Revert "Revert "Speed up plog_double ~1.7x with fast integer range reduction""

This reverts commit b1d2ce4c85
2026-04-10 11:34:33 +08:00 · 2026-04-08 13:10:27 -07:00
parent b1d2ce4c85
commit 111c4d23a9
2 changed files with 159 additions and 161 deletions
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -141,98 +141,83 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plog2_float(const Pac
  return plog_impl_float<Packet, /* base2 */ true>(_x);
 }

-/* Returns the base e (2.718...) or base 2 logarithm of x.
- * The argument is separated into its exponent and fractional parts.
- * The logarithm of the fraction in the interval [sqrt(1/2), sqrt(2)],
- * is approximated by
- *
- *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
- *
- * for more detail see: http://www.netlib.org/cephes/
- */
-template <typename Packet, bool base2>
-EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plog_impl_double(const Packet _x) {
-  Packet x = _x;
+// Core range reduction and polynomial evaluation for double logarithm.
+//
+// Same structure as plog_core_float but for double precision.
+// Given a positive double v (may be denormal), decomposes it as
+// v = 2^e * (1+f) with f in [sqrt(0.5)-1, sqrt(2)-1], then evaluates
+// log(1+f) ≈ f - 0.5*f^2 + f^3 * P(f)/Q(f) using the Cephes [5/5]
+// rational approximation.
+template <typename Packet>
+EIGEN_STRONG_INLINE void plog_core_double(const Packet v, Packet& log_mantissa, Packet& e) {
+  typedef typename unpacket_traits<Packet>::integer_packet PacketL;

-  const Packet cst_1 = pset1<Packet>(1.0);
-  const Packet cst_neg_half = pset1<Packet>(-0.5);
-  const Packet cst_minus_inf = pset1frombits<Packet>(static_cast<uint64_t>(0xfff0000000000000ull));
-  const Packet cst_pos_inf = pset1frombits<Packet>(static_cast<uint64_t>(0x7ff0000000000000ull));
+  const PacketL cst_min_normal = pset1<PacketL>(int64_t(0x0010000000000000LL));
+  const PacketL cst_mant_mask = pset1<PacketL>(int64_t(0x000fffffffffffffLL));
+  const PacketL cst_sqrt_half_offset = pset1<PacketL>(int64_t(0x00095f619980c433LL));
+  const PacketL cst_exp_bias = pset1<PacketL>(int64_t(0x3ff));                  // 1023
+  const PacketL cst_half_mant = pset1<PacketL>(int64_t(0x3fe6a09e667f3bcdLL));  // sqrt(0.5)

-  // Polynomial Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
-  //                             1/sqrt(2) <= x < sqrt(2)
-  const Packet cst_cephes_SQRTHF = pset1<Packet>(0.70710678118654752440E0);
-  const Packet cst_cephes_log_p0 = pset1<Packet>(1.01875663804580931796E-4);
-  const Packet cst_cephes_log_p1 = pset1<Packet>(4.97494994976747001425E-1);
-  const Packet cst_cephes_log_p2 = pset1<Packet>(4.70579119878881725854E0);
-  const Packet cst_cephes_log_p3 = pset1<Packet>(1.44989225341610930846E1);
-  const Packet cst_cephes_log_p4 = pset1<Packet>(1.79368678507819816313E1);
-  const Packet cst_cephes_log_p5 = pset1<Packet>(7.70838733755885391666E0);
+  // Normalize denormals by multiplying by 2^52.
+  PacketL vi = preinterpret<PacketL>(v);
+  PacketL is_denormal = pcmp_lt(vi, cst_min_normal);
+  Packet v_normalized = pmul(v, pset1<Packet>(4503599627370496.0));  // 2^52
+  vi = pselect(is_denormal, preinterpret<PacketL>(v_normalized), vi);
+  PacketL denorm_adj = pand(is_denormal, pset1<PacketL>(int64_t(52)));

