From 1c2b23cd7b2e6b5f0070f06b7e5b728c90ccea29 Mon Sep 17 00:00:00 2001
From: Paul Kienzle <pkienzle@nist.gov>
Date: Fri, 25 Jul 2025 19:28:43 -0400
Subject: [PATCH 1/5] adaptive integration for cylinder using qr heuristic

---
 sasmodels/models/cylinderp.c    |   104 +
 sasmodels/models/cylinderp.py   |   251 +
 sasmodels/models/lib/adaptive.c | 11213 ++++++++++++++++++++++++++++++
 3 files changed, 11568 insertions(+)
 create mode 100644 sasmodels/models/cylinderp.c
 create mode 100644 sasmodels/models/cylinderp.py
 create mode 100644 sasmodels/models/lib/adaptive.c

diff --git a/sasmodels/models/cylinderp.c b/sasmodels/models/cylinderp.c
new file mode 100644
index 00000000..e47ca2c9
--- /dev/null
+++ b/sasmodels/models/cylinderp.c
@@ -0,0 +1,104 @@
+static double
+form_volume(double radius, double length)
+{
+    return M_PI*radius*radius*length;
+}
+
+static double
+_fq(double qab, double qc, double radius, double length)
+{
+    return sas_2J1x_x(qab*radius) * sas_sinx_x(qc*0.5*length);
+}
+
+static double
+radius_from_excluded_volume(double radius, double length)
+{
+    return 0.5*cbrt(0.75*radius*(2.0*radius*length
+           + (radius + length)*(M_PI*radius + length)));
+}
+
+static double
+radius_from_volume(double radius, double length)
+{
+    return cbrt(M_PI*radius*radius*length/M_4PI_3);
+}
+
+static double
+radius_from_diagonal(double radius, double length)
+{
+    return sqrt(radius*radius + 0.25*length*length);
+}
+
+static double
+radius_effective(int mode, double radius, double length)
+{
+    switch (mode) {
+    default:
+    case 1:
+        return radius_from_excluded_volume(radius, length);
+    case 2:
+        return radius_from_volume(radius, length);
+    case 3:
+        return radius;
+    case 4:
+        return 0.5*length;
+    case 5:
+        return (radius < 0.5*length ? radius : 0.5*length);
+    case 6:
+        return (radius > 0.5*length ? radius : 0.5*length);
+    case 7:
+        return radius_from_diagonal(radius,length);
+    }
+}
+
+
+static void
+Fq(double q,
+    double *F1,
+    double *F2,
+    double sld,
+    double solvent_sld,
+    double radius,
+    double length)
+{
+    // translate a point in [-1,1] to a point in [0, pi/2]
+    const double zm = M_PI_4;
+    const double zb = M_PI_4;
+
+    double total_F1 = 0.0;
+    double total_F2 = 0.0;
+
+    double qr = q*(radius > length ? radius : length);
+    double *w, *z;
+    int n = gauss_weights(qr, &w, &z);
+    for (int i=0; i<n ;i++) {
+        const double theta = z[i]*zm + zb;
+        double sin_theta, cos_theta; // slots to hold sincos function output
+        // theta (theta,phi) the projection of the cylinder on the detector plane
+        SINCOS(theta , sin_theta, cos_theta);
+        const double form = _fq(q*sin_theta, q*cos_theta, radius, length);
+        total_F1 += w[i] * form * sin_theta;
+        total_F2 += w[i] * form * form * sin_theta;
+    }
+    // translate dx in [-1,1] to dx in [lower,upper]
+    total_F1 *= zm;
+    total_F2 *= zm;
+    const double s = (sld - solvent_sld) * form_volume(radius, length);
+    *F1 = 1e-2 * s * total_F1;
+    *F2 = 1e-4 * s * s * total_F2;
+}
+
+
+
+static double
+Iqac(double qab, double qc,
+    double sld,
+    double solvent_sld,
+    double radius,
+    double length)
+{
+    const double form = _fq(qab, qc, radius, length);
+    const double s = (sld-solvent_sld) * form_volume(radius, length);
+    return 1.0e-4 * square(s * form);
+}
+
diff --git a/sasmodels/models/cylinderp.py b/sasmodels/models/cylinderp.py
new file mode 100644
index 00000000..7f1ac3b5
--- /dev/null
+++ b/sasmodels/models/cylinderp.py
@@ -0,0 +1,251 @@
+# cylinder model
+# Note: model title and parameter table are inserted automatically
+r"""
+
+For information about polarised and magnetic scattering, see
+the :ref:`magnetism` documentation.
