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zig/lib/std/math.zig
zooster bc8e1e1de4
Improvements to docs and text 
* docs(std.math): elaborate on difference between absCast and absInt

* docs(std.rand.Random.weightedIndex): elaborate on likelihood

I think this makes it easier to understand.

* langref: add small reminder

* docs(std.fs.path.extension): brevity

* docs(std.bit_set.StaticBitSet): mention the specific types

* std.debug.TTY: explain what purpose this struct serves

This should also make it clearer that this struct is not supposed to provide unrelated terminal manipulation functionality such as setting the cursor position or something because terminals are complicated and we should keep this struct simple and focused on debugging.

* langref(package listing): brevity

* langref: explain what exactly `threadlocal` causes to happen

* std.array_list: link between swapRemove and orderedRemove

Maybe this can serve as a TLDR and make it easier to decide.

* PrefetchOptions.locality: clarify docs that this is a range

This confused me previously and I thought I can only use either 0 or 3.

* fix typos and more

* std.builtin.CallingConvention: document some CCs

* langref: explain possibly cryptic names

I think it helps knowing what exactly these acronyms (@clz and @ctz) and
abbreviations (@popCount) mean.

* variadic function error: add missing preposition

* std.fmt.format docs: nicely hyphenate

* help menu: say what to optimize for

I think this is slightly more specific than just calling it
"optimizations". These are speed optimizations. I used the word
"performance" here.
2023-04-23 21:06:21 +03:00