-  const Packet cst_cephes_log_q0 = pset1<Packet>(1.0);
-  const Packet cst_cephes_log_q1 = pset1<Packet>(1.12873587189167450590E1);
-  const Packet cst_cephes_log_q2 = pset1<Packet>(4.52279145837532221105E1);
-  const Packet cst_cephes_log_q3 = pset1<Packet>(8.29875266912776603211E1);
-  const Packet cst_cephes_log_q4 = pset1<Packet>(7.11544750618563894466E1);
-  const Packet cst_cephes_log_q5 = pset1<Packet>(2.31251620126765340583E1);
+  // Combined range reduction via integer bias (same trick as float version).
+  PacketL vi_biased = padd(vi, cst_sqrt_half_offset);
+  PacketL e_int = psub(psub(plogical_shift_right<52>(vi_biased), cst_exp_bias), denorm_adj);
+  e = pcast<PacketL, Packet>(e_int);
+  Packet f = psub(preinterpret<Packet>(padd(pand(vi_biased, cst_mant_mask), cst_half_mant)), pset1<Packet>(1.0));

-  Packet e;
-  // extract significant in the range [0.5,1) and exponent
-  x = pfrexp(x, e);
+  // Rational approximation log(1+f) = f - 0.5*f^2 + f^3 * P(f)/Q(f)
+  // from Cephes, [5/5] rational on [sqrt(0.5)-1, sqrt(2)-1].
+  Packet f2 = pmul(f, f);
+  Packet f3 = pmul(f2, f);

-  // Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2))
-  // and shift by -1. The values are then centered around 0, which improves
-  // the stability of the polynomial evaluation.
-  //   if( x < SQRTHF ) {
-  //     e -= 1;
-  //     x = x + x - 1.0;
-  //   } else { x = x - 1.0; }
-  Packet mask = pcmp_lt(x, cst_cephes_SQRTHF);
-  Packet tmp = pand(x, mask);
-  x = psub(x, cst_1);
-  e = psub(e, pand(cst_1, mask));
-  x = padd(x, tmp);
-
-  Packet x2 = pmul(x, x);
-  Packet x3 = pmul(x2, x);
-
-  // Evaluate the polynomial in factored form for better instruction-level parallelism.
-  // y = x - 0.5*x^2 + x^3 * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
+  // Evaluate P and Q in factored form for instruction-level parallelism.
  Packet y, y1, y_;
-  y = pmadd(cst_cephes_log_p0, x, cst_cephes_log_p1);
-  y1 = pmadd(cst_cephes_log_p3, x, cst_cephes_log_p4);
-  y = pmadd(y, x, cst_cephes_log_p2);
-  y1 = pmadd(y1, x, cst_cephes_log_p5);
-  y_ = pmadd(y, x3, y1);
+  y = pmadd(pset1<Packet>(1.01875663804580931796E-4), f, pset1<Packet>(4.97494994976747001425E-1));
+  y1 = pmadd(pset1<Packet>(1.44989225341610930846E1), f, pset1<Packet>(1.79368678507819816313E1));
+  y = pmadd(y, f, pset1<Packet>(4.70579119878881725854E0));
+  y1 = pmadd(y1, f, pset1<Packet>(7.70838733755885391666E0));
+  y_ = pmadd(y, f3, y1);

-  y = pmadd(cst_cephes_log_q0, x, cst_cephes_log_q1);
-  y1 = pmadd(cst_cephes_log_q3, x, cst_cephes_log_q4);
-  y = pmadd(y, x, cst_cephes_log_q2);
-  y1 = pmadd(y1, x, cst_cephes_log_q5);
-  y = pmadd(y, x3, y1);
+  y = pmadd(pset1<Packet>(1.0), f, pset1<Packet>(1.12873587189167450590E1));
+  y1 = pmadd(pset1<Packet>(8.29875266912776603211E1), f, pset1<Packet>(7.11544750618563894466E1));
+  y = pmadd(y, f, pset1<Packet>(4.52279145837532221105E1));
+  y1 = pmadd(y1, f, pset1<Packet>(2.31251620126765340583E1));
+  y = pmadd(y, f3, y1);

-  y_ = pmul(y_, x3);
+  y_ = pmul(y_, f3);
  y = pdiv(y_, y);

-  y = pmadd(cst_neg_half, x2, y);
-  x = padd(x, y);
+  y = pmadd(pset1<Packet>(-0.5), f2, y);
+  log_mantissa = padd(f, y);
+}