+
+Definition
+----------
+
+The output of the 2D scattering intensity function for oriented cylinders is
+given by (Guinier, 1955)
+
+.. math::
+
+    I(q,\alpha) = \frac{\text{scale}}{V} F^2(q,\alpha) + \text{background}
+
+where
+
+.. math::
+
+    F(q,\alpha) = 2 (\Delta \rho) V
+           \frac{\sin \left(\tfrac12 qL\cos\alpha \right)}
+                {\tfrac12 qL \cos \alpha}
+           \frac{J_1 \left(q R \sin \alpha\right)}{q R \sin \alpha}
+
+and $\alpha$ is the angle between the axis of the cylinder and $\vec q$,
+$V =\pi R^2L$ is the volume of the cylinder, $L$ is the length of the cylinder,
+$R$ is the radius of the cylinder, and $\Delta\rho$ (contrast) is the
+scattering length density difference between the scatterer and the solvent.
+$J_1$ is the first order Bessel function.
+
+For randomly oriented particles:
+
+.. math::
+
+    P(q)=F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha}
+
+
+The output of the 1D scattering intensity function for randomly oriented
+cylinders is thus given by
+
+.. math::
+
+    I(q) = \frac{\text{scale}}{V}
+        \int_0^{\pi/2} F^2(q,\alpha) \sin \alpha\ d\alpha + \text{background}
+
+
+NB: The 2nd virial coefficient of the cylinder is calculated based on the
+radius and length values, and used as the effective radius for $S(q)$
+when $P(q) \cdot S(q)$ is applied.
+
+For 2d scattering from oriented cylinders, we define the direction of the
+axis of the cylinder using two angles $\theta$ (note this is not the same as
+the scattering angle used in q) and $\phi$. Those angles are defined in
+:numref:`cylinder-angle-definition` , for further details see
+:ref:`orientation`.
+
+.. _cylinder-angle-definition:
+
+.. figure:: img/cylinder_angle_definition.png
+
+    Angles $\theta$ and $\phi$ orient the cylinder relative to the beam line
+    coordinates, where the beam is along the $z$ axis. Rotation $\theta$,
+    initially in the $xz$ plane, is carried out first, then rotation $\phi$
+    about the $z$ axis. Orientation distributions are described as rotations
+    about two perpendicular axes $\delta_1$ and $\delta_2$ in the frame of
+    the cylinder itself, which when $\theta = \phi = 0$ are parallel to the
+    $Y$ and $X$ axes.
+
+.. figure:: img/cylinder_angle_projection.png
+
+    Examples for oriented cylinders.
+
+The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the
+model when fitting 2d data.
+
+Validation
+----------
+
+Validation of the code was done by comparing the output of the 1D model
+to the output of the software provided by the NIST (Kline, 2006).
+The implementation of the intensity for fully oriented cylinders was done
+by averaging over a uniform distribution of orientations using
+
+.. math::
+
+    P(q) = \int_0^{\pi/2} d\phi
+        \int_0^\pi p(\theta) P_0(q,\theta) \sin \theta\ d\theta
+
+
+where $p(\theta,\phi) = 1$ is the probability distribution for the orientation
+and $P_0(q,\theta)$ is the scattering intensity for the fully oriented
+system, and then comparing to the 1D result.