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const builtin = @import("builtin");
const std = @import("std.zig");
const assert = std.debug.assert;
const mem = std.mem;
const testing = std.testing;
/// Euler's number (e)
pub const e = 2.71828182845904523536028747135266249775724709369995;
/// Archimedes' constant (π)
pub const pi = 3.14159265358979323846264338327950288419716939937510;
/// Phi or Golden ratio constant (Φ) = (1 + sqrt(5))/2
pub const phi = 1.6180339887498948482045868343656381177203091798057628621;
/// Circle constant (τ)
pub const tau = 2 * pi;
/// log2(e)
pub const log2e = 1.442695040888963407359924681001892137;
/// log10(e)
pub const log10e = 0.434294481903251827651128918916605082;
/// ln(2)
pub const ln2 = 0.693147180559945309417232121458176568;
/// ln(10)
pub const ln10 = 2.302585092994045684017991454684364208;
/// 2/sqrt(π)
pub const two_sqrtpi = 1.128379167095512573896158903121545172;
/// sqrt(2)
pub const sqrt2 = 1.414213562373095048801688724209698079;
/// 1/sqrt(2)
pub const sqrt1_2 = 0.707106781186547524400844362104849039;
pub const floatExponentBits = @import("math/float.zig").floatExponentBits;
pub const floatMantissaBits = @import("math/float.zig").floatMantissaBits;
pub const floatFractionalBits = @import("math/float.zig").floatFractionalBits;
pub const floatExponentMin = @import("math/float.zig").floatExponentMin;
pub const floatExponentMax = @import("math/float.zig").floatExponentMax;
pub const floatTrueMin = @import("math/float.zig").floatTrueMin;
pub const floatMin = @import("math/float.zig").floatMin;
pub const floatMax = @import("math/float.zig").floatMax;
pub const floatEps = @import("math/float.zig").floatEps;
pub const inf = @import("math/float.zig").inf;
// TODO Replace with @compileError("deprecated for foobar") after 0.10.0 is released.
pub const f16_true_min: comptime_float = floatTrueMin(f16); // prev: 0.000000059604644775390625
pub const f32_true_min: comptime_float = floatTrueMin(f32); // prev: 1.40129846432481707092e-45
pub const f64_true_min: comptime_float = floatTrueMin(f64); // prev: 4.94065645841246544177e-324
pub const f80_true_min = floatTrueMin(f80); // prev: make_f80(.{ .fraction = 1, .exp = 0 })
pub const f128_true_min = floatTrueMin(f128); // prev: @bitCast(f128, @as(u128, 0x00000000000000000000000000000001))
pub const f16_min: comptime_float = floatMin(f16); // prev: 0.00006103515625
pub const f32_min: comptime_float = floatMin(f32); // prev: 1.17549435082228750797e-38
pub const f64_min: comptime_float = floatMin(f64); // prev: 2.2250738585072014e-308
pub const f80_min = floatMin(f80); // prev: make_f80(.{ .fraction = 0x8000000000000000, .exp = 1 })
pub const f128_min = floatMin(f128); // prev: @bitCast(f128, @as(u128, 0x00010000000000000000000000000000))
pub const f16_max: comptime_float = floatMax(f16); // prev: 65504
pub const f32_max: comptime_float = floatMax(f32); // prev: 3.40282346638528859812e+38
pub const f64_max: comptime_float = floatMax(f64); // prev: 1.79769313486231570815e+308
pub const f80_max = floatMax(f80); // prev: make_f80(.{ .fraction = 0xFFFFFFFFFFFFFFFF, .exp = 0x7FFE })
pub const f128_max = floatMax(f128); // prev: @bitCast(f128, @as(u128, 0x7FFEFFFFFFFFFFFFFFFFFFFFFFFFFFFF))
pub const f16_epsilon: comptime_float = floatEps(f16); // prev: 0.0009765625
pub const f32_epsilon: comptime_float = floatEps(f32); // prev: 1.1920928955078125e-07
pub const f64_epsilon: comptime_float = floatEps(f64); // prev: 2.22044604925031308085e-16
pub const f80_epsilon = floatEps(f80); // prev: make_f80(.{ .fraction = 0x8000000000000000, .exp = 0x3FC0 })
pub const f128_epsilon = floatEps(f128); // prev: @bitCast(f128, @as(u128, 0x3F8F0000000000000000000000000000))
pub const f16_toint: comptime_float = 1.0 / f16_epsilon; // same as before
pub const f32_toint: comptime_float = 1.0 / f32_epsilon; // same as before
pub const f64_toint: comptime_float = 1.0 / f64_epsilon; // same as before
pub const f80_toint = 1.0 / f80_epsilon; // same as before
pub const f128_toint = 1.0 / f128_epsilon; // same as before
pub const inf_u16 = @bitCast(u16, inf_f16); // prev: @as(u16, 0x7C00)
pub const inf_f16 = inf(f16); // prev: @bitCast(f16, inf_u16)
pub const inf_u32 = @bitCast(u32, inf_f32); // prev: @as(u32, 0x7F800000)
pub const inf_f32 = inf(f32); // prev: @bitCast(f32, inf_u32)
pub const inf_u64 = @bitCast(u64, inf_f64); // prev: @as(u64, 0x7FF << 52)
pub const inf_f64 = inf(f64); // prev: @bitCast(f64, inf_u64)
pub const inf_f80 = inf(f80); // prev: make_f80(F80{ .fraction = 0x8000000000000000, .exp = 0x7fff })
pub const inf_u128 = @bitCast(u128, inf_f128); // prev: @as(u128, 0x7fff0000000000000000000000000000)
pub const inf_f128 = inf(f128); // prev: @bitCast(f128, inf_u128)
pub const epsilon = floatEps;
// End of "soft deprecated" section
pub const nan_u16 = @as(u16, 0x7C01);
pub const nan_f16 = @bitCast(f16, nan_u16);
pub const qnan_u16 = @as(u16, 0x7E00);
pub const qnan_f16 = @bitCast(f16, qnan_u16);
pub const nan_u32 = @as(u32, 0x7F800001);
pub const nan_f32 = @bitCast(f32, nan_u32);
pub const qnan_u32 = @as(u32, 0x7FC00000);
pub const qnan_f32 = @bitCast(f32, qnan_u32);
pub const nan_u64 = @as(u64, 0x7FF << 52) | 1;
pub const nan_f64 = @bitCast(f64, nan_u64);
pub const qnan_u64 = @as(u64, 0x7ff8000000000000);
pub const qnan_f64 = @bitCast(f64, qnan_u64);
pub const nan_f80 = make_f80(F80{ .fraction = 0xA000000000000000, .exp = 0x7fff });
pub const qnan_f80 = make_f80(F80{ .fraction = 0xC000000000000000, .exp = 0x7fff });
pub const nan_u128 = @as(u128, 0x7fff0000000000000000000000000001);
pub const nan_f128 = @bitCast(f128, nan_u128);
pub const qnan_u128 = @as(u128, 0x7fff8000000000000000000000000000);
pub const qnan_f128 = @bitCast(f128, qnan_u128);
pub const nan = @import("math/nan.zig").nan;
pub const snan = @import("math/nan.zig").snan;
/// Performs an approximate comparison of two floating point values `x` and `y`.
/// Returns true if the absolute difference between them is less or equal than
/// the specified tolerance.
///
/// The `tolerance` parameter is the absolute tolerance used when determining if
/// the two numbers are close enough; a good value for this parameter is a small
/// multiple of `floatEps(T)`.
///
/// Note that this function is recommended for comparing small numbers
/// around zero; using `approxEqRel` is suggested otherwise.
///
/// NaN values are never considered equal to any value.
pub fn approxEqAbs(comptime T: type, x: T, y: T, tolerance: T) bool {
assert(@typeInfo(T) == .Float);
assert(tolerance >= 0);
// Fast path for equal values (and signed zeros and infinites).
if (x == y)
return true;
if (isNan(x) or isNan(y))
return false;
return @fabs(x - y) <= tolerance;
}
/// Performs an approximate comparison of two floating point values `x` and `y`.
/// Returns true if the absolute difference between them is less or equal than
/// `max(|x|, |y|) * tolerance`, where `tolerance` is a positive number greater
/// than zero.
///
/// The `tolerance` parameter is the relative tolerance used when determining if
/// the two numbers are close enough; a good value for this parameter is usually
/// `sqrt(floatEps(T))`, meaning that the two numbers are considered equal if at
/// least half of the digits are equal.
///
/// Note that for comparisons of small numbers around zero this function won't
/// give meaningful results, use `approxEqAbs` instead.
///
/// NaN values are never considered equal to any value.
pub fn approxEqRel(comptime T: type, x: T, y: T, tolerance: T) bool {
assert(@typeInfo(T) == .Float);
assert(tolerance > 0);
// Fast path for equal values (and signed zeros and infinites).
if (x == y)
return true;
if (isNan(x) or isNan(y))
return false;
return @fabs(x - y) <= max(@fabs(x), @fabs(y)) * tolerance;
}
test "approxEqAbs and approxEqRel" {
inline for ([_]type{ f16, f32, f64, f128 }) |T| {
const eps_value = comptime floatEps(T);
const sqrt_eps_value = comptime sqrt(eps_value);
const nan_value = comptime nan(T);
const inf_value = comptime inf(T);
const min_value = comptime floatMin(T);
try testing.expect(approxEqAbs(T, 0.0, 0.0, eps_value));
try testing.expect(approxEqAbs(T, -0.0, -0.0, eps_value));
try testing.expect(approxEqAbs(T, 0.0, -0.0, eps_value));
try testing.expect(approxEqRel(T, 1.0, 1.0, sqrt_eps_value));
try testing.expect(!approxEqRel(T, 1.0, 0.0, sqrt_eps_value));
try testing.expect(!approxEqAbs(T, 1.0 + 2 * eps_value, 1.0, eps_value));
try testing.expect(approxEqAbs(T, 1.0 + 1 * eps_value, 1.0, eps_value));
try testing.expect(!approxEqRel(T, 1.0, nan_value, sqrt_eps_value));
try testing.expect(!approxEqRel(T, nan_value, nan_value, sqrt_eps_value));
try testing.expect(approxEqRel(T, inf_value, inf_value, sqrt_eps_value));
try testing.expect(approxEqRel(T, min_value, min_value, sqrt_eps_value));
try testing.expect(approxEqRel(T, -min_value, -min_value, sqrt_eps_value));
try testing.expect(approxEqAbs(T, min_value, 0.0, eps_value * 2));
try testing.expect(approxEqAbs(T, -min_value, 0.0, eps_value * 2));
}
}
pub fn doNotOptimizeAway(val: anytype) void {
return mem.doNotOptimizeAway(val);
}
pub fn raiseInvalid() void {
// Raise INVALID fpu exception
}
pub fn raiseUnderflow() void {
// Raise UNDERFLOW fpu exception
}
pub fn raiseOverflow() void {
