zig

blob dedd4d7e (5314B) - Raw

---

 // 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 "math.asin" {
     try expect(asin(@as(f32, 0.0)) == asin32(0.0));
     try expect(asin(@as(f64, 0.0)) == asin64(0.0));
 }
 
 test "math.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 "math.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 "math.asin32.special" {
     try expect(asin32(0.0) == 0.0);
     try expect(asin32(-0.0) == -0.0);
     try expect(math.isNan(asin32(-2)));
     try expect(math.isNan(asin32(1.5)));
 }
 
 test "math.asin64.special" {
     try expect(asin64(0.0) == 0.0);
     try expect(asin64(-0.0) == -0.0);
     try expect(math.isNan(asin64(-2)));
     try expect(math.isNan(asin64(1.5)));
 }