
fx_data_buffer resb 16384 ; Adjust size as needed
fy_data_buffer resb 16384 ; Adjust size as needed
interp_x_data_buffer resb 16384 ; Adjust size as needed
error_message_buffer resb 256 ; For storing error messages
result_length_send resd 1
result_buffer resb 16384 ; Adjust size as needed
extern printf
extern recv
extern send
extern close
extern struct_unpack
extern struct_pack
extern strlen
extern strcpy
extern hyperbolic_parabolic_interpolation_nd
section .text
global handle_client
handle_client:
push ebp
mov ebp, esp
push ebx
push esi
push edi
push ebp ; For backtrace
mov esi, [ebp+8] ; client_socket
mov edi, [ebp+12] ; addr (pointer to sockaddr_in)
; Extract client IP address for logging
mov eax, [edi+4] ; sin_addr
mov [client_address], eax
; Print "Handling client: "
push msg_handling
call printf
add esp, 4
; Print client address
push dword [client_address+0]
push dword [client_address+1]
push dword [client_address+2]
push dword [client_address+3]
push format_ip
call printf
add esp, 16
; Receive operation code (1 byte)
push 1
push esi
push operation_code_buffer
call recv
add esp, 12
cmp eax, 1
jl .client_disconnected_op_code
push operation_code_buffer
push struct_unpack_fmt_b
push operation_code_received
call struct_unpack
add esp, 12
cmp byte [operation_code_received], word [op_code_expected]
jne .invalid_op_code
; Receive the number of data dimensions (4 bytes)
push 4
push esi
push num_dimensions_buffer
call recv
add esp, 12
cmp eax, 4
jl .client_disconnected_num_dim
push num_dimensions_buffer
push struct_unpack_fmt_i
push dword [num_dimensions_received]
call struct_unpack
add esp, 12
mov ecx, [num_dimensions_received] ; Loop through dimensions
mov ebx, 0 ; Dimension counter
.dimension_loop:
cmp ebx, ecx
jge .receive_interp_x_count
inc ebx
; Receive the number of floats in the x array for this dimension (4 bytes)
push 4
push esi
push num_fx_buffer
call recv
add esp, 12
cmp eax, 4
jl .client_disconnected_x_len
push num_fx_buffer
push struct_unpack_fmt_i
push dword [num_fx_received]
call struct_unpack
add esp, 12
mov esi, [ebp+8] ; Reset socket for recv
mov eax, [num_fx_received]
mov edx, word [float_size]
mul edx ; Expected number of bytes for x data
mov [expected_bytes], eax
mov edi, fx_data_buffer
call receive_all
cmp eax, [expected_bytes]
jnz .client_disconnected_incomplete_x
; Receive the number of floats in the y array for this dimension (4 bytes)
push 4
push esi
push num_fy_buffer
call recv
add esp, 12
cmp eax, 4
jl .client_disconnected_y_len
push num_fy_buffer
push struct_unpack_fmt_i
push dword [num_fy_received]
call struct_unpack
add esp, 12
mov esi, [ebp+8] ; Reset socket for recv
mov eax, [num_fy_received]
mov edx, word [float_size]
mul edx ; Expected number of bytes for y data
mov [expected_bytes], eax
mov edi, fy_data_buffer
call receive_all
cmp eax, [expected_bytes]
jnz .client_disconnected_incomplete_y
; TODO: Store fx_data_buffer and fy_data_buffer pointers for interpolation
jmp .dimension_loop
.receive_interp_x_count:
; Receive the number of interpolation x values (4 bytes)
push 4
push esi
push num_interp_x_buffer
call recv
add esp, 12
cmp eax, 4
jl .client_disconnected_interp_x_len
push num_interp_x_buffer
push struct_unpack_fmt_i
push dword [num_interp_x_received]
call struct_unpack
add esp, 12
mov esi, [ebp+8] ; Reset socket for recv
mov eax, [num_interp_x_received]
mov edx, word [float_size]
mul edx ; Expected number of bytes for interpolation x data
mov [expected_bytes], eax
mov edi, interp_x_data_buffer
call receive_all
cmp eax, [expected_bytes]
jnz .client_disconnected_incomplete_interp_x
; TODO: Call the hyperbolic_parabolic_interpolation_nd function
; Need to set up arguments according to the C calling convention
; This will involve pushing pointers to the received data, the number of dimensions, etc.
