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Add f16, f80 and f128 support for acos and asin (#30997)
The software impl of `acos` and `asin` depends on the `sqrt` op. Since support for `sqrt` in `f16`, `f80`, and `f128` has been added, the impl of `acos` and `asin` for `f16`, `f80`, and `f128` is now being supplemented. Reviewed-on: https://codeberg.org/ziglang/zig/pulls/30997 Reviewed-by: Andrew Kelley <andrew@ziglang.org> Co-authored-by: lzm-build <3575188313@qq.com> Co-committed-by: lzm-build <3575188313@qq.com>
This commit is contained in:
lzm-build
+331
-78
@@ -3,10 +3,13 @@
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//
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// https://git.musl-libc.org/cgit/musl/tree/src/math/acosf.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/acos.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/acosl.c
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const std = @import("../std.zig");
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const math = std.math;
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const expect = std.testing.expect;
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const testing = std.testing;
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const builtin = @import("builtin");
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const native_endian = builtin.cpu.arch.endian();
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/// Returns the arc-cosine of x.
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///
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@@ -15,71 +18,120 @@ const expect = std.testing.expect;
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pub fn acos(x: anytype) @TypeOf(x) {
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const T = @TypeOf(x);
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return switch (T) {
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f32 => acos32(x),
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f64 => acos64(x),
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f16 => acosBinary16(x),
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f32 => acosBinary32(x),
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f64 => acosBinary64(x),
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f80 => acosExtended80(x),
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f128 => acosBinary128(x),
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else => @compileError("acos not implemented for " ++ @typeName(T)),
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};
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}
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fn r32(z: f32) f32 {
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const pS0 = 1.6666586697e-01;
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const pS1 = -4.2743422091e-02;
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const pS2 = -8.6563630030e-03;
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const qS1 = -7.0662963390e-01;
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fn approxBinary16(z: f32) f32 {
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const S0: f32 = 1.0000001e0;
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const S1: f32 = 1.6664918e-1;
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const S2: f32 = 7.55022e-2;
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const S3: f32 = 3.9513987e-2;
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const S4: f32 = 5.0883885e-2;
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return S0 + z * (S1 + z * (S2 + z * (S3 + z * S4)));
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}
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fn acosBinary16(x: f16) f16 {
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const pio2: f32 = math.pi / 2.0;
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const hx: u16 = @bitCast(x);
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const ix: u16 = hx & 0x7fff;
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// |x| >= 1 or nan
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if (ix >= 0x3c00) {
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if (ix == 0x3c00) {
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if (hx >> 15 != 0) {
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return @floatCast(2.0 * pio2 + 0x1p-120);
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}
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return 0.0;
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}
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return 0.0 / (x - x);
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}
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const xf: f32 = @floatCast(x);
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// |x| < 0.5
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if (ix < 0x3800) {
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return @floatCast(pio2 - xf * approxBinary16(xf * xf));
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}
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// x < -0.5
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if (hx >> 15 != 0) {
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const z = (1.0 + xf) * 0.5;
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const s = @sqrt(z);
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const w = approxBinary16(z) * s;
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return @floatCast(2.0 * (pio2 - w));
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}
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// x > 0.5
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const z = (1.0 - xf) * 0.5;
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const s = @sqrt(z);
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const w = approxBinary16(z) * s;
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return @floatCast(2.0 * w);
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}
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fn rationalApproxBinary32(z: f32) f32 {
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const pS0: f32 = 1.6666586697e-01;
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const pS1: f32 = -4.2743422091e-02;
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const pS2: f32 = -8.6563630030e-03;
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const qS1: f32 = -7.0662963390e-01;
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const p = z * (pS0 + z * (pS1 + z * pS2));
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const q = 1.0 + z * qS1;
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return p / q;
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}
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fn acos32(x: f32) f32 {
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const pio2_hi = 1.5707962513e+00;
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const pio2_lo = 7.5497894159e-08;
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fn acosBinary32(x: f32) f32 {
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const pio2_hi: f32 = 1.5707962513e+00;
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const pio2_lo: f32 = 7.5497894159e-08;
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const hx: u32 = @as(u32, @bitCast(x));
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const ix: u32 = hx & 0x7FFFFFFF;
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const hx: u32 = @bitCast(x);
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const ix: u32 = hx & 0x7fff_ffff;
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// |x| >= 1 or nan
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if (ix >= 0x3F800000) {
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if (ix == 0x3F800000) {
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if (ix >= 0x3f800000) {
