compiler-rt: math functions reorg

 * unify the logic for exporting math functions from compiler-rt,
   with the appropriate suffixes and prefixes.
   - add all missing f128 and f80 exports. Functions with missing
     implementations call other functions and have TODO comments.
   - also add f16 functions
 * move math functions from freestanding libc to compiler-rt (#7265)
 * enable all the f128 and f80 code in the stage2 compiler and behavior
   tests (#11161).
 * update std lib to use builtins rather than `std.math`.

1 files changed, 5 insertions, 179 deletions

diff --git a/lib/std/math/log2.zig b/lib/std/math/log2.zig
index 556c16f5cf..c83b170208 100644
--- a/lib/std/math/log2.zig
+++ b/lib/std/math/log2.zig
@@ -1,13 +1,6 @@
-// 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.zig");
 const math = std.math;
 const expect = std.testing.expect;
-const maxInt = std.math.maxInt;
 
 /// Returns the base-2 logarithm of x.
 ///
@@ -20,15 +13,9 @@ pub fn log2(x: anytype) @TypeOf(x) {
     const T = @TypeOf(x);
     switch (@typeInfo(T)) {
         .ComptimeFloat => {
-            return @as(comptime_float, log2_64(x));
-        },
-        .Float => {
-            return switch (T) {
-                f32 => log2_32(x),
-                f64 => log2_64(x),
-                else => @compileError("log2 not implemented for " ++ @typeName(T)),
-            };
+            return @as(comptime_float, @log2(x));
         },
+        .Float => return @log2(x),
         .ComptimeInt => comptime {
             var result = 0;
             var x_shifted = x;
@@ -46,168 +33,7 @@ pub fn log2(x: anytype) @TypeOf(x) {
     }
 }
 
-pub fn log2_32(x_: f32) 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 = @bitCast(u32, 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(u32, x);
-    } else if (ix >= 0x7F800000) {
-        return x;
-    } else if (ix == 0x3F800000) {
-        return 0;
-    }
-
-    // x into [sqrt(2) / 2, sqrt(2)]
-    ix += 0x3F800000 - 0x3F3504F3;
-    k += @intCast(i32, ix >> 23) - 0x7F;
-    ix = (ix & 0x007FFFFF) + 0x3F3504F3;
-    x = @bitCast(f32, 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(u32, hi);
-    u &= 0xFFFFF000;
-    hi = @bitCast(f32, u);
-    const lo = f - hi - hfsq + s * (hfsq + R);
-    return (lo + hi) * ivln2lo + lo * ivln2hi + hi * ivln2hi + @intToFloat(f32, k);
-}
-
-pub fn log2_64(x_: f64) 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 = @bitCast(u64, x);
-    var hx = @intCast(u32, 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(u32, @bitCast(u64, 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 += @intCast(i32, hx >> 20) - 0x3FF;
-    hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
-    ix = (@as(u64, hx) << 32) | (ix & 0xFFFFFFFF);
-    x = @bitCast(f64, 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 = @bitCast(u64, hi);
-    hii &= @as(u64, maxInt(u64)) << 32;
-    hi = @bitCast(f64, 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 = @intToFloat(f64, k);
-    const ww = y + val_hi;
-    val_lo += (y - ww) + val_hi;
-    val_hi = ww;
-
-    return val_lo + val_hi;
-}
-
-test "math.log2" {
-    try expect(log2(@as(f32, 0.2)) == log2_32(0.2));
-    try expect(log2(@as(f64, 0.2)) == log2_64(0.2));
-}
-
-test "math.log2_32" {
-    const epsilon = 0.000001;
-
-    try expect(math.approxEqAbs(f32, log2_32(0.2), -2.321928, epsilon));
-    try expect(math.approxEqAbs(f32, log2_32(0.8923), -0.164399, epsilon));
-    try expect(math.approxEqAbs(f32, log2_32(1.5), 0.584962, epsilon));
-    try expect(math.approxEqAbs(f32, log2_32(37.45), 5.226894, epsilon));
-    try expect(math.approxEqAbs(f32, log2_32(123123.234375), 16.909744, epsilon));
-}
-
-test "math.log2_64" {
-    const epsilon = 0.000001;
-
-    try expect(math.approxEqAbs(f64, log2_64(0.2), -2.321928, epsilon));
-    try expect(math.approxEqAbs(f64, log2_64(0.8923), -0.164399, epsilon));
-    try expect(math.approxEqAbs(f64, log2_64(1.5), 0.584962, epsilon));
-    try expect(math.approxEqAbs(f64, log2_64(37.45), 5.226894, epsilon));
-    try expect(math.approxEqAbs(f64, log2_64(123123.234375), 16.909744, epsilon));
-}
-
-test "math.log2_32.special" {
-    try expect(math.isPositiveInf(log2_32(math.inf(f32))));
-    try expect(math.isNegativeInf(log2_32(0.0)));
-    try expect(math.isNan(log2_32(-1.0)));
-    try expect(math.isNan(log2_32(math.nan(f32))));
-}
-
-test "math.log2_64.special" {
-    try expect(math.isPositiveInf(log2_64(math.inf(f64))));
-    try expect(math.isNegativeInf(log2_64(0.0)));
-    try expect(math.isNan(log2_64(-1.0)));
-    try expect(math.isNan(log2_64(math.nan(f64))));
+test "log2" {
+    try expect(log2(@as(f32, 0.2)) == @log2(0.2));
+    try expect(log2(@as(f64, 0.2)) == @log2(0.2));
 }