zig/lib/std /
math/powi.zig
Returns the power of x raised by the integer y (x^y). Errors: - Overflow: Integer overflow or Infinity - Underflow: Absolute value of result smaller than 1 Edge case rules ordered by precedence: - powi(T, x, 0) = 1 unless T is i1, i0, u0 - powi(T, 0, x) = 0 when x > 0 - powi(T, 0, x) = Overflow - powi(T, 1, y) = 1 - powi(T, -1, y) = -1 for y an odd integer - powi(T, -1, y) = 1 unless T is i1, i0, u0 - powi(T, -1, y) = Overflow - powi(T, x, y) = Overflow when y >= @bitSizeOf(x) - powi(T, x, y) = Underflow when y < 0
// 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
powi()
const std = @import("../std.zig");
const math = std.math;
const assert = std.debug.assert;
const testing = std.testing;
Test: powi
/// Returns the power of x raised by the integer y (x^y).
///
/// Errors:
/// - Overflow: Integer overflow or Infinity
/// - Underflow: Absolute value of result smaller than 1
/// Edge case rules ordered by precedence:
/// - powi(T, x, 0) = 1 unless T is i1, i0, u0
/// - powi(T, 0, x) = 0 when x > 0
/// - powi(T, 0, x) = Overflow
/// - powi(T, 1, y) = 1
/// - powi(T, -1, y) = -1 for y an odd integer
/// - powi(T, -1, y) = 1 unless T is i1, i0, u0
/// - powi(T, -1, y) = Overflow
/// - powi(T, x, y) = Overflow when y >= @bitSizeOf(x)
/// - powi(T, x, y) = Underflow when y < 0
pub fn powi(comptime T: type, x: T, y: T) (error{
Overflow,
Underflow,
}!T) {
const bit_size = @typeInfo(T).int.bits;
Test:
powi.special
// `y & 1 == 0` won't compile when `does_one_overflow`.
const does_one_overflow = math.maxInt(T) < 1;
const is_y_even = !does_one_overflow and y & 1 == 0;
Test:
powi.narrow
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 {
// Infinity/NaN, not overflow in strict sense
return error.Overflow;
}
}
// x >= 2 or x <= -2 from this point
if (y >= bit_size) {
return error.Overflow;
}
if (y < 0) {
return error.Underflow;
}
// invariant :
// return value = powi(T, base, exp) * acc;
var base = x;
var exp = y;
var acc: T = if (does_one_overflow) unreachable else 1;
while (exp > 1) {
if (exp & 1 == 1) {
const ov = @mulWithOverflow(acc, base);
if (ov[1] != 0) return error.Overflow;
acc = ov[0];
}
exp >>= 1;
const ov = @mulWithOverflow(base, base);
if (ov[1] != 0) return error.Overflow;
base = ov[0];
}
if (exp == 1) {
const ov = @mulWithOverflow(acc, base);
if (ov[1] != 0) return error.Overflow;
acc = ov[0];
}
return acc;
}
test 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 "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 "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);
}