+
+References
+----------
+
+#.  J. Pedersen, *Adv. Colloid Interface Sci.*, 70 (1997) 171-210
+#.  G. Fournet, *Bull. Soc. Fr. Mineral. Cristallogr.*, 74 (1951) 39-113
+#.  L. Onsager, *Ann. New York Acad. Sci.*, 51 (1949) 627-659
+
+Authorship and Verification
+----------------------------
+
+* **Author:**
+* **Last Modified by:** Paul Butler (docs only) November 10, 2022
+* **Last Reviewed by:**
+"""
+
+import numpy as np  # type: ignore
+from numpy import pi, inf  # type: ignore
+
+name = "cylinder"
+title = "Right circular cylinder with uniform scattering length density."
+description = """
+     f(q,alpha) = 2*(sld - sld_solvent)*V*sin(qLcos(alpha)/2))
+                /[qLcos(alpha)/2]*J1(qRsin(alpha))/[qRsin(alpha)]
+
+            P(q,alpha)= scale/V*f(q,alpha)^(2)+background
+            V: Volume of the cylinder
+            R: Radius of the cylinder
+            L: Length of the cylinder
+            J1: The Bessel function
+            alpha: angle between the axis of the
+            cylinder and the q-vector for 1D
+            :the ouput is P(q)=scale/V*integral
+            from pi/2 to zero of...
+            f(q,alpha)^(2)*sin(alpha)*dalpha + background
+"""
+category = "shape:cylinder"
+
+# pylint: disable=bad-whitespace, line-too-long
+#             [ "name", "units", default, [lower, upper], "type", "description"],
+parameters = [
+    ["sld",         "1e-6/Ang^2",   4, [-inf, inf], "sld",         "Cylinder scattering length density"],
+    ["sld_solvent", "1e-6/Ang^2",   1, [-inf, inf], "sld",         "Solvent scattering length density"],
+    ["radius",      "Ang",         20, [0, inf],    "volume",      "Cylinder radius"],
+    ["length",      "Ang",        400, [0, inf],    "volume",      "Cylinder length"],
+    ["theta",       "degrees",     60, [-360, 360], "orientation", "cylinder axis to beam angle"],
+    ["phi",         "degrees",     60, [-360, 360], "orientation", "rotation about beam"],
+    ]
+# pylint: enable=bad-whitespace, line-too-long
+
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "cylinderp.c"]
+valid = "radius >= 0.0 && length >= 0.0"
+have_Fq = True
+radius_effective_modes = [
+    "excluded volume", "equivalent volume sphere", "radius",
+    "half length", "half min dimension", "half max dimension", "half diagonal",
+    ]
+
+def random():
+    """Return a random parameter set for the model."""
+    volume = 10**np.random.uniform(5, 12)
+    length = 10**np.random.uniform(-2, 2)*volume**0.333
+    radius = np.sqrt(volume/length/np.pi)
+    pars = dict(
+        #scale=1,
+        #background=0,
+        length=length,
+        radius=radius,
+    )
+    return pars
+
+
+# Test 1-D and 2-D models
+qx, qy = 0.2 * np.cos(2.5), 0.2 * np.sin(2.5)
+theta, phi = 80.1534480601659, 10.1510817110481  # (10, 10) in sasview 3.x
+tests = [
+    [{}, 0.2, 0.042761386790780453],
+    [{}, [0.2], [0.042761386790780453]],
+    [{"scale": 1., "background": 0.}, [0.01, 0.05, 0.2],
+     # these numerical results NOT independently verified
+     [3.01823887e+02, 5.36661653e+01, 4.17613868e-02]],