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if (ix == 0x3f800000) {
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if (hx >> 31 != 0) {
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return 2.0 * pio2_hi + 0x1.0p-120;
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} else {
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return 0.0;
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}
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} else {
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return (x - x) / 0;
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return 0.0;
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}
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return 0.0 / (x - x);
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}
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// |x| < 0.5
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if (ix < 0x3F000000) {
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if (ix <= 0x32800000) { // |x| < 2^(-26)
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if (ix < 0x3f00_0000) {
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// |x| < 2^(-26)
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if (ix <= 0x3280_0000) {
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return pio2_hi + 0x1.0p-120;
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} else {
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return pio2_hi - (x - (pio2_lo - x * r32(x * x)));
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}
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return pio2_hi - (x - (pio2_lo - x * rationalApproxBinary32(x * x)));
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}
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// x < -0.5
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if (hx >> 31 != 0) {
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const z = (1 + x) * 0.5;
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const s = @sqrt(z);
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const w = r32(z) * s - pio2_lo;
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return 2 * (pio2_hi - (s + w));
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const w = rationalApproxBinary32(z) * s - pio2_lo;
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return 2.0 * (pio2_hi - (s + w));
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}
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// x > 0.5
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const z = (1.0 - x) * 0.5;
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const s = @sqrt(z);
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const jx = @as(u32, @bitCast(s));
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const df = @as(f32, @bitCast(jx & 0xFFFFF000));
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const hs: u32 = @bitCast(s);
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const df: f32 = @bitCast(hs & 0xffff_f000);
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const c = (z - df * df) / (s + df);
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const w = r32(z) * s + c;
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return 2 * (df + w);
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const w = rationalApproxBinary32(z) * s + c;
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return 2.0 * (df + w);
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}
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fn r64(z: f64) f64 {
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fn rationalApproxBinary64(z: f64) f64 {
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const pS0: f64 = 1.66666666666666657415e-01;
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const pS1: f64 = -3.25565818622400915405e-01;
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const pS2: f64 = 2.01212532134862925881e-01;
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@@ -96,91 +148,292 @@ fn r64(z: f64) f64 {
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return p / q;
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}
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fn acos64(x: f64) f64 {
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fn acosBinary64(x: f64) f64 {
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const pio2_hi: f64 = 1.57079632679489655800e+00;
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const pio2_lo: f64 = 6.12323399573676603587e-17;
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const ux = @as(u64, @bitCast(x));
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const hx = @as(u32, @intCast(ux >> 32));
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const ix = hx & 0x7FFFFFFF;
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const hx: u32 = @intCast(@as(u64, @bitCast(x)) >> 32);
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const ix: u32 = hx & 0x7fff_ffff;
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// |x| >= 1 or nan
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if (ix >= 0x3FF00000) {
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const lx = @as(u32, @intCast(ux & 0xFFFFFFFF));
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// acos(1) = 0, acos(-1) = pi
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if ((ix - 0x3FF00000) | lx == 0) {
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if (ix >= 0x3ff0_0000) {
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const lx: u32 = @truncate(@as(u64, @bitCast(x)));
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if ((ix - 0x3ff0_0000 | lx) == 0) {
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if (hx >> 31 != 0) {
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return 2 * pio2_hi + 0x1.0p-120;
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} else {
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return 0;
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return 2.0 * pio2_hi + 0x1.0p-120;
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}
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return 0.0;
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}
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return (x - x) / 0;
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return 0.0 / (x - x);
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}
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// |x| < 0.5
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if (ix < 0x3FE00000) {
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if (ix < 0x3fe0_0000) {
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// |x| < 2^(-57)
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if (ix <= 0x3C600000) {
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if (ix <= 0x3c60_0000) {
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return pio2_hi + 0x1.0p-120;
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} else {
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return pio2_hi - (x - (pio2_lo - x * r64(x * x)));
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}
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return pio2_hi - (x - (pio2_lo - x * rationalApproxBinary64(x * x)));
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}
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// x < -0.5
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if (hx >> 31 != 0) {
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const z = (1.0 + x) * 0.5;
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const s = @sqrt(z);
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const w = r64(z) * s - pio2_lo;
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const w = rationalApproxBinary64(z) * s - pio2_lo;
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return 2 * (pio2_hi - (s + w));
