From a999fc9059cf4daad462294a08874cc1c2d402af Mon Sep 17 00:00:00 2001
From: Christophe Delage <christ@ophe.net>
Date: Mon, 13 Apr 2026 15:17:29 +0200
Subject: [PATCH] Add @exp(f128) and @exp2(f128)

---
 lib/compiler_rt/exp.zig      |   5 +-
 lib/compiler_rt/exp2.zig     |   5 +-
 lib/compiler_rt/exp_f128.zig | 377 +++++++++++++++++++++++++++++++++++
 3 files changed, 379 insertions(+), 8 deletions(-)
 create mode 100644 lib/compiler_rt/exp_f128.zig

diff --git a/lib/compiler_rt/exp.zig b/lib/compiler_rt/exp.zig
index c5a980ac72..3b0e593af0 100644
--- a/lib/compiler_rt/exp.zig
+++ b/lib/compiler_rt/exp.zig
@@ -194,10 +194,7 @@ pub fn __expx(a: f80) callconv(.c) f80 {
     return @floatCast(expq(a));
 }
 
-pub fn expq(a: f128) callconv(.c) f128 {
-    // TODO: more correct implementation
-    return exp(@floatCast(a));
-}
+const expq = @import("exp_f128.zig").exp;
 
 pub fn expl(x: c_longdouble) callconv(.c) c_longdouble {
     switch (@typeInfo(c_longdouble).float.bits) {
diff --git a/lib/compiler_rt/exp2.zig b/lib/compiler_rt/exp2.zig
index 4e41db2f2d..94f19bef2c 100644
--- a/lib/compiler_rt/exp2.zig
+++ b/lib/compiler_rt/exp2.zig
@@ -161,10 +161,7 @@ pub fn __exp2x(x: f80) callconv(.c) f80 {
     return @floatCast(exp2q(x));
 }
 
-pub fn exp2q(x: f128) callconv(.c) f128 {
-    // TODO: more correct implementation
-    return exp2(@floatCast(x));
-}
+pub const exp2q = @import("exp_f128.zig").exp2;
 
 pub fn exp2l(x: c_longdouble) callconv(.c) c_longdouble {
     switch (@typeInfo(c_longdouble).float.bits) {
diff --git a/lib/compiler_rt/exp_f128.zig b/lib/compiler_rt/exp_f128.zig
new file mode 100644
index 0000000000..ac09308ff3
--- /dev/null
+++ b/lib/compiler_rt/exp_f128.zig
@@ -0,0 +1,377 @@
+/// Implementation of f128 exp and exp2 based on:
+///
+/// * "Table-Driven Implementation of the Exponential Function in IEEE Floating-Point Arithmetic"
+///   ACM Transactions on Mathematical Software (TOMS), Volume 15, Issue 2 pp. 144-157
+///
+/// and
+///
+/// * "Table-driven implementation of the Expm1 function in IEEE floating-point arithmetic"
+///   ACM Transactions on Mathematical Software (TOMS), Volume 18, Issue 2 pp. 211-222
+///
+/// Both by Ping Tak Peter Tang.
+///
+/// Adapted by Christophe Delage to work with 128 bit floats and with base 2 and 10.