+    [{"scale": 1., "background": 0.},
+     # the longer list here checks  F1, F2=I(Q)*V, R_eff, volume, volume_ratio
+     0.05, 2214.9614083, 26975556.88749548, 73.34013315261608,
+     502654.8245743669, 1.0],
+#2345678901234567890123456789012345678901234567890123456789012345678901234567890
+    [{"@S": "hardsphere",         # MONODISPERSE
+      "scale": 5., "background": 0., "volfraction": 0.2,
+      "structure_factor_mode": 0,  # normal decoupling approx
+      "radius_effective_mode": 1,  # Reff "excluded volume"
+     }, [0.01, 0.05, 0.2], [7.35571916e+01, 5.78147797e+01, 4.15623248e-2]
+     ],
+    [{"@S": "hardsphere",
+      "scale": 5., "background": 0., "volfraction": 0.2,
+      "structure_factor_mode": 1,  # beta approx
+      "radius_effective_mode": 1,  # Reff "excluded volume"
+     }, [0.01, 0.05, 0.2], [8.29729770e+01, 5.44206752e+01, 4.17598382e-2]
+     ],
+    [{"@S": "hardsphere",         # POLYDISPERSE
+      "scale": 5., "background": 0., "volfraction": 0.2,
+      "radius_pd": 0.2, "radius_pd_n": 15, "length_pd": 0.1,
+      "structure_factor_mode": 0,  # normal decoupling approx
+      "radius_effective_mode": 1,  # Reff "excluded volume"
+     }, [0.01, 0.05, 0.2], [87.50350037, 63.95202427, 0.27889988]
+     ],
+    [{"@S": "hardsphere",
+      "scale": 5., "background": 0., "volfraction": 0.2,
+      "radius_pd": 0.2, "radius_pd_n": 15, "length_pd": 0.1,
+      "structure_factor_mode": 1,  # beta approx
+      "radius_effective_mode": 1,  # Reff "excluded volume"
+     }, [0.01, 0.05, 0.2], [132.2101165, 59.89948174, 0.28048784]
+     ],
+    #
+    [{'theta': theta, 'phi': phi}, (qx, qy), 0.03514647218513852],
+    [{'theta': theta, 'phi': phi}, [(qx, qy)], [0.03514647218513852]],
+]
+del qx, qy, theta, phi  # not necessary to delete, but cleaner
+
+def _extend_with_reff_tests(radius, length):
+    """Test R_eff and form volume calculations"""
+    # V and Vr are the same for each R_eff mode
+    V = pi*radius**2*length  # shell volume = form volume for solid objects
+    Vr = 1.0  # form:shell volume ratio
+    # Use test value for I(0.2) from above to check Fsq value.  Need to
+    # remove scale and background before testing.
+    q = 0.2
+    scale, background = V, 0.001
+    Fsq = (0.042761386790780453 - background)*scale
+    F = None  # Need target value for <F>
+    # Various values for R_eff, depending on mode
+    r_effs = [
+        0.,
+        0.5*(0.75*radius*(2.0*radius*length
+                          + (radius + length)*(pi*radius + length)))**(1./3.),
+        (0.75*radius**2*length)**(1./3.),
+        radius,
+        length/2.,
+        min(radius, length/2.),
+        max(radius, length/2.),
+        np.sqrt(4*radius**2 + length**2)/2.,
+    ]
+    tests.extend([
+        ({'radius_effective_mode': 0}, q, F, Fsq, r_effs[0], V, Vr),
+        ({'radius_effective_mode': 1}, q, F, Fsq, r_effs[1], V, Vr),
+        ({'radius_effective_mode': 2}, q, F, Fsq, r_effs[2], V, Vr),
+        ({'radius_effective_mode': 3}, q, F, Fsq, r_effs[3], V, Vr),
