// 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 // https://git.musl-libc.org/cgit/musl/tree/src/math/asinl.c // // Ported from ARM-software, which is licensed under the MIT license: // https://github.com/ARM-software/optimized-routines/blob/master/LICENSE // // https://github.com/ARM-software/optimized-routines/blob/master/math/aarch64/advsimd/asinf.c // https://github.com/ARM-software/optimized-routines/blob/master/math/aarch64/advsimd/asin.c const std = @import("../std.zig"); const math = std.math; const mem = std.mem; const testing = std.testing; const builtin = @import("builtin"); const native_endian = builtin.cpu.arch.endian(); /// 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); switch (@typeInfo(T)) { .float => |info| switch (info.bits) { 16 => return asinBinary16(x), 32 => return asinBinary32(x), 64 => return asinBinary64(x), 80 => return asinExtended80(x), 128 => return asinBinary128(x), else => comptime unreachable, }, .vector => |info| switch (info.child) { f32 => return asinBinary32Vec(info.len, x), f64 => return asinBinary64Vec(info.len, x), else => @compileError("unimplemented"), }, else => comptime unreachable, } } fn approxBinary16(z: f32) f32 { const S0: f32 = 1.0000001e0; const S1: f32 = 1.6664918e-1; const S2: f32 = 7.55022e-2; const S3: f32 = 3.9513987e-2; const S4: f32 = 5.0883885e-2; return S0 + z * (S1 + z * (S2 + z * (S3 + z * S4))); } fn asinBinary16(x: f16) f16 { const pio2: f32 = math.pi / 2.0; const hx: u16 = @bitCast(x); const ix = hx & 0x7fff; // |x| >= 1 if (ix >= 0x3c00) { // |x| == 1 if (ix == 0x3c00) { // asin(+-1) = +-pi/2 with inexact return @floatCast(x * pio2 + 0x1.0p-120); } // asin(|x| > 1) is nan return 0.0 / (x - x); } // |x| < 0.5 if (ix < 0x3800) { return @floatCast(x * approxBinary16(x * x)); } // 1 > |x| >= 0.5 const z = (1.0 - @abs(x)) * 0.5; const s = @sqrt(z); const x_local = pio2 - 2.0 * s * approxBinary16(z); if (hx >> 15 != 0) { return @floatCast(-x_local); } return @floatCast(x_local); } fn rationalApproxBinary32(z: f32) f32 { const pS0: f32 = 1.6666586697e-01; const pS1: f32 = -4.2743422091e-02; const pS2: f32 = -8.6563630030e-03; const qS1: f32 = -7.0662963390e-01; const p = z * (pS0 + z * (pS1 + z * pS2)); const q = 1.0 + z * qS1; return p / q; } fn asinBinary32(x: f32) f32 { const pio2: f64 = 1.570796326794896558e+00; const hx: u32 = @bitCast(x); const ix = hx & 0x7fff_ffff; // |x| >= 1 if (ix >= 0x3f80_0000) { // |x| == 1 if (ix == 0x3f80_0000) { // asin(+-1) = +-pi/2 with inexact return @floatCast(@as(f64, @floatCast(x)) * pio2 + 0x1.0p-120); } // asin(|x| > 1) is nan return 0.0 / (x - x); } // |x| < 0.5 if (ix < 0x3f00_0000) { // 0x1p-126 <= |x| < 0x1p-12 if (ix < 0x3980_0000 and ix >= 0x0080_0000) { return x; } return x + x * rationalApproxBinary32(x * x); } // 1 > |x| >= 0.5 const z = (1.0 - @abs(x)) * 0.5; const s: f64 = @floatCast(@sqrt(z)); const x_local: f32 = @floatCast(pio2 - 2.0 * (s + s * @as(f64, @floatCast(rationalApproxBinary32(z))))); return if (hx >> 31 != 0) -x_local else x_local; } fn rationalApproxBinary64(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 asinBinary64(x: f64) f64 { const pio2_hi: f64 = 1.57079632679489655800e+00; const pio2_lo: f64 = 6.12323399573676603587e-17; const hx: u32 = @intCast(@as(u64, @bitCast(x)) >> 32); const ix = hx & 0x7fffffff; // |x| >= 1 or nan if (ix >= 