// Raise OVERFLOW fpu exception
}
pub fn raiseInexact() void {
// Raise INEXACT fpu exception
}
pub fn raiseDivByZero() void {
// Raise INEXACT fpu exception
}
pub const isNan = @import("math/isnan.zig").isNan;
pub const isSignalNan = @import("math/isnan.zig").isSignalNan;
pub const frexp = @import("math/frexp.zig").frexp;
pub const Frexp = @import("math/frexp.zig").Frexp;
pub const modf = @import("math/modf.zig").modf;
pub const modf32_result = @import("math/modf.zig").modf32_result;
pub const modf64_result = @import("math/modf.zig").modf64_result;
pub const copysign = @import("math/copysign.zig").copysign;
pub const isFinite = @import("math/isfinite.zig").isFinite;
pub const isInf = @import("math/isinf.zig").isInf;
pub const isPositiveInf = @import("math/isinf.zig").isPositiveInf;
pub const isNegativeInf = @import("math/isinf.zig").isNegativeInf;
pub const isNormal = @import("math/isnormal.zig").isNormal;
pub const signbit = @import("math/signbit.zig").signbit;
pub const scalbn = @import("math/scalbn.zig").scalbn;
pub const ldexp = @import("math/ldexp.zig").ldexp;
pub const pow = @import("math/pow.zig").pow;
pub const powi = @import("math/powi.zig").powi;
pub const sqrt = @import("math/sqrt.zig").sqrt;
pub const cbrt = @import("math/cbrt.zig").cbrt;
pub const acos = @import("math/acos.zig").acos;
pub const asin = @import("math/asin.zig").asin;
pub const atan = @import("math/atan.zig").atan;
pub const atan2 = @import("math/atan2.zig").atan2;
pub const hypot = @import("math/hypot.zig").hypot;
pub const expm1 = @import("math/expm1.zig").expm1;
pub const ilogb = @import("math/ilogb.zig").ilogb;
pub const ln = @import("math/ln.zig").ln;
pub const log = @import("math/log.zig").log;
pub const log2 = @import("math/log2.zig").log2;
pub const log10 = @import("math/log10.zig").log10;
pub const log10_int = @import("math/log10.zig").log10_int;
pub const log1p = @import("math/log1p.zig").log1p;
pub const asinh = @import("math/asinh.zig").asinh;
pub const acosh = @import("math/acosh.zig").acosh;
pub const atanh = @import("math/atanh.zig").atanh;
pub const sinh = @import("math/sinh.zig").sinh;
pub const cosh = @import("math/cosh.zig").cosh;
pub const tanh = @import("math/tanh.zig").tanh;
pub const gcd = @import("math/gcd.zig").gcd;
/// Sine trigonometric function on a floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @sin
pub inline fn sin(value: anytype) @TypeOf(value) {
return @sin(value);
}
/// Cosine trigonometric function on a floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @cos
pub inline fn cos(value: anytype) @TypeOf(value) {
return @cos(value);
}
/// Tangent trigonometric function on a floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @tan
pub inline fn tan(value: anytype) @TypeOf(value) {
return @tan(value);
}
/// Converts an angle in radians to degrees. T must be a float type.
pub fn radiansToDegrees(comptime T: type, angle_in_radians: T) T {
if (@typeInfo(T) != .Float and @typeInfo(T) != .ComptimeFloat)
@compileError("T must be a float type");
return angle_in_radians * 180.0 / pi;
}
test "radiansToDegrees" {
try std.testing.expectApproxEqAbs(@as(f32, 0), radiansToDegrees(f32, 0), 1e-6);
try std.testing.expectApproxEqAbs(@as(f32, 90), radiansToDegrees(f32, pi / 2.0), 1e-6);
try std.testing.expectApproxEqAbs(@as(f32, -45), radiansToDegrees(f32, -pi / 4.0), 1e-6);
try std.testing.expectApproxEqAbs(@as(f32, 180), radiansToDegrees(f32, pi), 1e-6);
try std.testing.expectApproxEqAbs(@as(f32, 360), radiansToDegrees(f32, 2.0 * pi), 1e-6);
}
/// Converts an angle in degrees to radians. T must be a float type.
pub fn degreesToRadians(comptime T: type, angle_in_degrees: T) T {
if (@typeInfo(T) != .Float and @typeInfo(T) != .ComptimeFloat)
@compileError("T must be a float type");
return angle_in_degrees * pi / 180.0;
}
test "degreesToRadians" {
try std.testing.expectApproxEqAbs(@as(f32, pi / 2.0), degreesToRadians(f32, 90), 1e-6);
try std.testing.expectApproxEqAbs(@as(f32, -3 * pi / 2.0), degreesToRadians(f32, -270), 1e-6);
try std.testing.expectApproxEqAbs(@as(f32, 2 * pi), degreesToRadians(f32, 360), 1e-6);
}
/// Base-e exponential function on a floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @exp
pub inline fn exp(value: anytype) @TypeOf(value) {
return @exp(value);
}
/// Base-2 exponential function on a floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @exp2
pub inline fn exp2(value: anytype) @TypeOf(value) {
return @exp2(value);
}
pub const complex = @import("math/complex.zig");
pub const Complex = complex.Complex;
pub const big = @import("math/big.zig");
test {
std.testing.refAllDecls(@This());
}
/// Given two types, returns the smallest one which is capable of holding the
/// full range of the minimum value.
pub fn Min(comptime A: type, comptime B: type) type {
switch (@typeInfo(A)) {
.Int => |a_info| switch (@typeInfo(B)) {
.Int => |b_info| if (a_info.signedness == .unsigned and b_info.signedness == .unsigned) {
if (a_info.bits < b_info.bits) {
return A;
} else {
return B;
}
},
else => {},
},
else => {},
}
return @TypeOf(@as(A, 0) + @as(B, 0));
}
/// Returns the smaller number. When one parameter's type's full range
/// fits in the other, the return type is the smaller type.
pub fn min(x: anytype, y: anytype) Min(@TypeOf(x), @TypeOf(y)) {
const Result = Min(@TypeOf(x), @TypeOf(y));
if (x < y) {
// TODO Zig should allow this as an implicit cast because x is
// immutable and in this scope it is known to fit in the
// return type.
switch (@typeInfo(Result)) {
.Int => return @intCast(Result, x),
else => return x,
}
} else {
// TODO Zig should allow this as an implicit cast because y is
// immutable and in this scope it is known to fit in the
// return type.
switch (@typeInfo(Result)) {
.Int => return @intCast(Result, y),
else => return y,
}
}
}
test "min" {
try testing.expect(min(@as(i32, -1), @as(i32, 2)) == -1);
{
var a: u16 = 999;
var b: u32 = 10;
var result = min(a, b);
try testing.expect(@TypeOf(result) == u16);
try testing.expect(result == 10);
}
{
var a: f64 = 10.34;
var b: f32 = 999.12;
var result = min(a, b);
try testing.expect(@TypeOf(result) == f64);
try testing.expect(result == 10.34);
}
{
var a: i8 = -127;
var b: i16 = -200;
var result = min(a, b);
try testing.expect(@TypeOf(result) == i16);
try testing.expect(result == -200);
}
{
const a = 10.34;
var b: f32 = 999.12;
var result = min(a, b);
try testing.expect(@TypeOf(result) == f32);
try testing.expect(result == 10.34);
}
}
/// Finds the minimum of three numbers.
pub fn min3(x: anytype, y: anytype, z: anytype) @TypeOf(x, y, z) {
return min(x, min(y, z));
}
test "min3" {
try testing.expect(min3(@as(i32, 0), @as(i32, 1), @as(i32, 2)) == 0);
try testing.expect(min3(@as(i32, 0), @as(i32, 2), @as(i32, 1)) == 0);
try testing.expect(min3(@as(i32, 1), @as(i32, 0), @as(i32, 2)) == 0);
try testing.expect(min3(@as(i32, 1), @as(i32, 2), @as(i32, 0)) == 0);
try testing.expect(min3(@as(i32, 2), @as(i32, 0), @as(i32, 1)) == 0);
try testing.expect(min3(@as(i32, 2), @as(i32, 1), @as(i32, 0)) == 0);
}
/// Returns the maximum of two numbers. Return type is the one with the
/// larger range.
pub fn max(x: anytype, y: anytype) @TypeOf(x, y) {
return if (x > y) x else y;
}
test "max" {
try testing.expect(max(@as(i32, -1), @as(i32, 2)) == 2);
try testing.expect(max(@as(i32, 2), @as(i32, -1)) == 2);
}
/// Finds the maximum of three numbers.
pub fn max3(x: anytype, y: anytype, z: anytype) @TypeOf(x, y, z) {
return max(x, max(y, z));
}
test "max3" {
try testing.expect(max3(@as(i32, 0), @as(i32, 1), @as(i32, 2)) == 2);
try testing.expect(max3(@as(i32, 0), @as(i32, 2), @as(i32, 1)) == 2);
try testing.expect(max3(@as(i32, 1), @as(i32, 0), @as(i32, 2)) == 2);
try testing.expect(max3(@as(i32, 1), @as(i32, 2), @as(i32, 0)) == 2);
try testing.expect(max3(@as(i32, 2), @as(i32, 0), @as(i32, 1)) == 2);
try testing.expect(max3(@as(i32, 2), @as(i32, 1), @as(i32, 0)) == 2);
}
/// Limit val to the inclusive range [lower, upper].
pub fn clamp(val: anytype, lower: anytype, upper: anytype) @TypeOf(val, lower, upper) {
assert(lower <= upper);
return max(lower, min(val, upper));
}
test "clamp" {
// Within range
try testing.expect(std.math.clamp(@as(i32, -1), @as(i32, -4), @as(i32, 7)) == -1);
// Below
try testing.expect(std.math.clamp(@as(i32, -5), @as(i32, -4), @as(i32, 7)) == -4);
// Above
try testing.expect(std.math.clamp(@as(i32, 8), @as(i32, -4), @as(i32, 7)) == 7);
// Floating point
try testing.expect(std.math.clamp(@as(f32, 1.1), @as(f32, 0.0), @as(f32, 1.0)) == 1.0);
try testing.expect(std.math.clamp(@as(f32, -127.5), @as(f32, -200), @as(f32, -100)) == -127.5);
// Mix of comptime and non-comptime
var i: i32 = 1;
try testing.expect(std.math.clamp(i, 0, 1) == 1);
}
/// Returns the product of a and b. Returns an error on overflow.
pub fn mul(comptime T: type, a: T, b: T) (error{Overflow}!T) {
if (T == comptime_int) return a * b;
const ov = @mulWithOverflow(a, b);
if (ov[1] != 0) return error.Overflow;
return ov[0];
}
/// Returns the sum of a and b. Returns an error on overflow.
pub fn add(comptime T: type, a: T, b: T) (error{Overflow}!T) {
if (T == comptime_int) return a + b;
const ov = @addWithOverflow(a, b);
if (ov[1] != 0) return error.Overflow;
return ov[0];
}
/// Returns a - b, or an error on overflow.