+        ({'radius_effective_mode': 4}, q, F, Fsq, r_effs[4], V, Vr),
+        ({'radius_effective_mode': 5}, q, F, Fsq, r_effs[5], V, Vr),
+        ({'radius_effective_mode': 6}, q, F, Fsq, r_effs[6], V, Vr),
+        ({'radius_effective_mode': 7}, q, F, Fsq, r_effs[7], V, Vr),
+    ])
+
+# Test Reff and volume with default model parameters
+_extend_with_reff_tests(parameters[2][2], parameters[3][2])
+del _extend_with_reff_tests
+
+# ADDED by:  RKH  ON: 18Mar2016 renamed sld's etc
diff --git a/sasmodels/models/lib/adaptive.c b/sasmodels/models/lib/adaptive.c
new file mode 100644
index 00000000..bd4a0f50
--- /dev/null
+++ b/sasmodels/models/lib/adaptive.c
@@ -0,0 +1,11213 @@
+// Created by Andrew Jackson on 4/23/07
+
+#ifdef GAUSS_N
+# undef GAUSS_N
+# undef GAUSS_Z
+# undef GAUSS_W
+#endif
+#define GAUSS_N 76
+#define GAUSS_Z Gauss76Z
+#define GAUSS_W Gauss76Wt
+
+// Gaussians
+constant double Gauss76Wt[76] = {
+   .00126779163408536,		//0
+   .00294910295364247,
+   .00462793522803742,
+   .00629918049732845,
+   .00795984747723973,
+   .00960710541471375,
+   .0112381685696677,
+   .0128502838475101,
+   .0144407317482767,
+   .0160068299122486,
+   .0175459372914742,		//10
+   .0190554584671906,
+   .020532847967908,
+   .0219756145344162,
+   .0233813253070112,
+   .0247476099206597,
+   .026072164497986,
+   .0273527555318275,
+   .028587223650054,
+   .029773487255905,
+   .0309095460374916,		//20
+   .0319934843404216,
+   .0330234743977917,
+   .0339977794120564,
+   .0349147564835508,
+   .0357728593807139,
+   .0365706411473296,
+   .0373067565423816,
+   .0379799643084053,
+   .0385891292645067,
+   .0391332242205184,		//30
+   .0396113317090621,
+   .0400226455325968,
+   .040366472122844,
+   .0406422317102947,
+   .0408494593018285,
+   .040987805464794,
+   .0410570369162294,
+   .0410570369162294,
+   .040987805464794,
+   .0408494593018285,		//40
+   .0406422317102947,
+   .040366472122844,
+   .0400226455325968,
+   .0396113317090621,
+   .0391332242205184,
+   .0385891292645067,
+   .0379799643084053,
+   .0373067565423816,
+   .0365706411473296,
+   .0357728593807139,		//50
+   .0349147564835508,
+   .0339977794120564,
+   .0330234743977917,
+   .0319934843404216,
+   .0309095460374916,
+   .029773487255905,
+   .028587223650054,
+   .0273527555318275,
+   .026072164497986,
+   .0247476099206597,		//60
+   .0233813253070112,
+   .0219756145344162,
+   .020532847967908,
+   .0190554584671906,
+   .0175459372914742,
+   .0160068299122486,
+   .0144407317482767,
+   .0128502838475101,
+   .0112381685696677,
+   .00960710541471375,		//70
+   .00795984747723973,
+   .00629918049732845,
+   .00462793522803742,
+   .00294910295364247,
+   .00126779163408536		//75 (indexed from 0)
+};
+
+constant double Gauss76Z[76] = {
+   -.999505948362153,		//0
+   -.997397786355355,
+   -.993608772723527,
+   -.988144453359837,
+   -.981013938975656,
+   -.972229228520377,
+   -.961805126758768,
+   -.949759207710896,
+   -.936111781934811,
+   -.92088586125215,
+   -.904107119545567,		//10
+   -.885803849292083,
+   -.866006913771982,
+   -.844749694983342,