0x3ff0_0000) { const lx: u32 = @truncate(@as(u64, @bitCast(x))); // asin(1) = +-pi/2 with inexact if ((ix - 0x3ff0_0000 | lx) == 0) { return x * pio2_hi + 0x1.0p-120; } return 0.0 / (x - x); } // |x| < 0.5 if (ix < 0x3fe0_0000) { // if 0x1p-1022 <= |x| < 0x1p-26 avoid raising overflow if (ix < 0x3e50_0000 and ix >= 0x0010_0000) { return x; } return x + x * rationalApproxBinary64(x * x); } // 1 > |x| >= 0.5 const z = (1.0 - @abs(x)) * 0.5; const s = @sqrt(z); const r = rationalApproxBinary64(z); // |x| > 0.975 if (ix >= 0x3fef_3333) { const x_local = pio2_hi - (2 * (s + s * r) - pio2_lo); return if (hx >> 31 != 0) -x_local else x_local; } // f+c = sqrt(z) const hs: u64 = @bitCast(s); const f: f64 = @bitCast(hs & 0xffff_ffff_0000_0000); const c: f64 = (z - f * f) / (s + f); const x_local = 0.5 * pio2_hi - (2.0 * s * r - (pio2_lo - 2.0 * c) - (0.5 * pio2_hi - 2.0 * f)); return if (hx >> 31 != 0) -x_local else x_local; } fn rationalApproxExtended80(z: f80) f80 { const pS0: f80 = 1.66666666666666666631e-01; const pS1: f80 = -4.16313987993683104320e-01; const pS2: f80 = 3.69068046323246813704e-01; const pS3: f80 = -1.36213932016738603108e-01; const pS4: f80 = 1.78324189708471965733e-02; const pS5: f80 = -2.19216428382605211588e-04; const pS6: f80 = -7.10526623669075243183e-06; const qS1: f80 = -2.94788392796209867269e+00; const qS2: f80 = 3.27309890266528636716e+00; const qS3: f80 = -1.68285799854822427013e+00; const qS4: f80 = 3.90699412641738801874e-01; const qS5: f80 = -3.14365703596053263322e-02; const p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * (pS5 + z * pS6)))))); const q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * (qS4 + z * qS5)))); return p / q; } fn asinExtended80(x: f80) f80 { const pio2_hi: f80 = 1.57079632679489661926; const pio2_lo: f80 = -2.50827880633416601173e-20; const hx: u80 = @bitCast(x); const se: u16 = @truncate(hx >> 64); const e = se & 0x7fff; const sign = se >> 15 != 0; // |x| >= 1 or nan if (e >= 0x3fff) { // asin(+-1)=+-pi/2 with inexact if (x == 1.0 or x == -1.0) { return x * pio2_hi + 0x1p-120; } return 0.0 / (x - x); } // |x| < 0.5 if (e < 0x3fff - 1) { if (e < 0x3fff - (math.floatMantissaBits(f80) + 1) / 2) { // return x with inexact if x!=0 mem.doNotOptimizeAway(x + 0x1p120); return x; } return x + x * rationalApproxExtended80(x * x); } // 1 > |x| >= 0.5 const z = (1.0 - @abs(x)) * 0.5; const s = @sqrt(z); const r = rationalApproxExtended80(z); const m: u64 = @truncate(hx & 0x0000_ffff_ffff_ffff_ffff); if ((m >> 56) >= 0xf7) { const x_local = pio2_hi - (2.0 * (s + s * r) - pio2_lo); return if (sign) -x_local else x_local; } const hs: u80 = @bitCast(s); const f: f80 = @bitCast(hs & 0xffff_ffff_ffff_0000_0000); const c = (z - f * f) / (s + f); const x_local = 0.5 * pio2_hi - (2.0 * s * r - (pio2_lo - 2.0 * c) - (0.5 * pio2_hi - 2.0 * f)); return if (sign) -x_local else x_local; } fn rationalApproxBinary128(z: f128) f128 { const pS0: f128 = 1.66666666666666666666666666666700314e-01; const pS1: f128 = -7.32816946414566252574527475428622708e-01; const pS2: f128 = 1.34215708714992334609030036562143589e+00; const pS3: f128 = -1.32483151677116409805070261790752040e+00; const pS4: f128 = 7.61206183613632558824485341162121989e-01; const pS5: f128 = -2.56165783329023486777386833928147375e-01; const pS6: f128 = 4.80718586374448793411019434585413855e-02; const pS7: