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Merge branch 'std.math.atan: Add @Vector(?,f32) and @Vector(?,f64) support'
Add SIMD support for atan (f32 and f64), based on the [ARM impl](https://github.com/ARM-software/optimized-routines/blob/master/math/aarch64/advsimd/atanf.c). To reduce branching, more polynomial approximation is used. Reviewed-on: https://codeberg.org/ziglang/zig/pulls/31195
This commit is contained in:
Andrew Kelley
commit
e262a32ad1
1 changed files with 205 additions and 8 deletions
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@ -4,6 +4,12 @@
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// https://git.musl-libc.org/cgit/musl/tree/src/math/atanf.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/atan.c
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// https://git.musl-libc.org/cgit/musl/tree/src/math/atanl.c
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//
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// Ported from ARM-software, which is licensed under the MIT license:
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// https://github.com/ARM-software/optimized-routines/blob/master/LICENSE
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//
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// https://github.com/ARM-software/optimized-routines/blob/master/math/aarch64/advsimd/atanf.c
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// https://github.com/ARM-software/optimized-routines/blob/master/math/aarch64/advsimd/atan.c
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const std = @import("../std.zig");
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const math = std.math;
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@ -17,14 +23,22 @@ const testing = std.testing;
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/// - atan(+-inf) = +-pi/2
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pub fn atan(x: anytype) @TypeOf(x) {
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const T = @TypeOf(x);
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return switch (T) {
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f16 => atanBinary16(x),
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f32 => atanBinary32(x),
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f64 => atanBinary64(x),
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f80 => atanExtended80(x),
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f128 => atanBinary128(x),
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else => @compileError("atan not implemented for " ++ @typeName(T)),
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};
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switch (@typeInfo(T)) {
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.float => |info| switch (info.bits) {
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16 => return atanBinary16(x),
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32 => return atanBinary32(x),
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64 => return atanBinary64(x),
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80 => return atanExtended80(x),
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128 => return atanBinary128(x),
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else => comptime unreachable,
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},
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.vector => |info| switch (info.child) {
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f32 => return atanBinary32Vec(info.len, x),
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f64 => return atanBinary64Vec(info.len, x),
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else => @compileError("unimplemented"),
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},
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else => comptime unreachable,
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}
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}
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fn atanBinary16(x: f16) f16 {
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@ -579,3 +593,186 @@ test "atanBinary128" {
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try testing.expectApproxEqAbs(atanBinary128(0x1.299d54ac7d6afc5154643b601519p1), 0x1.2a24e22d861debfd6f974500567fp0, math.floatEpsAt(f128, 0x1.2a24e22d861debfd6f974500567fp0));
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try testing.expectApproxEqAbs(atanBinary128(-0x1.0264fb9f3d50e4f0f966f0686064p1), -0x1.1c617825f97512b7f38656ab12cdp0, math.floatEpsAt(f128, -0x1.1c617825f97512b7f38656ab12cdp0));
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}
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fn atanBinary32Vec(comptime vec_len: comptime_int, x: @Vector(vec_len, f32)) @TypeOf(x) {
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const sign_mask: @Vector(vec_len, u32) = @splat(0x80000000);
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const neg_one: @Vector(vec_len, f32) = @splat(-1.0);
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const pi_over_2: @Vector(vec_len, u32) = @splat(0x3fc90fdb);
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const zero: @Vector(vec_len, u32) = @splat(0);
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const c0: @Vector(vec_len, f32) = @splat(-0x1.5554dcp-2);
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const c1: @Vector(vec_len, f32) = @splat(0x1.9978ecp-3);
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const c2: @Vector(vec_len, f32) = @splat(-0x1.230a94p-3);
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const c3: @Vector(vec_len, f32) = @splat(0x1.b4debp-4);