+   -.822068037328975,
+   -.7980001871612,
+   -.77258672828181,
+   -.74587051350361,
+   -.717896592387704,
+   -.688712135277641,
+   -.658366353758143,		//20
+   -.626910417672267,
+   -.594397368836793,
+   -.560882031601237,
+   -.526420920401243,
+   -.491072144462194,
+   -.454895309813726,
+   -.417951418780327,
+   -.380302767117504,
+   -.342012838966962,
+   -.303146199807908,		//30
+   -.263768387584994,
+   -.223945802196474,
+   -.183745593528914,
+   -.143235548227268,
+   -.102483975391227,
+   -.0615595913906112,
+   -.0205314039939986,
+   .0205314039939986,
+   .0615595913906112,
+   .102483975391227,			//40
+   .143235548227268,
+   .183745593528914,
+   .223945802196474,
+   .263768387584994,
+   .303146199807908,
+   .342012838966962,
+   .380302767117504,
+   .417951418780327,
+   .454895309813726,
+   .491072144462194,		//50
+   .526420920401243,
+   .560882031601237,
+   .594397368836793,
+   .626910417672267,
+   .658366353758143,
+   .688712135277641,
+   .717896592387704,
+   .74587051350361,
+   .77258672828181,
+   .7980001871612,	//60
+   .822068037328975,
+   .844749694983342,
+   .866006913771982,
+   .885803849292083,
+   .904107119545567,
+   .92088586125215,
+   .936111781934811,
+   .949759207710896,
+   .961805126758768,
+   .972229228520377,		//70
+   .981013938975656,
+   .988144453359837,
+   .993608772723527,
+   .997397786355355,
+   .999505948362153		//75
+};
+
+// Generated by sasmodels.gengauss.gengauss(500)
+
+#ifdef GAUSS_N
+# undef GAUSS_N
+# undef GAUSS_Z
+# undef GAUSS_W
+#endif
+#define GAUSS_N 500
+#define GAUSS_Z Gauss500Z
+#define GAUSS_W Gauss500Wt
+
+constant double Gauss500Wt[500]={
+	 2.962364450557860e-05,
+	 6.895707281791116e-05,
+	 1.083460286937404e-04,
+	 1.477357747700011e-04,
+	 1.871207158564209e-04,
+	 2.264985887109888e-04,
+	 2.658676532622232e-04,
+	 3.052262942691012e-04,
+	 3.445729352095938e-04,
+	 3.839060141358958e-04,
+	 4.232239754797495e-04,
+	 4.625252670006160e-04,
+	 5.018083384642759e-04,
+	 5.410716410674521e-04,
+	 5.803136271950050e-04,
+	 6.195327503018360e-04,
+	 6.587274648935693e-04,
+	 6.978962265241736e-04,
+	 7.370374918307137e-04,
+	 7.761497185724180e-04,
+	 8.152313656795385e-04,
+	 8.542808933021538e-04,
+	 8.932967628764972e-04,
+	 9.322774371650196e-04,
+	 9.712213803292585e-04,
+	 1.010127057980878e-03,
+	 1.048992937247853e-03,
+	 1.087817486819192e-03,
+	 1.126599177025894e-03,
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+	 3.928969029489244e-03,
+	 3.959617995624711e-03,
+	 3.990110954990701e-03,
+	 4.020446706180265e-03,
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+	 4.750212946261104e-03,
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+	 4.826629602276532e-03,
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+	 4.876624879582988e-03,
+	 4.901334804294905e-03,
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+	 5.137656166300713e-03,
+	 5.160190028971708e-03,
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+	 5.333068932823244e-03,
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+	 5.414492476193605e-03,