f128 = -4.42523267167024279410230886239774718e-03; const pS8: f128 = 1.44551535183911458253205638280410064e-04; const pS9: f128 = -2.10558957916600254061591040482706179e-07; const qS1: f128 = -4.84690167848739751544716485245697428e+00; const qS2: f128 = 9.96619113536172610135016921140206980e+00; const qS3: f128 = -1.13177895428973036660836798461641458e+01; const qS4: f128 = 7.74004374389488266169304117714658761e+00; const qS5: f128 = -3.25871986053534084709023539900339905e+00; const qS6: f128 = 8.27830318881232209752469022352928864e-01; const qS7: f128 = -1.18768052702942805423330715206348004e-01; const qS8: f128 = 8.32600764660522313269101537926539470e-03; const qS9: f128 = -1.99407384882605586705979504567947007e-04; const p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * (pS5 + z * (pS6 + z * (pS7 + z * (pS8 + z * pS9))))))))); const q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * (qS4 + z * (qS5 + z * (qS6 + z * (qS7 + z * (qS8 + z * qS9)))))))); return p / q; } fn asinBinary128(x: f128) f128 { const pio2_hi: f128 = 1.57079632679489661923132169163975140; const pio2_lo: f128 = 4.33590506506189051239852201302167613e-35; const hx: u128 = @bitCast(x); const se: u16 = @truncate(hx >> 112); const e = se & 0x7fff; const sign = se >> 15 != 0; // |x| >= 1 or nan if (e >= 0x3fff) { // asin(+-1)=+-pi/2 with inexact if (x == 1.0 or x == -1.0) { return x * pio2_hi + 0x1p-120; } return 0.0 / (x - x); } // |x| < 0.5 if (e < 0x3fff - 1) { if (e < 0x3fff - (math.floatMantissaBits(f128) + 2) / 2) { // return x with inexact if x!=0 mem.doNotOptimizeAway(x + 0x1p120); return x; } return x + x * rationalApproxBinary128(x * x); } // 1 > |x| >= 0.5 const z = (1.0 - @abs(x)) * 0.5; const s = @sqrt(z); const r = rationalApproxBinary128(z); const top: u16 = @truncate((hx >> 96) & 0x0000_ffff); if (top >= 0xee00) { const x_local = pio2_hi - (2.0 * (s + s * r) - pio2_lo); return if (sign) -x_local else x_local; } const hs: u128 = @bitCast(s); const f: f128 = @bitCast(hs & 0xffff_ffff_ffff_ffff_0000_0000_0000_0000); const c = (z - f * f) / (s + f); const x_local = 0.5 * pio2_hi - (2.0 * s * r - (pio2_lo - 2.0 * c) - (0.5 * pio2_hi - 2.0 * f)); return if (sign) -x_local else x_local; } test "asinBinary16.special" { try testing.expectApproxEqAbs(0x1.92p0, asinBinary16(0x1p+0), math.floatEpsAt(f16, 0x1.92p0)); try testing.expectApproxEqAbs(-0x1.92p0, asinBinary16(-0x1p+0), math.floatEpsAt(f16, -0x1.92p0)); try testing.expectEqual(0x0p+0, asinBinary16(0x0p+0)); try testing.expectEqual(0x0p+0, asinBinary16(-0x0p+0)); try testing.expect(math.isNan(asinBinary16(0x1.004p0))); try testing.expect(math.isNan(asinBinary16(-0x1.004p0))); try testing.expect(math.isNan(asinBinary16(math.inf(f16)))); try testing.expect(math.isNan(asinBinary16(-math.inf(f16)))); try testing.expect(math.isNan(asinBinary16(math.nan(f16)))); } test "asinBinary16" { try testing.expectApproxEqAbs(-0x1.e4cp-6, asinBinary16(-0x1.e4cp-6), math.floatEpsAt(f16, -0x1.e4cp-6)); try testing.expectApproxEqAbs(0x1.2a8p0, asinBinary16(0x1.d68p-1), math.floatEpsAt(f16, 0x1.2a8p0)); try testing.expectApproxEqAbs(-0x1.eep-1, asinBinary16(-0x1.a4cp-1), math.floatEpsAt(f16, -0x1.eep-1)); try testing.expectApproxEqAbs(-0x1.0d4p-2, asinBinary16(-0x1.0a4p-2), math.floatEpsAt(f16, -0x1.0d4p-2)); try testing.expectApproxEqAbs(0x1.3c8p-1, asinBinary16(0x1.28cp-1), math.floatEpsAt(f16, 