zig/std/math/hypot.zig

164 lines
4.6 KiB
Zig

// Special Cases:
//
// - hypot(+-inf, y) = +inf
// - hypot(x, +-inf) = +inf
// - hypot(nan, y) = nan
// - hypot(x, nan) = nan
const math = @import("index.zig");
const assert = @import("../debug.zig").assert;
// TODO issue #393
pub const hypot = hypot_workaround;
pub fn hypot_workaround(comptime T: type, x: T, y: T) -> T {
switch (T) {
f32 => @inlineCall(hypot32, x, y),
f64 => @inlineCall(hypot64, x, y),
else => @compileError("hypot not implemented for " ++ @typeName(T)),
}
}
fn hypot32(x: f32, y: f32) -> f32 {
var ux = @bitCast(u32, x);
var uy = @bitCast(u32, y);
ux &= @maxValue(u32) >> 1;
uy &= @maxValue(u32) >> 1;
if (ux < uy) {
const tmp = ux;
ux = uy;
uy = tmp;
}
var xx = @bitCast(f32, ux);
var yy = @bitCast(f32, uy);
if (uy == 0xFF << 23) {
return yy;
}
if (ux >= 0xFF << 23 or uy == 0 or ux - uy >= (25 << 23)) {
return xx + yy;
}
var z: f32 = 1.0;
if (ux >= (0x7F+60) << 23) {
z = 0x1.0p90;
xx *= 0x1.0p-90;
yy *= 0x1.0p-90;
} else if (uy < (0x7F-60) << 23) {
z = 0x1.0p-90;
xx *= 0x1.0p-90;
yy *= 0x1.0p-90;
}
z * math.sqrt(f32(f64(x) * x + f64(y) * y))
}
fn sq(hi: &f64, lo: &f64, x: f64) {
const split: f64 = 0x1.0p27 + 1.0;
const xc = x * split;
const xh = x - xc + xc;
const xl = x - xh;
*hi = x * x;
*lo = xh * xh - *hi + 2 * xh * xl + xl * xl;
}
fn hypot64(x: f64, y: f64) -> f64 {
var ux = @bitCast(u64, x);
var uy = @bitCast(u64, y);
ux &= @maxValue(u64) >> 1;
uy &= @maxValue(u64) >> 1;
if (ux < uy) {
const tmp = ux;
ux = uy;
uy = tmp;
}
const ex = ux >> 52;
const ey = uy >> 52;
var xx = @bitCast(f64, ux);
var yy = @bitCast(f64, uy);
// hypot(inf, nan) == inf
if (ey == 0x7FF) {
return yy;
}
if (ex == 0x7FF or uy == 0) {
return xx;
}
// hypot(x, y) ~= x + y * y / x / 2 with inexact for small y/x
if (ex - ey > 64) {
return xx + yy;
}
var z: f64 = 1;
if (ex > 0x3FF + 510) {
z = 0x1.0p700;
xx *= 0x1.0p-700;
yy *= 0x1.0p-700;
} else if (ey < 0x3FF - 450) {
z = 0x1.0p-700;
xx *= 0x1.0p700;
yy *= 0x1.0p700;
}
var hx: f64 = undefined;
var lx: f64 = undefined;
var hy: f64 = undefined;
var ly: f64 = undefined;
sq(&hx, &lx, x);
sq(&hy, &ly, y);
z * math.sqrt(ly + lx + hy + hx)
}
test "math.hypot" {
assert(hypot(f32, 0.0, -1.2) == hypot32(0.0, -1.2));
assert(hypot(f64, 0.0, -1.2) == hypot64(0.0, -1.2));
}
test "math.hypot32" {
const epsilon = 0.000001;
assert(math.approxEq(f32, hypot32(0.0, -1.2), 1.2, epsilon));
assert(math.approxEq(f32, hypot32(0.2, -0.34), 0.394462, epsilon));
assert(math.approxEq(f32, hypot32(0.8923, 2.636890), 2.783772, epsilon));
assert(math.approxEq(f32, hypot32(1.5, 5.25), 5.460083, epsilon));
assert(math.approxEq(f32, hypot32(37.45, 159.835), 164.163742, epsilon));
assert(math.approxEq(f32, hypot32(89.123, 382.028905), 392.286865, epsilon));
assert(math.approxEq(f32, hypot32(123123.234375, 529428.707813), 543556.875, epsilon));
}
test "math.hypot64" {
const epsilon = 0.000001;
assert(math.approxEq(f64, hypot64(0.0, -1.2), 1.2, epsilon));
assert(math.approxEq(f64, hypot64(0.2, -0.34), 0.394462, epsilon));
assert(math.approxEq(f64, hypot64(0.8923, 2.636890), 2.783772, epsilon));
assert(math.approxEq(f64, hypot64(1.5, 5.25), 5.460082, epsilon));
assert(math.approxEq(f64, hypot64(37.45, 159.835), 164.163728, epsilon));
assert(math.approxEq(f64, hypot64(89.123, 382.028905), 392.286876, epsilon));
assert(math.approxEq(f64, hypot64(123123.234375, 529428.707813), 543556.885247, epsilon));
}
test "math.hypot32.special" {
assert(math.isPositiveInf(hypot32(math.inf(f32), 0.0)));
assert(math.isPositiveInf(hypot32(-math.inf(f32), 0.0)));
assert(math.isPositiveInf(hypot32(0.0, math.inf(f32))));
assert(math.isPositiveInf(hypot32(0.0, -math.inf(f32))));
assert(math.isNan(hypot32(math.nan(f32), 0.0)));
assert(math.isNan(hypot32(0.0, math.nan(f32))));
}
test "math.hypot64.special" {
assert(math.isPositiveInf(hypot64(math.inf(f64), 0.0)));
assert(math.isPositiveInf(hypot64(-math.inf(f64), 0.0)));
assert(math.isPositiveInf(hypot64(0.0, math.inf(f64))));
assert(math.isPositiveInf(hypot64(0.0, -math.inf(f64))));
assert(math.isNan(hypot64(math.nan(f64), 0.0)));
assert(math.isNan(hypot64(0.0, math.nan(f64))));
}