+	 5.434317026139552e-03,
+	 5.453927466985097e-03,
+	 5.473323026089901e-03,
+	 5.492502939279533e-03,
+	 5.511466450875843e-03,
+	 5.530212813727135e-03,
+	 5.548741289236909e-03,
+	 5.567051147393411e-03,
+	 5.585141666798417e-03,
+	 5.603012134695263e-03,
+	 5.620661846997404e-03,
+	 5.638090108315933e-03,
+	 5.655296231986907e-03,
+	 5.672279540098574e-03,
+	 5.689039363517862e-03,
+	 5.705575041916975e-03,
+	 5.721885923799350e-03,
+	 5.737971366525110e-03,
+	 5.753830736336734e-03,
+	 5.769463408383798e-03,
+	 5.784868766747535e-03,
+	 5.800046204465426e-03,
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+	 6.176735106227958e-03,
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+	 6.219833035671504e-03,
+	 6.225011456591986e-03,
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+	 6.269951029757533e-03,
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+	 4.483482614589342e-03,
+	 4.455820389211089e-03,
+	 4.427982606961833e-03,
+	 4.399970364634929e-03,
+	 4.371784765896547e-03,
+	 4.343426921244611e-03,
+	 4.314897947962091e-03,
+	 4.286198970075190e-03,
+	 4.257331118307538e-03,
+	 4.228295530036851e-03,
+	 4.199093349248971e-03,
+	 4.169725726493931e-03,
+	 4.140193818840021e-03,
+	 4.110498789828263e-03,
+	 4.080641809426477e-03,
+	 4.050624053982856e-03,
+	 4.020446706180265e-03,
+	 3.990110954990701e-03,
+	 3.959617995624711e-03,
+	 3.928969029489244e-03,
+	 3.898165264136193e-03,
+	 3.867207913216764e-03,
+	 3.836098196433846e-03,
+	 3.804837339493179e-03,
+	 3.773426574055379e-03,
+	 3.741867137686732e-03,
+	 3.710160273812769e-03,
+	 3.678307231665397e-03,
+	 3.646309266237678e-03,
+	 3.614167638231078e-03,
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+	 3.549458465543619e-03,
+	 3.516893470368361e-03,
+	 3.484189911525201e-03,
+	 3.451349077517390e-03,
+	 3.418372262255511e-03,
+	 3.385260765007777e-03,
+	 3.352015890349086e-03,
+	 3.318638948108751e-03,
+	 3.285131253320412e-03,
+	 3.251494126168971e-03,
+	 3.217728891937877e-03,
+	 3.183836880959549e-03,
+	 3.149819428560841e-03,
+	 3.115677875009653e-03,
+	 3.081413565465073e-03,
+	 3.047027849921952e-03,
+	 3.012522083158995e-03,
+	 2.977897624683573e-03,
+	 2.943155838680763e-03,
+	 2.908298093958407e-03,
+	 2.873325763891207e-03,
+	 2.838240226370725e-03,
+	 2.803042863747321e-03,
+	 2.767735062778413e-03,
+	 2.732318214571477e-03,
+	 2.696793714530561e-03,
+	 2.661162962301745e-03,
+	 2.625427361717589e-03,
+	 2.589588320740147e-03,
+	 2.553647251408908e-03,
+	 2.517605569780848e-03,
+	 2.481464695880025e-03,
+	 2.445226053636986e-03,
+	 2.408891070833094e-03,
+	 2.372461179047613e-03,
+	 2.335937813598022e-03,
+	 2.299322413484867e-03,
+	 2.262616421335232e-03,
+	 2.225821283344425e-03,
+	 2.188938449220948e-03,
+	 2.151969372128613e-03,
+	 2.114915508628630e-03,
+	 2.077778318622784e-03,
+	 2.040559265296571e-03,
+	 2.003259815059579e-03,
+	 1.965881437489817e-03,
+	 1.928425605276330e-03,
+	 1.890893794157173e-03,
+	 1.853287482865413e-03,
+	 1.815608153070388e-03,
+	 1.777857289316139e-03,