0x1.3c8p-1)); try testing.expectApproxEqAbs(0x1.298p-3, asinBinary16(0x1.284p-3), math.floatEpsAt(f16, 0x1.298p-3)); try testing.expectApproxEqAbs(-0x1.784p-1, asinBinary16(-0x1.574p-1), math.floatEpsAt(f16, -0x1.784p-1)); try testing.expectApproxEqAbs(-0x1.6a4p-1, asinBinary16(-0x1.4ccp-1), math.floatEpsAt(f16, -0x1.6a4p-1)); try testing.expectApproxEqAbs(0x1.e84p-1, asinBinary16(0x1.a18p-1), math.floatEpsAt(f16, 0x1.e84p-1)); try testing.expectApproxEqAbs(0x1.83cp-2, asinBinary16(0x1.7a8p-2), math.floatEpsAt(f16, 0x1.83cp-2)); } test "asinBinary32.special" { try testing.expectApproxEqAbs(0x1.921fb6p+0, asinBinary32(0x1p+0), math.floatEpsAt(f32, 0x1.921fb6p+0)); try testing.expectApproxEqAbs(-0x1.921fb6p+0, asinBinary32(-0x1p+0), math.floatEpsAt(f32, -0x1.921fb6p+0)); try testing.expectEqual(0x0p+0, asinBinary32(0x0p+0)); try testing.expectEqual(0x0p+0, asinBinary32(-0x0p+0)); try testing.expect(math.isNan(asinBinary32(0x1.000002p+0))); try testing.expect(math.isNan(asinBinary32(-0x1.000002p+0))); try testing.expect(math.isNan(asinBinary32(math.inf(f32)))); try testing.expect(math.isNan(asinBinary32(-math.inf(f32)))); try testing.expect(math.isNan(asinBinary32(math.nan(f32)))); } test "asinBinary32" { try testing.expectApproxEqAbs(-0x1.4c868p-4, asinBinary32(-0x1.4c2906p-4), math.floatEpsAt(f32, -0x1.4c868p-4)); try testing.expectApproxEqAbs(0x1.130648p-1, asinBinary32(0x1.05fcfap-1), math.floatEpsAt(f32, 0x1.130648p-1)); try testing.expectApproxEqAbs(0x1.090abcp-1, asinBinary32(0x1.fab976p-2), math.floatEpsAt(f32, 0x1.090abcp-1)); try testing.expectApproxEqAbs(0x1.c39fa2p-1, asinBinary32(0x1.8b4b8cp-1), math.floatEpsAt(f32, 0x1.c39fa2p-1)); try testing.expectApproxEqAbs(0x1.9c332p-1, asinBinary32(0x1.7117c2p-1), math.floatEpsAt(f32, 0x1.9c332p-1)); try testing.expectApproxEqAbs(0x1.e62a1cp-5, asinBinary32(0x1.e5e112p-5), math.floatEpsAt(f32, 0x1.e62a1cp-5)); try testing.expectApproxEqAbs(-0x1.0a65dep-2, asinBinary32(-0x1.07673p-2), math.floatEpsAt(f32, -0x1.0a65dep-2)); try testing.expectApproxEqAbs(-0x1.25046p-2, asinBinary32(-0x1.2108dep-2), math.floatEpsAt(f32, -0x1.25046p-2)); try testing.expectApproxEqAbs(-0x1.6c6f0cp-1, asinBinary32(-0x1.4e6e6cp-1), math.floatEpsAt(f32, -0x1.6c6f0cp-1)); try testing.expectApproxEqAbs(0x1.350f7ap-1, asinBinary32(0x1.22a16ap-1), math.floatEpsAt(f32, 0x1.350f7ap-1)); } test "asinBinary64.special" { try testing.expectApproxEqAbs(0x1.921fb54442d18p+0, asinBinary64(0x1p+0), math.floatEpsAt(f64, 0x1.921fb54442d18p+0)); try testing.expectApproxEqAbs(-0x1.921fb54442d18p+0, asinBinary64(-0x1p+0), math.floatEpsAt(f64, -0x1.921fb54442d18p+0)); try testing.expectEqual(0x0p+0, asinBinary64(0x0p+0)); try testing.expectEqual(0x0p+0, asinBinary64(-0x0p+0)); try testing.expect(math.isNan(asinBinary64(0x1.000002p+0))); try testing.expect(math.isNan(asinBinary64(-0x1.000002p+0))); try testing.expect(math.isNan(asinBinary64(math.inf(f64)))); try testing.expect(math.isNan(asinBinary64(-math.inf(f64)))); try testing.expect(math.isNan(asinBinary64(math.nan(f64)))); } test "asinBinary64" { try testing.expectApproxEqAbs(0x1.fae86c5941692p-2, asinBinary64(0x1.e674fba3e40d5p-2), math.floatEpsAt(f64, 0x1.fae86c5941692p-2)); try testing.expectApproxEqAbs(-0x1.46b6ad730c93ap-1, asinBinary64(-0x1.30fd0566fd979p-1), math.floatEpsAt(f64, -0x1.46b6ad730c93ap-1)); try