//! 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/log2f.c //! https://git.musl-libc.org/cgit/musl/tree/src/math/log2.c const std = @import("std"); const builtin = @import("builtin"); const math = std.math; const expect = std.testing.expect; const expectEqual = std.testing.expectEqual; const maxInt = std.math.maxInt; const arch = builtin.cpu.arch; const common = @import("common.zig"); pub const panic = common.panic; comptime { @export(&__log2h, .{ .name = "__log2h", .linkage = common.linkage, .visibility = common.visibility }); @export(&log2f, .{ .name = "log2f", .linkage = common.linkage, .visibility = common.visibility }); @export(&log2, .{ .name = "log2", .linkage = common.linkage, .visibility = common.visibility }); @export(&__log2x, .{ .name = "__log2x", .linkage = common.linkage, .visibility = common.visibility }); if (common.want_ppc_abi) { @export(&log2q, .{ .name = "log2f128", .linkage = common.linkage, .visibility = common.visibility }); } @export(&log2q, .{ .name = "log2q", .linkage = common.linkage, .visibility = common.visibility }); @export(&log2l, .{ .name = "log2l", .linkage = common.linkage, .visibility = common.visibility }); } pub fn __log2h(a: f16) callconv(.c) f16 { // TODO: more efficient implementation return @floatCast(log2f(a)); } pub fn log2f(x_: f32) callconv(.c) f32 { const ivln2hi: f32 = 1.4428710938e+00; const ivln2lo: f32 = -1.7605285393e-04; const Lg1: f32 = 0xaaaaaa.0p-24; const Lg2: f32 = 0xccce13.0p-25; const Lg3: f32 = 0x91e9ee.0p-25; const Lg4: f32 = 0xf89e26.0p-26; var x = x_; var u: u32 = @bitCast(x); var ix = u; var k: i32 = 0; // x < 2^(-126) if (ix < 0x00800000 or ix >> 31 != 0) { // log(+-0) = -inf if (ix << 1 == 0) { return -math.inf(f32); } // log(-#) = nan if (ix >> 31 != 0) { return math.nan(f32); } k -= 25; x *= 0x1.0p25; ix = @bitCast(x); } else if (ix >= 0x7F800000) { return x; } else if (ix == 0x3F800000) { return 0; } // x into [sqrt(2) / 2, sqrt(2)] ix += 0x3F800000 - 0x3F3504F3; k += @as(i32, @intCast(ix >> 23)) - 0x7F; ix = (ix & 0x007FFFFF) + 0x3F3504F3; x = @bitCast(ix); const f = x - 1.0; const s = f / (2.0 + f); const z = s * s; const w = z * z; const t1 = w * (Lg2 + w * Lg4); const t2 = z * (Lg1 + w * Lg3); const R = t2 + t1; const hfsq = 0.5 * f * f; var hi = f - hfsq; u = @bitCast(hi); u &= 0xFFFFF000; hi = @bitCast(u); const lo = f - hi - hfsq + s * (hfsq + R); return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + @as(f32, @floatFromInt(k)); } pub fn log2(x_: f64) callconv(.c) f64 { const ivln2hi: f64 = 1.44269504072144627571e+00; const ivln2lo: f64 = 1.67517131648865118353e-10; const Lg1: f64 = 6.666666666666735130e-01; const Lg2: f64 = 3.999999999940941908e-01; const Lg3: f64 = 2.857142874366239149e-01; const Lg4: f64 = 2.222219843214978396e-01; const Lg5: f64 = 1.818357216161805012e-01; const Lg6: f64 = 1.531383769920937332e-01; const Lg7: f64 = 1.479819860511658591e-01; var x = x_; var ix: u64 = @bitCast(x); var hx: u32 = @intCast(ix >> 32); var k: i32 = 0; if (hx < 0x00100000 or hx >> 31 != 0) { // log(+-0) = -inf if (ix << 1 == 0) { return -math.inf(f64); } // log(-#) = nan if (hx >> 31 != 0) { return math.nan(f64); } // subnormal, scale x k -= 54; x *= 0x1.0p54; hx = @intCast(@as(u64, @bitCast(x)) >> 32); } else if (hx >= 0x7FF00000) { return x; } else if (hx == 0x3FF00000 and ix << 32 == 0) { return 0; } // x into [sqrt(2) / 2, sqrt(2)] hx += 0x3FF00000 - 0x3FE6A09E; k += @as(i32, @intCast(hx >> 20)) - 0x3FF; hx = (hx & 0x000FFFFF) + 0x3FE6A09E; ix = (@as(u64, hx) << 32) | (ix & 0xFFFFFFFF); x = @bitCast(ix); const f = x - 1.0; const hfsq = 0.5 * f * f; const s = f / (2.0 + f); const z = s * s; const w = z * z; const t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); const t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); const R = t2 + t1; // hi + lo = f - hfsq + s * (hfsq + R) ~ log(1 + f) var hi = f - hfsq; var hii = @as(u64, @bitCast(hi)); hii &= @as(u64, maxInt(u64)) << 32; hi = @bitCast(hii); const