pub fn sub(comptime T: type, a: T, b: T) (error{Overflow}!T) {
if (T == comptime_int) return a - b;
const ov = @subWithOverflow(a, b);
if (ov[1] != 0) return error.Overflow;
return ov[0];
}
pub fn negate(x: anytype) !@TypeOf(x) {
return sub(@TypeOf(x), 0, x);
}
/// Shifts a left by shift_amt. Returns an error on overflow. shift_amt
/// is unsigned.
pub fn shlExact(comptime T: type, a: T, shift_amt: Log2Int(T)) !T {
if (T == comptime_int) return a << shift_amt;
const ov = @shlWithOverflow(a, shift_amt);
if (ov[1] != 0) return error.Overflow;
return ov[0];
}
/// Shifts left. Overflowed bits are truncated.
/// A negative shift amount results in a right shift.
pub fn shl(comptime T: type, a: T, shift_amt: anytype) T {
const abs_shift_amt = absCast(shift_amt);
const casted_shift_amt = blk: {
if (@typeInfo(T) == .Vector) {
const C = @typeInfo(T).Vector.child;
const len = @typeInfo(T).Vector.len;
if (abs_shift_amt >= @typeInfo(C).Int.bits) return @splat(len, @as(C, 0));
break :blk @splat(len, @intCast(Log2Int(C), abs_shift_amt));
} else {
if (abs_shift_amt >= @typeInfo(T).Int.bits) return 0;
break :blk @intCast(Log2Int(T), abs_shift_amt);
}
};
if (@TypeOf(shift_amt) == comptime_int or @typeInfo(@TypeOf(shift_amt)).Int.signedness == .signed) {
if (shift_amt < 0) {
return a >> casted_shift_amt;
}
}
return a << casted_shift_amt;
}
test "shl" {
if (builtin.zig_backend == .stage2_llvm and builtin.cpu.arch == .aarch64) {
// https://github.com/ziglang/zig/issues/12012
return error.SkipZigTest;
}
try testing.expect(shl(u8, 0b11111111, @as(usize, 3)) == 0b11111000);
try testing.expect(shl(u8, 0b11111111, @as(usize, 8)) == 0);
try testing.expect(shl(u8, 0b11111111, @as(usize, 9)) == 0);
try testing.expect(shl(u8, 0b11111111, @as(isize, -2)) == 0b00111111);
try testing.expect(shl(u8, 0b11111111, 3) == 0b11111000);
try testing.expect(shl(u8, 0b11111111, 8) == 0);
try testing.expect(shl(u8, 0b11111111, 9) == 0);
try testing.expect(shl(u8, 0b11111111, -2) == 0b00111111);
try testing.expect(shl(@Vector(1, u32), @Vector(1, u32){42}, @as(usize, 1))[0] == @as(u32, 42) << 1);
try testing.expect(shl(@Vector(1, u32), @Vector(1, u32){42}, @as(isize, -1))[0] == @as(u32, 42) >> 1);
try testing.expect(shl(@Vector(1, u32), @Vector(1, u32){42}, 33)[0] == 0);
}
/// Shifts right. Overflowed bits are truncated.
/// A negative shift amount results in a left shift.
pub fn shr(comptime T: type, a: T, shift_amt: anytype) T {
const abs_shift_amt = absCast(shift_amt);
const casted_shift_amt = blk: {
if (@typeInfo(T) == .Vector) {
const C = @typeInfo(T).Vector.child;
const len = @typeInfo(T).Vector.len;
if (abs_shift_amt >= @typeInfo(C).Int.bits) return @splat(len, @as(C, 0));
break :blk @splat(len, @intCast(Log2Int(C), abs_shift_amt));
} else {
if (abs_shift_amt >= @typeInfo(T).Int.bits) return 0;
break :blk @intCast(Log2Int(T), abs_shift_amt);
}
};
if (@TypeOf(shift_amt) == comptime_int or @typeInfo(@TypeOf(shift_amt)).Int.signedness == .signed) {
if (shift_amt < 0) {
return a << casted_shift_amt;
}
}
return a >> casted_shift_amt;
}
test "shr" {
if (builtin.zig_backend == .stage2_llvm and builtin.cpu.arch == .aarch64) {
// https://github.com/ziglang/zig/issues/12012
return error.SkipZigTest;
}
try testing.expect(shr(u8, 0b11111111, @as(usize, 3)) == 0b00011111);
try testing.expect(shr(u8, 0b11111111, @as(usize, 8)) == 0);
try testing.expect(shr(u8, 0b11111111, @as(usize, 9)) == 0);
try testing.expect(shr(u8, 0b11111111, @as(isize, -2)) == 0b11111100);
try testing.expect(shr(u8, 0b11111111, 3) == 0b00011111);
try testing.expect(shr(u8, 0b11111111, 8) == 0);
try testing.expect(shr(u8, 0b11111111, 9) == 0);
try testing.expect(shr(u8, 0b11111111, -2) == 0b11111100);
try testing.expect(shr(@Vector(1, u32), @Vector(1, u32){42}, @as(usize, 1))[0] == @as(u32, 42) >> 1);
try testing.expect(shr(@Vector(1, u32), @Vector(1, u32){42}, @as(isize, -1))[0] == @as(u32, 42) << 1);
try testing.expect(shr(@Vector(1, u32), @Vector(1, u32){42}, 33)[0] == 0);
}
/// Rotates right. Only unsigned values can be rotated. Negative shift
/// values result in shift modulo the bit count.
pub fn rotr(comptime T: type, x: T, r: anytype) T {
if (@typeInfo(T) == .Vector) {
const C = @typeInfo(T).Vector.child;
if (C == u0) return 0;
if (@typeInfo(C).Int.signedness == .signed) {
@compileError("cannot rotate signed integers");
}
const ar = @intCast(Log2Int(C), @mod(r, @typeInfo(C).Int.bits));
return (x >> @splat(@typeInfo(T).Vector.len, ar)) | (x << @splat(@typeInfo(T).Vector.len, 1 + ~ar));
} else if (@typeInfo(T).Int.signedness == .signed) {
@compileError("cannot rotate signed integer");
} else {
if (T == u0) return 0;
if (isPowerOfTwo(@typeInfo(T).Int.bits)) {
const ar = @intCast(Log2Int(T), @mod(r, @typeInfo(T).Int.bits));
return x >> ar | x << (1 +% ~ar);
} else {
const ar = @mod(r, @typeInfo(T).Int.bits);
return shr(T, x, ar) | shl(T, x, @typeInfo(T).Int.bits - ar);
}
}
}
test "rotr" {
if (builtin.zig_backend == .stage2_llvm and builtin.cpu.arch == .aarch64) {
// https://github.com/ziglang/zig/issues/12012
return error.SkipZigTest;
}
try testing.expect(rotr(u0, 0b0, @as(usize, 3)) == 0b0);
try testing.expect(rotr(u5, 0b00001, @as(usize, 0)) == 0b00001);
try testing.expect(rotr(u6, 0b000001, @as(usize, 7)) == 0b100000);
try testing.expect(rotr(u8, 0b00000001, @as(usize, 0)) == 0b00000001);
try testing.expect(rotr(u8, 0b00000001, @as(usize, 9)) == 0b10000000);
try testing.expect(rotr(u8, 0b00000001, @as(usize, 8)) == 0b00000001);
try testing.expect(rotr(u8, 0b00000001, @as(usize, 4)) == 0b00010000);
try testing.expect(rotr(u8, 0b00000001, @as(isize, -1)) == 0b00000010);
try testing.expect(rotr(@Vector(1, u32), @Vector(1, u32){1}, @as(usize, 1))[0] == @as(u32, 1) << 31);
try testing.expect(rotr(@Vector(1, u32), @Vector(1, u32){1}, @as(isize, -1))[0] == @as(u32, 1) << 1);
}
/// Rotates left. Only unsigned values can be rotated. Negative shift
/// values result in shift modulo the bit count.
pub fn rotl(comptime T: type, x: T, r: anytype) T {
if (@typeInfo(T) == .Vector) {
const C = @typeInfo(T).Vector.child;
if (C == u0) return 0;
if (@typeInfo(C).Int.signedness == .signed) {
@compileError("cannot rotate signed integers");
}
const ar = @intCast(Log2Int(C), @mod(r, @typeInfo(C).Int.bits));
return (x << @splat(@typeInfo(T).Vector.len, ar)) | (x >> @splat(@typeInfo(T).Vector.len, 1 +% ~ar));
} else if (@typeInfo(T).Int.signedness == .signed) {
@compileError("cannot rotate signed integer");
} else {
if (T == u0) return 0;
if (isPowerOfTwo(@typeInfo(T).Int.bits)) {
const ar = @intCast(Log2Int(T), @mod(r, @typeInfo(T).Int.bits));
return x << ar | x >> 1 +% ~ar;
} else {
const ar = @mod(r, @typeInfo(T).Int.bits);
return shl(T, x, ar) | shr(T, x, @typeInfo(T).Int.bits - ar);
}
}
}
test "rotl" {
if (builtin.zig_backend == .stage2_llvm and builtin.cpu.arch == .aarch64) {
// https://github.com/ziglang/zig/issues/12012
return error.SkipZigTest;
}
try testing.expect(rotl(u0, 0b0, @as(usize, 3)) == 0b0);
try testing.expect(rotl(u5, 0b00001, @as(usize, 0)) == 0b00001);
try testing.expect(rotl(u6, 0b000001, @as(usize, 7)) == 0b000010);
try testing.expect(rotl(u8, 0b00000001, @as(usize, 0)) == 0b00000001);
try testing.expect(rotl(u8, 0b00000001, @as(usize, 9)) == 0b00000010);
try testing.expect(rotl(u8, 0b00000001, @as(usize, 8)) == 0b00000001);
try testing.expect(rotl(u8, 0b00000001, @as(usize, 4)) == 0b00010000);
try testing.expect(rotl(u8, 0b00000001, @as(isize, -1)) == 0b10000000);
try testing.expect(rotl(@Vector(1, u32), @Vector(1, u32){1 << 31}, @as(usize, 1))[0] == 1);
try testing.expect(rotl(@Vector(1, u32), @Vector(1, u32){1 << 31}, @as(isize, -1))[0] == @as(u32, 1) << 30);
}
/// Returns an unsigned int type that can hold the number of bits in T
/// - 1. Suitable for 0-based bit indices of T.
pub fn Log2Int(comptime T: type) type {
// comptime ceil log2
comptime var count = 0;
comptime var s = @typeInfo(T).Int.bits - 1;
inline while (s != 0) : (s >>= 1) {
count += 1;
}
return std.meta.Int(.unsigned, count);
}
/// Returns an unsigned int type that can hold the number of bits in T.
pub fn Log2IntCeil(comptime T: type) type {
// comptime ceil log2
comptime var count = 0;
comptime var s = @typeInfo(T).Int.bits;
inline while (s != 0) : (s >>= 1) {
count += 1;
}
return std.meta.Int(.unsigned, count);
}
/// Returns the smallest integer type that can hold both from and to.
pub fn IntFittingRange(comptime from: comptime_int, comptime to: comptime_int) type {
assert(from <= to);
if (from == 0 and to == 0) {
return u0;
}
const signedness: std.builtin.Signedness = if (from < 0) .signed else .unsigned;
const largest_positive_integer = max(if (from < 0) (-from) - 1 else from, to); // two's complement
const base = log2(largest_positive_integer);
const upper = (1 << base) - 1;
var magnitude_bits = if (upper >= largest_positive_integer) base else base + 1;
if (signedness == .signed) {
magnitude_bits += 1;
}
return std.meta.Int(signedness, magnitude_bits);
}
test "IntFittingRange" {
try testing.expect(IntFittingRange(0, 0) == u0);
try testing.expect(IntFittingRange(0, 1) == u1);
try testing.expect(IntFittingRange(0, 2) == u2);
try testing.expect(IntFittingRange(0, 3) == u2);
try testing.expect(IntFittingRange(0, 4) == u3);
try testing.expect(IntFittingRange(0, 7) == u3);