testing.expectApproxEqAbs(0x1.6be0be8074eep-2, asinBinary64(0x1.6444a25abfeaap-2), math.floatEpsAt(f64, 0x1.6be0be8074eep-2)); try testing.expectApproxEqAbs(0x1.5a7e98f53f717p-1, asinBinary64(0x1.40a53228d1a13p-1), math.floatEpsAt(f64, 0x1.5a7e98f53f717p-1)); try testing.expectApproxEqAbs(-0x1.1ea2602d14e8p0, asinBinary64(-0x1.ccc6d64845cfdp-1), math.floatEpsAt(f64, -0x1.1ea2602d14e8p0)); try testing.expectApproxEqAbs(-0x1.d2c2634193158p-1, asinBinary64(-0x1.94bd91b7fc74bp-1), math.floatEpsAt(f64, -0x1.d2c2634193158p-1)); try testing.expectApproxEqAbs(-0x1.982d5f1895d2p-2, asinBinary64(-0x1.8d741b5797fccp-2), math.floatEpsAt(f64, -0x1.982d5f1895d2p-2)); try testing.expectApproxEqAbs(-0x1.3fdaf7dfdc864p-3, asinBinary64(-0x1.3e8e7e15881c5p-3), math.floatEpsAt(f64, -0x1.3fdaf7dfdc864p-3)); try testing.expectApproxEqAbs(-0x1.9269540735b7bp-2, asinBinary64(-0x1.88222d8ab8ca9p-2), math.floatEpsAt(f64, -0x1.9269540735b7bp-2)); try testing.expectApproxEqAbs(-0x1.474c4c6625527p-2, asinBinary64(-0x1.41c0e9babcbd2p-2), math.floatEpsAt(f64, -0x1.474c4c6625527p-2)); } test "asinExtended80.special" { try testing.expectApproxEqAbs(0x1.921fb54442d1846ap+0, asinExtended80(0x1p+0), math.floatEpsAt(f80, 0x1.921fb54442d1846ap+0)); try testing.expectApproxEqAbs(-0x1.921fb54442d1846ap+0, asinExtended80(-0x1p+0), math.floatEpsAt(f80, -0x1.921fb54442d1846ap+0)); try testing.expectEqual(0x0p+0, asinExtended80(0x0p+0)); try testing.expectEqual(0x0p+0, asinExtended80(-0x0p+0)); try testing.expect(math.isNan(asinExtended80(0x1.0000000000000002p+0))); try testing.expect(math.isNan(asinExtended80(-0x1.0000000000000002p+0))); try testing.expect(math.isNan(asinExtended80(math.inf(f80)))); try testing.expect(math.isNan(asinExtended80(-math.inf(f80)))); try testing.expect(math.isNan(asinExtended80(math.nan(f80)))); } test "asinExtended80" { try testing.expectApproxEqAbs(0x1.63cfb560149daa9p-9, asinExtended80(0x1.63cf98bc52ce0da8p-9), math.floatEpsAt(f80, 0x1.63cfb560149daa9p-9)); try testing.expectApproxEqAbs(-0x1.113cbacd8cd1b96cp-1, asinExtended80(-0x1.0473756f7ae930dp-1), math.floatEpsAt(f80, -0x1.113cbacd8cd1b96cp-1)); try testing.expectApproxEqAbs(-0x1.2721b231d197b064p-2, asinExtended80(-0x1.2310057e005cc288p-2), math.floatEpsAt(f80, -0x1.2721b231d197b064p-2)); try testing.expectApproxEqAbs(0x1.547c408c5d2b05aap0, asinExtended80(0x1.f13b03bd685d96eap-1), math.floatEpsAt(f80, 0x1.547c408c5d2b05aap0)); try testing.expectApproxEqAbs(-0x1.296b76bfadbb5cecp0, asinExtended80(-0x1.d5c507e3ef84041cp-1), math.floatEpsAt(f80, -0x1.296b76bfadbb5cecp0)); try testing.expectApproxEqAbs(0x1.b572da8729a84f2ap-1, asinExtended80(0x1.8222cbc9147153d8p-1), math.floatEpsAt(f80, 0x1.b572da8729a84f2ap-1)); try testing.expectApproxEqAbs(-0x1.42c9e80ac0524dap-11, asinExtended80(-0x1.42c9e6b4a088a246p-11), math.floatEpsAt(f80, -0x1.42c9e80ac0524dap-11)); try testing.expectApproxEqAbs(-0x1.920ca86aef6c3028p-3, asinExtended80(-0x1.8f78d49deadb521cp-3), math.floatEpsAt(f80, -0x1.920ca86aef6c3028p-3)); try testing.expectApproxEqAbs(-0x1.b91cb4f7204d92fp-2, asinExtended80(-0x1.ab98792783515774p-2), math.floatEpsAt(f80, -0x1.b91cb4f7204d92fp-2)); try testing.expectApproxEqAbs(-0x1.1f20815fdc4c5304p-1, asinExtended80(-0x1.104fe30cef6800aap-1), math.floatEpsAt(f80, -0x1.1f20815fdc4c5304p-1)); } test "asinBinary128.special" { try