-  // Add the logarithm of the exponent back to the result of the interpolation.
+// Natural or base-2 logarithm for double packets.
+template <typename Packet, bool base2>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet plog_impl_double(const Packet _x) {
+  Packet log_mantissa, e;
+  plog_core_double(_x, log_mantissa, e);
+
+  // Add the logarithm of the exponent back to the result.
+  Packet x;
  if (base2) {
    const Packet cst_log2e = pset1<Packet>(static_cast<double>(EIGEN_LOG2E));
-    x = pmadd(x, cst_log2e, e);
+    x = pmadd(log_mantissa, cst_log2e, e);
  } else {
    const Packet cst_ln2 = pset1<Packet>(static_cast<double>(EIGEN_LN2));
-    x = pmadd(e, cst_ln2, x);
+    x = pmadd(e, cst_ln2, log_mantissa);
  }

+  const Packet cst_minus_inf = pset1frombits<Packet>(static_cast<uint64_t>(0xfff0000000000000ull));
+  const Packet cst_pos_inf = pset1frombits<Packet>(static_cast<uint64_t>(0x7ff0000000000000ull));
  Packet invalid_mask = pcmp_lt_or_nan(_x, pzero(_x));
  Packet iszero_mask = pcmp_eq(_x, pzero(_x));
  Packet pos_inf_mask = pcmp_eq(_x, cst_pos_inf);
-  // Filter out invalid inputs, i.e.:
-  //  - negative arg will be NAN
-  //  - 0 will be -INF
-  //  - +INF will be +INF
  return pselect(iszero_mask, cst_minus_inf, por(pselect(pos_inf_mask, cst_pos_inf, x), invalid_mask));
 }

@@ -287,7 +272,10 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_log1p_float(c
 }

 /** \internal \returns log(1 + x) for double precision float.
-    Same direct approach as the float version.
+    Computes log(1+x) using plog_core_double for the core range reduction
+    and polynomial evaluation. The rounding error from forming u = fl(1+x)
+    is recovered as dx = x - (u - 1), and folded in as a first-order
+    correction dx/u after the polynomial evaluation.
 */
 template <typename Packet>
 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_log1p_double(const Packet& x) {
@@ -295,61 +283,25 @@ EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet generic_log1p_double(
  const Packet cst_minus_inf = pset1frombits<Packet>(static_cast<uint64_t>(0xfff0000000000000ull));
  const Packet cst_pos_inf = pset1frombits<Packet>(static_cast<uint64_t>(0x7ff0000000000000ull));

+  // u = 1 + x, with rounding. Recover the lost low bits: dx = x - (u - 1).
  Packet u = padd(one, x);
  Packet dx = psub(x, psub(u, one));

+  // For |x| tiny enough that u rounds to 1, return x directly.
  Packet small_mask = pcmp_eq(u, one);
+  // For u = +inf (x very large), return +inf.
  Packet inf_mask = pcmp_eq(u, cst_pos_inf);

-  const Packet cst_cephes_SQRTHF = pset1<Packet>(0.70710678118654752440E0);
-  Packet e;
-  Packet m = pfrexp(u, e);
-  Packet mask = pcmp_lt(m, cst_cephes_SQRTHF);
-  Packet tmp = pand(m, mask);
-  m = psub(m, one);
-  e = psub(e, pand(one, mask));
-  m = padd(m, tmp);
+  // Core range reduction and polynomial on u.
+  Packet log_u, e;
+  plog_core_double(u, log_u, e);

