zig/std/math.zig
Andrew Kelley 29b488245d add setFloatMode builtin and std.math.floor
* skip installing std/rand_test.zig as it's not needed beyond running
   the std lib tests
 * add std.math.floor function
 * add setFloatMode builtin function to choose between
   builtin.FloatMode.Optimized (default) and builtin.FloatMode.Strict
   (Optimized is equivalent to -ffast-math in gcc)
2017-05-20 23:06:32 -04:00

344 lines
9.8 KiB
Zig

const assert = @import("debug.zig").assert;
const builtin = @import("builtin");
pub const Cmp = enum {
Less,
Equal,
Greater,
};
pub fn min(x: var, y: var) -> @typeOf(x + y) {
if (x < y) x else y
}
test "math.min" {
assert(min(i32(-1), i32(2)) == -1);
}
pub fn max(x: var, y: var) -> @typeOf(x + y) {
if (x > y) x else y
}
test "math.max" {
assert(max(i32(-1), i32(2)) == 2);
}
error Overflow;
pub fn mul(comptime T: type, a: T, b: T) -> %T {
var answer: T = undefined;
if (@mulWithOverflow(T, a, b, &answer)) error.Overflow else answer
}
error Overflow;
pub fn add(comptime T: type, a: T, b: T) -> %T {
var answer: T = undefined;
if (@addWithOverflow(T, a, b, &answer)) error.Overflow else answer
}
error Overflow;
pub fn sub(comptime T: type, a: T, b: T) -> %T {
var answer: T = undefined;
if (@subWithOverflow(T, a, b, &answer)) error.Overflow else answer
}
error Overflow;
pub fn shl(comptime T: type, a: T, b: T) -> %T {
var answer: T = undefined;
if (@shlWithOverflow(T, a, b, &answer)) error.Overflow else answer
}
test "math overflow functions" {
testOverflow();
comptime testOverflow();
}
fn testOverflow() {
assert(%%mul(i32, 3, 4) == 12);
assert(%%add(i32, 3, 4) == 7);
assert(%%sub(i32, 3, 4) == -1);
assert(%%shl(i32, 0b11, 4) == 0b110000);
}
pub fn log(comptime base: usize, value: var) -> @typeOf(value) {
const T = @typeOf(value);
switch (@typeId(T)) {
builtin.TypeId.Int => {
if (base == 2) {
return T.bit_count - 1 - @clz(value);
} else {
@compileError("TODO implement log for non base 2 integers");
}
},
builtin.TypeId.Float => {
@compileError("TODO implement log for floats");
},
else => {
@compileError("log expects integer or float, found '" ++ @typeName(T) ++ "'");
},
}
}
error Overflow;
pub fn absInt(x: var) -> %@typeOf(x) {
const T = @typeOf(x);
comptime assert(@typeId(T) == builtin.TypeId.Int); // must pass an integer to absInt
comptime assert(T.is_signed); // must pass a signed integer to absInt
if (x == @minValue(@typeOf(x)))
return error.Overflow;
{
@setDebugSafety(this, false);
return if (x < 0) -x else x;
}
}
test "math.absInt" {
testAbsInt();
comptime testAbsInt();
}
fn testAbsInt() {
assert(%%absInt(i32(-10)) == 10);
assert(%%absInt(i32(10)) == 10);
}
pub fn absFloat(x: var) -> @typeOf(x) {
comptime assert(@typeId(@typeOf(x)) == builtin.TypeId.Float);
return if (x < 0) -x else x;
}
test "math.absFloat" {
testAbsFloat();
comptime testAbsFloat();
}
fn testAbsFloat() {
assert(absFloat(f32(-10.0)) == 10.0);
assert(absFloat(f32(10.0)) == 10.0);
}
error DivisionByZero;
error Overflow;
pub fn divTrunc(comptime T: type, numerator: T, denominator: T) -> %T {
@setDebugSafety(this, false);
if (denominator == 0)
return error.DivisionByZero;