try testing.expect(IntFittingRange(0, 8) == u4);
try testing.expect(IntFittingRange(0, 9) == u4);
try testing.expect(IntFittingRange(0, 15) == u4);
try testing.expect(IntFittingRange(0, 16) == u5);
try testing.expect(IntFittingRange(0, 17) == u5);
try testing.expect(IntFittingRange(0, 4095) == u12);
try testing.expect(IntFittingRange(2000, 4095) == u12);
try testing.expect(IntFittingRange(0, 4096) == u13);
try testing.expect(IntFittingRange(2000, 4096) == u13);
try testing.expect(IntFittingRange(0, 4097) == u13);
try testing.expect(IntFittingRange(2000, 4097) == u13);
try testing.expect(IntFittingRange(0, 123456789123456798123456789) == u87);
try testing.expect(IntFittingRange(0, 123456789123456798123456789123456789123456798123456789) == u177);
try testing.expect(IntFittingRange(-1, -1) == i1);
try testing.expect(IntFittingRange(-1, 0) == i1);
try testing.expect(IntFittingRange(-1, 1) == i2);
try testing.expect(IntFittingRange(-2, -2) == i2);
try testing.expect(IntFittingRange(-2, -1) == i2);
try testing.expect(IntFittingRange(-2, 0) == i2);
try testing.expect(IntFittingRange(-2, 1) == i2);
try testing.expect(IntFittingRange(-2, 2) == i3);
try testing.expect(IntFittingRange(-1, 2) == i3);
try testing.expect(IntFittingRange(-1, 3) == i3);
try testing.expect(IntFittingRange(-1, 4) == i4);
try testing.expect(IntFittingRange(-1, 7) == i4);
try testing.expect(IntFittingRange(-1, 8) == i5);
try testing.expect(IntFittingRange(-1, 9) == i5);
try testing.expect(IntFittingRange(-1, 15) == i5);
try testing.expect(IntFittingRange(-1, 16) == i6);
try testing.expect(IntFittingRange(-1, 17) == i6);
try testing.expect(IntFittingRange(-1, 4095) == i13);
try testing.expect(IntFittingRange(-4096, 4095) == i13);
try testing.expect(IntFittingRange(-1, 4096) == i14);
try testing.expect(IntFittingRange(-4097, 4095) == i14);
try testing.expect(IntFittingRange(-1, 4097) == i14);
try testing.expect(IntFittingRange(-1, 123456789123456798123456789) == i88);
try testing.expect(IntFittingRange(-1, 123456789123456798123456789123456789123456798123456789) == i178);
}
test "overflow functions" {
try testOverflow();
comptime try testOverflow();
}
fn testOverflow() !void {
try testing.expect((mul(i32, 3, 4) catch unreachable) == 12);
try testing.expect((add(i32, 3, 4) catch unreachable) == 7);
try testing.expect((sub(i32, 3, 4) catch unreachable) == -1);
try testing.expect((shlExact(i32, 0b11, 4) catch unreachable) == 0b110000);
}
/// Returns the absolute value of x, where x is a value of a signed integer type.
/// Does not convert and returns a value of a signed integer type.
/// Use `absCast` if you want to convert the result and get an unsigned type.
pub fn absInt(x: anytype) !@TypeOf(x) {
const T = @TypeOf(x);
return switch (@typeInfo(T)) {
.Int => |info| {
comptime assert(info.signedness == .signed); // must pass a signed integer to absInt
if (x == minInt(T)) {
return error.Overflow;
} else {
@setRuntimeSafety(false);
return if (x < 0) -x else x;
}
},
.Vector => |vinfo| blk: {
switch (@typeInfo(vinfo.child)) {
.Int => |info| {
comptime assert(info.signedness == .signed); // must pass a signed integer to absInt
if (@reduce(.Or, x == @splat(vinfo.len, @as(vinfo.child, minInt(vinfo.child))))) {
return error.Overflow;
}
const zero = @splat(vinfo.len, @as(vinfo.child, 0));
break :blk @select(vinfo.child, x > zero, x, -x);
},
else => @compileError("Expected vector of ints, found " ++ @typeName(T)),
}
},
else => @compileError("Expected an int or vector, found " ++ @typeName(T)),
};
}
test "absInt" {
try testAbsInt();
comptime try testAbsInt();
}
fn testAbsInt() !void {
try testing.expect((absInt(@as(i32, -10)) catch unreachable) == 10);
try testing.expect((absInt(@as(i32, 10)) catch unreachable) == 10);
try testing.expectEqual(@Vector(3, i32){ 10, 10, 0 }, (absInt(@Vector(3, i32){ -10, 10, 0 }) catch unreachable));
try testing.expectError(error.Overflow, absInt(@as(i32, minInt(i32))));
try testing.expectError(error.Overflow, absInt(@Vector(3, i32){ 10, -10, minInt(i32) }));
}
/// Divide numerator by denominator, rounding toward zero. Returns an
/// error on overflow or when denominator is zero.
pub fn divTrunc(comptime T: type, numerator: T, denominator: T) !T {
@setRuntimeSafety(false);
if (denominator == 0) return error.DivisionByZero;
if (@typeInfo(T) == .Int and @typeInfo(T).Int.signedness == .signed and numerator == minInt(T) and denominator == -1) return error.Overflow;
return @divTrunc(numerator, denominator);
}
test "divTrunc" {
try testDivTrunc();
comptime try testDivTrunc();
}
fn testDivTrunc() !void {
try testing.expect((divTrunc(i32, 5, 3) catch unreachable) == 1);
try testing.expect((divTrunc(i32, -5, 3) catch unreachable) == -1);
try testing.expectError(error.DivisionByZero, divTrunc(i8, -5, 0));
try testing.expectError(error.Overflow, divTrunc(i8, -128, -1));
try testing.expect((divTrunc(f32, 5.0, 3.0) catch unreachable) == 1.0);
try testing.expect((divTrunc(f32, -5.0, 3.0) catch unreachable) == -1.0);
}
/// Divide numerator by denominator, rounding toward negative
/// infinity. Returns an error on overflow or when denominator is
/// zero.
pub fn divFloor(comptime T: type, numerator: T, denominator: T) !T {
@setRuntimeSafety(false);
if (denominator == 0) return error.DivisionByZero;
if (@typeInfo(T) == .Int and @typeInfo(T).Int.signedness == .signed and numerator == minInt(T) and denominator == -1) return error.Overflow;
return @divFloor(numerator, denominator);
}
test "divFloor" {
try testDivFloor();
comptime try testDivFloor();
}
fn testDivFloor() !void {
try testing.expect((divFloor(i32, 5, 3) catch unreachable) == 1);
try testing.expect((divFloor(i32, -5, 3) catch unreachable) == -2);
try testing.expectError(error.DivisionByZero, divFloor(i8, -5, 0));
try testing.expectError(error.Overflow, divFloor(i8, -128, -1));
try testing.expect((divFloor(f32, 5.0, 3.0) catch unreachable) == 1.0);
try testing.expect((divFloor(f32, -5.0, 3.0) catch unreachable) == -2.0);
}
/// Divide numerator by denominator, rounding toward positive
/// infinity. Returns an error on overflow or when denominator is
/// zero.
pub fn divCeil(comptime T: type, numerator: T, denominator: T) !T {
@setRuntimeSafety(false);
if ((comptime std.meta.trait.isNumber(T)) and denominator == 0) return error.DivisionByZero;
const info = @typeInfo(T);
switch (info) {
.ComptimeFloat, .Float => return @ceil(numerator / denominator),
.ComptimeInt, .Int => {
if (numerator < 0 and denominator < 0) {
if (info == .Int and numerator == minInt(T) and denominator == -1)
return error.Overflow;
return @divFloor(numerator + 1, denominator) + 1;
}
if (numerator > 0 and denominator > 0)
return @divFloor(numerator - 1, denominator) + 1;
return @divTrunc(numerator, denominator);
},
else => @compileError("divCeil unsupported on " ++ @typeName(T)),
}
}
test "divCeil" {
try testDivCeil();
comptime try testDivCeil();
}
fn testDivCeil() !void {
try testing.expectEqual(@as(i32, 2), divCeil(i32, 5, 3) catch unreachable);
try testing.expectEqual(@as(i32, -1), divCeil(i32, -5, 3) catch unreachable);
try testing.expectEqual(@as(i32, -1), divCeil(i32, 5, -3) catch unreachable);
try testing.expectEqual(@as(i32, 2), divCeil(i32, -5, -3) catch unreachable);
try testing.expectEqual(@as(i32, 0), divCeil(i32, 0, 5) catch unreachable);
try testing.expectEqual(@as(u32, 0), divCeil(u32, 0, 5) catch unreachable);
try testing.expectError(error.DivisionByZero, divCeil(i8, -5, 0));
try testing.expectError(error.Overflow, divCeil(i8, -128, -1));
try testing.expectEqual(@as(f32, 0.0), divCeil(f32, 0.0, 5.0) catch unreachable);
try testing.expectEqual(@as(f32, 2.0), divCeil(f32, 5.0, 3.0) catch unreachable);
try testing.expectEqual(@as(f32, -1.0), divCeil(f32, -5.0, 3.0) catch unreachable);
try testing.expectEqual(@as(f32, -1.0), divCeil(f32, 5.0, -3.0) catch unreachable);
try testing.expectEqual(@as(f32, 2.0), divCeil(f32, -5.0, -3.0) catch unreachable);
try testing.expectEqual(6, divCeil(comptime_int, 23, 4) catch unreachable);
try testing.expectEqual(-5, divCeil(comptime_int, -23, 4) catch unreachable);
try testing.expectEqual(-5, divCeil(comptime_int, 23, -4) catch unreachable);
try testing.expectEqual(6, divCeil(comptime_int, -23, -4) catch unreachable);
try testing.expectError(error.DivisionByZero, divCeil(comptime_int, 23, 0));
try testing.expectEqual(6.0, divCeil(comptime_float, 23.0, 4.0) catch unreachable);
try testing.expectEqual(-5.0, divCeil(comptime_float, -23.0, 4.0) catch unreachable);
try testing.expectEqual(-5.0, divCeil(comptime_float, 23.0, -4.0) catch unreachable);
try testing.expectEqual(6.0, divCeil(comptime_float, -23.0, -4.0) catch unreachable);
try testing.expectError(error.DivisionByZero, divCeil(comptime_float, 23.0, 0.0));
}
/// Divide numerator by denominator. Return an error if quotient is
/// not an integer, denominator is zero, or on overflow.
pub fn divExact(comptime T: type, numerator: T, denominator: T) !T {
@setRuntimeSafety(false);
if (denominator == 0) return error.DivisionByZero;
if (@typeInfo(T) == .Int and @typeInfo(T).Int.signedness == .signed and numerator == minInt(T) and denominator == -1) return error.Overflow;
const result = @divTrunc(numerator, denominator);