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}
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// x > 0.5
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const z = (1.0 - x) * 0.5;
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const s = @sqrt(z);
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const jx = @as(u64, @bitCast(s));
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const df = @as(f64, @bitCast(jx & 0xFFFFFFFF00000000));
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const df: f64 = @bitCast(@as(u64, @bitCast(s)) & 0xffff_ffff_0000_0000);
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const c = (z - df * df) / (s + df);
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const w = r64(z) * s + c;
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return 2 * (df + w);
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const w = rationalApproxBinary64(z) * s + c;
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return 2.0 * (df + w);
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}
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test acos {
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try expect(acos(@as(f32, 0.0)) == acos32(0.0));
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try expect(acos(@as(f64, 0.0)) == acos64(0.0));
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fn rationalApproxExtended80(z: f80) f80 {
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const pS0: f80 = 1.66666666666666666631e-01;
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const pS1: f80 = -4.16313987993683104320e-01;
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const pS2: f80 = 3.69068046323246813704e-01;
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const pS3: f80 = -1.36213932016738603108e-01;
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const pS4: f80 = 1.78324189708471965733e-02;
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const pS5: f80 = -2.19216428382605211588e-04;
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const pS6: f80 = -7.10526623669075243183e-06;
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const qS1: f80 = -2.94788392796209867269e+00;
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const qS2: f80 = 3.27309890266528636716e+00;
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const qS3: f80 = -1.68285799854822427013e+00;
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const qS4: f80 = 3.90699412641738801874e-01;
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const qS5: f80 = -3.14365703596053263322e-02;
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const p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * (pS5 + z * pS6))))));
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const q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * (qS4 + z * qS5))));
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return p / q;
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}
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test acos32 {
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const epsilon = 0.000001;
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fn acosExtended80(x: f80) f80 {
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const pio2_hi: f80 = 1.57079632679489661926;
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const pio2_lo: f80 = -2.50827880633416601173e-20;
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try expect(math.approxEqAbs(f32, acos32(0.0), 1.570796, epsilon));
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try expect(math.approxEqAbs(f32, acos32(0.2), 1.369438, epsilon));
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try expect(math.approxEqAbs(f32, acos32(0.3434), 1.220262, epsilon));
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try expect(math.approxEqAbs(f32, acos32(0.5), 1.047198, epsilon));
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try expect(math.approxEqAbs(f32, acos32(0.8923), 0.468382, epsilon));
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try expect(math.approxEqAbs(f32, acos32(-0.2), 1.772154, epsilon));
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const hx: u80 = @bitCast(x);
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const se: u16 = @truncate(hx >> 64);
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const e = se & 0x7fff;
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// |x| >= 1 or nan
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if (e >= 0x3fff) {
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if (x == 1.0) {
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return 0.0;
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}
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if (x == -1.0) {
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return 2.0 * pio2_hi + 0x1p-120;
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}
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return 0.0 / (x - x);
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}
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// |x| < 0.5
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if (e < 0x3fff - 1) {
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if (e < 0x3fff - math.floatFractionalBits(f80)) {
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return pio2_hi + 0x1p-120;
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}
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return pio2_hi - (rationalApproxExtended80(x * x) * x - pio2_lo + x);
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}
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// x < -0.5
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if (se >> 15 != 0) {
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const z = (1 + x) * 0.5;
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const s = @sqrt(z);
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return 2.0 * (pio2_hi - (rationalApproxExtended80(z) * s - pio2_lo + s));
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}
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// x > 0.5
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const z = (1.0 - x) * 0.5;
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const s = @sqrt(z);
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const hs: u80 = @bitCast(s);
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const f: f80 = @bitCast(hs & 0xffff_ffff_ffff_0000_0000);
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const c = (z - f * f) / (s + f);
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return 2.0 * (rationalApproxExtended80(z) * s + c + f);
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}
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test acos64 {
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const epsilon = 0.000001;
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fn rationalApproxBinary128(z: f128) f128 {
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const pS0: f128 = 1.66666666666666666666666666666700314e-01;
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const pS1: f128 = -7.32816946414566252574527475428622708e-01;
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const pS2: f128 = 1.34215708714992334609030036562143589e+00;
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const pS3: f128 = -1.32483151677116409805070261790752040e+00;
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const pS4: f128 = 7.61206183613632558824485341162121989e-01;
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const pS5: f128 = -2.56165783329023486777386833928147375e-01;
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const pS6: f128 = 4.80718586374448793411019434585413855e-02;
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const pS7: f128 = -4.42523267167024279410230886239774718e-03;