testing.expectApproxEqAbs(0x1.921fb54442d18469898cc51701b8p0, asinBinary128(0x1p+0), math.floatEpsAt(f128, 0x1.921fb54442d18469898cc51701b8p0)); try testing.expectApproxEqAbs(-0x1.921fb54442d18469898cc51701b8p0, asinBinary128(-0x1p+0), math.floatEpsAt(f128, -0x1.921fb54442d18469898cc51701b8p0)); try testing.expectEqual(0x0p+0, asinBinary128(0x0p+0)); try testing.expectEqual(0x0p+0, asinBinary128(-0x0p+0)); try testing.expect(math.isNan(asinBinary128(0x1.0000000000000000000000000001p0))); try testing.expect(math.isNan(asinBinary128(-0x1.0000000000000000000000000001p0))); try testing.expect(math.isNan(asinBinary128(math.inf(f128)))); try testing.expect(math.isNan(asinBinary128(-math.inf(f128)))); try testing.expect(math.isNan(asinBinary128(math.nan(f128)))); } test "asinBinary128" { try testing.expectApproxEqAbs(0x1.87e9c740d7837f8e8fa667988fbep-3, asinBinary128(0x1.85868ce287ca0196b01c25fec5ffp-3), math.floatEpsAt(f128, 0x1.87e9c740d7837f8e8fa667988fbep-3)); try testing.expectApproxEqAbs(0x1.bd11a474e864213b48e0f005f1f4p-1, asinBinary128(0x1.8718d6d30b4daed08d04ef59f478p-1), math.floatEpsAt(f128, 0x1.bd11a474e864213b48e0f005f1f4p-1)); try testing.expectApproxEqAbs(0x1.20b56f8b42649fe72d1f8d68a378p-1, asinBinary128(0x1.11a67640cd7f0ba5d5e362f3abfap-1), math.floatEpsAt(f128, 0x1.20b56f8b42649fe72d1f8d68a378p-1)); try testing.expectApproxEqAbs(-0x1.0dc3a7ddb9736e5ad699bf338566p0, asinBinary128(-0x1.bd13bf14a9dce22188e52650daa7p-1), math.floatEpsAt(f128, -0x1.0dc3a7ddb9736e5ad699bf338566p0)); try testing.expectApproxEqAbs(-0x1.f250716038f70fa50a5826c03802p-2, asinBinary128(-0x1.dee0bc217fc462af57c484eefa71p-2), math.floatEpsAt(f128, -0x1.f250716038f70fa50a5826c03802p-2)); try testing.expectApproxEqAbs(-0x1.47a8b4cdd327f90056722feddbabp0, asinBinary128(-0x1.ea7df9139371c10b9d6fd2bbccd3p-1), math.floatEpsAt(f128, -0x1.47a8b4cdd327f90056722feddbabp0)); try testing.expectApproxEqAbs(0x1.079178d52be662dec67e2cd7f6e9p-2, asinBinary128(0x1.04aaea6de3b5a616460702f26dfcp-2), math.floatEpsAt(f128, 0x1.079178d52be662dec67e2cd7f6e9p-2)); try testing.expectApproxEqAbs(-0x1.192df5a8d71702cf1e27014887b2p0, asinBinary128(-0x1.c7ea85e6b61be666435a7d99444cp-1), math.floatEpsAt(f128, -0x1.192df5a8d71702cf1e27014887b2p0)); try testing.expectApproxEqAbs(-0x1.97f1092fd94ac0fdfddae2e1222bp-1, asinBinary128(-0x1.6e210214e40edf6c8479998189d1p-1), math.floatEpsAt(f128, -0x1.97f1092fd94ac0fdfddae2e1222bp-1)); try testing.expectApproxEqAbs(-0x1.97b62bc5ae6512093828828325e1p-3, asinBinary128(-0x1.95061bf93ed6986a45d20f0e1064p-3), math.floatEpsAt(f128, -0x1.97b62bc5ae6512093828828325e1p-3)); } fn asinBinary32Vec(comptime vec_len: comptime_int, x: @Vector(vec_len, f32)) @TypeOf(x) { const pi_over_2: @Vector(vec_len, f32) = @splat(math.pi / 2.0); const zero: @Vector(vec_len, f32) = @splat(0.0); const half: @Vector(vec_len, f32) = @splat(0.5); const neg_two: @Vector(vec_len, f32) = @splat(-2.0); const c0: @Vector(vec_len, f32) = @splat(0x1.55555ep-3); const c1: @Vector(vec_len, f32) = @splat(0x1.33261ap-4); const c2: @Vector(vec_len, f32) = @splat(0x1.70d7dcp-5); const c3: @Vector(vec_len, f32) = @splat(0x1.b059dp-6); const c4: @Vector(vec_len, f32) = @splat(0x1.3af7d8p-5); const ax = @abs(x); const ax_lt_half = ax < half; const z2 = @select(f32, ax_lt_half, x * x, @mulAdd(@Vector(vec_len, f32), -half, ax, half)); const z = @select(f32, ax_lt_half, ax, @sqrt(z2)); const