if (result * denominator != numerator) return error.UnexpectedRemainder;
return result;
}
test "divExact" {
try testDivExact();
comptime try testDivExact();
}
fn testDivExact() !void {
try testing.expect((divExact(i32, 10, 5) catch unreachable) == 2);
try testing.expect((divExact(i32, -10, 5) catch unreachable) == -2);
try testing.expectError(error.DivisionByZero, divExact(i8, -5, 0));
try testing.expectError(error.Overflow, divExact(i8, -128, -1));
try testing.expectError(error.UnexpectedRemainder, divExact(i32, 5, 2));
try testing.expect((divExact(f32, 10.0, 5.0) catch unreachable) == 2.0);
try testing.expect((divExact(f32, -10.0, 5.0) catch unreachable) == -2.0);
try testing.expectError(error.UnexpectedRemainder, divExact(f32, 5.0, 2.0));
}
/// Returns numerator modulo denominator, or an error if denominator is
/// zero or negative. Negative numerators never result in negative
/// return values.
pub fn mod(comptime T: type, numerator: T, denominator: T) !T {
@setRuntimeSafety(false);
if (denominator == 0) return error.DivisionByZero;
if (denominator < 0) return error.NegativeDenominator;
return @mod(numerator, denominator);
}
test "mod" {
try testMod();
comptime try testMod();
}
fn testMod() !void {
try testing.expect((mod(i32, -5, 3) catch unreachable) == 1);
try testing.expect((mod(i32, 5, 3) catch unreachable) == 2);
try testing.expectError(error.NegativeDenominator, mod(i32, 10, -1));
try testing.expectError(error.DivisionByZero, mod(i32, 10, 0));
try testing.expect((mod(f32, -5, 3) catch unreachable) == 1);
try testing.expect((mod(f32, 5, 3) catch unreachable) == 2);
try testing.expectError(error.NegativeDenominator, mod(f32, 10, -1));
try testing.expectError(error.DivisionByZero, mod(f32, 10, 0));
}
/// Returns the remainder when numerator is divided by denominator, or
/// an error if denominator is zero or negative. Negative numerators
/// can give negative results.
pub fn rem(comptime T: type, numerator: T, denominator: T) !T {
@setRuntimeSafety(false);
if (denominator == 0) return error.DivisionByZero;
if (denominator < 0) return error.NegativeDenominator;
return @rem(numerator, denominator);
}
test "rem" {
try testRem();
comptime try testRem();
}
fn testRem() !void {
try testing.expect((rem(i32, -5, 3) catch unreachable) == -2);
try testing.expect((rem(i32, 5, 3) catch unreachable) == 2);
try testing.expectError(error.NegativeDenominator, rem(i32, 10, -1));
try testing.expectError(error.DivisionByZero, rem(i32, 10, 0));
try testing.expect((rem(f32, -5, 3) catch unreachable) == -2);
try testing.expect((rem(f32, 5, 3) catch unreachable) == 2);
try testing.expectError(error.NegativeDenominator, rem(f32, 10, -1));
try testing.expectError(error.DivisionByZero, rem(f32, 10, 0));
}
/// Returns the absolute value of a floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @fabs
pub inline fn fabs(value: anytype) @TypeOf(value) {
return @fabs(value);
}
/// Returns the absolute value of the integer parameter.
/// Converts result type to unsigned if needed and returns a value of an unsigned integer type.
/// Use `absInt` if you want to keep your integer type signed.
pub fn absCast(x: anytype) switch (@typeInfo(@TypeOf(x))) {
.ComptimeInt => comptime_int,
.Int => |int_info| std.meta.Int(.unsigned, int_info.bits),
else => @compileError("absCast only accepts integers"),
} {
switch (@typeInfo(@TypeOf(x))) {
.ComptimeInt => {
if (x < 0) {
return -x;
} else {
return x;
}
},
.Int => |int_info| {
if (int_info.signedness == .unsigned) return x;
const Uint = std.meta.Int(.unsigned, int_info.bits);
if (x < 0) {
return ~@bitCast(Uint, x +% -1);
} else {
return @intCast(Uint, x);
}
},
else => unreachable,
}
}
test "absCast" {
try testing.expectEqual(@as(u1, 1), absCast(@as(i1, -1)));
try testing.expectEqual(@as(u32, 999), absCast(@as(i32, -999)));
try testing.expectEqual(@as(u32, 999), absCast(@as(i32, 999)));
try testing.expectEqual(@as(u32, -minInt(i32)), absCast(@as(i32, minInt(i32))));
try testing.expectEqual(999, absCast(-999));
}
/// Returns the negation of the integer parameter.
/// Result is a signed integer.
pub fn negateCast(x: anytype) !std.meta.Int(.signed, @bitSizeOf(@TypeOf(x))) {
if (@typeInfo(@TypeOf(x)).Int.signedness == .signed) return negate(x);
const int = std.meta.Int(.signed, @bitSizeOf(@TypeOf(x)));
if (x > -minInt(int)) return error.Overflow;
if (x == -minInt(int)) return minInt(int);
return -@intCast(int, x);
}
test "negateCast" {
try testing.expect((negateCast(@as(u32, 999)) catch unreachable) == -999);
try testing.expect(@TypeOf(negateCast(@as(u32, 999)) catch unreachable) == i32);
try testing.expect((negateCast(@as(u32, -minInt(i32))) catch unreachable) == minInt(i32));
try testing.expect(@TypeOf(negateCast(@as(u32, -minInt(i32))) catch unreachable) == i32);
try testing.expectError(error.Overflow, negateCast(@as(u32, maxInt(i32) + 10)));
}
/// Cast an integer to a different integer type. If the value doesn't fit,
/// return null.
pub fn cast(comptime T: type, x: anytype) ?T {
comptime assert(@typeInfo(T) == .Int); // must pass an integer
const is_comptime = @TypeOf(x) == comptime_int;
comptime assert(is_comptime or @typeInfo(@TypeOf(x)) == .Int); // must pass an integer
if ((is_comptime or maxInt(@TypeOf(x)) > maxInt(T)) and x > maxInt(T)) {
return null;
} else if ((is_comptime or minInt(@TypeOf(x)) < minInt(T)) and x < minInt(T)) {
return null;
} else {
return @intCast(T, x);
}
}
test "cast" {
try testing.expect(cast(u8, 300) == null);
try testing.expect(cast(u8, @as(u32, 300)) == null);
try testing.expect(cast(i8, -200) == null);
try testing.expect(cast(i8, @as(i32, -200)) == null);
try testing.expect(cast(u8, -1) == null);
try testing.expect(cast(u8, @as(i8, -1)) == null);
try testing.expect(cast(u64, -1) == null);
try testing.expect(cast(u64, @as(i8, -1)) == null);
try testing.expect(cast(u8, 255).? == @as(u8, 255));
try testing.expect(cast(u8, @as(u32, 255)).? == @as(u8, 255));
try testing.expect(@TypeOf(cast(u8, 255).?) == u8);
try testing.expect(@TypeOf(cast(u8, @as(u32, 255)).?) == u8);
}
pub const AlignCastError = error{UnalignedMemory};
/// Align cast a pointer but return an error if it's the wrong alignment
pub fn alignCast(comptime alignment: u29, ptr: anytype) AlignCastError!@TypeOf(@alignCast(alignment, ptr)) {
const addr = @ptrToInt(ptr);
if (addr % alignment != 0) {
return error.UnalignedMemory;
}
return @alignCast(alignment, ptr);
}
pub fn isPowerOfTwo(v: anytype) bool {
assert(v != 0);
return (v & (v - 1)) == 0;
}
/// Rounds the given floating point number to an integer, away from zero.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @round
pub inline fn round(value: anytype) @TypeOf(value) {
return @round(value);
}
/// Rounds the given floating point number to an integer, towards zero.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @trunc
pub inline fn trunc(value: anytype) @TypeOf(value) {
return @trunc(value);
}
/// Returns the largest integral value not greater than the given floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @floor
pub inline fn floor(value: anytype) @TypeOf(value) {
return @floor(value);
}
/// Returns the nearest power of two less than or equal to value, or
/// zero if value is less than or equal to zero.
pub fn floorPowerOfTwo(comptime T: type, value: T) T {
const uT = std.meta.Int(.unsigned, @typeInfo(T).Int.bits);
if (value <= 0) return 0;
return @as(T, 1) << log2_int(uT, @intCast(uT, value));
}
test "floorPowerOfTwo" {
try testFloorPowerOfTwo();
comptime try testFloorPowerOfTwo();
}
fn testFloorPowerOfTwo() !void {
try testing.expect(floorPowerOfTwo(u32, 63) == 32);
try testing.expect(floorPowerOfTwo(u32, 64) == 64);
try testing.expect(floorPowerOfTwo(u32, 65) == 64);
try testing.expect(floorPowerOfTwo(u32, 0) == 0);
try testing.expect(floorPowerOfTwo(u4, 7) == 4);
try testing.expect(floorPowerOfTwo(u4, 8) == 8);
try testing.expect(floorPowerOfTwo(u4, 9) == 8);
try testing.expect(floorPowerOfTwo(u4, 0) == 0);
try testing.expect(floorPowerOfTwo(i4, 7) == 4);
try testing.expect(floorPowerOfTwo(i4, -8) == 0);
try testing.expect(floorPowerOfTwo(i4, -1) == 0);
try testing.expect(floorPowerOfTwo(i4, 0) == 0);
}
/// Returns the smallest integral value not less than the given floating point number.
/// Uses a dedicated hardware instruction when available.
/// This is the same as calling the builtin @ceil
pub inline fn ceil(value: anytype) @TypeOf(value) {
return @ceil(value);
}
/// Returns the next power of two (if the value is not already a power of two).
/// Only unsigned integers can be used. Zero is not an allowed input.
/// Result is a type with 1 more bit than the input type.
pub fn ceilPowerOfTwoPromote(comptime T: type, value: T) std.meta.Int(@typeInfo(T).Int.signedness, @typeInfo(T).Int.bits + 1) {
comptime assert(@typeInfo(T) == .Int);
comptime assert(@typeInfo(T).Int.signedness == .unsigned);
assert(value != 0);
const PromotedType = std.meta.Int(@typeInfo(T).Int.signedness, @typeInfo(T).Int.bits + 1);
const ShiftType = std.math.Log2Int(PromotedType);
return @as(PromotedType, 1) << @intCast(ShiftType, @typeInfo(T).Int.bits - @clz(value - 1));
}
/// Returns the next power of two (if the value is not already a power of two).
/// Only unsigned integers can be used. Zero is not an allowed input.