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const pS8: f128 = 1.44551535183911458253205638280410064e-04;
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const pS9: f128 = -2.10558957916600254061591040482706179e-07;
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const qS1: f128 = -4.84690167848739751544716485245697428e+00;
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const qS2: f128 = 9.96619113536172610135016921140206980e+00;
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const qS3: f128 = -1.13177895428973036660836798461641458e+01;
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const qS4: f128 = 7.74004374389488266169304117714658761e+00;
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const qS5: f128 = -3.25871986053534084709023539900339905e+00;
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const qS6: f128 = 8.27830318881232209752469022352928864e-01;
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const qS7: f128 = -1.18768052702942805423330715206348004e-01;
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const qS8: f128 = 8.32600764660522313269101537926539470e-03;
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const qS9: f128 = -1.99407384882605586705979504567947007e-04;
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try expect(math.approxEqAbs(f64, acos64(0.0), 1.570796, epsilon));
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try expect(math.approxEqAbs(f64, acos64(0.2), 1.369438, epsilon));
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try expect(math.approxEqAbs(f64, acos64(0.3434), 1.220262, epsilon));
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try expect(math.approxEqAbs(f64, acos64(0.5), 1.047198, epsilon));
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try expect(math.approxEqAbs(f64, acos64(0.8923), 0.468382, epsilon));
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try expect(math.approxEqAbs(f64, acos64(-0.2), 1.772154, epsilon));
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const p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * (pS5 + z * (pS6 + z * (pS7 + z * (pS8 + z * pS9)))))))));
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const q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * (qS4 + z * (qS5 + z * (qS6 + z * (qS7 + z * (qS8 + z * qS9))))))));
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return p / q;
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}
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test "acos32.special" {
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try expect(math.isNan(acos32(-2)));
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try expect(math.isNan(acos32(1.5)));
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fn acosBinary128(x: f128) f128 {
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const pio2_hi: f128 = 1.57079632679489661923132169163975140;
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const pio2_lo: f128 = 4.33590506506189051239852201302167613e-35;
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const hx: u128 = @bitCast(x);
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const se: u16 = @truncate(hx >> 112);
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const e = se & 0x7fff;
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// |x| >= 1 or nan
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if (e >= 0x3fff) {
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if (x == 1.0) {
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return 0.0;
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}
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if (x == -1.0) {
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return 2 * pio2_hi + 0x1p-120;
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}
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return 0.0 / (x - x);
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}
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// |x| < 0.5
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if (e < 0x3fff - 1) {
|
||||
if (e < 0x3fff - math.floatFractionalBits(f128)) {
|
||||
return pio2_hi + 0x1p-120;
|
||||
}
|
||||
return pio2_hi - (rationalApproxBinary128(x * x) * x - pio2_lo + x);
|
||||
}
|
||||
// x < -0.5
|
||||
if (se >> 15 != 0) {
|
||||
const z = (1 + x) * 0.5;
|
||||
const s = @sqrt(z);
|
||||
return 2 * (pio2_hi - (rationalApproxBinary128(z) * s - pio2_lo + s));
|
||||
}
|
||||
// x > 0.5
|
||||
const z = (1.0 - x) * 0.5;
|
||||
const s = @sqrt(z);
|
||||
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);
|
||||
return 2.0 * (rationalApproxBinary128(z) * s + c + f);
|
||||
}
|
||||
|
||||
test "acos64.special" {
|
||||
try expect(math.isNan(acos64(-2)));
|
||||
try expect(math.isNan(acos64(1.5)));
|
||||
test "acosBinary16.special" {
|
||||
try testing.expectApproxEqAbs(acosBinary16(0x0p+0), 0x1.92p0, math.floatEpsAt(f16, 0x1.92p0));
|
||||
try testing.expectApproxEqAbs(acosBinary16(-0x1p+0), 0x1.92p1, math.floatEpsAt(f16, 0x1.92p1));
|
||||
try testing.expectEqual(acosBinary16(0x1p+0), 0x0p+0);
|
||||
try testing.expect(math.isNan(acosBinary16(0x1.004p0)));
|
||||
try testing.expect(math.isNan(acosBinary16(-0x1.004p0)));
|
||||
try testing.expect(math.isNan(acosBinary16(math.inf(f16))));
|
||||
try testing.expect(math.isNan(acosBinary16(-math.inf(f16))));
|
||||
try testing.expect(math.isNan(acosBinary16(math.nan(f16))));
|
||||
}
|
||||
|
||||
test "acosBinary16" {
|
||||
try testing.expectApproxEqAbs(acosBinary16(0x1.db4p-5), 0x1.834p0, math.floatEpsAt(f16, 0x1.834p0));
|
||||
try testing.expectApproxEqAbs(acosBinary16(-0x1.068p-2), 0x1.d48p0, math.floatEpsAt(f16, 0x1.d48p0));
|
||||
try testing.expectApproxEqAbs(acosBinary16(-0x1.2c4p-3), 0x1.b7cp0, math.floatEpsAt(f16, 0x1.b7cp0));
|
||||
try testing.expectApproxEqAbs(acosBinary16(0x1.65p-3), 0x1.654p0, math.floatEpsAt(f16, 0x1.654p0));
|
||||
try testing.expectApproxEqAbs(acosBinary16(0x1.dfcp-1), 0x1.6d8p-2, math.floatEpsAt(f16, 0x1.6d8p-2));
|
||||
try testing.expectApproxEqAbs(acosBinary16(-0x1.764p-1), 0x1.32p1, math.floatEpsAt(f16, 0x1.32p1));
|
||||
try testing.expectApproxEqAbs(acosBinary16(0x1.b18p-3), 0x1.5b8p0, math.floatEpsAt(f16, 0x1.5b8p0));
|
||||
try testing.expectApproxEqAbs(acosBinary16(0x1.5acp-3), 0x1.668p0, math.floatEpsAt(f16, 0x1.668p0));
|
||||
try testing.expectApproxEqAbs(acosBinary16(-0x1.18cp-1), 0x1.134p1, math.floatEpsAt(f16, 0x1.134p1));
|
||||
try testing.expectApproxEqAbs(acosBinary16(-0x1.03p-1), 0x1.0dp1, math.floatEpsAt(f16, 0x1.0dp1));
|
||||
}
|
||||
|
||||
test "acosBinary32.special" {
|
||||
try testing.expectApproxEqAbs(acosBinary32(0x0p+0), 0x1.921fb6p+0, math.floatEpsAt(f32, 0x1.921fb6p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary32(-0x1p+0), 0x1.921fb6p+1, math.floatEpsAt(f32, 0x1.921fb6p+1));
|
||||
try testing.expectEqual(acosBinary32(0x1p+0), 0x0p+0);
|
||||
try testing.expect(math.isNan(acosBinary32(0x1.000002p+0)));
|
||||
try testing.expect(math.isNan(acosBinary32(-0x1.000002p+0)));
|
||||
try testing.expect(math.isNan(acosBinary32(math.inf(f32))));
|
||||
try testing.expect(math.isNan(acosBinary32(-math.inf(f32))));
|
||||
try testing.expect(math.isNan(acosBinary32(math.nan(f32))));
|
||||
}
|
||||
|
||||
test "acosBinary32" {
|
||||
try testing.expectApproxEqAbs(acosBinary32(-0x1.13284cp-2), 0x1.d7c4e6p+0, math.floatEpsAt(f32, 0x1.d7c4e6p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary32(0x1.6ca8ep-1), 0x1.8e6756p-1, math.floatEpsAt(f32, 0x1.8e6756p-1));
|
||||
try testing.expectApproxEqAbs(acosBinary32(0x1.c2ca6p-1), 0x1.f9d74cp-2, math.floatEpsAt(f32, 0x1.f9d74cp-2));
|
||||
try testing.expectApproxEqAbs(acosBinary32(-0x1.55f12p-1), 0x1.26abdcp+1, math.floatEpsAt(f32, 0x1.26abdcp+1));
|
||||
try testing.expectApproxEqAbs(acosBinary32(-0x1.15679ep-2), 0x1.d85a44p+0, math.floatEpsAt(f32, 0x1.d85a44p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary32(-0x1.41e132p-5), 0x1.9c2f68p+0, math.floatEpsAt(f32, 0x1.9c2f68p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary32(0x1.281b0ep-1), 0x1.e881bp-1, math.floatEpsAt(f32, 0x1.e881bp-1));
