// Based on Rust, which is licensed under the MIT license. // https://github.com/rust-lang/rust/blob/360432f1e8794de58cd94f34c9c17ad65871e5b5/LICENSE-MIT // // https://github.com/rust-lang/rust/blob/360432f1e8794de58cd94f34c9c17ad65871e5b5/src/libcore/num/mod.rs#L3423 const builtin = @import("builtin"); const std = @import("../std.zig"); const math = std.math; const assert = std.debug.assert; const testing = std.testing; /// Returns the power of x raised by the integer y (x^y). /// /// Special Cases: /// - powi(x, +-0) = 1 for any x /// - powi(0, y) = 0 for any y /// - powi(1, y) = 1 for any y /// - powi(-1, y) = -1 for y an odd integer /// - powi(-1, y) = 1 for y an even integer /// - powi(x, y) = Overflow for y >= @sizeOf(x) - 1 or y > 0 /// - powi(x, y) = Underflow for y > @sizeOf(x) - 1 or y < 0 pub fn powi(comptime T: type, x: T, y: T) (error{ Overflow, Underflow, }!T) { const info = @typeInfo(T); comptime assert(@typeInfo(T) == .Int); // powi(x, +-0) = 1 for any x if (y == 0 or y == -0) { return 1; } switch (x) { // powi(0, y) = 0 for any y 0 => return 0, // powi(1, y) = 1 for any y 1 => return 1, else => { // powi(x, y) = Overflow for for y >= @sizeOf(x) - 1 y > 0 // powi(x, y) = Underflow for for y > @sizeOf(x) - 1 y < 0 const bit_size = @sizeOf(T) * 8; if (info.Int.is_signed) { if (x == -1) { // powi(-1, y) = -1 for for y an odd integer // powi(-1, y) = 1 for for y an even integer if (@mod(y, 2) == 0) { return 1; } else { return -1; } } if (x > 0 and y >= bit_size - 1) { return error.Overflow; } else if (x < 0 and y > bit_size - 1) { return error.Underflow; } } else { if (y >= bit_size) { return error.Overflow; } } var base = x; var exp = y; var acc: T = 1; while (exp > 1) { if (exp & 1 == 1) { if (@mulWithOverflow(T, acc, base, &acc)) { if (x > 0) { return error.Overflow; } else { return error.Underflow; } } } exp >>= 1; if (@mulWithOverflow(T, base, base, &base)) { if (x > 0) { return error.Overflow; } else { return error.Underflow; } } } if (exp == 1) { if (@mulWithOverflow(T, acc, base, &acc)) { if (x > 0) { return error.Overflow; } else { return error.Underflow; } } } return acc; }, } } test "math.powi" { testing.expectError(error.Underflow, powi(i8, -66, 6)); testing.expectError(error.Underflow, powi(i16, -13, 13)); testing.expectError(error.Underflow, powi(i32, -32, 21)); testing.expectError(error.Underflow, powi(i64, -24, 61)); testing.expectError(error.Underflow, powi(i17, -15, 15)); testing.expectError(error.Underflow, powi(i42, -6, 40)); testing.expect((try powi(i8, -5, 3)) == -125); testing.expect((try powi(i16, -16, 3)) == -4096); testing.expect((try powi(i32, -91, 3)) == -753571); testing.expect((try powi(i64, -36, 6)) == 2176782336); testing.expect((try powi(i17, -2, 15)) == -32768); testing.expect((try powi(i42, -5, 7)) == -78125); testing.expect((try powi(u8, 6, 2)) == 36); testing.expect((try powi(u16, 5, 4)) == 625); testing.expect((try powi(u32, 12, 6)) == 2985984); testing.expect((try powi(u64, 34, 2)) == 1156); testing.expect((try powi(u17, 16, 3)) == 4096); testing.expect((try powi(u42, 34, 6)) == 1544804416); testing.expectError(error.Overflow, powi(i8, 120, 7)); testing.expectError(error.Overflow, powi(i16, 73, 15)); testing.expectError(error.Overflow, powi(i32, 23, 31)); testing.expectError(error.Overflow, powi(i64, 68, 61)); testing.expectError(error.Overflow, powi(i17, 15, 15)); testing.expectError(error.Overflow, powi(i42, 121312, 41)); testing.expectError(error.Overflow, powi(u8, 123, 7)); testing.expectError(error.Overflow, powi(u16, 2313, 15)); testing.expectError(error.Overflow, powi(u32, 8968, 31)); testing.expectError(error.Overflow, powi(u64, 2342, 63)); testing.expectError(error.Overflow, powi(u17, 2723, 16)); testing.expectError(error.Overflow, powi(u42, 8234, 41)); } test "math.powi.special" { testing.expectError(error.Underflow, powi(i8, -2, 8)); testing.expectError(error.Underflow, powi(i16, -2, 16)); testing.expectError(error.Underflow, powi(i32, -2, 32)); testing.expectError(error.Underflow, powi(i64, -2, 64)); testing.expectError(error.Underflow, powi(i17, -2, 17)); testing.expectError(error.Underflow, powi(i42, -2, 42)); testing.expect((try powi(i8, -1, 3)) == -1); testing.expect((try powi(i16, -1, 2)) == 1); testing.expect((try powi(i32, -1, 16)) == 1); testing.expect((try powi(i64, -1, 6)) == 1); testing.expect((try powi(i17, -1, 15)) == -1); testing.expect((try powi(i42, -1, 7)) == -1); testing.expect((try powi(u8, 1, 2)) == 1); testing.expect((try powi(u16, 1, 4)) == 1); testing.expect((try powi(u32, 1, 6)) == 1); testing.expect((try powi(u64, 1, 2)) == 1); testing.expect((try powi(u17, 1, 3)) == 1); testing.expect((try powi(u42, 1, 6)) == 1); testing.expectError(error.Overflow, powi(i8, 2, 7)); testing.expectError(error.Overflow, powi(i16, 2, 15)); testing.expectError(error.Overflow, powi(i32, 2, 31)); testing.expectError(error.Overflow, powi(i64, 2, 63)); testing.expectError(error.Overflow, powi(i17, 2, 16)); testing.expectError(error.Overflow, powi(i42, 2, 41)); testing.expectError(error.Overflow, powi(u8, 2, 8)); testing.expectError(error.Overflow, powi(u16, 2, 16)); testing.expectError(error.Overflow, powi(u32, 2, 32)); testing.expectError(error.Overflow, powi(u64, 2, 64)); testing.expectError(error.Overflow, powi(u17, 2, 17)); testing.expectError(error.Overflow, powi(u42, 2, 42)); testing.expect((try powi(u8, 6, 0)) == 1); testing.expect((try powi(u16, 5, 0)) == 1); testing.expect((try powi(u32, 12, 0)) == 1); testing.expect((try powi(u64, 34, 0)) == 1); testing.expect((try powi(u17, 16, 0)) == 1); testing.expect((try powi(u42, 34, 0)) == 1); }