189 lines
6.9 KiB
Zig
189 lines
6.9 KiB
Zig
// Based on Rust, which is licensed under the MIT license.
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// https://github.com/rust-lang/rust/blob/360432f1e8794de58cd94f34c9c17ad65871e5b5/LICENSE-MIT
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//
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// https://github.com/rust-lang/rust/blob/360432f1e8794de58cd94f34c9c17ad65871e5b5/src/libcore/num/mod.rs#L3423
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const builtin = @import("builtin");
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const std = @import("../std.zig");
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const math = std.math;
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const assert = std.debug.assert;
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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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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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comptime assert(@typeInfo(T) == .Int);
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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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}
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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.is_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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}
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}
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test "math.powi" {
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testing.expectError(error.Underflow, powi(i8, -66, 6));
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testing.expectError(error.Underflow, powi(i16, -13, 13));
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testing.expectError(error.Underflow, powi(i32, -32, 21));
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testing.expectError(error.Underflow, powi(i64, -24, 61));
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testing.expectError(error.Underflow, powi(i17, -15, 15));
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testing.expectError(error.Underflow, powi(i42, -6, 40));
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testing.expect((try powi(i8, -5, 3)) == -125);
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testing.expect((try powi(i16, -16, 3)) == -4096);
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testing.expect((try powi(i32, -91, 3)) == -753571);
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testing.expect((try powi(i64, -36, 6)) == 2176782336);
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testing.expect((try powi(i17, -2, 15)) == -32768);
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testing.expect((try powi(i42, -5, 7)) == -78125);
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testing.expect((try powi(u8, 6, 2)) == 36);
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testing.expect((try powi(u16, 5, 4)) == 625);
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testing.expect((try powi(u32, 12, 6)) == 2985984);
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testing.expect((try powi(u64, 34, 2)) == 1156);
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testing.expect((try powi(u17, 16, 3)) == 4096);
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testing.expect((try powi(u42, 34, 6)) == 1544804416);
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testing.expectError(error.Overflow, powi(i8, 120, 7));
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testing.expectError(error.Overflow, powi(i16, 73, 15));
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testing.expectError(error.Overflow, powi(i32, 23, 31));
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testing.expectError(error.Overflow, powi(i64, 68, 61));
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testing.expectError(error.Overflow, powi(i17, 15, 15));
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testing.expectError(error.Overflow, powi(i42, 121312, 41));
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testing.expectError(error.Overflow, powi(u8, 123, 7));
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testing.expectError(error.Overflow, powi(u16, 2313, 15));
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testing.expectError(error.Overflow, powi(u32, 8968, 31));
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testing.expectError(error.Overflow, powi(u64, 2342, 63));
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testing.expectError(error.Overflow, powi(u17, 2723, 16));
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testing.expectError(error.Overflow, powi(u42, 8234, 41));
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}
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test "math.powi.special" {
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testing.expectError(error.Underflow, powi(i8, -2, 8));
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testing.expectError(error.Underflow, powi(i16, -2, 16));
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testing.expectError(error.Underflow, powi(i32, -2, 32));
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testing.expectError(error.Underflow, powi(i64, -2, 64));
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testing.expectError(error.Underflow, powi(i17, -2, 17));
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testing.expectError(error.Underflow, powi(i42, -2, 42));
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testing.expect((try powi(i8, -1, 3)) == -1);
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testing.expect((try powi(i16, -1, 2)) == 1);
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testing.expect((try powi(i32, -1, 16)) == 1);
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testing.expect((try powi(i64, -1, 6)) == 1);
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testing.expect((try powi(i17, -1, 15)) == -1);
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testing.expect((try powi(i42, -1, 7)) == -1);
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testing.expect((try powi(u8, 1, 2)) == 1);
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testing.expect((try powi(u16, 1, 4)) == 1);
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testing.expect((try powi(u32, 1, 6)) == 1);
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testing.expect((try powi(u64, 1, 2)) == 1);
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testing.expect((try powi(u17, 1, 3)) == 1);
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testing.expect((try powi(u42, 1, 6)) == 1);
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testing.expectError(error.Overflow, powi(i8, 2, 7));
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testing.expectError(error.Overflow, powi(i16, 2, 15));
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testing.expectError(error.Overflow, powi(i32, 2, 31));
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testing.expectError(error.Overflow, powi(i64, 2, 63));
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testing.expectError(error.Overflow, powi(i17, 2, 16));
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testing.expectError(error.Overflow, powi(i42, 2, 41));
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testing.expectError(error.Overflow, powi(u8, 2, 8));
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testing.expectError(error.Overflow, powi(u16, 2, 16));
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testing.expectError(error.Overflow, powi(u32, 2, 32));
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testing.expectError(error.Overflow, powi(u64, 2, 64));
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testing.expectError(error.Overflow, powi(u17, 2, 17));
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testing.expectError(error.Overflow, powi(u42, 2, 42));
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testing.expect((try powi(u8, 6, 0)) == 1);
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testing.expect((try powi(u16, 5, 0)) == 1);
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testing.expect((try powi(u32, 12, 0)) == 1);
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testing.expect((try powi(u64, 34, 0)) == 1);
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testing.expect((try powi(u17, 16, 0)) == 1);
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testing.expect((try powi(u42, 34, 0)) == 1);
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}
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