|
||||
try testing.expectApproxEqAbs(acosBinary32(0x1.b5ce34p-1), 0x1.1713f6p-1, math.floatEpsAt(f32, 0x1.1713f6p-1));
|
||||
try testing.expectApproxEqAbs(acosBinary32(-0x1.583482p-3), 0x1.bd5accp+0, math.floatEpsAt(f32, 0x1.bd5accp+0));
|
||||
try testing.expectApproxEqAbs(acosBinary32(-0x1.ea8224p-1), 0x1.6ce7d8p+1, math.floatEpsAt(f32, 0x1.6ce7d8p+1));
|
||||
}
|
||||
|
||||
test "acosBinary64.special" {
|
||||
try testing.expectApproxEqAbs(acosBinary64(0x0p+0), 0x1.921fb54442d18p+0, math.floatEpsAt(f64, 0x1.921fb54442d18p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary64(-0x1p+0), 0x1.921fb54442d18p+1, math.floatEpsAt(f64, 0x1.921fb54442d18p+1));
|
||||
try testing.expectEqual(acosBinary64(0x1p+0), 0x0p+0);
|
||||
try testing.expect(math.isNan(acosBinary64(0x1.0000000000001p+0)));
|
||||
try testing.expect(math.isNan(acosBinary64(-0x1.0000000000001p+0)));
|
||||
try testing.expect(math.isNan(acosBinary64(math.inf(f64))));
|
||||
try testing.expect(math.isNan(acosBinary64(-math.inf(f64))));
|
||||
try testing.expect(math.isNan(acosBinary64(math.nan(f64))));
|
||||
}
|
||||
|
||||
test "acosBinary64" {
|
||||
try testing.expectApproxEqAbs(acosBinary64(-0x1.13284b2b5006dp-2), 0x1.d7c4e61020905p+0, math.floatEpsAt(f64, 0x1.d7c4e61020905p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary64(0x1.6ca8dfb825911p-1), 0x1.8e6756e27c366p-1, math.floatEpsAt(f64, 0x1.8e6756e27c366p-1));
|
||||
try testing.expectApproxEqAbs(acosBinary64(0x1.c2ca609de7505p-1), 0x1.f9d748eaf956p-2, math.floatEpsAt(f64, 0x1.f9d748eaf956p-2));
|
||||
try testing.expectApproxEqAbs(acosBinary64(-0x1.55f11fba96889p-1), 0x1.26abdc68d07aap+1, math.floatEpsAt(f64, 0x1.26abdc68d07aap+1));
|
||||
try testing.expectApproxEqAbs(acosBinary64(-0x1.15679e27084ddp-2), 0x1.d85a44ea44fe4p+0, math.floatEpsAt(f64, 0x1.d85a44ea44fe4p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary64(-0x1.41e131b093c41p-5), 0x1.9c2f688eee8abp+0, math.floatEpsAt(f64, 0x1.9c2f688eee8abp+0));
|
||||
try testing.expectApproxEqAbs(acosBinary64(0x1.281b0d18455f5p-1), 0x1.e881b1d4eb2a1p-1, math.floatEpsAt(f64, 0x1.e881b1d4eb2a1p-1));
|
||||
try testing.expectApproxEqAbs(acosBinary64(0x1.b5ce34a51b239p-1), 0x1.1713f567a87efp-1, math.floatEpsAt(f64, 0x1.1713f567a87efp-1));
|
||||
try testing.expectApproxEqAbs(acosBinary64(-0x1.583481079de4dp-3), 0x1.bd5acbe8fcc59p+0, math.floatEpsAt(f64, 0x1.bd5acbe8fcc59p+0));
|
||||
try testing.expectApproxEqAbs(acosBinary64(-0x1.ea8223103b871p-1), 0x1.6ce7d66f628e5p+1, math.floatEpsAt(f64, 0x1.6ce7d66f628e5p+1));
|
||||
}
|
||||
|
||||
test "acosExtended80.special" {
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x0p+0), 0x1.921fb54442d1846ap+0, math.floatEpsAt(f80, 0x1.921fb54442d1846ap+0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(-0x1p+0), 0x1.921fb54442d1846ap+1, math.floatEpsAt(f80, 0x1.921fb54442d1846ap+1));
|
||||
try testing.expectEqual(acosExtended80(0x1p+0), 0x0p+0);
|
||||
try testing.expect(math.isNan(acosExtended80(0x1.0000000000000002p+0)));
|
||||
try testing.expect(math.isNan(acosExtended80(-0x1.0000000000000002p+0)));
|
||||
try testing.expect(math.isNan(acosExtended80(math.inf(f80))));
|
||||
try testing.expect(math.isNan(acosExtended80(-math.inf(f80))));
|
||||
try testing.expect(math.isNan(acosExtended80(math.nan(f80))));
|
||||
}
|
||||
|
||||
test "acosExtended80" {
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x1.72068a321edc8804p-1), 0x1.86b349040d28f794p-1, math.floatEpsAt(f80, 0x1.86b349040d28f794p-1));
|
||||
try testing.expectApproxEqAbs(acosExtended80(-0x1.06d0a467d22977ecp-2), 0x1.d4923ade73ec379cp0, math.floatEpsAt(f80, 0x1.d4923ade73ec379cp0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x1.77d21385faa9798ap-3), 0x1.62e0e8898c6d04f2p0, math.floatEpsAt(f80, 0x1.62e0e8898c6d04f2p0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(-0x1.73ee3e8bc2a44dbep-1), 0x1.3123cbcd5dc4bd58p1, math.floatEpsAt(f80, 0x1.3123cbcd5dc4bd58p1));
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x1.0a2dd1f6ffcf668ap-1), 0x1.062a6d562df2d316p0, math.floatEpsAt(f80, 0x1.062a6d562df2d316p0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x1.8e835c490a3aff9ep-3), 0x1.5ffd68b520aa55fap0, math.floatEpsAt(f80, 0x1.5ffd68b520aa55fap0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x1.add20cdc1565064cp-3), 0x1.5bfe6cabda700684p0, math.floatEpsAt(f80, 0x1.5bfe6cabda700684p0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x1.21986d43727fca72p-8), 0x1.90fe1c993b571924p0, math.floatEpsAt(f80, 0x1.90fe1c993b571924p0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(0x1.d61e0b3fae6a0564p-2), 0x1.18044ccc626e7f9ep0, math.floatEpsAt(f80, 0x1.18044ccc626e7f9ep0));
|
||||
try testing.expectApproxEqAbs(acosExtended80(-0x1.171e7c4a41883ccap-4), 0x1.a39513b6c16532b4p0, math.floatEpsAt(f80, 0x1.a39513b6c16532b4p0));
|
||||
}
|
||||
|
||||
test "acosBinary128.special" {
|
||||
try testing.expectApproxEqAbs(acosBinary128(0x0p+0), 0x1.921fb54442d18469898cc51701b8p0, math.floatEpsAt(f128, 0x1.921fb54442d18469898cc51701b8p0));
|
||||
try testing.expectApproxEqAbs(acosBinary128(-0x1p+0), 0x1.921fb54442d18469898cc51701b8p1, math.floatEpsAt(f128, 0x1.921fb54442d18469898cc51701b8p1));
|
||||
try testing.expectEqual(acosBinary128(0x1p+0), 0x0p+0);
|
||||
try testing.expect(math.isNan(acosBinary128(0x1.0000000000000000000000000001p0)));
|
||||
try testing.expect(math.isNan(acosBinary128(-0x1.0000000000000000000000000001p0)));
|
||||
try testing.expect(math.isNan(acosBinary128(math.inf(f128))));
|
||||
try testing.expect(math.isNan(acosBinary128(-math.inf(f128))));
|
||||
try testing.expect(math.isNan(acosBinary128(math.nan(f128))));
|
||||
}
|
||||
|
||||
test "acosBinary128" {
|
||||
try testing.expectApproxEqAbs(acosBinary128(-0x1.511bdb99a3c4373bedf834ef4f68p-1), 0x1.250e9a58f049eeafa99db4360c88p1, math.floatEpsAt(f128, 0x1.250e9a58f049eeafa99db4360c88p1));
|
||||
try testing.expectApproxEqAbs(acosBinary128(-0x1.5879cc3ad6dfd2a52e9891c69808p-1), 0x1.2786664b1c676c99437b68590004p1, math.floatEpsAt(f128, 0x1.2786664b1c676c99437b68590004p1));
|
||||
try testing.expectApproxEqAbs(acosBinary128(0x1.3f988ba64a7eb97a751c5f0b3077p-1), 0x1.cb190cd361c7c03a09c470b4caebp-1, math.floatEpsAt(f128, 0x1.cb190cd361c7c03a09c470b4caebp-1));
|
||||
try testing.expectApproxEqAbs(acosBinary128(-0x1.3f2d96c7768e4c4fa02315727959p-1), 0x1.1f373be697880111758f582b1a96p1, math.floatEpsAt(f128, 0x1.1f373be697880111758f582b1a96p1));
|
||||
try testing.expectApproxEqAbs(acosBinary128(0x1.fad303c2e28c1f4d8f9fd0e5686fp-2), 0x1.0d92fd2a0a6ca3e4853c1de9ea6ap0, math.floatEpsAt(f128, 0x1.0d92fd2a0a6ca3e4853c1de9ea6ap0));
|
||||
try testing.expectApproxEqAbs(acosBinary128(0x1.ddde322bd1a2ee50c5ba30c9c617p-2), 0x1.15d4b306e16fbf9ea4f29e82b154p0, math.floatEpsAt(f128, 0x1.15d4b306e16fbf9ea4f29e82b154p0));
|
||||
try testing.expectApproxEqAbs(acosBinary128(-0x1.b02f6adefcbeb1d48666b827ff17p-1), 0x1.49b0a0355a5539052388e8a6dc11p1, math.floatEpsAt(f128, 0x1.49b0a0355a5539052388e8a6dc11p1));
|
||||
try testing.expectApproxEqAbs(acosBinary128(0x1.c8581cce7cd3f6efab0fc60d9b7dp-2), 0x1.1be0b757f4cef022f5d2422b9c78p0, math.floatEpsAt(f128, 0x1.1be0b757f4cef022f5d2422b9c78p0));
|
||||
try testing.expectApproxEqAbs(acosBinary128(-0x1.bf887b8c4e33cbef59993056f3dep-1), 0x1.513270e671db2d840f20b0186c2cp1, math.floatEpsAt(f128, 0x1.513270e671db2d840f20b0186c2cp1));
|
||||
try testing.expectApproxEqAbs(acosBinary128(0x1.0c0f600ab6f9c84c6102942044cep-3), 0x1.70851a509f0e8bfbe780aa8f29f9p0, math.floatEpsAt(f128, 0x1.70851a509f0e8bfbe780aa8f29f9p0));
|
||||
}
|
||||
|
||||
+345
-91
@@ -3,10 +3,14 @@
|
||||
//
|
||||
// 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
|
||||
|
||||
const std = @import("../std.zig");
|
||||
const math = std.math;
|
||||
const expect = std.testing.expect;
|
||||
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.
