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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/asinf.c
// https://git.musl-libc.org/cgit/musl/tree/src/math/asin.c
const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
/// Returns the arc-sin of x.
///
/// Special Cases:
/// - asin(+-0) = +-0
/// - asin(x) = nan if x < -1 or x > 1
pub fn asin(x: anytype) @TypeOf(x) {
const T = @TypeOf(x);
return switch (T) {
f32 => asin32(x),
f64 => asin64(x),
else => @compileError("asin 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 asin32(x: f32) f32 {
const pio2 = 1.570796326794896558e+00;
const hx: u32 = @as(u32, @bitCast(x));
const ix: u32 = hx & 0x7FFFFFFF;
// |x| >= 1
if (ix >= 0x3F800000) {
// |x| >= 1
if (ix == 0x3F800000) {
return x * pio2 + 0x1.0p-120; // asin(+-1) = +-pi/2 with inexact
} else {
return math.nan(f32); // asin(|x| > 1) is nan
}
}
// |x| < 0.5
if (ix < 0x3F000000) {
// 0x1p-126 <= |x| < 0x1p-12
if (ix < 0x39800000 and ix >= 0x00800000) {
return x;
} else {
return x + x * r32(x * x);
}
}
// 1 > |x| >= 0.5
const z = (1 - @abs(x)) * 0.5;
const s = @sqrt(z);
const fx = pio2 - 2 * (s + s * r32(z));
if (hx >> 31 != 0) {
return -fx;
} else {
return fx;
}
}
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 asin64(x: f64) f64 {
const pio2_hi: f64 = 1.57079632679489655800e+00;
const pio2_lo: f64 = 6.12323399573676603587e-17;
const ux = @as(u64, @bitCast(x));
const hx = @as(u32, @intCast(ux >> 32));
const ix = hx & 0x7FFFFFFF;
// |x| >= 1 or nan
if (ix >= 0x3FF00000) {
const lx = @as(u32, @intCast(ux & 0xFFFFFFFF));
// asin(1) = +-pi/2 with inexact
if ((ix - 0x3FF00000) | lx == 0) {
return x * pio2_hi + 0x1.0p-120;
} else {
return math.nan(f64);
}
}
// |x| < 0.5
if (ix < 0x3FE00000) {
// if 0x1p-1022 <= |x| < 0x1p-26 avoid raising overflow
if (ix < 0x3E500000 and ix >= 0x00100000) {
return x;
} else {
return x + x * r64(x * x);
}
}
// 1 > |x| >= 0.5
const z = (1 - @abs(x)) * 0.5;
const s = @sqrt(z);
const r = r64(z);
var fx: f64 = undefined;
// |x| > 0.975
if (ix >= 0x3FEF3333) {
fx = pio2_hi - 2 * (s + s * r);
} else {
const jx = @as(u64, @bitCast(s));
const df = @as(f64, @bitCast(jx & 0xFFFFFFFF00000000));
const c = (z - df * df) / (s + df);
fx = 0.5 * pio2_hi - (2 * s * r - (pio2_lo - 2 * c) - (0.5 * pio2_hi - 2 * df));
}
if (hx >> 31 != 0) {
return -fx;
} else {
return fx;
}
}
test asin {
try expect(asin(@as(f32, 0.0)) == asin32(0.0));
try expect(asin(@as(f64, 0.0)) == asin64(0.0));
}
test asin32 {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f32, asin32(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f32, asin32(0.2), 0.201358, epsilon));
try expect(math.approxEqAbs(f32, asin32(-0.2), -0.201358, epsilon));
try expect(math.approxEqAbs(f32, asin32(0.3434), 0.350535, epsilon));
try expect(math.approxEqAbs(f32, asin32(0.5), 0.523599, epsilon));
try expect(math.approxEqAbs(f32, asin32(0.8923), 1.102415, epsilon));
}
test asin64 {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f64, asin64(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f64, asin64(0.2), 0.201358, epsilon));
try expect(math.approxEqAbs(f64, asin64(-0.2), -0.201358, epsilon));
try expect(math.approxEqAbs(f64, asin64(0.3434), 0.350535, epsilon));
try expect(math.approxEqAbs(f64, asin64(0.5), 0.523599, epsilon));
try expect(math.approxEqAbs(f64, asin64(0.8923), 1.102415, epsilon));
}
test "asin32.special" {
try expect(math.isPositiveZero(asin32(0.0)));
try expect(math.isNegativeZero(asin32(-0.0)));
try expect(math.isNan(asin32(-2)));
try expect(math.isNan(asin32(1.5)));
}
test "asin64.special" {
try expect(math.isPositiveZero(asin64(0.0)));
try expect(math.isNegativeZero(asin64(-0.0)));
try expect(math.isNan(asin64(-2)));
try expect(math.isNan(asin64(1.5)));
}
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