+///
+/// Accuracy tested on 100 million uniformly distributed random values:
+///
+/// exp:
+///     when result is normal:    <= 0.5 ulp: 99.83%, worst case: 0.512
+///     when result is subnormal: <= 0.5 ulp: 99.80%, worst case: 0.628
+/// exp2:
+///     when result is normal:    <= 0.5 ulp: 99.82%, worst case: 0.514
+///     when result is subnormal: <= 0.5 ulp: 99.56%, worst case: 0.752
+///
+const exp_f128 = @This();
+
+const std = @import("std");
+const math = std.math;
+
+pub fn exp(x: f128) callconv(.c) f128 {
+    if (!math.isFinite(x)) {
+        if (math.isNan(x)) {
+            if (math.isSignalNan(x)) math.raiseInvalid();
+            return math.nan(f128);
+        }
+        return if (math.signbit(x)) 0 else x;
+    }
+    if (@abs(x) > 12000) {
+        if (math.signbit(x)) {
+            math.raiseUnderflow();
+            return 0;
+        } else {
+            math.raiseOverflow();
+            return math.inf(f128);
+        }
+    }
+
+    if (@abs(x) < 0x1p-114)
+        return 1 + x;
+
+    return proc1(cfg_e, x);
+}
+
+const cfg_e: Config = .{
+    .inv_log_size = 92.33248261689365807103517958412109,
+    .log_size_hi = 1.0830424696249145459644251897780967e-2,
+    .neg_log_size_lo = -3.0422579568449217993561868333332404e-33,
+    .poly = expPoly,
+    .finalize = expFinalize,
+};
+
+/// Approximates e^(r_hi + r_lo) - 1.
+fn expPoly(r_hi: f128, r_lo: f128) f128 {
+    const a2: f128 = 0.5000000000000000000000000000000001;
+    const a3: f128 = 0.16666666666666666666666666666666673;
+    const a4: f128 = 4.16666666666666666666666665159063e-2;
+    const a5: f128 = 8.333333333333333333333333293907277e-3;
+    const a6: f128 = 1.3888888888888888889300177029864553e-3;
+    const a7: f128 = 1.984126984126984127049928848046117e-4;
+    const a8: f64 = 2.4801587301583374475925191558926944e-5;
+    const a9: f64 = 2.7557319223981316410138550193306495e-6;
+    const a10: f64 = 2.75573345290144319034653394989056e-7;
+    const a11: f64 = 2.5052122512857680160207187885276378e-8;
+
+    const r = r_hi + r_lo;
+    const s: f64 = @floatCast(r);
+    const rr = r * r;
+    const ss = s * s;
+
+    // Do the upper degree computation in f64 and try to get better ILP
+    // by deviating from Horner's method. This does not measurably hurt
+    // accuracy.
+    const a10_11 = a10 + s * a11;
+    const a8_9 = a8 + s * a9;
+    const a8_11 = a8_9 + ss * a10_11;
+    const a6_7 = a6 + r * a7;
+    const a4_5 = a4 + r * a5;
+    const a2_3 = a2 + r * a3;
+    const a2_11 = a2_3 + rr * (a4_5 + rr * (a6_7 + rr * a8_11));
+
+    return r_hi + (r_lo + rr * a2_11);
+}
+
+/// Computes 2^x
+pub fn exp2(x: f128) callconv(.c) f128 {
+    if (!math.isFinite(x)) {
+        if (math.isNan(x)) {
+            if (math.isSignalNan(x)) math.raiseInvalid();
+            return math.nan(f128);
+        }
+        return if (math.signbit(x)) 0 else x;
+    }
+    if (@abs(x) > 17000) {
+        if (math.signbit(x)) {
+            math.raiseUnderflow();
+            return 0;
+        } else {
+            math.raiseOverflow();
+            return math.inf(f128);
+        }
+    }
+    if (@abs(x) < 0x1p-114 * math.log2e)
+        return 1 + x;
+
+    return proc1(cfg_2, x);
+}
+
+/// Compute a^`x` or a^`x` - 1, depending on `cfg`.
+fn proc1(comptime cfg: Config, x: f128) f128 {
+    // Argument reduction: x = r * 2^(j / size + m)
+    // with r in [-log_a(2) / 2 / size, log_a(2) / 2 / size].
+    //
+    // r computed as r_hi + r_lo to simulate higher precision.