|
||||
///
|
||||
@@ -16,62 +20,101 @@ const expect = std.testing.expect;
|
||||
pub fn asin(x: anytype) @TypeOf(x) {
|
||||
const T = @TypeOf(x);
|
||||
return switch (T) {
|
||||
f32 => asin32(x),
|
||||
f64 => asin64(x),
|
||||
f16 => asinBinary16(x),
|
||||
f32 => asinBinary32(x),
|
||||
f64 => asinBinary64(x),
|
||||
f80 => asinExtended80(x),
|
||||
f128 => asinBinary128(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;
|
||||
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 asin32(x: f32) f32 {
|
||||
const pio2 = 1.570796326794896558e+00;
|
||||
fn asinBinary32(x: f32) f32 {
|
||||
const pio2: f64 = 1.570796326794896558e+00;
|
||||
|
||||
const hx: u32 = @as(u32, @bitCast(x));
|
||||
const ix: u32 = hx & 0x7FFFFFFF;
|
||||
const hx: u32 = @bitCast(x);
|
||||
const ix = hx & 0x7fff_ffff;
|
||||
|
||||
// |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
|
||||
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 < 0x3F000000) {
|
||||
if (ix < 0x3f00_0000) {
|
||||
// 0x1p-126 <= |x| < 0x1p-12
|
||||
if (ix < 0x39800000 and ix >= 0x00800000) {
|
||||
if (ix < 0x3980_0000 and ix >= 0x0080_0000) {
|
||||
return x;
|
||||
} else {
|
||||
return x + x * r32(x * x);
|
||||
}
|
||||
return x + x * rationalApproxBinary32(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;
|
||||
}
|
||||
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 r64(z: f64) f64 {
|
||||
fn rationalApproxBinary64(z: f64) f64 {
|
||||
const pS0: f64 = 1.66666666666666657415e-01;
|
||||
const pS1: f64 = -3.25565818622400915405e-01;
|
||||
const pS2: f64 = 2.01212532134862925881e-01;
|
||||
@@ -88,96 +131,307 @@ fn r64(z: f64) f64 {
|
||||
return p / q;
|
||||
}
|
||||
|
||||
fn asin64(x: f64) f64 {
|
||||
fn asinBinary64(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;
|
||||
const hx: u32 = @intCast(@as(u64, @bitCast(x)) >> 32);
|
||||
const ix = hx & 0x7fffffff;
|
||||
|
||||
// |x| >= 1 or nan
|
||||
if (ix >= 0x3FF00000) {
|
||||
const lx = @as(u32, @intCast(ux & 0xFFFFFFFF));
|
||||
|
||||
if (ix >= 0x3ff0_0000) {
|
||||
const lx: u32 = @truncate(@as(u64, @bitCast(x)));
|
||||
// asin(1) = +-pi/2 with inexact
|
||||
if ((ix - 0x3FF00000) | lx == 0) {
|
||||
if ((ix - 0x3ff0_0000 | lx) == 0) {
|
||||
return x * pio2_hi + 0x1.0p-120;
|
||||
} else {
|
||||
return math.nan(f64);
|
||||
}
|
||||
return 0.0 / (x - x);
|
||||
}
|
||||
|
||||
// |x| < 0.5
|
||||
if (ix < 0x3FE00000) {
|
||||
if (ix < 0x3fe0_0000) {
|
||||
// if 0x1p-1022 <= |x| < 0x1p-26 avoid raising overflow
|
||||
if (ix < 0x3E500000 and ix >= 0x00100000) {
|
||||
if (ix < 0x3e50_0000 and ix >= 0x0010_0000) {
|
||||
return x;
|
||||
} else {
|
||||
return x + x * r64(x * x);
|
||||
}
|
||||
return x + x * rationalApproxBinary64(x * x);
|
||||
}
|
||||
|
||||
// 1 > |x| >= 0.5
|
||||
const z = (1 - @abs(x)) * 0.5;
|
||||
const z = (1.0 - @abs(x)) * 0.5;
|
||||
const s = @sqrt(z);
|
||||
const r = r64(z);
|
||||
var fx: f64 = undefined;
|
||||
|
||||
const r = rationalApproxBinary64(z);
|
||||
// |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 (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);
|
||||
}
|
||||
|
||||
if (hx >> 31 != 0) {
|
||||
return -fx;
|
||||
} else {
|
||||
return fx;
|
||||
// |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;
|
||||
}
|
||||
|
||||
test asin {
|
||||
try expect(asin(@as(f32, 0.0)) == asin32(0.0));
|
||||
try expect(asin(@as(f64, 0.0)) == asin64(0.0));
|
||||
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;
|
||||
}
|
||||
|
||||
test asin32 {
|
||||
const epsilon = 0.000001;
|
||||
fn asinBinary128(x: f128) f128 {
|
||||
const pio2_hi: f128 = 1.57079632679489661923132169163975140;
|
||||
const pio2_lo: f128 = 4.33590506506189051239852201302167613e-35;
|
||||
|
||||
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));
|
||||
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 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 "asinBinary16.special" {
|
||||
try testing.expectApproxEqAbs(asinBinary16(0x1p+0), 0x1.92p0, math.floatEpsAt(f16, 0x1.92p0));
|
||||
try testing.expectApproxEqAbs(asinBinary16(-0x1p+0), -0x1.92p0, math.floatEpsAt(f16, -0x1.92p0));
|
||||
try testing.expectEqual(asinBinary16(0x0p+0), 0x0p+0);
|
||||
try testing.expectEqual(asinBinary16(-0x0p+0), 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 "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 "asinBinary16" {
|
||||
try testing.expectApproxEqAbs(asinBinary16(-0x1.e4cp-6), -0x1.e4cp-6, math.floatEpsAt(f16, -0x1.e4cp-6));