z3 = z2 * z; const p3_4 = @mulAdd(@Vector(vec_len, f32), z2, c4, c3); const p2_4 = @mulAdd(@Vector(vec_len, f32), z2, p3_4, c2); const p1_4 = @mulAdd(@Vector(vec_len, f32), z2, p2_4, c1); const p0_4 = @mulAdd(@Vector(vec_len, f32), z2, p1_4, c0); const p = @mulAdd(@Vector(vec_len, f32), z3, p0_4, z); const y = @select(f32, ax_lt_half, p, @mulAdd(@Vector(vec_len, f32), p, neg_two, pi_over_2)); return @select(f32, x < zero, -y, y); } fn asinBinary64Vec(comptime vec_len: comptime_int, x: @Vector(vec_len, f64)) @TypeOf(x) { const pi_over_2: @Vector(vec_len, f64) = @splat(math.pi / 2.0); const zero: @Vector(vec_len, f64) = @splat(0.0); const half: @Vector(vec_len, f64) = @splat(0.5); const neg_two: @Vector(vec_len, f64) = @splat(-2.0); const c0: @Vector(vec_len, f64) = @splat(0x1.555555555554ep-3); const c1: @Vector(vec_len, f64) = @splat(0x1.3333333337233p-4); const c2: @Vector(vec_len, f64) = @splat(0x1.6db6db67f6d9fp-5); const c3: @Vector(vec_len, f64) = @splat(0x1.f1c71fbd29fbbp-6); const c4: @Vector(vec_len, f64) = @splat(0x1.6e8b264d467d6p-6); const c5: @Vector(vec_len, f64) = @splat(0x1.1c5997c357e9dp-6); const c6: @Vector(vec_len, f64) = @splat(0x1.c86a22cd9389dp-7); const c7: @Vector(vec_len, f64) = @splat(0x1.856073c22ebbep-7); const c8: @Vector(vec_len, f64) = @splat(0x1.fd1151acb6bedp-8); const c9: @Vector(vec_len, f64) = @splat(0x1.087182f799c1dp-6); const c10: @Vector(vec_len, f64) = @splat(-0x1.6602748120927p-7); const c11: @Vector(vec_len, f64) = @splat(0x1.cfa0dd1f9478p-6); const ax = @abs(x); const ax_lt_half = ax < half; const z2 = @select(f64, ax_lt_half, x * x, @mulAdd(@Vector(vec_len, f64), -half, ax, half)); const z = @select(f64, ax_lt_half, ax, @sqrt(z2)); const z3 = z2 * z; const z4 = z2 * z2; const z8 = z4 * z4; const p0_1 = @mulAdd(@Vector(vec_len, f64), z2, c1, c0); const p2_3 = @mulAdd(@Vector(vec_len, f64), z2, c3, c2); const p0_3 = @mulAdd(@Vector(vec_len, f64), z4, p2_3, p0_1); const p4_5 = @mulAdd(@Vector(vec_len, f64), z2, c5, c4); const p6_7 = @mulAdd(@Vector(vec_len, f64), z2, c7, c6); const p4_7 = @mulAdd(@Vector(vec_len, f64), z4, p6_7, p4_5); const p8_9 = @mulAdd(@Vector(vec_len, f64), z2, c9, c8); const p10_11 = @mulAdd(@Vector(vec_len, f64), z2, c11, c10); const p8_11 = @mulAdd(@Vector(vec_len, f64), z4, p10_11, p8_9); const p4_11 = @mulAdd(@Vector(vec_len, f64), z8, p8_11, p4_7); const p0_11 = @mulAdd(@Vector(vec_len, f64), z8, p4_11, p0_3); const p = @mulAdd(@Vector(vec_len, f64), z3, p0_11, z); const y = @select(f64, ax_lt_half, p, @mulAdd(@Vector(vec_len, f64), p, neg_two, pi_over_2)); return @select(f64, x < zero, -y, y); } test "asinBinary32Vec.special" { const input: @Vector(9, f32) = .{ 0x1p+0, -0x1p+0, 0x0p+0, -0x0p+0, 0x1.000002p+0, -0x1.000002p+0, math.inf(f32), -math.inf(f32), math.nan(f32), }; const output = asinBinary32Vec(9, input); try testing.expectApproxEqAbs(0x1.921fb6p+0, output[0], math.floatEpsAt(f32, 0x1.921fb6p+0)); try testing.expectApproxEqAbs(-0x1.921fb6p+0, output[1], math.floatEpsAt(f32, -0x1.921fb6p+0)); try testing.expectEqual(0x0p+0, output[2]); try testing.expectEqual(0x0p+0, output[3]); try testing.expect(math.isNan(output[4])); try testing.expect(math.isNan(output[5])); try testing.expect(math.isNan(output[6])); try testing.expect(math.isNan(output[7])); try testing.expect(math.isNan(output[8])); } test "asinBinary32Vec" { const input: @Vector(10, f32) = .