+    const n = @round(x * cfg.inv_log_size);
+    const ni: i32 = @intFromFloat(n);
+    const n2 = @mod(ni, size);
+    const n1 = ni - n2;
+    const m = @divExact(n1, size);
+    const j: usize = @intCast(n2);
+
+    const r_hi = x - n * cfg.log_size_hi;
+    const r_lo = n * cfg.neg_log_size_lo;
+
+    const pr = cfg.poly(r_hi, r_lo);
+
+    return cfg.finalize(pr, j, m);
+}
+
+const cfg_2: Config = .{
+    .inv_log_size = 64,
+    .log_size_hi = 1.5625e-2,
+    .neg_log_size_lo = 0,
+    .poly = exp2Poly,
+    .finalize = expFinalize,
+};
+
+/// Approximates 2^(r_hi + r_lo) - 1.
+fn exp2Poly(r_hi: f128, r_lo: f128) f128 {
+    const a1: f128 = 0.6931471805599453094172321214581766;
+    const a2: f128 = 0.24022650695910071233355126316333273;
+    const a3: f128 = 5.5504108664821579953142263768621824e-2;
+    const a4: f128 = 9.618129107628477161979071497097137e-3;
+    const a5: f128 = 1.3333558146428443423412221872998745e-3;
+    const a6: f128 = 1.5403530393381609955139554247429082e-4;
+    const a7: f128 = 1.5252733804059840280740292411812167e-5;
+    const a8: f64 = 1.321548679014167884759296382063556e-6;
+    const a9: f64 = 1.0178086009237659848870888288504849e-7;
+    const a10: f64 = 7.0549159308426003613013130647805315e-9;
+    const a11: f64 = 4.445540987582123304209680731453203e-10;
+
+    const r = r_hi + r_lo;
+    const s: f64 = @floatCast(r);
+    const rr = r * r;
+    const ss = s * s;
+
+    // Do the upper degree computation in f64 and try to get better ILP
+    // by deviating from Horner's method. This does not measurably hurt
+    // accuracy.
+    const a10_11 = a10 + s * a11;
+    const a8_9 = a8 + s * a9;
+    const a8_11 = a8_9 + ss * a10_11;
+    const a6_7 = a6 + r * a7;
+    const a4_5 = a4 + r * a5;
+    const a2_3 = a2 + r * a3;
+    const a2_11 = a2_3 + rr * (a4_5 + rr * (a6_7 + rr * a8_11));
+
+    return r * (a1 + r * a2_11);
+}
+
+/// Configuration for computing a^x, a in {e, 2, 10}, or e^x - 1.
+const Config = struct {
+    /// size / log(a)
+    inv_log_size: f128,
+
+    // High bits of log(a) / size, with the 12 last bits set to 0
+    log_size_hi: f128,
+    // Low bits of log(a) / size, negated
+    neg_log_size_lo: f128,
+
+    /// Approximates a^(r_hi + r_lo) - 1.
+    poly: fn (f128, f128) f128,
+
+    /// Compute the final value, a^x or e^x - 1.
+    finalize: fn (pr: f128, j: usize, m: i32) f128,
+};
+
+/// computes (1 + pr) * 2^(j / 32) * 2^m.