if (@typeId(T) == builtin.TypeId.Int and T.is_signed and numerator == @minValue(T) and denominator == -1)
return error.Overflow;
return @divTrunc(numerator, denominator);
}
test "math.divTrunc" {
testDivTrunc();
comptime testDivTrunc();
}
fn testDivTrunc() {
assert(%%divTrunc(i32, 5, 3) == 1);
assert(%%divTrunc(i32, -5, 3) == -1);
if (divTrunc(i8, -5, 0)) |_| unreachable else |err| assert(err == error.DivisionByZero);
if (divTrunc(i8, -128, -1)) |_| unreachable else |err| assert(err == error.Overflow);
assert(%%divTrunc(f32, 5.0, 3.0) == 1.0);
assert(%%divTrunc(f32, -5.0, 3.0) == -1.0);
}
error DivisionByZero;
error Overflow;
pub fn divFloor(comptime T: type, numerator: T, denominator: T) -> %T {
@setDebugSafety(this, false);
if (denominator == 0)
return error.DivisionByZero;
if (@typeId(T) == builtin.TypeId.Int and T.is_signed and numerator == @minValue(T) and denominator == -1)
return error.Overflow;
return @divFloor(numerator, denominator);
}
test "math.divFloor" {
testDivFloor();
comptime testDivFloor();
}
fn testDivFloor() {
assert(%%divFloor(i32, 5, 3) == 1);
assert(%%divFloor(i32, -5, 3) == -2);
if (divFloor(i8, -5, 0)) |_| unreachable else |err| assert(err == error.DivisionByZero);
if (divFloor(i8, -128, -1)) |_| unreachable else |err| assert(err == error.Overflow);
assert(%%divFloor(f32, 5.0, 3.0) == 1.0);
assert(%%divFloor(f32, -5.0, 3.0) == -2.0);
}
error DivisionByZero;
error Overflow;
error UnexpectedRemainder;
pub fn divExact(comptime T: type, numerator: T, denominator: T) -> %T {
@setDebugSafety(this, false);
if (denominator == 0)
return error.DivisionByZero;
if (@typeId(T) == builtin.TypeId.Int and T.is_signed and numerator == @minValue(T) and denominator == -1)
return error.Overflow;
const result = @divTrunc(numerator, denominator);
if (result * denominator != numerator)
return error.UnexpectedRemainder;
return result;
}
test "math.divExact" {
testDivExact();
comptime testDivExact();
}
fn testDivExact() {
assert(%%divExact(i32, 10, 5) == 2);
assert(%%divExact(i32, -10, 5) == -2);
if (divExact(i8, -5, 0)) |_| unreachable else |err| assert(err == error.DivisionByZero);
if (divExact(i8, -128, -1)) |_| unreachable else |err| assert(err == error.Overflow);
if (divExact(i32, 5, 2)) |_| unreachable else |err| assert(err == error.UnexpectedRemainder);
assert(%%divExact(f32, 10.0, 5.0) == 2.0);
assert(%%divExact(f32, -10.0, 5.0) == -2.0);
if (divExact(f32, 5.0, 2.0)) |_| unreachable else |err| assert(err == error.UnexpectedRemainder);
}
error DivisionByZero;
error NegativeDenominator;
pub fn mod(comptime T: type, numerator: T, denominator: T) -> %T {
@setDebugSafety(this, false);
if (denominator == 0)
return error.DivisionByZero;
if (denominator < 0)
return error.NegativeDenominator;
return @mod(numerator, denominator);
}
test "math.mod" {
testMod();
comptime testMod();
}
fn testMod() {
assert(%%mod(i32, -5, 3) == 1);
assert(%%mod(i32, 5, 3) == 2);
if (mod(i32, 10, -1)) |_| unreachable else |err| assert(err == error.NegativeDenominator);
if (mod(i32, 10, 0)) |_| unreachable else |err| assert(err == error.DivisionByZero);
assert(%%mod(f32, -5, 3) == 1);