{ -0x1.4c2906p-4, 0x1.05fcfap-1, 0x1.fab976p-2, 0x1.8b4b8cp-1, 0x1.7117c2p-1, 0x1.e5e112p-5, -0x1.07673p-2, -0x1.2108dep-2, -0x1.4e6e6cp-1, 0x1.22a16ap-1, }; const output = asinBinary32Vec(10, input); try testing.expectApproxEqAbs(-0x1.4c868p-4, output[0], math.floatEpsAt(f32, -0x1.4c868p-4)); try testing.expectApproxEqAbs(0x1.130648p-1, output[1], math.floatEpsAt(f32, 0x1.130648p-1)); try testing.expectApproxEqAbs(0x1.090abcp-1, output[2], math.floatEpsAt(f32, 0x1.090abcp-1)); try testing.expectApproxEqAbs(0x1.c39fa2p-1, output[3], math.floatEpsAt(f32, 0x1.c39fa2p-1)); try testing.expectApproxEqAbs(0x1.9c332p-1, output[4], math.floatEpsAt(f32, 0x1.9c332p-1)); try testing.expectApproxEqAbs(0x1.e62a1cp-5, output[5], math.floatEpsAt(f32, 0x1.e62a1cp-5)); try testing.expectApproxEqAbs(-0x1.0a65dep-2, output[6], math.floatEpsAt(f32, -0x1.0a65dep-2)); try testing.expectApproxEqAbs(-0x1.25046p-2, output[7], math.floatEpsAt(f32, -0x1.25046p-2)); try testing.expectApproxEqAbs(-0x1.6c6f0cp-1, output[8], math.floatEpsAt(f32, -0x1.6c6f0cp-1)); try testing.expectApproxEqAbs(0x1.350f7ap-1, output[9], math.floatEpsAt(f32, 0x1.350f7ap-1)); } test "asinBinary64Vec.special" { const input: @Vector(9, f64) = .{ 0x1p+0, -0x1p+0, 0x0p+0, -0x0p+0, 0x1.000002p+0, -0x1.000002p+0, math.inf(f64), -math.inf(f64), math.nan(f64), }; const output = asinBinary64Vec(9, input); try testing.expectApproxEqAbs(0x1.921fb54442d18p+0, output[0], math.floatEpsAt(f64, 0x1.921fb54442d18p+0)); try testing.expectApproxEqAbs(-0x1.921fb54442d18p+0, output[1], math.floatEpsAt(f64, -0x1.921fb54442d18p+0)); try testing.expectEqual(0x0p+0, output[2]); try testing.expectEqual(0x0p+0, output[3]); try testing.expect(math.isNan(output[4])); try testing.expect(math.isNan(output[5])); try testing.expect(math.isNan(output[6])); try testing.expect(math.isNan(output[7])); try testing.expect(math.isNan(output[8])); } test "asinBinary64Vec" { const input: @Vector(10, f64) = .{ 0x1.e674fba3e40d5p-2, -0x1.30fd0566fd979p-1, 0x1.6444a25abfeaap-2, 0x1.40a53228d1a13p-1, -0x1.ccc6d64845cfdp-1, -0x1.94bd91b7fc74bp-1, -0x1.8d741b5797fccp-2, -0x1.3e8e7e15881c5p-3, -0x1.88222d8ab8ca9p-2, -0x1.41c0e9babcbd2p-2, }; const output = asinBinary64Vec(10, input); try testing.expectApproxEqAbs(0x1.fae86c5941692p-2, output[0], math.floatEpsAt(f64, 0x1.fae86c5941692p-2)); try testing.expectApproxEqAbs(-0x1.46b6ad730c93ap-1, output[1], math.floatEpsAt(f64, -0x1.46b6ad730c93ap-1)); try testing.expectApproxEqAbs(0x1.6be0be8074eep-2, output[2], math.floatEpsAt(f64, 0x1.6be0be8074eep-2)); try testing.expectApproxEqAbs(0x1.5a7e98f53f717p-1, output[3], math.floatEpsAt(f64, 0x1.5a7e98f53f717p-1)); try testing.expectApproxEqAbs(-0x1.1ea2602d14e8p0, output[4], math.floatEpsAt(f64, -0x1.1ea2602d14e8p0)); try testing.expectApproxEqAbs(-0x1.d2c2634193158p-1, output[5], math.floatEpsAt(f64, -0x1.d2c2634193158p-1)); try testing.expectApproxEqAbs(-0x1.982d5f1895d2p-2, output[6], math.floatEpsAt(f64, -0x1.982d5f1895d2p-2)); try testing.expectApproxEqAbs(-0x1.3fdaf7dfdc864p-3, output[7], math.floatEpsAt(f64, -0x1.3fdaf7dfdc864p-3)); try testing.expectApproxEqAbs(-0x1.9269540735b7bp-2, output[8], math.floatEpsAt(f64, -0x1.9269540735b7bp-2)); try testing.expectApproxEqAbs(-0x1.474c4c6625527p-2, output[9], math.floatEpsAt(f64, -0x1.474c4c6625527p-2)); }