/// If the value doesn't fit, returns an error.
pub fn ceilPowerOfTwo(comptime T: type, value: T) (error{Overflow}!T) {
comptime assert(@typeInfo(T) == .Int);
const info = @typeInfo(T).Int;
comptime assert(info.signedness == .unsigned);
const PromotedType = std.meta.Int(info.signedness, info.bits + 1);
const overflowBit = @as(PromotedType, 1) << info.bits;
var x = ceilPowerOfTwoPromote(T, value);
if (overflowBit & x != 0) {
return error.Overflow;
}
return @intCast(T, x);
}
/// Returns the next power of two (if the value is not already a power
/// of two). Only unsigned integers can be used. Zero is not an
/// allowed input. Asserts that the value fits.
pub fn ceilPowerOfTwoAssert(comptime T: type, value: T) T {
return ceilPowerOfTwo(T, value) catch unreachable;
}
test "ceilPowerOfTwoPromote" {
try testCeilPowerOfTwoPromote();
comptime try testCeilPowerOfTwoPromote();
}
fn testCeilPowerOfTwoPromote() !void {
try testing.expectEqual(@as(u33, 1), ceilPowerOfTwoPromote(u32, 1));
try testing.expectEqual(@as(u33, 2), ceilPowerOfTwoPromote(u32, 2));
try testing.expectEqual(@as(u33, 64), ceilPowerOfTwoPromote(u32, 63));
try testing.expectEqual(@as(u33, 64), ceilPowerOfTwoPromote(u32, 64));
try testing.expectEqual(@as(u33, 128), ceilPowerOfTwoPromote(u32, 65));
try testing.expectEqual(@as(u6, 8), ceilPowerOfTwoPromote(u5, 7));
try testing.expectEqual(@as(u6, 8), ceilPowerOfTwoPromote(u5, 8));
try testing.expectEqual(@as(u6, 16), ceilPowerOfTwoPromote(u5, 9));
try testing.expectEqual(@as(u5, 16), ceilPowerOfTwoPromote(u4, 9));
}
test "ceilPowerOfTwo" {
try testCeilPowerOfTwo();
comptime try testCeilPowerOfTwo();
}
fn testCeilPowerOfTwo() !void {
try testing.expectEqual(@as(u32, 1), try ceilPowerOfTwo(u32, 1));
try testing.expectEqual(@as(u32, 2), try ceilPowerOfTwo(u32, 2));
try testing.expectEqual(@as(u32, 64), try ceilPowerOfTwo(u32, 63));
try testing.expectEqual(@as(u32, 64), try ceilPowerOfTwo(u32, 64));
try testing.expectEqual(@as(u32, 128), try ceilPowerOfTwo(u32, 65));
try testing.expectEqual(@as(u5, 8), try ceilPowerOfTwo(u5, 7));
try testing.expectEqual(@as(u5, 8), try ceilPowerOfTwo(u5, 8));
try testing.expectEqual(@as(u5, 16), try ceilPowerOfTwo(u5, 9));
try testing.expectError(error.Overflow, ceilPowerOfTwo(u4, 9));
}
/// Return the log base 2 of integer value x, rounding down to the
/// nearest integer.
pub fn log2_int(comptime T: type, x: T) Log2Int(T) {
if (@typeInfo(T) != .Int or @typeInfo(T).Int.signedness != .unsigned)
@compileError("log2_int requires an unsigned integer, found " ++ @typeName(T));
assert(x != 0);
return @intCast(Log2Int(T), @typeInfo(T).Int.bits - 1 - @clz(x));
}
/// Return the log base 2 of integer value x, rounding up to the
/// nearest integer.
pub fn log2_int_ceil(comptime T: type, x: T) Log2IntCeil(T) {
if (@typeInfo(T) != .Int or @typeInfo(T).Int.signedness != .unsigned)
@compileError("log2_int_ceil requires an unsigned integer, found " ++ @typeName(T));
assert(x != 0);
if (x == 1) return 0;
const log2_val: Log2IntCeil(T) = log2_int(T, x - 1);
return log2_val + 1;
}
test "std.math.log2_int_ceil" {
try testing.expect(log2_int_ceil(u32, 1) == 0);
try testing.expect(log2_int_ceil(u32, 2) == 1);
try testing.expect(log2_int_ceil(u32, 3) == 2);
try testing.expect(log2_int_ceil(u32, 4) == 2);
try testing.expect(log2_int_ceil(u32, 5) == 3);
try testing.expect(log2_int_ceil(u32, 6) == 3);
try testing.expect(log2_int_ceil(u32, 7) == 3);
try testing.expect(log2_int_ceil(u32, 8) == 3);
try testing.expect(log2_int_ceil(u32, 9) == 4);
try testing.expect(log2_int_ceil(u32, 10) == 4);
}
/// Cast a value to a different type. If the value doesn't fit in, or
/// can't be perfectly represented by, the new type, it will be
/// converted to the closest possible representation.
pub fn lossyCast(comptime T: type, value: anytype) T {
switch (@typeInfo(T)) {
.Float => {
switch (@typeInfo(@TypeOf(value))) {
.Int => return @intToFloat(T, value),
.Float => return @floatCast(T, value),
.ComptimeInt => return @as(T, value),
.ComptimeFloat => return @as(T, value),
else => @compileError("bad type"),
}
},
.Int => {
switch (@typeInfo(@TypeOf(value))) {
.Int, .ComptimeInt => {
if (value >= maxInt(T)) {
return @as(T, maxInt(T));
} else if (value <= minInt(T)) {
return @as(T, minInt(T));
} else {
return @intCast(T, value);
}
},
.Float, .ComptimeFloat => {
if (value >= maxInt(T)) {
return @as(T, maxInt(T));
} else if (value <= minInt(T)) {
return @as(T, minInt(T));
} else {
return @floatToInt(T, value);
}
},
else => @compileError("bad type"),
}
},
else => @compileError("bad result type"),
}
}
test "lossyCast" {
try testing.expect(lossyCast(i16, 70000.0) == @as(i16, 32767));
try testing.expect(lossyCast(u32, @as(i16, -255)) == @as(u32, 0));
try testing.expect(lossyCast(i9, @as(u32, 200)) == @as(i9, 200));
try testing.expect(lossyCast(u32, @as(f32, maxInt(u32))) == maxInt(u32));
}
/// Performs linear interpolation between *a* and *b* based on *t*.
/// *t* must be in range 0.0 to 1.0. Supports floats and vectors of floats.
///
/// This does not guarantee returning *b* if *t* is 1 due to floating-point errors.
/// This is monotonic.
pub fn lerp(a: anytype, b: anytype, t: anytype) @TypeOf(a, b, t) {
const Type = @TypeOf(a, b, t);
switch (@typeInfo(Type)) {
.Float, .ComptimeFloat => assert(t >= 0 and t <= 1),
.Vector => |vector| {
const lower_bound = @reduce(.And, t >= @splat(vector.len, @as(vector.child, 0)));
const upper_bound = @reduce(.And, t <= @splat(vector.len, @as(vector.child, 1)));
assert(lower_bound and upper_bound);
},
else => comptime unreachable,
}
return @mulAdd(Type, b - a, t, a);
}
test "lerp" {
try testing.expectEqual(@as(f64, 75), lerp(50, 100, 0.5));
try testing.expectEqual(@as(f32, 43.75), lerp(50, 25, 0.25));
try testing.expectEqual(@as(f64, -31.25), lerp(-50, 25, 0.25));
try testing.expectApproxEqRel(@as(f32, -7.16067345e+03), lerp(-10000.12345, -5000.12345, 0.56789), 1e-19);
try testing.expectApproxEqRel(@as(f64, 7.010987590521e+62), lerp(0.123456789e-64, 0.123456789e64, 0.56789), 1e-33);
try testing.expectEqual(@as(f32, 0.0), lerp(@as(f32, 1.0e8), 1.0, 1.0));
try testing.expectEqual(@as(f64, 0.0), lerp(@as(f64, 1.0e16), 1.0, 1.0));
try testing.expectEqual(@as(f32, 1.0), lerp(@as(f32, 1.0e7), 1.0, 1.0));
try testing.expectEqual(@as(f64, 1.0), lerp(@as(f64, 1.0e15), 1.0, 1.0));
try testing.expectEqual(
lerp(@splat(3, @as(f32, 0)), @splat(3, @as(f32, 50)), @splat(3, @as(f32, 0.5))),
@Vector(3, f32){ 25, 25, 25 },
);
try testing.expectEqual(
lerp(@splat(3, @as(f64, 50)), @splat(3, @as(f64, 100)), @splat(3, @as(f64, 0.5))),
@Vector(3, f64){ 75, 75, 75 },
);
}
/// Returns the maximum value of integer type T.
pub fn maxInt(comptime T: type) comptime_int {
const info = @typeInfo(T);
const bit_count = info.Int.bits;
if (bit_count == 0) return 0;
return (1 << (bit_count - @boolToInt(info.Int.signedness == .signed))) - 1;
}
/// Returns the minimum value of integer type T.
pub fn minInt(comptime T: type) comptime_int {
const info = @typeInfo(T);
const bit_count = info.Int.bits;
if (info.Int.signedness == .unsigned) return 0;
if (bit_count == 0) return 0;
return -(1 << (bit_count - 1));
}
test "minInt and maxInt" {
try testing.expect(maxInt(u0) == 0);
try testing.expect(maxInt(u1) == 1);
try testing.expect(maxInt(u8) == 255);
try testing.expect(maxInt(u16) == 65535);
try testing.expect(maxInt(u32) == 4294967295);
try testing.expect(maxInt(u64) == 18446744073709551615);
try testing.expect(maxInt(u128) == 340282366920938463463374607431768211455);
try testing.expect(maxInt(i0) == 0);
try testing.expect(maxInt(i1) == 0);
try testing.expect(maxInt(i8) == 127);
try testing.expect(maxInt(i16) == 32767);
try testing.expect(maxInt(i32) == 2147483647);
try testing.expect(maxInt(i63) == 4611686018427387903);
try testing.expect(maxInt(i64) == 9223372036854775807);
try testing.expect(maxInt(i128) == 170141183460469231731687303715884105727);
try testing.expect(minInt(u0) == 0);
try testing.expect(minInt(u1) == 0);
try testing.expect(minInt(u8) == 0);
try testing.expect(minInt(u16) == 0);
try testing.expect(minInt(u32) == 0);
try testing.expect(minInt(u63) == 0);
try testing.expect(minInt(u64) == 0);
try testing.expect(minInt(u128) == 0);
try testing.expect(minInt(i0) == 0);
try testing.expect(minInt(i1) == -1);
try testing.expect(minInt(i8) == -128);
try testing.expect(minInt(i16) == -32768);
try testing.expect(minInt(i32) == -2147483648);
try testing.expect(minInt(i63) == -4611686018427387904);
try testing.expect(minInt(i64) == -9223372036854775808);
try testing.expect(minInt(i128) == -170141183460469231731687303715884105728);
}
test "max value type" {
const x: u32 = maxInt(i32);
try testing.expect(x == 2147483647);
}
/// Multiply a and b. Return type is wide enough to guarantee no
/// overflow.
pub fn mulWide(comptime T: type, a: T, b: T) std.meta.Int(
@typeInfo(T).Int.signedness,
@typeInfo(T).Int.bits * 2,
) {
const ResultInt = std.meta.Int(
@typeInfo(T).Int.signedness,
@typeInfo(T).Int.bits * 2,
);
return @as(ResultInt, a) * @as(ResultInt, b);
}
test "mulWide" {
try testing.expect(mulWide(u8, 5, 5) == 25);
try testing.expect(mulWide(i8, 5, -5) == -25);
try testing.expect(mulWide(u8, 100, 100) == 10000);
}
/// See also `CompareOperator`.
pub const Order = enum {