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const c4: @Vector(vec_len, f32) = @splat(-0x1.3550dap-4);
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const c5: @Vector(vec_len, f32) = @splat(0x1.61eebp-5);
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const c6: @Vector(vec_len, f32) = @splat(-0x1.0c17d4p-6);
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const c7: @Vector(vec_len, f32) = @splat(0x1.7ea694p-9);
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const ix: @Vector(vec_len, u32) = @bitCast(x);
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const sign = ix & sign_mask;
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const pred = @abs(x) > @abs(neg_one);
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const z = @select(f32, pred, neg_one / x, x);
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const shift: @Vector(vec_len, f32) = @bitCast(@select(u32, pred, pi_over_2 ^ sign, zero));
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const z2 = z * z;
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const z3 = z * z2;
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const z4 = z2 * z2;
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const z8 = z4 * z4;
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const p0_1 = @mulAdd(@Vector(vec_len, f32), z2, c1, c0);
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const p2_3 = @mulAdd(@Vector(vec_len, f32), z2, c3, c2);
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const p4_5 = @mulAdd(@Vector(vec_len, f32), z2, c5, c4);
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const p6_7 = @mulAdd(@Vector(vec_len, f32), z2, c7, c6);
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const p0_3 = @mulAdd(@Vector(vec_len, f32), z4, p2_3, p0_1);
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const p4_7 = @mulAdd(@Vector(vec_len, f32), z4, p6_7, p4_5);
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const p0_7 = @mulAdd(@Vector(vec_len, f32), z8, p4_7, p0_3);
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return @mulAdd(@Vector(vec_len, f32), z3, p0_7, shift + z);
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}
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fn atanBinary64Vec(comptime vec_len: comptime_int, x: @Vector(vec_len, f64)) @TypeOf(x) {
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const sign_mask: @Vector(vec_len, u64) = @splat(0x8000000000000000);
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const neg_one: @Vector(vec_len, f64) = @splat(-1.0);
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const pi_over_2: @Vector(vec_len, u64) = @splat(0x3ff921fb54442d18);
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const zero: @Vector(vec_len, u64) = @splat(0);
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const c0: @Vector(vec_len, f64) = @splat(-0x1.555555555552ap-2);
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const c1: @Vector(vec_len, f64) = @splat(0x1.9999999995aebp-3);
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const c2: @Vector(vec_len, f64) = @splat(-0x1.24924923923f6p-3);
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const c3: @Vector(vec_len, f64) = @splat(0x1.c71c7184288a2p-4);
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const c4: @Vector(vec_len, f64) = @splat(-0x1.745d11fb3d32bp-4);
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const c5: @Vector(vec_len, f64) = @splat(0x1.3b136a18051b9p-4);
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const c6: @Vector(vec_len, f64) = @splat(-0x1.110e6d985f496p-4);
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const c7: @Vector(vec_len, f64) = @splat(0x1.e1bcf7f08801dp-5);
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const c8: @Vector(vec_len, f64) = @splat(-0x1.ae644e28058c3p-5);
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const c9: @Vector(vec_len, f64) = @splat(0x1.82eeb1fed85c6p-5);
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const c10: @Vector(vec_len, f64) = @splat(-0x1.59d7f901566cbp-5);
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const c11: @Vector(vec_len, f64) = @splat(0x1.2c982855ab069p-5);
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const c12: @Vector(vec_len, f64) = @splat(-0x1.eb49592998177p-6);
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const c13: @Vector(vec_len, f64) = @splat(0x1.69d8b396e3d38p-6);
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const c14: @Vector(vec_len, f64) = @splat(-0x1.ca980345c4204p-7);
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const c15: @Vector(vec_len, f64) = @splat(0x1.dc050eafde0b3p-8);
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const c16: @Vector(vec_len, f64) = @splat(-0x1.7ea70755b8eccp-9);
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const c17: @Vector(vec_len, f64) = @splat(0x1.ba3da3de903e8p-11);
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const c18: @Vector(vec_len, f64) = @splat(-0x1.44a4b059b6f67p-13);
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const c19: @Vector(vec_len, f64) = @splat(0x1.c4a45029e5a91p-17);
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const ix: @Vector(vec_len, u64) = @bitCast(x);
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const sign = ix & sign_mask;
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const pred = @abs(x) > @abs(neg_one);
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const shift: @Vector(vec_len, f64) = @bitCast(@select(u64, pred, pi_over_2 ^ sign, zero));
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const z = @select(f64, pred, neg_one / x, x);
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const z2 = z * z;