push dword [num_interp_x_received] ; Length of x_interp
push interp_x_data_buffer ; Pointer to x_interp
; Need to reconstruct the all_fx_data and all_fy_data lists
; This will require knowing the lengths of each array within these lists
; The Python code iterates through dimensions, so we need to do something similar
; This part is complex and requires careful memory management and passing of data structures
; A direct assembly implementation of the Python list of numpy arrays is non-trivial
; Placeholder for calling the interpolation function
; push dword [num_dimensions_received]
; push pointer to all_fy_data
; push pointer to all_fx_data
; call hyperbolic_parabolic_interpolation_nd
; add esp, ... ; Clean up stack
; Assume the result is now in result_buffer and its length is in result_length_received
; Send the float result back to the client
mov eax, [result_length_received]
push eax ; Length of result
push struct_pack_fmt_i
push result_length_send
call struct_pack
add esp, 12
push dword [result_length_send]
push esi
push dword [result_length_send]
call send
add esp, 12
cmp eax, dword [result_length_send]
jnz .connection_error_send_result_len
push dword [result_length_received]
mov ecx, eax
push esi
push result_buffer
push ecx
call send
add esp, 12
cmp eax, ecx
jnz .connection_error_send_result
jmp .cleanup
.invalid_op_code:
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push dword [operation_code_received]
push msg_invalid_op_code
call printf
add esp, 20
jmp .cleanup_socket
.client_disconnected_op_code:
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_op_code
call printf
add esp, 16
jmp .cleanup_socket
.client_disconnected_num_dim:
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_num_dim
call printf
add esp, 16
jmp .cleanup_socket
.client_disconnected_x_len:
push ebx ; Dimension number
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_x_len
call printf
add esp, 20
jmp .cleanup_socket
.client_disconnected_incomplete_x:
push ebx ; Dimension number
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_incomplete_x
call printf
add esp, 20
jmp .cleanup_socket
.client_disconnected_y_len:
push ebx ; Dimension number
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_y_len
call printf
add esp, 20
jmp .cleanup_socket
.client_disconnected_incomplete_y:
push ebx ; Dimension number
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_incomplete_y
call printf
add esp, 20
jmp .cleanup_socket
.client_disconnected_interp_x_len:
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_interp_x_len
call printf
add esp, 16
jmp .cleanup_socket
.client_disconnected_incomplete_interp_x:
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_disconnected_incomplete_interp_x
call printf
add esp, 16
jmp .cleanup_socket
.value_error:
; Assume error message is in error_message_buffer
push dword [error_message_length]
push error_message_buffer
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_value_error
call printf
add esp, 20
jmp .cleanup_socket
.connection_reset_error:
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_connection_reset
call printf
add esp, 16
jmp .cleanup_socket
.unexpected_error:
; Assume error message is in error_message_buffer
push dword [error_message_length]
push error_message_buffer
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_unexpected_error
call printf
add esp, 20
jmp .cleanup_socket
.connection_error_send_result_len:
; Handle error sending result length
jmp .cleanup_socket
.connection_error_send_result:
; Handle error sending result data
jmp .cleanup_socket
.cleanup_socket:
push dword [esi]
call close
add esp, 4
.cleanup:
push dword [client_address+3]
push dword [client_address+2]
push dword [client_address+1]
push dword [client_address+0]
push msg_connection_closed
call printf
add esp, 16
pop ebp
pop edi
pop esi
pop ebx
pop ebp
ret
; Helper function to receive a specific number of bytes
receive_all:
push ebp
mov ebp, esp
mov edi, [ebp+8] ; Buffer
mov esi, [ebp+12] ; Socket
mov ecx, [expected_bytes] ; Number of bytes to receive
xor eax, eax ; Total bytes received
.receive_loop:
cmp eax, ecx
jge .receive_done
push ecx
sub ecx, eax ; Remaining bytes
cmp ecx, word [chunk_size]
jle .receive_chunk_size
mov ecx, word [chunk_size]
.receive_chunk_size:
push ecx
push esi
push edi
call recv
add esp, 12
cmp eax, 0
jle .receive_error ; Connection closed
add edi, eax
add eax, [ebp-4] ; Add to total received
mov [ebp-4], eax
pop ecx
jmp .receive_loop
.receive_done:
mov eax, [ebp-4] ; Return total bytes received
jmp .receive_exit
.receive_error:
mov eax, -1
jmp .receive_exit
.receive_exit:
mov esp, ebp
pop ebp
ret
section .bss
operation_code_buffer resb 1
num_dimensions_buffer resb 4
num_fx_buffer resb 4
num_fy
