const std = @import("../std.zig");
const math = std.math;
const assert = std.debug.assert;
const testing = std.testing;
pub fn powi(comptime T: type, x: T, y: T) (error{
    Overflow,
    Underflow,
}!T) {
    const bit_size = @typeInfo(T).Int.bits;
    
    const does_one_overflow = math.maxInt(T) < 1;
    const is_y_even = !does_one_overflow and y & 1 == 0;
    if (x == 1 or y == 0 or (x == -1 and is_y_even)) {
        if (does_one_overflow) {
            return error.Overflow;
        } else {
            return 1;
        }
    }
    if (x == -1) {
        return -1;
    }
    if (x == 0) {
        if (y > 0) {
            return 0;
        } else {
            
            return error.Overflow;
        }
    }
    
    if (y >= bit_size) {
        return error.Overflow;
    }
    if (y < 0) {
        return error.Underflow;
    }
    
    
    var base = x;
    var exp = y;
    var acc: T = if (does_one_overflow) unreachable else 1;
    while (exp > 1) {
        if (exp & 1 == 1) {
            if (@mulWithOverflow(T, acc, base, &acc)) {
                return error.Overflow;
            }
        }
        exp >>= 1;
        if (@mulWithOverflow(T, base, base, &base)) {
            return error.Overflow;
        }
    }
    if (exp == 1) {
        if (@mulWithOverflow(T, acc, base, &acc)) {
            return error.Overflow;
        }
    }
    return acc;
}
test "math.powi" {
    try testing.expectError(error.Overflow, powi(i8, -66, 6));
    try testing.expectError(error.Overflow, powi(i16, -13, 13));
    try testing.expectError(error.Overflow, powi(i32, -32, 21));
    try testing.expectError(error.Overflow, powi(i64, -24, 61));
    try testing.expectError(error.Overflow, powi(i17, -15, 15));
    try testing.expectError(error.Overflow, powi(i42, -6, 40));
    try testing.expect((try powi(i8, -5, 3)) == -125);
    try testing.expect((try powi(i16, -16, 3)) == -4096);
    try testing.expect((try powi(i32, -91, 3)) == -753571);
    try testing.expect((try powi(i64, -36, 6)) == 2176782336);
    try testing.expect((try powi(i17, -2, 15)) == -32768);
    try testing.expect((try powi(i42, -5, 7)) == -78125);
    try testing.expect((try powi(u8, 6, 2)) == 36);
    try testing.expect((try powi(u16, 5, 4)) == 625);
    try testing.expect((try powi(u32, 12, 6)) == 2985984);
    try testing.expect((try powi(u64, 34, 2)) == 1156);
    try testing.expect((try powi(u17, 16, 3)) == 4096);
    try testing.expect((try powi(u42, 34, 6)) == 1544804416);
    try testing.expectError(error.Overflow, powi(i8, 120, 7));
    try testing.expectError(error.Overflow, powi(i16, 73, 15));
    try testing.expectError(error.Overflow, powi(i32, 23, 31));
    try testing.expectError(error.Overflow, powi(i64, 68, 61));
    try testing.expectError(error.Overflow, powi(i17, 15, 15));
    try testing.expectError(error.Overflow, powi(i42, 121312, 41));
    try testing.expectError(error.Overflow, powi(u8, 123, 7));
    try testing.expectError(error.Overflow, powi(u16, 2313, 15));
    try testing.expectError(error.Overflow, powi(u32, 8968, 31));
    try testing.expectError(error.Overflow, powi(u64, 2342, 63));
    try testing.expectError(error.Overflow, powi(u17, 2723, 16));
    try testing.expectError(error.Overflow, powi(u42, 8234, 41));
    const minInt = std.math.minInt;
    try testing.expect((try powi(i8, -2, 7)) == minInt(i8));
    try testing.expect((try powi(i16, -2, 15)) == minInt(i16));
    try testing.expect((try powi(i32, -2, 31)) == minInt(i32));
    try testing.expect((try powi(i64, -2, 63)) == minInt(i64));
    try testing.expectError(error.Underflow, powi(i8, 6, -2));
    try testing.expectError(error.Underflow, powi(i16, 5, -4));
    try testing.expectError(error.Underflow, powi(i32, 12, -6));
    try testing.expectError(error.Underflow, powi(i64, 34, -2));
    try testing.expectError(error.Underflow, powi(i17, 16, -3));
    try testing.expectError(error.Underflow, powi(i42, 34, -6));
}
test "math.powi.special" {
    try testing.expectError(error.Overflow, powi(i8, -2, 8));
    try testing.expectError(error.Overflow, powi(i16, -2, 16));
    try testing.expectError(error.Overflow, powi(i32, -2, 32));
    try testing.expectError(error.Overflow, powi(i64, -2, 64));
    try testing.expectError(error.Overflow, powi(i17, -2, 17));
    try testing.expectError(error.Overflow, powi(i17, -2, 16));
    try testing.expectError(error.Overflow, powi(i42, -2, 42));
    try testing.expect((try powi(i8, -1, 3)) == -1);
    try testing.expect((try powi(i16, -1, 2)) == 1);
    try testing.expect((try powi(i32, -1, 16)) == 1);
    try testing.expect((try powi(i64, -1, 6)) == 1);
    try testing.expect((try powi(i17, -1, 15)) == -1);
    try testing.expect((try powi(i42, -1, 7)) == -1);
    try testing.expect((try powi(u8, 1, 2)) == 1);
    try testing.expect((try powi(u16, 1, 4)) == 1);
    try testing.expect((try powi(u32, 1, 6)) == 1);
    try testing.expect((try powi(u64, 1, 2)) == 1);
    try testing.expect((try powi(u17, 1, 3)) == 1);
    try testing.expect((try powi(u42, 1, 6)) == 1);
    try testing.expectError(error.Overflow, powi(i8, 2, 7));
    try testing.expectError(error.Overflow, powi(i16, 2, 15));
    try testing.expectError(error.Overflow, powi(i32, 2, 31));
    try testing.expectError(error.Overflow, powi(i64, 2, 63));
    try testing.expectError(error.Overflow, powi(i17, 2, 16));
    try testing.expectError(error.Overflow, powi(i42, 2, 41));
    try testing.expectError(error.Overflow, powi(u8, 2, 8));
    try testing.expectError(error.Overflow, powi(u16, 2, 16));
    try testing.expectError(error.Overflow, powi(u32, 2, 32));
    try testing.expectError(error.Overflow, powi(u64, 2, 64));
    try testing.expectError(error.Overflow, powi(u17, 2, 17));
    try testing.expectError(error.Overflow, powi(u42, 2, 42));
    try testing.expect((try powi(u8, 6, 0)) == 1);
    try testing.expect((try powi(u16, 5, 0)) == 1);
    try testing.expect((try powi(u32, 12, 0)) == 1);
    try testing.expect((try powi(u64, 34, 0)) == 1);
    try testing.expect((try powi(u17, 16, 0)) == 1);
    try testing.expect((try powi(u42, 34, 0)) == 1);
}
test "math.powi.narrow" {
    try testing.expectError(error.Overflow, powi(u0, 0, 0));
    try testing.expectError(error.Overflow, powi(i0, 0, 0));
    try testing.expectError(error.Overflow, powi(i1, 0, 0));
    try testing.expectError(error.Overflow, powi(i1, -1, 0));
    try testing.expectError(error.Overflow, powi(i1, 0, -1));
    try testing.expect((try powi(i1, -1, -1)) == -1);
}