|
||||
try testing.expectApproxEqAbs(asinBinary16(0x1.d68p-1), 0x1.2a8p0, math.floatEpsAt(f16, 0x1.2a8p0));
|
||||
try testing.expectApproxEqAbs(asinBinary16(-0x1.a4cp-1), -0x1.eep-1, math.floatEpsAt(f16, -0x1.eep-1));
|
||||
try testing.expectApproxEqAbs(asinBinary16(-0x1.0a4p-2), -0x1.0d4p-2, math.floatEpsAt(f16, -0x1.0d4p-2));
|
||||
try testing.expectApproxEqAbs(asinBinary16(0x1.28cp-1), 0x1.3c8p-1, math.floatEpsAt(f16, 0x1.3c8p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary16(0x1.284p-3), 0x1.298p-3, math.floatEpsAt(f16, 0x1.298p-3));
|
||||
try testing.expectApproxEqAbs(asinBinary16(-0x1.574p-1), -0x1.784p-1, math.floatEpsAt(f16, -0x1.784p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary16(-0x1.4ccp-1), -0x1.6a4p-1, math.floatEpsAt(f16, -0x1.6a4p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary16(0x1.a18p-1), 0x1.e84p-1, math.floatEpsAt(f16, 0x1.e84p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary16(0x1.7a8p-2), 0x1.83cp-2, math.floatEpsAt(f16, 0x1.83cp-2));
|
||||
}
|
||||
|
||||
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)));
|
||||
test "asinBinary32.special" {
|
||||
try testing.expectApproxEqAbs(asinBinary32(0x1p+0), 0x1.921fb6p+0, math.floatEpsAt(f32, 0x1.921fb6p+0));
|
||||
try testing.expectApproxEqAbs(asinBinary32(-0x1p+0), -0x1.921fb6p+0, math.floatEpsAt(f32, -0x1.921fb6p+0));
|
||||
try testing.expectEqual(asinBinary32(0x0p+0), 0x0p+0);
|
||||
try testing.expectEqual(asinBinary32(-0x0p+0), 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(asinBinary32(-0x1.4c2906p-4), -0x1.4c868p-4, math.floatEpsAt(f32, -0x1.4c868p-4));
|
||||
try testing.expectApproxEqAbs(asinBinary32(0x1.05fcfap-1), 0x1.130648p-1, math.floatEpsAt(f32, 0x1.130648p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary32(0x1.fab976p-2), 0x1.090abcp-1, math.floatEpsAt(f32, 0x1.090abcp-1));
|
||||
try testing.expectApproxEqAbs(asinBinary32(0x1.8b4b8cp-1), 0x1.c39fa2p-1, math.floatEpsAt(f32, 0x1.c39fa2p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary32(0x1.7117c2p-1), 0x1.9c332p-1, math.floatEpsAt(f32, 0x1.9c332p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary32(0x1.e5e112p-5), 0x1.e62a1cp-5, math.floatEpsAt(f32, 0x1.e62a1cp-5));
|
||||
try testing.expectApproxEqAbs(asinBinary32(-0x1.07673p-2), -0x1.0a65dep-2, math.floatEpsAt(f32, -0x1.0a65dep-2));
|
||||
try testing.expectApproxEqAbs(asinBinary32(-0x1.2108dep-2), -0x1.25046p-2, math.floatEpsAt(f32, -0x1.25046p-2));
|
||||
try testing.expectApproxEqAbs(asinBinary32(-0x1.4e6e6cp-1), -0x1.6c6f0cp-1, math.floatEpsAt(f32, -0x1.6c6f0cp-1));
|
||||
try testing.expectApproxEqAbs(asinBinary32(0x1.22a16ap-1), 0x1.350f7ap-1, math.floatEpsAt(f32, 0x1.350f7ap-1));
|
||||
}
|
||||
|
||||
test "asinBinary64.special" {
|
||||
try testing.expectApproxEqAbs(asinBinary64(0x1p+0), 0x1.921fb54442d18p+0, math.floatEpsAt(f64, 0x1.921fb54442d18p+0));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1p+0), -0x1.921fb54442d18p+0, math.floatEpsAt(f64, -0x1.921fb54442d18p+0));
|
||||
try testing.expectEqual(asinBinary64(0x0p+0), 0x0p+0);
|
||||
try testing.expectEqual(asinBinary64(-0x0p+0), 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(asinBinary64(0x1.e674fba3e40d5p-2), 0x1.fae86c5941692p-2, math.floatEpsAt(f64, 0x1.fae86c5941692p-2));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1.30fd0566fd979p-1), -0x1.46b6ad730c93ap-1, math.floatEpsAt(f64, -0x1.46b6ad730c93ap-1));
|
||||
try testing.expectApproxEqAbs(asinBinary64(0x1.6444a25abfeaap-2), 0x1.6be0be8074eep-2, math.floatEpsAt(f64, 0x1.6be0be8074eep-2));
|
||||
try testing.expectApproxEqAbs(asinBinary64(0x1.40a53228d1a13p-1), 0x1.5a7e98f53f717p-1, math.floatEpsAt(f64, 0x1.5a7e98f53f717p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1.ccc6d64845cfdp-1), -0x1.1ea2602d14e8p0, math.floatEpsAt(f64, -0x1.1ea2602d14e8p0));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1.94bd91b7fc74bp-1), -0x1.d2c2634193158p-1, math.floatEpsAt(f64, -0x1.d2c2634193158p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1.8d741b5797fccp-2), -0x1.982d5f1895d2p-2, math.floatEpsAt(f64, -0x1.982d5f1895d2p-2));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1.3e8e7e15881c5p-3), -0x1.3fdaf7dfdc864p-3, math.floatEpsAt(f64, -0x1.3fdaf7dfdc864p-3));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1.88222d8ab8ca9p-2), -0x1.9269540735b7bp-2, math.floatEpsAt(f64, -0x1.9269540735b7bp-2));
|
||||
