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std.math.powi: use standard definition of underflow/overflow, implement u0, i0, i1 edge case (#11499)
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leesongun
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@ -10,108 +10,94 @@ const testing = std.testing;
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/// Returns the power of x raised by the integer y (x^y).
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///
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/// Special Cases:
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/// - powi(x, +-0) = 1 for any x
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/// - powi(0, y) = 0 for any y
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/// - powi(1, y) = 1 for any y
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/// - powi(-1, y) = -1 for y an odd integer
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/// - powi(-1, y) = 1 for y an even integer
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/// - powi(x, y) = Overflow for y >= @sizeOf(x) - 1 or y > 0
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/// - powi(x, y) = Underflow for y > @sizeOf(x) - 1 or y < 0
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/// Errors:
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/// - Overflow: Integer overflow or Infinity
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/// - Underflow: Absolute value of result smaller than 1
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/// Edge case rules ordered by precedence:
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/// - powi(T, x, 0) = 1 unless T is i1, i0, u0
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/// - powi(T, 0, x) = 0 when x > 0
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/// - powi(T, 0, x) = Overflow
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/// - powi(T, 1, y) = 1
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/// - powi(T, -1, y) = -1 for y an odd integer
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/// - powi(T, -1, y) = 1 unless T is i1, i0, u0
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/// - powi(T, -1, y) = Overflow
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/// - powi(T, x, y) = Overflow when y >= @bitSizeOf(x)
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/// - powi(T, x, y) = Underflow when y < 0
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pub fn powi(comptime T: type, x: T, y: T) (error{
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Overflow,
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Underflow,
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}!T) {
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const info = @typeInfo(T);
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const bit_size = @typeInfo(T).Int.bits;
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comptime assert(@typeInfo(T) == .Int);
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// `y & 1 == 0` won't compile when `does_one_overflow`.
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const does_one_overflow = math.maxInt(T) < 1;
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const is_y_even = !does_one_overflow and y & 1 == 0;
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// powi(x, +-0) = 1 for any x
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if (y == 0 or y == -0) {
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return 1;
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if (x == 1 or y == 0 or (x == -1 and is_y_even)) {
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if (does_one_overflow) {
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return error.Overflow;
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} else {
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return 1;
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}
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}
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switch (x) {
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// powi(0, y) = 0 for any y
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0 => return 0,
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// powi(1, y) = 1 for any y
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1 => return 1,
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else => {
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// powi(x, y) = Overflow for for y >= @sizeOf(x) - 1 y > 0
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// powi(x, y) = Underflow for for y > @sizeOf(x) - 1 y < 0
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const bit_size = @sizeOf(T) * 8;
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if (info.Int.signedness == .signed) {
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if (x == -1) {
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// powi(-1, y) = -1 for for y an odd integer
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// powi(-1, y) = 1 for for y an even integer
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if (@mod(y, 2) == 0) {
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return 1;
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} else {
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return -1;
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}
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}
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if (x > 0 and y >= bit_size - 1) {
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return error.Overflow;
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} else if (x < 0 and y > bit_size - 1) {
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return error.Underflow;
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}
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} else {
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if (y >= bit_size) {
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return error.Overflow;
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}
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}
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var base = x;
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var exp = y;
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var acc: T = 1;
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while (exp > 1) {
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if (exp & 1 == 1) {
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if (@mulWithOverflow(T, acc, base, &acc)) {
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if (x > 0) {
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return error.Overflow;
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} else {
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return error.Underflow;
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}
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}
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}
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exp >>= 1;
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if (@mulWithOverflow(T, base, base, &base)) {
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if (x > 0) {
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return error.Overflow;
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} else {
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return error.Underflow;
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}
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}
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}
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if (exp == 1) {
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if (@mulWithOverflow(T, acc, base, &acc)) {
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if (x > 0) {
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return error.Overflow;
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} else {
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return error.Underflow;
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}
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}
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}
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return acc;
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},
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if (x == -1) {
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return -1;
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}
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if (x == 0) {
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if (y > 0) {
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return 0;