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const z3 = z * z2;
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const z4 = z2 * z2;
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const z8 = z4 * z4;
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const z16 = z8 * z8;
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const p0_1 = @mulAdd(@Vector(vec_len, f64), z2, c1, c0);
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const p2_3 = @mulAdd(@Vector(vec_len, f64), z2, c3, c2);
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const p0_3 = @mulAdd(@Vector(vec_len, f64), z4, p2_3, p0_1);
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const p4_5 = @mulAdd(@Vector(vec_len, f64), z2, c5, c4);
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const p6_7 = @mulAdd(@Vector(vec_len, f64), z2, c7, c6);
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const p4_7 = @mulAdd(@Vector(vec_len, f64), z4, p6_7, p4_5);
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const p0_7 = @mulAdd(@Vector(vec_len, f64), z8, p4_7, p0_3);
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const p8_9 = @mulAdd(@Vector(vec_len, f64), z2, c9, c8);
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const p10_11 = @mulAdd(@Vector(vec_len, f64), z2, c11, c10);
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const p8_11 = @mulAdd(@Vector(vec_len, f64), z4, p10_11, p8_9);
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const p12_13 = @mulAdd(@Vector(vec_len, f64), z2, c13, c12);
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const p14_15 = @mulAdd(@Vector(vec_len, f64), z2, c15, c14);
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const p12_15 = @mulAdd(@Vector(vec_len, f64), z4, p14_15, p12_13);
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const p16_17 = @mulAdd(@Vector(vec_len, f64), z2, c17, c16);
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const p18_19 = @mulAdd(@Vector(vec_len, f64), z2, c19, c18);
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const p16_19 = @mulAdd(@Vector(vec_len, f64), z4, p18_19, p16_17);
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const p8_15 = @mulAdd(@Vector(vec_len, f64), z8, p12_15, p8_11);
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const p8_19 = @mulAdd(@Vector(vec_len, f64), z16, p16_19, p8_15);
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const p0_19 = @mulAdd(@Vector(vec_len, f64), p8_19, z16, p0_7);
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return @mulAdd(@Vector(vec_len, f64), z3, p0_19, shift + z);
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}
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test "atanBinary32Vec.special" {
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const input: @Vector(7, f32) = .{
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0x0p+0,
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-0x0p+0,
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0x1p+0,
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-0x1p+0,
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math.inf(f32),
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-math.inf(f32),
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math.nan(f32),
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};
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const output = atanBinary32Vec(7, input);
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try testing.expectEqual(output[0], 0x0p+0);
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try testing.expectEqual(output[1], -0x0p+0);
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try testing.expectApproxEqAbs(output[2], 0x1.921fb6p-1, math.floatEpsAt(f32, 0x1.921fb6p-1));
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try testing.expectApproxEqAbs(output[3], -0x1.921fb6p-1, math.floatEpsAt(f32, -0x1.921fb6p-1));
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try testing.expectApproxEqAbs(output[4], 0x1.921fb6p+0, math.floatEpsAt(f32, 0x1.921fb6p+0));
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try testing.expectApproxEqAbs(output[5], -0x1.921fb6p+0, math.floatEpsAt(f32, -0x1.921fb6p+0));
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try testing.expect(math.isNan(output[6]));
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}
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test "atanBinary32Vec" {
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const input: @Vector(10, f32) = .{
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-0x1.8629dp-2,
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-0x1.59d42ep1,
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-0x1.d2dbe2p0,
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-0x1.5f314ep-1,
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0x1.5869bp1,
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-0x1.b13a06p-2,
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0x1.3cb0f2p1,
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-0x1.0ed746p-2,
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0x1.299d54p1,
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-0x1.0264fcp1,
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};
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const output = atanBinary32Vec(10, input);
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try testing.expectApproxEqAbs(output[0], -0x1.74c62p-2, math.floatEpsAt(f32, -0x1.74c62p-2));
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try testing.expectApproxEqAbs(output[1], -0x1.375fd8p0, math.floatEpsAt(f32, -0x1.375fd8p0));