/// Less than (`<`)
lt,
/// Equal (`==`)
eq,
/// Greater than (`>`)
gt,
pub fn invert(self: Order) Order {
return switch (self) {
.lt => .gt,
.eq => .eq,
.gt => .lt,
};
}
pub fn compare(self: Order, op: CompareOperator) bool {
return switch (self) {
.lt => switch (op) {
.lt => true,
.lte => true,
.eq => false,
.gte => false,
.gt => false,
.neq => true,
},
.eq => switch (op) {
.lt => false,
.lte => true,
.eq => true,
.gte => true,
.gt => false,
.neq => false,
},
.gt => switch (op) {
.lt => false,
.lte => false,
.eq => false,
.gte => true,
.gt => true,
.neq => true,
},
};
}
};
/// Given two numbers, this function returns the order they are with respect to each other.
pub fn order(a: anytype, b: anytype) Order {
if (a == b) {
return .eq;
} else if (a < b) {
return .lt;
} else if (a > b) {
return .gt;
} else {
unreachable;
}
}
/// See also `Order`.
pub const CompareOperator = enum {
/// Less than (`<`)
lt,
/// Less than or equal (`<=`)
lte,
/// Equal (`==`)
eq,
/// Greater than or equal (`>=`)
gte,
/// Greater than (`>`)
gt,
/// Not equal (`!=`)
neq,
/// Reverse the direction of the comparison.
/// Use when swapping the left and right hand operands.
pub fn reverse(op: CompareOperator) CompareOperator {
return switch (op) {
.lt => .gt,
.lte => .gte,
.gt => .lt,
.gte => .lte,
.eq => .eq,
.neq => .neq,
};
}
};
/// This function does the same thing as comparison operators, however the
/// operator is a runtime-known enum value. Works on any operands that
/// support comparison operators.
pub fn compare(a: anytype, op: CompareOperator, b: anytype) bool {
return switch (op) {
.lt => a < b,
.lte => a <= b,
.eq => a == b,
.neq => a != b,
.gt => a > b,
.gte => a >= b,
};
}
test "compare between signed and unsigned" {
try testing.expect(compare(@as(i8, -1), .lt, @as(u8, 255)));
try testing.expect(compare(@as(i8, 2), .gt, @as(u8, 1)));
try testing.expect(!compare(@as(i8, -1), .gte, @as(u8, 255)));
try testing.expect(compare(@as(u8, 255), .gt, @as(i8, -1)));
try testing.expect(!compare(@as(u8, 255), .lte, @as(i8, -1)));
try testing.expect(compare(@as(i8, -1), .lt, @as(u9, 255)));
try testing.expect(!compare(@as(i8, -1), .gte, @as(u9, 255)));
try testing.expect(compare(@as(u9, 255), .gt, @as(i8, -1)));
try testing.expect(!compare(@as(u9, 255), .lte, @as(i8, -1)));
try testing.expect(compare(@as(i9, -1), .lt, @as(u8, 255)));
try testing.expect(!compare(@as(i9, -1), .gte, @as(u8, 255)));
try testing.expect(compare(@as(u8, 255), .gt, @as(i9, -1)));
try testing.expect(!compare(@as(u8, 255), .lte, @as(i9, -1)));
try testing.expect(compare(@as(u8, 1), .lt, @as(u8, 2)));
try testing.expect(@bitCast(u8, @as(i8, -1)) == @as(u8, 255));
try testing.expect(!compare(@as(u8, 255), .eq, @as(i8, -1)));
try testing.expect(compare(@as(u8, 1), .eq, @as(u8, 1)));
}
test "order" {
try testing.expect(order(0, 0) == .eq);
try testing.expect(order(1, 0) == .gt);
try testing.expect(order(-1, 0) == .lt);
}
test "order.invert" {
try testing.expect(Order.invert(order(0, 0)) == .eq);
try testing.expect(Order.invert(order(1, 0)) == .lt);
try testing.expect(Order.invert(order(-1, 0)) == .gt);
}
test "order.compare" {
try testing.expect(order(-1, 0).compare(.lt));
try testing.expect(order(-1, 0).compare(.lte));
try testing.expect(order(0, 0).compare(.lte));
try testing.expect(order(0, 0).compare(.eq));
try testing.expect(order(0, 0).compare(.gte));
try testing.expect(order(1, 0).compare(.gte));
try testing.expect(order(1, 0).compare(.gt));
try testing.expect(order(1, 0).compare(.neq));
}
test "compare.reverse" {
inline for (@typeInfo(CompareOperator).Enum.fields) |op_field| {
const op = @intToEnum(CompareOperator, op_field.value);
try testing.expect(compare(2, op, 3) == compare(3, op.reverse(), 2));
try testing.expect(compare(3, op, 3) == compare(3, op.reverse(), 3));
try testing.expect(compare(4, op, 3) == compare(3, op.reverse(), 4));
}
}
/// Returns a mask of all ones if value is true,
/// and a mask of all zeroes if value is false.
/// Compiles to one instruction for register sized integers.
pub inline fn boolMask(comptime MaskInt: type, value: bool) MaskInt {
if (@typeInfo(MaskInt) != .Int)
@compileError("boolMask requires an integer mask type.");
if (MaskInt == u0 or MaskInt == i0)
@compileError("boolMask cannot convert to u0 or i0, they are too small.");
// The u1 and i1 cases tend to overflow,
// so we special case them here.
if (MaskInt == u1) return @boolToInt(value);
if (MaskInt == i1) {
// The @as here is a workaround for #7950
return @bitCast(i1, @as(u1, @boolToInt(value)));
}
return -%@intCast(MaskInt, @boolToInt(value));
}
test "boolMask" {
const runTest = struct {
fn runTest() !void {
try testing.expectEqual(@as(u1, 0), boolMask(u1, false));
try testing.expectEqual(@as(u1, 1), boolMask(u1, true));
try testing.expectEqual(@as(i1, 0), boolMask(i1, false));
try testing.expectEqual(@as(i1, -1), boolMask(i1, true));
try testing.expectEqual(@as(u13, 0), boolMask(u13, false));
try testing.expectEqual(@as(u13, 0x1FFF), boolMask(u13, true));
try testing.expectEqual(@as(i13, 0), boolMask(i13, false));
try testing.expectEqual(@as(i13, -1), boolMask(i13, true));
try testing.expectEqual(@as(u32, 0), boolMask(u32, false));
try testing.expectEqual(@as(u32, 0xFFFF_FFFF), boolMask(u32, true));
try testing.expectEqual(@as(i32, 0), boolMask(i32, false));
try testing.expectEqual(@as(i32, -1), boolMask(i32, true));
}
}.runTest;
try runTest();
comptime try runTest();
}
/// Return the mod of `num` with the smallest integer type
pub fn comptimeMod(num: anytype, comptime denom: comptime_int) IntFittingRange(0, denom - 1) {
return @intCast(IntFittingRange(0, denom - 1), @mod(num, denom));
}
pub const F80 = struct {
fraction: u64,
exp: u16,
};
pub fn make_f80(repr: F80) f80 {
const int = (@as(u80, repr.exp) << 64) | repr.fraction;
return @bitCast(f80, int);
}
pub fn break_f80(x: f80) F80 {
const int = @bitCast(u80, x);
return .{
.fraction = @truncate(u64, int),
.exp = @truncate(u16, int >> 64),
};
}
/// Returns -1, 0, or 1.
/// Supports integer and float types and vectors of integer and float types.
/// Unsigned integer types will always return 0 or 1.
/// Branchless.
pub inline fn sign(i: anytype) @TypeOf(i) {
const T = @TypeOf(i);
return switch (@typeInfo(T)) {
.Int, .ComptimeInt => @as(T, @boolToInt(i > 0)) - @boolToInt(i < 0),
.Float, .ComptimeFloat => @intToFloat(T, @boolToInt(i > 0)) - @intToFloat(T, @boolToInt(i < 0)),
.Vector => |vinfo| blk: {
switch (@typeInfo(vinfo.child)) {
.Int, .Float => {
const zero = @splat(vinfo.len, @as(vinfo.child, 0));
const one = @splat(vinfo.len, @as(vinfo.child, 1));
break :blk @select(vinfo.child, i > zero, one, zero) - @select(vinfo.child, i < zero, one, zero);
},
else => @compileError("Expected vector of ints or floats, found " ++ @typeName(T)),
}
},
else => @compileError("Expected an int, float or vector of one, found " ++ @typeName(T)),
};
}
fn testSign() !void {
// each of the following blocks checks the inputs
// 2, -2, 0, { 2, -2, 0 } provide expected output
// 1, -1, 0, { 1, -1, 0 } for the given T
// (negative values omitted for unsigned types)
{
const T = i8;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, -1), sign(@as(T, -2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(3, T){ 1, -1, 0 }, sign(@Vector(3, T){ 2, -2, 0 }));
}
{
const T = i32;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, -1), sign(@as(T, -2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(3, T){ 1, -1, 0 }, sign(@Vector(3, T){ 2, -2, 0 }));
}
{
const T = i64;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, -1), sign(@as(T, -2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(3, T){ 1, -1, 0 }, sign(@Vector(3, T){ 2, -2, 0 }));
}
{
const T = u8;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(2, T){ 1, 0 }, sign(@Vector(2, T){ 2, 0 }));
}
{
const T = u32;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(2, T){ 1, 0 }, sign(@Vector(2, T){ 2, 0 }));
}
{
const T = u64;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(2, T){ 1, 0 }, sign(@Vector(2, T){ 2, 0 }));
}
{
const T = f16;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, -1), sign(@as(T, -2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(3, T){ 1, -1, 0 }, sign(@Vector(3, T){ 2, -2, 0 }));
}
{
const T = f32;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, -1), sign(@as(T, -2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(3, T){ 1, -1, 0 }, sign(@Vector(3, T){ 2, -2, 0 }));
}
{
const T = f64;
try std.testing.expectEqual(@as(T, 1), sign(@as(T, 2)));
try std.testing.expectEqual(@as(T, -1), sign(@as(T, -2)));
try std.testing.expectEqual(@as(T, 0), sign(@as(T, 0)));
try std.testing.expectEqual(@Vector(3, T){ 1, -1, 0 }, sign(@Vector(3, T){ 2, -2, 0 }));
}
// comptime_int
try std.testing.expectEqual(-1, sign(-10));
try std.testing.expectEqual(1, sign(10));
try std.testing.expectEqual(0, sign(0));
// comptime_float
try std.testing.expectEqual(-1.0, sign(-10.0));
try std.testing.expectEqual(1.0, sign(10.0));
try std.testing.expectEqual(0.0, sign(0.0));
}
test "sign" {
if (builtin.zig_backend == .stage2_llvm) {
// https://github.com/ziglang/zig/issues/12012
return error.SkipZigTest;
}
try testSign();
comptime try testSign();
}
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