-  // Same polynomial as plog_double.
-  const Packet cst_neg_half = pset1<Packet>(-0.5);
-  const Packet cst_cephes_log_p0 = pset1<Packet>(1.01875663804580931796E-4);
-  const Packet cst_cephes_log_p1 = pset1<Packet>(4.97494994976747001425E-1);
-  const Packet cst_cephes_log_p2 = pset1<Packet>(4.70579119878881725854E0);
-  const Packet cst_cephes_log_p3 = pset1<Packet>(1.44989225341610930846E1);
-  const Packet cst_cephes_log_p4 = pset1<Packet>(1.79368678507819816313E1);
-  const Packet cst_cephes_log_p5 = pset1<Packet>(7.70838733755885391666E0);
-  const Packet cst_cephes_log_q0 = pset1<Packet>(1.0);
-  const Packet cst_cephes_log_q1 = pset1<Packet>(1.12873587189167450590E1);
-  const Packet cst_cephes_log_q2 = pset1<Packet>(4.52279145837532221105E1);
-  const Packet cst_cephes_log_q3 = pset1<Packet>(8.29875266912776603211E1);
-  const Packet cst_cephes_log_q4 = pset1<Packet>(7.11544750618563894466E1);
-  const Packet cst_cephes_log_q5 = pset1<Packet>(2.31251620126765340583E1);
-
-  Packet m2 = pmul(m, m);
-  Packet m3 = pmul(m2, m);
-
-  Packet y, y1, y_;
-  y = pmadd(cst_cephes_log_p0, m, cst_cephes_log_p1);
-  y1 = pmadd(cst_cephes_log_p3, m, cst_cephes_log_p4);
-  y = pmadd(y, m, cst_cephes_log_p2);
-  y1 = pmadd(y1, m, cst_cephes_log_p5);
-  y_ = pmadd(y, m3, y1);
-
-  y = pmadd(cst_cephes_log_q0, m, cst_cephes_log_q1);
-  y1 = pmadd(cst_cephes_log_q3, m, cst_cephes_log_q4);
-  y = pmadd(y, m, cst_cephes_log_q2);
-  y1 = pmadd(y1, m, cst_cephes_log_q5);
-  y = pmadd(y, m3, y1);
-
-  y_ = pmul(y_, m3);
-  Packet log_m = pdiv(y_, y);
-  log_m = pmadd(cst_neg_half, m2, log_m);
-  log_m = padd(m, log_m);
-
-  // result = e * ln2 + log(m) + dx/u.
+  // result = e * ln2 + log(u) + dx/u.
+  // The dx/u term corrects for the rounding error in u = fl(1+x).
  const Packet cst_ln2 = pset1<Packet>(static_cast<double>(EIGEN_LN2));
-  Packet result = pmadd(e, cst_ln2, padd(log_m, pdiv(dx, u)));
+  Packet result = pmadd(e, cst_ln2, padd(log_u, pdiv(dx, u)));

+  // Handle special cases.
  Packet neg_mask = pcmp_lt(u, pzero(u));
  Packet zero_mask = pcmp_eq(x, pset1<Packet>(-1.0));
  result = pselect(small_mask, x, result);
--- a/test/ulp_accuracy/ulp_accuracy.cpp
+++ b/test/ulp_accuracy/ulp_accuracy.cpp
@@ -233,15 +233,17 @@ static std::vector<FuncEntry<Scalar>> build_func_table() {
 // Range iteration helpers
 // ============================================================================

-// Advances x toward +inf by at least 1 ULP. When step_eps > 0, additionally
-// jumps by a relative factor of (1 + step_eps) to sample the range sparsely.
+// Advances a non-negative value toward +inf by at least 1 ULP. When step_eps > 0,
+// additionally jumps by max(|x|, min_normal) * step_eps. For normals this is
+// equivalent to x * (1 + eps). For denormals where x * eps < smallest_denormal,
+// the min_normal floor ensures we still skip through the denormal region at a
+// rate matching the smallest normals rather than stalling at 1 ULP per step.
 template <typename Scalar>
-static inline Scalar advance_by_step(Scalar x, double step_eps) {
+static inline Scalar advance_positive(Scalar x, double step_eps) {
  Scalar next = std::nextafter(x, std::numeric_limits<Scalar>::infinity());
  if (step_eps > 0.0 && std::isfinite(next)) {
-    // Try to jump further by a relative amount.
-    Scalar jumped = next > 0 ? next * static_cast<Scalar>(1.0 + step_eps) : next / static_cast<Scalar>(1.0 + step_eps);
-    // Use the jump only if it actually advances further (handles denormal stalling).
+    Scalar base = std::max(next, std::numeric_limits<Scalar>::min());
+    Scalar jumped = next + base * static_cast<Scalar>(step_eps);
    if (jumped > next) next = jumped;
  }
  return next;
@@ -281,26 +283,60 @@ static double linear_to_scalar(int64_t lin, double /*tag*/) {
 // Dynamic work queue: threads atomically claim chunks for load balancing
 // ============================================================================