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try testing.expectApproxEqAbs(output[2], -0x1.11b8aep0, math.floatEpsAt(f32, -0x1.11b8aep0));
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try testing.expectApproxEqAbs(output[3], -0x1.33d28cp-1, math.floatEpsAt(f32, -0x1.33d28cp-1));
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try testing.expectApproxEqAbs(output[4], 0x1.37082ep0, math.floatEpsAt(f32, 0x1.37082ep0));
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try testing.expectApproxEqAbs(output[5], -0x1.99d7cap-2, math.floatEpsAt(f32, -0x1.99d7cap-2));
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try testing.expectApproxEqAbs(output[6], 0x1.2fcb12p0, math.floatEpsAt(f32, 0x1.2fcb12p0));
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try testing.expectApproxEqAbs(output[7], -0x1.08c71ap-2, math.floatEpsAt(f32, -0x1.08c71ap-2));
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try testing.expectApproxEqAbs(output[8], 0x1.2a24e2p0, math.floatEpsAt(f32, 0x1.2a24e2p0));
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try testing.expectApproxEqAbs(output[9], -0x1.1c6178p0, math.floatEpsAt(f32, -0x1.1c6178p0));
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}
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test "atanBinary64Vec.special" {
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const input: @Vector(7, f64) = .{
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0x0p+0,
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-0x0p+0,
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0x1p+0,
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-0x1p+0,
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math.inf(f64),
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-math.inf(f64),
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math.nan(f64),
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};
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const output = atanBinary64Vec(7, input);
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try testing.expectEqual(output[0], 0x0p+0);
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try testing.expectEqual(output[1], -0x0p+0);
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try testing.expectApproxEqAbs(output[2], 0x1.921fb54442d18p-1, math.floatEpsAt(f64, 0x1.921fb54442d18p-1));
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try testing.expectApproxEqAbs(output[3], -0x1.921fb54442d18p-1, math.floatEpsAt(f64, -0x1.921fb54442d18p-1));
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try testing.expectApproxEqAbs(output[4], 0x1.921fb54442d18p+0, math.floatEpsAt(f64, 0x1.921fb54442d18p+0));
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try testing.expectApproxEqAbs(output[5], -0x1.921fb54442d18p+0, math.floatEpsAt(f64, -0x1.921fb54442d18p+0));
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try testing.expect(math.isNan(output[6]));
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}
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test "atanBinary64Vec" {
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const input: @Vector(10, f64) = .{
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-0x1.8629d0244cdccp-2,
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-0x1.59d42d4659937p1,
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-0x1.d2dbe23d04f06p0,
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-0x1.5f314e72398e8p-1,
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0x1.5869af37b7d08p1,
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-0x1.b13a05a662618p-2,
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0x1.3cb0f12f39d8ap1,
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-0x1.0ed746b39cbb7p-2,
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0x1.299d54ac7d6bp1,
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-0x1.0264fb9f3d50ep1,
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};
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const output = atanBinary64Vec(10, input);
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try testing.expectApproxEqAbs(output[0], -0x1.74c61f4377016p-2, math.floatEpsAt(f64, -0x1.74c61f4377016p-2));
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try testing.expectApproxEqAbs(output[1], -0x1.375fd7987cc2p0, math.floatEpsAt(f64, -0x1.375fd7987cc2p0));
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try testing.expectApproxEqAbs(output[2], -0x1.11b8adeba5616p0, math.floatEpsAt(f64, -0x1.11b8adeba5616p0));
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try testing.expectApproxEqAbs(output[3], -0x1.33d28ca762539p-1, math.floatEpsAt(f64, -0x1.33d28ca762539p-1));
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try testing.expectApproxEqAbs(output[4], 0x1.37082ce2dd03p0, math.floatEpsAt(f64, 0x1.37082ce2dd03p0));
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try testing.expectApproxEqAbs(output[5], -0x1.99d7cac66dd44p-2, math.floatEpsAt(f64, -0x1.99d7cac66dd44p-2));
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try testing.expectApproxEqAbs(output[6], 0x1.2fcb120468e8ep0, math.floatEpsAt(f64, 0x1.2fcb120468e8ep0));
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try testing.expectApproxEqAbs(output[7], -0x1.08c71aa0e509p-2, math.floatEpsAt(f64, -0x1.08c71aa0e509p-2));
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try testing.expectApproxEqAbs(output[8], 0x1.2a24e22d861dfp0, math.floatEpsAt(f64, 0x1.2a24e22d861dfp0));
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try testing.expectApproxEqAbs(output[9], -0x1.1c617825f9751p0, math.floatEpsAt(f64, -0x1.1c617825f9751p0));
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}
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