assert(%%mod(f32, 5, 3) == 2);
if (mod(f32, 10, -1)) |_| unreachable else |err| assert(err == error.NegativeDenominator);
if (mod(f32, 10, 0)) |_| unreachable else |err| assert(err == error.DivisionByZero);
}
error DivisionByZero;
error NegativeDenominator;
pub fn rem(comptime T: type, numerator: T, denominator: T) -> %T {
@setDebugSafety(this, false);
if (denominator == 0)
return error.DivisionByZero;
if (denominator < 0)
return error.NegativeDenominator;
return @rem(numerator, denominator);
}
test "math.rem" {
testRem();
comptime testRem();
}
fn testRem() {
assert(%%rem(i32, -5, 3) == -2);
assert(%%rem(i32, 5, 3) == 2);
if (rem(i32, 10, -1)) |_| unreachable else |err| assert(err == error.NegativeDenominator);
if (rem(i32, 10, 0)) |_| unreachable else |err| assert(err == error.DivisionByZero);
assert(%%rem(f32, -5, 3) == -2);
assert(%%rem(f32, 5, 3) == 2);
if (rem(f32, 10, -1)) |_| unreachable else |err| assert(err == error.NegativeDenominator);
if (rem(f32, 10, 0)) |_| unreachable else |err| assert(err == error.DivisionByZero);
}
fn isNan(comptime T: type, x: T) -> bool {
assert(@typeId(T) == builtin.TypeId.Float);
if (T == f32) {
const bits = bitCast(u32, x);
return (bits & 0x7fffffff) > 0x7f800000;
} else if (T == f64) {
const bits = bitCast(u64, x);
return (bits & (@maxValue(u64) >> 1)) > (u64(0x7ff) << 52);
} else if (T == c_longdouble) {
@compileError("TODO support isNan for c_longdouble");
} else {
unreachable;
}
}
// TODO this should be a builtin
fn bitCast(comptime DestType: type, value: var) -> DestType {
assert(@sizeOf(DestType) == @sizeOf(@typeOf(value)));
return *@ptrCast(&const DestType, &value);
}
pub fn floor(x: var) -> @typeOf(x) {
switch (@typeOf(x)) {
f32 => floor_f32(x),
f64 => floor_f64(x),
c_longdouble => @compileError("TODO support floor for c_longdouble"),
else => @compileError("Invalid type for floor: " ++ @typeName(@typeOf(x))),
}
}
fn floor_f32(x: f32) -> f32 {
var i = bitCast(u32, x);
const e = i32((i >> 23) & 0xff) -% 0x7f;
if (e >= 23)
return x;
if (e >= 0) {
const m = bitCast(u32, 0x007fffff >> e);
if ((i & m) == 0)
return x;
if (i >> 31 != 0)
i +%= m;
i &= ~m;
} else {
if (i >> 31 == 0)
return 0;
if (i <<% 1 != 0)
return -1.0;
}
return bitCast(f32, i);
}
fn floor_f64(x: f64) -> f64 {
const DBL_EPSILON = 2.22044604925031308085e-16;
const toint = 1.0 / DBL_EPSILON;
var i = bitCast(u64, x);
const e = (i >> 52) & 0x7ff;
if (e >= 0x3ff +% 52 or x == 0)
return x;
// y = int(x) - x, where int(x) is an integer neighbor of x
const y = {
@setFloatMode(this, builtin.FloatMode.Strict);
if (i >> 63 != 0) {
x - toint + toint - x
} else {
x + toint - toint - x
}
};
// special case because of non-nearest rounding modes
if (e <= 0x3ff - 1) {
if (i >> 63 != 0)
return -1.0;
return 0.0;
}
if (y > 0)
return x + y - 1;
return x + y;
}
test "math.floor" {
assert(floor(f32(1.234)) == 1.0);
assert(floor(f32(-1.234)) == -2.0);
assert(floor(f32(999.0)) == 999.0);
assert(floor(f32(-999.0)) == -999.0);
assert(floor(f64(1.234)) == 1.0);
assert(floor(f64(-1.234)) == -2.0);
assert(floor(f64(999.0)) == 999.0);
assert(floor(f64(-999.0)) == -999.0);
}