+// Work queue that distributes chunks in positive absolute-value linear space.
+// Iteration goes outward from 0: the worker tests both +|x| and -|x| for
+// each sampled magnitude, so the multiplicative step (1 + eps) always works
+// cleanly — no special handling for negative values needed.
 template <typename Scalar>
 struct WorkQueue {
  int64_t range_hi_lin;
  int64_t chunk_size;
  double step_eps;
  std::atomic<int64_t> next_lin;
+  Scalar orig_lo;  // original range for sign filtering
+  Scalar orig_hi;
+  bool test_pos;  // whether any positive values are in [lo, hi]
+  bool test_neg;  // whether any negative values are in [lo, hi]

-  void init(Scalar lo, Scalar hi, int64_t csz, double step) {
-    range_hi_lin = scalar_to_linear(hi);
-    chunk_size = csz;
+  void init(Scalar lo, Scalar hi, int num_threads, double step) {
+    orig_lo = lo;
+    orig_hi = hi;
+    test_pos = (hi >= Scalar(0));
+    test_neg = (lo < Scalar(0));
+
+    // Compute absolute-value iteration range.
+    Scalar abs_lo, abs_hi;
+    if (lo <= Scalar(0) && hi >= Scalar(0)) {
+      abs_lo = Scalar(0);
+      abs_hi = std::max(std::abs(lo), hi);
+    } else {
+      abs_lo = std::min(std::abs(lo), std::abs(hi));
+      abs_hi = std::max(std::abs(lo), std::abs(hi));
+    }
+
+    range_hi_lin = scalar_to_linear(abs_hi);
    step_eps = step;
-    next_lin.store(scalar_to_linear(lo), std::memory_order_relaxed);
+    next_lin.store(scalar_to_linear(abs_lo), std::memory_order_relaxed);
+
+    uint64_t total_abs = count_scalars_in_range(abs_lo, abs_hi);
+    chunk_size = std::max(int64_t(1), static_cast<int64_t>(total_abs / (num_threads * 16)));
+    if (step > 0.0) {
+      // Ensure chunks are large enough that advance_positive's min_normal floor
+      // can actually skip the denormal region.  The denormal region contains
+      // count_scalars_in_range(0, min_normal) ULPs; any chunk must span at
+      // least that many so the min_normal-based jump lands past chunk_hi.
+      int64_t denorm_span = static_cast<int64_t>(count_scalars_in_range(Scalar(0), std::numeric_limits<Scalar>::min()));
+      chunk_size = std::max(chunk_size, denorm_span);
+    }
  }

-  // Claim the next chunk. Returns false when no work remains.
+  // Claim the next chunk of absolute values. Returns false when no work remains.
  bool claim(Scalar& chunk_lo, Scalar& chunk_hi) {
    int64_t lo_lin = next_lin.fetch_add(chunk_size, std::memory_order_relaxed);
-    if (lo_lin > range_hi_lin) return false;
-    int64_t hi_lin = lo_lin + chunk_size - 1;
-    if (hi_lin > range_hi_lin) hi_lin = range_hi_lin;
+    if (lo_lin > range_hi_lin || lo_lin < 0) return false;
+    // Compute hi_lin carefully to avoid int64_t overflow.
+    int64_t remaining = range_hi_lin - lo_lin;
+    int64_t hi_lin = (remaining < chunk_size - 1) ? range_hi_lin : lo_lin + chunk_size - 1;
    chunk_lo = linear_to_scalar(lo_lin, Scalar(0));
    chunk_hi = linear_to_scalar(hi_lin, Scalar(0));
    return true;
@@ -322,8 +358,12 @@ static void worker(const FuncEntry<Scalar>& func, WorkQueue<Scalar>& queue, int
 #ifdef EIGEN_HAS_MPFR
  mpfr_t mp_in, mp_out;
  if (use_mpfr) {
-    mpfr_init2(mp_in, 128);
-    mpfr_init2(mp_out, 128);
+    // Use 2x the mantissa bits of Scalar for the reference: 48 for float (24-bit
+    // mantissa), 106 for double (53-bit mantissa). This is sufficient for correctly-
+    // rounded results while keeping MPFR evaluation fast.
+    constexpr int kMpfrBits = std::is_same<Scalar, float>::value ? 48 : 106;
+    mpfr_init2(mp_in, kMpfrBits);
+    mpfr_init2(mp_out, kMpfrBits);
  }
 #else
  (void)use_mpfr;
@@ -348,32 +388,42 @@ static void worker(const FuncEntry<Scalar>& func, WorkQueue<Scalar>& queue, int
    }
  };