lo = f - hi - hfsq + s * (hfsq + R); var val_hi = hi * ivln2hi; var val_lo = (lo + hi) * ivln2lo + lo * ivln2hi; // spadd(val_hi, val_lo, y) const y: f64 = @floatFromInt(k); const ww = y + val_hi; val_lo += (y - ww) + val_hi; val_hi = ww; return val_lo + val_hi; } pub fn __log2x(a: f80) callconv(.c) f80 { // TODO: more efficient implementation return @floatCast(log2q(a)); } pub fn log2q(a: f128) callconv(.c) f128 { // TODO: more correct implementation return log2(@floatCast(a)); } pub fn log2l(x: c_longdouble) callconv(.c) c_longdouble { switch (@typeInfo(c_longdouble).float.bits) { 16 => return __log2h(x), 32 => return log2f(x), 64 => return log2(x), 80 => return __log2x(x), 128 => return log2q(x), else => @compileError("unreachable"), } } test "log2f() special" { try expectEqual(log2f(0.0), -math.inf(f32)); try expectEqual(log2f(-0.0), -math.inf(f32)); try expect(math.isPositiveZero(log2f(1.0))); try expectEqual(log2f(2.0), 1.0); try expectEqual(log2f(math.inf(f32)), math.inf(f32)); try expect(math.isNan(log2f(-1.0))); try expect(math.isNan(log2f(-math.inf(f32)))); try expect(math.isNan(log2f(math.nan(f32)))); try expect(math.isNan(log2f(math.snan(f32)))); } test "log2f() sanity" { try expect(math.isNan(log2f(-0x1.0223a0p+3))); try expectEqual(log2f(0x1.161868p+2), 0x1.0f49acp+1); try expect(math.isNan(log2f(-0x1.0c34b4p+3))); try expect(math.isNan(log2f(-0x1.a206f0p+2))); try expectEqual(log2f(0x1.288bbcp+3), 0x1.9b2676p+1); try expectEqual(log2f(0x1.52efd0p-1), -0x1.30b494p-1); // Disagrees with GCC in last bit try expect(math.isNan(log2f(-0x1.a05cc8p-2))); try expectEqual(log2f(0x1.1f9efap-1), -0x1.a9f89ap-1); try expectEqual(log2f(0x1.8c5db0p-1), -0x1.7a2c96p-2); try expect(math.isNan(log2f(-0x1.5b86eap-1))); } test "log2f() boundary" { try expectEqual(log2f(0x1.fffffep+127), 0x1p+7); // Max input value try expectEqual(log2f(0x1p-149), -0x1.2ap+7); // Min positive input value try expect(math.isNan(log2f(-0x1p-149))); // Min negative input value try expectEqual(log2f(0x1.000002p+0), 0x1.715474p-23); // Last value before result reaches +0 try expectEqual(log2f(0x1.fffffep-1), -0x1.715478p-24); // Last value before result reaches -0 try expectEqual(log2f(0x1p-126), -0x1.f8p+6); // First subnormal try expect(math.isNan(log2f(-0x1p-126))); // First negative subnormal } test "log2() special" { try expectEqual(log2(0.0), -math.inf(f64)); try expectEqual(log2(-0.0), -math.inf(f64)); try expect(math.isPositiveZero(log2(1.0))); try expectEqual(log2(2.0), 1.0); try expectEqual(log2(math.inf(f64)), math.inf(f64)); try expect(math.isNan(log2(-1.0))); try expect(math.isNan(log2(-math.inf(f64)))); try expect(math.isNan(log2(math.nan(f64)))); try expect(math.isNan(log2(math.snan(f64)))); } test "log2() sanity" { try expect(math.isNan(log2(-0x1.02239f3c6a8f1p+3))); try expectEqual(log2(0x1.161868e18bc67p+2), 0x1.0f49ac3838580p+1); try expect(math.isNan(log2(-0x1.0c34b3e01e6e7p+3))); try expect(math.isNan(log2(-0x1.a206f0a19dcc4p+2))); try expectEqual(log2(0x1.288bbb0d6a1e6p+3), 0x1.9b26760c2a57ep+1); try expectEqual(log2(0x1.52efd0cd80497p-1), -0x1.30b490ef684c7p-1); try expect(math.isNan(log2(-0x1.a05cc754481d1p-2))); try expectEqual(log2(0x1.1f9ef934745cbp-1), -0x1.a9f89b5f5acb8p-1); try expectEqual(log2(0x1.8c5db097f7442p-1), -0x1.7a2c947173f06p-2); try expect(math.isNan(log2(-0x1.5b86ea8118a0ep-1))); } test "log2() boundary" { try expectEqual(log2(0x1.fffffffffffffp+1023), 0x1p+10); // Max input value try expectEqual(log2(0x1p-1074), -0x1.0c8p+10); // Min positive input value try expect(math.isNan(log2(-0x1p-1074))); // Min negative input value try expectEqual(log2(0x1.0000000000001p+0), 0x1.71547652b82fdp-52); // Last value before result reaches +0 try expectEqual(log2(0x1.fffffffffffffp-1), -0x1.71547652b82fep-53); // Last value before result reaches -0 try expectEqual(log2(0x1p-1022), -0x1.ffp+9); // First subnormal try expect(math.isNan(log2(-0x1p-1022))); // First negative subnormal }