+fn expFinalize(pr: f128, j: usize, m: i32) f128 {
+    const sj_hi = exp2_tab[j].hi;
+    const sj_lo = exp2_tab[j].lo;
+    const sj = sj_hi + sj_lo;
+
+    const x = sj_hi + (sj_lo + sj * pr);
+
+    return math.ldexp(x, m);
+}
+
+const expect = std.testing.expect;
+const expectEqual = std.testing.expectEqual;
+
+test "expq() special" {
+    try expectEqual(exp(0.0), 1.0);
+    try expectEqual(exp(-0.0), 1.0);
+    try expectEqual(exp(1.0), math.e);
+    try expectEqual(exp(math.ln2), 2.0);
+    try expect(math.isPositiveInf(exp(math.inf(f128))));
+    try expect(math.isPositiveZero(exp(-math.inf(f128))));
+    try expect(math.isNan(exp(math.nan(f128))));
+    try expect(math.isNan(exp(math.snan(f128))));
+}
+
+test "expq() sanity" {
+    try expectEqual(exp(0x1.161ba065182111ea1cf73db026b2p12), 0x1.83a48fa990038d5b6aebb7cac716p6419);
+    try expectEqual(exp(-0x1.49ce1b7b0e51027f6db3fe83bff7p9), 0x1.4dfac2418bdadddd6cf1fa1fefddp-952);
+    try expectEqual(exp(0x1.35395ecd9c471cb5a122e54421ap8), 0x1.1572fcd2d80a52183b1bc955dcb7p446);
+    try expectEqual(exp(0x1.2dfaba39016894e707847c6440b4p13), 0x1.314a408dab5852acfb4370713cdbp13941);
+    try expectEqual(exp(0x1.101337475539dd36e833c7d40d91p11), 0x1.2029e18fbabc334f851f14221089p3140);
+    try expectEqual(exp(0x1.2df2675a752767aa05874af1118cp13), 0x1.af6cbcf21a569f825eaa6879d87dp13939);
+    try expectEqual(exp(-0x1.c9900887871caf097d99f8398542p12), 0x1.04c39baa5c766f3de6233e8f07dp-10562);
+    try expectEqual(exp(0x1.9bc48fe7bfa2ac7128ebbd4939e9p12), 0x1.d931cb3d966a597631fde3c69694p9504);
+    try expectEqual(exp(-0x1.8868d9a1dd219debf76c9f0fb392p12), 0x1.f2dfb4906d3071c2df3e80934569p-9059);
+    try expectEqual(exp(0x1.5f41cc1bcb930c61a05f067fc442p13), 0x1.296ca19217f05a510f9811aa0e9cp16216);
+    try expectEqual(exp(0x1.35e8dfcc0cde6a334b9038fa98e6p13), 0x1.498de58f228e3c83d7e47400d686p14307);
+    try expectEqual(exp(0x1.ffea26d2e6e91cd9f621e730bbd2p12), 0x1.80bdb34340cb9136969a18505dd6p11816);
+    try expectEqual(exp(0x1.afc460feee0dc9db39bf49d3c112p11), 0x1.33d9f1d36aa9a75ecb5223a08282p4983);
+    try expectEqual(exp(-0x1.15511240004039de7beb770b122p13), 0x1.42058fe87c73fe2eed08e91eb0ccp-12803);
+    try expectEqual(exp(-0x1.a5e28048748f388fefc535e90fafp6), 0x1.c95ffed3eae71936b30ebdc29bfp-153);
+    try expectEqual(exp(0x1.3110993e3603ad8aea31e268ee83p12), 0x1.ccf37b60dd3e26bb7fb6b5d9f8cdp7041);
+    try expectEqual(exp(-0x1.a11e9d8a913df7ab8dcdef2179c4p12), 0x1.7e3089dc5ff6b84df2d1e042564cp-9629);
+    try expectEqual(exp(-0x1.4bcbe608a6526310c7fc13922e9p13), 0x1.26d226f1f40ab0e96bf9a717535p-15318);
+    try expectEqual(exp(0x1.410cb56d92bc5ae8986384c4299p13), 0x1.93300e94463e8e934eaff7563284p14821);
+    try expectEqual(exp(-0x1.f78f1935bf343246826d6769415fp11), 0x1.1ace810ef509fd05b4870388788ap-5812);
+}
+
+test "expq() boundary" {
+    // largest value before the result is infinite