try testing.expectApproxEqAbs(asinBinary64(-0x1.41c0e9babcbd2p-2), -0x1.474c4c6625527p-2, math.floatEpsAt(f64, -0x1.474c4c6625527p-2));
|
||||
}
|
||||
|
||||
test "asinExtended80.special" {
|
||||
try testing.expectApproxEqAbs(asinExtended80(0x1p+0), 0x1.921fb54442d1846ap+0, math.floatEpsAt(f80, 0x1.921fb54442d1846ap+0));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1p+0), -0x1.921fb54442d1846ap+0, math.floatEpsAt(f80, -0x1.921fb54442d1846ap+0));
|
||||
try testing.expectEqual(asinExtended80(0x0p+0), 0x0p+0);
|
||||
try testing.expectEqual(asinExtended80(-0x0p+0), 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(asinExtended80(0x1.63cf98bc52ce0da8p-9), 0x1.63cfb560149daa9p-9, math.floatEpsAt(f80, 0x1.63cfb560149daa9p-9));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1.0473756f7ae930dp-1), -0x1.113cbacd8cd1b96cp-1, math.floatEpsAt(f80, -0x1.113cbacd8cd1b96cp-1));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1.2310057e005cc288p-2), -0x1.2721b231d197b064p-2, math.floatEpsAt(f80, -0x1.2721b231d197b064p-2));
|
||||
try testing.expectApproxEqAbs(asinExtended80(0x1.f13b03bd685d96eap-1), 0x1.547c408c5d2b05aap0, math.floatEpsAt(f80, 0x1.547c408c5d2b05aap0));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1.d5c507e3ef84041cp-1), -0x1.296b76bfadbb5cecp0, math.floatEpsAt(f80, -0x1.296b76bfadbb5cecp0));
|
||||
try testing.expectApproxEqAbs(asinExtended80(0x1.8222cbc9147153d8p-1), 0x1.b572da8729a84f2ap-1, math.floatEpsAt(f80, 0x1.b572da8729a84f2ap-1));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1.42c9e6b4a088a246p-11), -0x1.42c9e80ac0524dap-11, math.floatEpsAt(f80, -0x1.42c9e80ac0524dap-11));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1.8f78d49deadb521cp-3), -0x1.920ca86aef6c3028p-3, math.floatEpsAt(f80, -0x1.920ca86aef6c3028p-3));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1.ab98792783515774p-2), -0x1.b91cb4f7204d92fp-2, math.floatEpsAt(f80, -0x1.b91cb4f7204d92fp-2));
|
||||
try testing.expectApproxEqAbs(asinExtended80(-0x1.104fe30cef6800aap-1), -0x1.1f20815fdc4c5304p-1, math.floatEpsAt(f80, -0x1.1f20815fdc4c5304p-1));
|
||||
}
|
||||
|
||||
test "asinBinary128.special" {
|
||||
try testing.expectApproxEqAbs(asinBinary128(0x1p+0), 0x1.921fb54442d18469898cc51701b8p0, math.floatEpsAt(f128, 0x1.921fb54442d18469898cc51701b8p0));
|
||||
try testing.expectApproxEqAbs(asinBinary128(-0x1p+0), -0x1.921fb54442d18469898cc51701b8p0, math.floatEpsAt(f128, -0x1.921fb54442d18469898cc51701b8p0));
|
||||
try testing.expectEqual(asinBinary128(0x0p+0), 0x0p+0);
|
||||
try testing.expectEqual(asinBinary128(-0x0p+0), 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(asinBinary128(0x1.85868ce287ca0196b01c25fec5ffp-3), 0x1.87e9c740d7837f8e8fa667988fbep-3, math.floatEpsAt(f128, 0x1.87e9c740d7837f8e8fa667988fbep-3));
|
||||
try testing.expectApproxEqAbs(asinBinary128(0x1.8718d6d30b4daed08d04ef59f478p-1), 0x1.bd11a474e864213b48e0f005f1f4p-1, math.floatEpsAt(f128, 0x1.bd11a474e864213b48e0f005f1f4p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary128(0x1.11a67640cd7f0ba5d5e362f3abfap-1), 0x1.20b56f8b42649fe72d1f8d68a378p-1, math.floatEpsAt(f128, 0x1.20b56f8b42649fe72d1f8d68a378p-1));
|
||||
try testing.expectApproxEqAbs(asinBinary128(-0x1.bd13bf14a9dce22188e52650daa7p-1), -0x1.0dc3a7ddb9736e5ad699bf338566p0, math.floatEpsAt(f128, -0x1.0dc3a7ddb9736e5ad699bf338566p0));
|
||||
try testing.expectApproxEqAbs(asinBinary128(-0x1.dee0bc217fc462af57c484eefa71p-2), -0x1.f250716038f70fa50a5826c03802p-2, math.floatEpsAt(f128, -0x1.f250716038f70fa50a5826c03802p-2));
|
||||
try testing.expectApproxEqAbs(asinBinary128(-0x1.ea7df9139371c10b9d6fd2bbccd3p-1), -0x1.47a8b4cdd327f90056722feddbabp0, math.floatEpsAt(f128, -0x1.47a8b4cdd327f90056722feddbabp0));
|
||||
try testing.expectApproxEqAbs(asinBinary128(0x1.04aaea6de3b5a616460702f26dfcp-2), 0x1.079178d52be662dec67e2cd7f6e9p-2, math.floatEpsAt(f128, 0x1.079178d52be662dec67e2cd7f6e9p-2));
|
||||
try testing.expectApproxEqAbs(asinBinary128(-0x1.c7ea85e6b61be666435a7d99444cp-1), -0x1.192df5a8d71702cf1e27014887b2p0, math.floatEpsAt(f128, -0x1.192df5a8d71702cf1e27014887b2p0));
|
||||
try testing.expectApproxEqAbs(asinBinary128(-0x1.6e210214e40edf6c8479998189d1p-1), -0x1.97f1092fd94ac0fdfddae2e1222bp-1, math.floatEpsAt(f128, -0x1.97f1092fd94ac0fdfddae2e1222bp-1));
|
||||
try testing.expectApproxEqAbs(asinBinary128(-0x1.95061bf93ed6986a45d20f0e1064p-3), -0x1.97b62bc5ae6512093828828325e1p-3, math.floatEpsAt(f128, -0x1.97b62bc5ae6512093828828325e1p-3));
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user