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// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/math/acosf.c
// https://git.musl-libc.org/cgit/musl/tree/src/math/acos.c
const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
/// Returns the arc-cosine of x.
///
/// Special cases:
/// - acos(x) = nan if x < -1 or x > 1
pub fn acos(x: var) @typeOf(x) {
const T = @typeOf(x);
return switch (T) {
f32 => acos32(x),
f64 => acos64(x),
else => @compileError("acos not implemented for " ++ @typeName(T)),
};
}
fn r32(z: f32) f32 {
const pS0 = 1.6666586697e-01;
const pS1 = -4.2743422091e-02;
const pS2 = -8.6563630030e-03;
const qS1 = -7.0662963390e-01;
const p = z * (pS0 + z * (pS1 + z * pS2));
const q = 1.0 + z * qS1;
return p / q;
}
fn acos32(x: f32) f32 {
const pio2_hi = 1.5707962513e+00;
const pio2_lo = 7.5497894159e-08;
const hx: u32 = @bitCast(u32, x);
const ix: u32 = hx & 0x7FFFFFFF;
// |x| >= 1 or nan
if (ix >= 0x3F800000) {
if (ix == 0x3F800000) {
if (hx >> 31 != 0) {
return 2.0 * pio2_hi + 0x1.0p-120;
} else {
return 0.0;
}
} else {
return math.nan(f32);
}
}
// |x| < 0.5
if (ix < 0x3F000000) {
if (ix <= 0x32800000) { // |x| < 2^(-26)
return pio2_hi + 0x1.0p-120;
} else {
return pio2_hi - (x - (pio2_lo - x * r32(x * x)));
}
}
// x < -0.5
if (hx >> 31 != 0) {
const z = (1 + x) * 0.5;
const s = math.sqrt(z);
const w = r32(z) * s - pio2_lo;
return 2 * (pio2_hi - (s + w));
}
// x > 0.5
const z = (1.0 - x) * 0.5;
const s = math.sqrt(z);
const jx = @bitCast(u32, s);
const df = @bitCast(f32, jx & 0xFFFFF000);
const c = (z - df * df) / (s + df);
const w = r32(z) * s + c;
return 2 * (df + w);
}
fn r64(z: f64) f64 {
const pS0: f64 = 1.66666666666666657415e-01;
const pS1: f64 = -3.25565818622400915405e-01;
const pS2: f64 = 2.01212532134862925881e-01;
const pS3: f64 = -4.00555345006794114027e-02;
const pS4: f64 = 7.91534994289814532176e-04;
const pS5: f64 = 3.47933107596021167570e-05;
const qS1: f64 = -2.40339491173441421878e+00;
const qS2: f64 = 2.02094576023350569471e+00;
const qS3: f64 = -6.88283971605453293030e-01;
const qS4: f64 = 7.70381505559019352791e-02;
const p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
const q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
return p / q;
}
fn acos64(x: f64) f64 {
const pio2_hi: f64 = 1.57079632679489655800e+00;
const pio2_lo: f64 = 6.12323399573676603587e-17;
const ux = @bitCast(u64, x);
const hx = @intCast(u32, ux >> 32);
const ix = hx & 0x7FFFFFFF;
// |x| >= 1 or nan
if (ix >= 0x3FF00000) {
const lx = @intCast(u32, ux & 0xFFFFFFFF);
// acos(1) = 0, acos(-1) = pi
if ((ix - 0x3FF00000) | lx == 0) {
if (hx >> 31 != 0) {
return 2 * pio2_hi + 0x1.0p-120;
} else {
return 0;
}
}
return math.nan(f32);
}
// |x| < 0.5
if (ix < 0x3FE00000) {
// |x| < 2^(-57)
if (ix <= 0x3C600000) {
return pio2_hi + 0x1.0p-120;
} else {
return pio2_hi - (x - (pio2_lo - x * r64(x * x)));
}
}
// x < -0.5
if (hx >> 31 != 0) {
const z = (1.0 + x) * 0.5;
const s = math.sqrt(z);
const w = r64(z) * s - pio2_lo;
return 2 * (pio2_hi - (s + w));
}
// x > 0.5
const z = (1.0 - x) * 0.5;
const s = math.sqrt(z);
const jx = @bitCast(u64, s);
const df = @bitCast(f64, jx & 0xFFFFFFFF00000000);
const c = (z - df * df) / (s + df);
const w = r64(z) * s + c;
return 2 * (df + w);
}
test "math.acos" {
expect(acos(f32(0.0)) == acos32(0.0));
expect(acos(f64(0.0)) == acos64(0.0));
}
test "math.acos32" {
const epsilon = 0.000001;
expect(math.approxEq(f32, acos32(0.0), 1.570796, epsilon));
expect(math.approxEq(f32, acos32(0.2), 1.369438, epsilon));
expect(math.approxEq(f32, acos32(0.3434), 1.220262, epsilon));
expect(math.approxEq(f32, acos32(0.5), 1.047198, epsilon));
expect(math.approxEq(f32, acos32(0.8923), 0.468382, epsilon));
expect(math.approxEq(f32, acos32(-0.2), 1.772154, epsilon));
}
test "math.acos64" {
const epsilon = 0.000001;
expect(math.approxEq(f64, acos64(0.0), 1.570796, epsilon));
expect(math.approxEq(f64, acos64(0.2), 1.369438, epsilon));
expect(math.approxEq(f64, acos64(0.3434), 1.220262, epsilon));
expect(math.approxEq(f64, acos64(0.5), 1.047198, epsilon));
expect(math.approxEq(f64, acos64(0.8923), 0.468382, epsilon));
expect(math.approxEq(f64, acos64(-0.2), 1.772154, epsilon));
}
test "math.acos32.special" {
expect(math.isNan(acos32(-2)));
expect(math.isNan(acos32(1.5)));
}
test "math.acos64.special" {
expect(math.isNan(acos64(-2)));
expect(math.isNan(acos64(1.5)));
}
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