+    try expectEqual(exp(0x1.62e42fefa39ef35793c7673007e5p13), 0x1.ffffffffffffffffffffffffc4a8p16383);
+    // first value that gives inf
+    try expect(math.isPositiveInf(exp(0x1.62e42fefa39ef35793c7673007e6p13)));
+    try expect(math.isPositiveInf(exp(math.floatMax(f128))));
+    try expectEqual(exp(0x1p-16494), 1.0);
+    try expectEqual(exp(-0x1p-16494), 1.0);
+    try expectEqual(exp(0x1p-16382), 1.0);
+    try expectEqual(exp(-0x1p-16382), 1.0);
+    try expectEqual(exp(-0x1.654bb3b2c73ebb059fabb506ff33p13), 0x1p-16494);
+    try expectEqual(exp(-0x1.654bb3b2c73ebb059fabb506ff34p13), 0);
+    try expectEqual(exp(-0x1.62d918ce2421d65ff90ac8f4ce65p13), 0x1.00000000000000000000000015c6p-16382);
+    try expectEqual(exp(-0x1.62d918ce2421d65ff90ac8f4ce66p13), 0x1.ffffffffffffffffffffffffeb8cp-16383);
+}
+
+test "exp2q() special" {
+    try expectEqual(exp2(0.0), 1.0);
+    try expectEqual(exp2(-0.0), 1.0);
+    try expectEqual(exp2(1.0), 2.0);
+    try expectEqual(exp2(-1.0), 0.5);
+    try expectEqual(exp2(math.inf(f128)), math.inf(f128));
+    try expect(math.isPositiveZero(exp2(-math.inf(f128))));
+    try expect(math.isNan(exp2(math.nan(f128))));
+    try expect(math.isNan(exp2(math.snan(f128))));
+}
+
+test "exp2q() boundary" {
+    try expectEqual(exp2(0x1.ffffffffffffffffffffffffffffp13), 0x1.ffffffffffffffffffffffffd3a3p16383);
+    try expect(math.isPositiveInf(exp2(0x1p14)));
+    try expect(math.isPositiveInf(exp2(math.floatMax(f128))));
+    try expectEqual(exp2(-0x1.01bcp14), 0);
+    try expectEqual(exp2(-0x1.01bbffffffffffffffffffffffffp14), 0x1p-16494);
+    try expectEqual(exp2(-0x1.fff0000000000000000000000001p13), 0x1.ffffffffffffffffffffffffd3a4p-16383);
+    try expectEqual(exp2(-0x1.fffp13), 0x1p-16382);
+    try expectEqual(exp2(0x1p-16494), 1.0);
+    try expectEqual(exp2(-0x1p-16494), 1.0);
+    try expectEqual(exp2(0x1p-16382), 1.0);
+    try expectEqual(exp2(-0x1p-16382), 1.0);
+}
+
+test "exp2q() sanity" {
+    try expectEqual(exp2(0x1.89e197c1a4509481147ae147ae16p12), 0x1.1249d5e676aa9feec3a5953b7c02p6302);
+    try expectEqual(exp2(-0x1.b411f0cfad25fc1b5c28f5c28f57p9), 0x1.d09909ac25bf2b1e11958781a70ap-873);
+    try expectEqual(exp2(0x1.e83de574e1a8b96e147ae147ae2p8), 0x1.2eb5386c57c57bc388716eaccd12p488);
+    try expectEqual(exp2(0x1.a9b613bed67b5f363d70a3d70a3ep13), 0x1.b16d037cd2c9626236091147b746p13622);
+    try expectEqual(exp2(0x1.84c9c52432be7a8a28f5c28f5c2bp11), 0x1.3c5614f7f1ddbadb57dc669669e2p3110);
+    try expectEqual(exp2(0x1.a9aa63b33e07e2bd23d70a3d70a5p13), 0x1.3ae2967925b501adb329d3bdc999p13621);
+    try expectEqual(exp2(-0x1.3f8d7f1b5b5ad15a028f5c28f5c2p13), 0x1.3e02ffbf66c581bd049af0ba1014p-10226);
+    try expectEqual(exp2(0x1.22c788348289d077a3d70a3d70a4p13), 0x1.eba8052f961ea5fb455eb7fd72c5p9304);
+    try expectEqual(exp2(-0x1.11cf846583d5645a628f5c28f5c2p13), 0x1.0aefc431a531a66384b8682fd26p-8762);