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} else {
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// Infinity/NaN, not overflow in strict sense
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return error.Overflow;
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}
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}
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// x >= 2 or x <= -2 from this point
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if (y >= bit_size) {
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return error.Overflow;
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}
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if (y < 0) {
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return error.Underflow;
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}
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// invariant :
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// return value = powi(T, base, exp) * acc;
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var base = x;
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var exp = y;
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var acc: T = if (does_one_overflow) unreachable else 1;
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while (exp > 1) {
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if (exp & 1 == 1) {
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if (@mulWithOverflow(T, acc, base, &acc)) {
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return error.Overflow;
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}
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}
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exp >>= 1;
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if (@mulWithOverflow(T, base, base, &base)) {
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return error.Overflow;
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}
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}
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if (exp == 1) {
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if (@mulWithOverflow(T, acc, base, &acc)) {
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return error.Overflow;
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}
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}
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return acc;
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}
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test "math.powi" {
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try testing.expectError(error.Underflow, powi(i8, -66, 6));
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try testing.expectError(error.Underflow, powi(i16, -13, 13));
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try testing.expectError(error.Underflow, powi(i32, -32, 21));
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try testing.expectError(error.Underflow, powi(i64, -24, 61));
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try testing.expectError(error.Underflow, powi(i17, -15, 15));
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try testing.expectError(error.Underflow, powi(i42, -6, 40));
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try testing.expectError(error.Overflow, powi(i8, -66, 6));
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try testing.expectError(error.Overflow, powi(i16, -13, 13));
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try testing.expectError(error.Overflow, powi(i32, -32, 21));
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try testing.expectError(error.Overflow, powi(i64, -24, 61));
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try testing.expectError(error.Overflow, powi(i17, -15, 15));
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try testing.expectError(error.Overflow, powi(i42, -6, 40));
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try testing.expect((try powi(i8, -5, 3)) == -125);
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try testing.expect((try powi(i16, -16, 3)) == -4096);
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@ -140,15 +126,29 @@ test "math.powi" {
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try testing.expectError(error.Overflow, powi(u64, 2342, 63));
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try testing.expectError(error.Overflow, powi(u17, 2723, 16));
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try testing.expectError(error.Overflow, powi(u42, 8234, 41));
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const minInt = std.math.minInt;
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try testing.expect((try powi(i8, -2, 7)) == minInt(i8));
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try testing.expect((try powi(i16, -2, 15)) == minInt(i16));
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try testing.expect((try powi(i32, -2, 31)) == minInt(i32));
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try testing.expect((try powi(i64, -2, 63)) == minInt(i64));
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try testing.expectError(error.Underflow, powi(i8, 6, -2));
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try testing.expectError(error.Underflow, powi(i16, 5, -4));
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try testing.expectError(error.Underflow, powi(i32, 12, -6));
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try testing.expectError(error.Underflow, powi(i64, 34, -2));
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try testing.expectError(error.Underflow, powi(i17, 16, -3));
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try testing.expectError(error.Underflow, powi(i42, 34, -6));
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}
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test "math.powi.special" {
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try testing.expectError(error.Underflow, powi(i8, -2, 8));
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try testing.expectError(error.Underflow, powi(i16, -2, 16));
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try testing.expectError(error.Underflow, powi(i32, -2, 32));
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try testing.expectError(error.Underflow, powi(i64, -2, 64));
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try testing.expectError(error.Underflow, powi(i17, -2, 17));
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try testing.expectError(error.Underflow, powi(i42, -2, 42));
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try testing.expectError(error.Overflow, powi(i8, -2, 8));
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try testing.expectError(error.Overflow, powi(i16, -2, 16));
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try testing.expectError(error.Overflow, powi(i32, -2, 32));
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try testing.expectError(error.Overflow, powi(i64, -2, 64));
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try testing.expectError(error.Overflow, powi(i17, -2, 17));
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try testing.expectError(error.Overflow, powi(i17, -2, 16));
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try testing.expectError(error.Overflow, powi(i42, -2, 42));
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try testing.expect((try powi(i8, -1, 3)) == -1);
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try testing.expect((try powi(i16, -1, 2)) == 1);
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@ -185,3 +185,12 @@ test "math.powi.special" {
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try testing.expect((try powi(u17, 16, 0)) == 1);
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try testing.expect((try powi(u42, 34, 0)) == 1);
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}
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test "math.powi.narrow" {
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try testing.expectError(error.Overflow, powi(u0, 0, 0));
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try testing.expectError(error.Overflow, powi(i0, 0, 0));
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try testing.expectError(error.Overflow, powi(i1, 0, 0));
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try testing.expectError(error.Overflow, powi(i1, -1, 0));
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try testing.expectError(error.Overflow, powi(i1, 0, -1));
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try testing.expect((try powi(i1, -1, -1)) == -1);
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}
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