+  auto flush_batch = [&](int& idx) {
+    if (idx == 0) return;
+    for (int i = idx; i < batch_size; i++) input[i] = input[idx - 1];
+    func.eigen_eval(eigen_out, input);
+    process_batch(idx, input, eigen_out);
+    idx = 0;
+  };
+
+  auto push_value = [&](Scalar v, int& idx) {
+    input[idx++] = v;
+    if (idx == batch_size) flush_batch(idx);
+  };
+
  Scalar chunk_lo, chunk_hi;
  while (queue.claim(chunk_lo, chunk_hi)) {
    int idx = 0;
-    Scalar x = chunk_lo;
+    Scalar abs_x = chunk_lo;
    for (;;) {
-      input[idx] = x;
-      idx++;
-
-      if (idx == batch_size) {
-        func.eigen_eval(eigen_out, input);
-        process_batch(batch_size, input, eigen_out);
-        idx = 0;
+      // Test +|x| if positive values are in range.
+      if (queue.test_pos && abs_x >= queue.orig_lo && abs_x <= queue.orig_hi) {
+        push_value(abs_x, idx);
+      }
+      // Test -|x| if negative values are in range (skip -0 to avoid testing 0 twice).
+      if (queue.test_neg && abs_x != Scalar(0)) {
+        Scalar neg_x = -abs_x;
+        if (neg_x >= queue.orig_lo && neg_x <= queue.orig_hi) {
+          push_value(neg_x, idx);
+        }
      }

-      if (x >= chunk_hi) break;
-      Scalar next = advance_by_step(x, queue.step_eps);
-      x = (next > chunk_hi) ? chunk_hi : next;
+      if (abs_x >= chunk_hi) break;
+      Scalar next = advance_positive(abs_x, queue.step_eps);
+      abs_x = (next > chunk_hi) ? chunk_hi : next;
    }

-    // Process remaining partial batch.  Pad unused slots with the last valid
-    // input so the full-size vectorized eval doesn't read uninitialized memory.
-    if (idx > 0) {
-      for (int i = idx; i < batch_size; i++) input[i] = input[idx - 1];
-      func.eigen_eval(eigen_out, input);
-      process_batch(idx, input, eigen_out);
-    }
+    flush_batch(idx);
  }

 #ifdef EIGEN_HAS_MPFR
@@ -439,11 +489,12 @@ static int run_test(const Options& opts) {
  std::printf("Function: %s (%s)\n", opts.func_name.c_str(), kTypeName);
  std::printf("Range: [%.*g, %.*g]\n", kDigits, double(lo), kDigits, double(hi));
  if (opts.step_eps > 0.0) {
-    std::printf("Sampling step: (1 + %g) * nextafter(x)\n", opts.step_eps);
+    std::printf("Sampling step: |x| * (1 + %g)\n", opts.step_eps);
  } else {
    std::printf("Representable values in range: %lu\n", static_cast<unsigned long>(total_scalars));
  }
-  std::printf("Reference: %s\n", opts.use_mpfr ? "MPFR (128-bit)" : "std C++ math");
+  std::printf("Reference: %s\n",
+              opts.use_mpfr ? (opts.use_double ? "MPFR (106-bit)" : "MPFR (48-bit)") : "std C++ math");
  std::printf("Threads: %d\n", num_threads);
  std::printf("Batch size: %d\n", opts.batch_size);
  std::printf("\n");
@@ -459,13 +510,8 @@ static int run_test(const Options& opts) {
    results.back()->init(opts.hist_width);
  }

-  // Use dynamic work distribution: threads claim small chunks from a shared
-  // queue.  This ensures even load balancing regardless of how per-value
-  // work varies across the range (e.g. log on negatives is trivial).
-  // Choose chunk_size so we get ~16 chunks per thread for good balancing.
-  int64_t chunk_size = std::max(int64_t(1), static_cast<int64_t>(total_scalars / (num_threads * 16)));
  WorkQueue<Scalar> queue;
-  queue.init(lo, hi, chunk_size, opts.step_eps);
+  queue.init(lo, hi, num_threads, opts.step_eps);

  std::vector<std::thread> threads;
  auto start_time = std::chrono::steady_clock::now();