+    try expectEqual(exp2(0x1.eee7707f597161b90a3d70a3d70bp13), 0x1.e7ba24db2ff207c89727d80fca5dp15836);
+    try expectEqual(exp2(0x1.b4d8b18ce858fe773d70a3d70a3ep13), 0x1.0fdaed7d8d2bd78a08575b84b9edp13979);
+    try expectEqual(exp2(0x1.6916f408801b3f7ebd70a3d70a3ep13), 0x1.d39bbbe66e1288441ef91fb6c4f8p11554);
+    try expectEqual(exp2(0x1.32826286d5689c66147ae147ae15p12), 0x1.1bdd18f576fffb40d7a7c4600473p4904);
+    try expectEqual(exp2(-0x1.83b40cdd8603c81b65c28f5c28f6p13), 0x1.687736e6ce5610f434444b20f2a5p-12407);
+    try expectEqual(exp2(-0x1.7832ea6506b0b2f47ae147ae144dp6), 0x1.eea794ee31522277606ff7a2c8ep-95);
+    try expectEqual(exp2(0x1.afbb8b6830cac8c2e147ae147ae2p12), 0x1.a620a1f8a46335e10818a504693cp6907);
+    try expectEqual(exp2(-0x1.2328a820e1db0e1b028f5c28f5c2p13), 0x1.e3add1a5b805ac7fa39b1ecf7a2ap-9318);
+    try expectEqual(exp2(-0x1.d03363f43eb86051c5c28f5c28f6p13), 0x1.7dac5a9d06f845523a229370d6fbp-14855);
+    try expectEqual(exp2(0x1.c47d13ba4001d5d6a3d70a3d70a5p13), 0x1.8d7369b8ad7bd5aace25ccb030dbp14479);
+    try expectEqual(exp2(-0x1.5e280f18074b0b38d1eb851eb851p12), 0x1.691d77d02a99bab87b9bd0aeb82ep-5603);
+}
+
+const size = 64;
+
+/// exp2_tab[j].hi + exp2_tab[j].lo ~= 2^(j / size)
+/// where exp2_tab[j].hi has its 30 trailing bits set to 0
+const exp2_tab = [size]struct { hi: f128, lo: f128 }{
+    .{ .hi = 1, .lo = 0 },
+    .{ .hi = 1.0108892860517004600204097572469746, .lo = 3.331488596564031210563288051982794e-26 },
+    .{ .hi = 1.0218971486541166782344800872427626, .lo = 4.754053684121973789288755464722138e-26 },
+    .{ .hi = 1.0330248790212284225001081883964135, .lo = 9.557404741840277960546616586298063e-26 },
+    .{ .hi = 1.044273782427413840321966300719135, .lo = 1.7802079401409229639033486606835582e-25 },
+    .{ .hi = 1.0556451783605571588083412749313592, .lo = 5.022157947196508429749069389839003e-26 },
+    .{ .hi = 1.0671404006768236181695209696174248, .lo = 1.5137538440721428405259778473587436e-25 },
+    .{ .hi = 1.0787607977571197937406800254939246, .lo = 1.1944558390181437089024030105545753e-26 },
+    .{ .hi = 1.0905077326652576592070106394193907, .lo = 1.6341317298466358429137337862221883e-26 },
+    .{ .hi = 1.1023825833078409435564140763781162, .lo = 1.3304753063524778951752027959085558e-25 },
+    .{ .hi = 1.1143867425958925363088128257407598, .lo = 1.3117884324019192923687629273175252e-25 },
+    .{ .hi = 1.1265216186082418997947985102919192, .lo = 1.3349511554260129942233288245148925e-25 },
+    .{ .hi = 1.1387886347566916537038301230733987, .lo = 1.6076811251744575806878211946090158e-25 },
+    .{ .hi = 1.1511892299529827058177595055860644, .lo = 1.296159181480888798344830542672908e-25 },
+    .{ .hi = 1.1637248587775775138135734257915416, .lo = 1.7330064367522746277589854745025186e-25 },
+    .{ .hi = 1.1763969916502812762846455513693297, .lo = 1.771145189358715817500494171124228e-25 },
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