+	 1.740036378965917e-03,
+	 1.702146912144630e-03,
+	 1.664190381676313e-03,
+	 1.626168283026832e-03,
+	 1.588082114248213e-03,
+	 1.549933375914893e-03,
+	 1.511723571066077e-03,
+	 1.473454205149692e-03,
+	 1.435126785955841e-03,
+	 1.396742823568952e-03,
+	 1.358303830294452e-03,
+	 1.319811320611454e-03,
+	 1.281266811103701e-03,
+	 1.242671820408409e-03,
+	 1.204027869149601e-03,
+	 1.165336479880733e-03,
+	 1.126599177025894e-03,
+	 1.087817486819192e-03,
+	 1.048992937247853e-03,
+	 1.010127057980878e-03,
+	 9.712213803292585e-04,
+	 9.322774371650196e-04,
+	 8.932967628764972e-04,
+	 8.542808933021538e-04,
+	 8.152313656795385e-04,
+	 7.761497185724180e-04,
+	 7.370374918307137e-04,
+	 6.978962265241736e-04,
+	 6.587274648935693e-04,
+	 6.195327503018360e-04,
+	 5.803136271950050e-04,
+	 5.410716410674521e-04,
+	 5.018083384642759e-04,
+	 4.625252670006160e-04,
+	 4.232239754797495e-04,
+	 3.839060141358958e-04,
+	 3.445729352095938e-04,
+	 3.052262942691012e-04,
+	 2.658676532622232e-04,
+	 2.264985887109888e-04,
+	 1.871207158564209e-04,
+	 1.477357747700011e-04,
+	 1.083460286937404e-04,
+	 6.895707281791116e-05,
+	 2.962364450557860e-05
+};
+constant double Gauss500Z[500]={
+	-9.999884567522129e-01,
+	-9.999391798145371e-01,
+	-9.998505288592006e-01,
+	-9.997224876879449e-01,
+	-9.995550589335447e-01,
+	-9.993482486165864e-01,
+	-9.991020646933555e-01,
+	-9.988165167849478e-01,
+	-9.984916161049857e-01,
+	-9.981273754352636e-01,
+	-9.977238091159455e-01,
+	-9.972809330409360e-01,
+	-9.967987646553128e-01,
+	-9.962773229536412e-01,
+	-9.957166284786823e-01,
+	-9.951167033202715e-01,
+	-9.944775711142633e-01,
+	-9.937992570414846e-01,
+	-9.930817878266696e-01,
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+};
+
+// Generated by sasmodels.gengauss.gengauss(5000)
+
+#ifdef GAUSS_N
+# undef GAUSS_N
+# undef GAUSS_Z
+# undef GAUSS_W
+#endif
+#define GAUSS_N 5000
+#define GAUSS_Z Gauss5000Z
+#define GAUSS_W Gauss5000Wt
+
+constant double Gauss5000Wt[5000]={
+	 2.967708115050575e-07,
+	 6.908266104348143e-07,
+	 1.085465123675602e-06,
+	 1.480153958519865e-06,
+	 1.874852422670078e-06,
+	 2.269553150625779e-06,
+	 2.664254217133740e-06,
+	 3.058954680077266e-06,
+	 3.453654255165420e-06,
+	 3.848352564833629e-06,
+	 4.243049412429516e-06,
+	 4.637744673454331e-06,
+	 5.032438122689845e-06,
+	 5.427129630022263e-06,
+	 5.821818973682805e-06,
+	 6.216506078925673e-06,
+	 6.611190683273135e-06,
+	 7.005872720375008e-06,
+	 7.400551980805749e-06,
+	 7.795228314173757e-06,
+	 8.189901580852119e-06,
+	 8.584571627627556e-06,
+	 8.979238283446009e-06,
+	 9.373901382873813e-06,
+	 9.768560793783854e-06,
+	 1.016321635593315e-05,
+	 1.055786790041504e-05,
+	 1.095251528286557e-05,
+	 1.134715833669453e-05,
+	 1.174179691045990e-05,
+	 1.213643086235614e-05,
+	 1.253106000748985e-05,
+	 1.292568421694196e-05,
+	 1.332030331747572e-05,
+	 1.371491717226208e-05,
+	 1.410952559792103e-05,
+	 1.450412847643540e-05,
+	 1.489872561233522e-05,
+	 1.529331687261776e-05,
+	 1.568790209278624e-05,
+	 1.608248112171249e-05,
+	 1.647705380774646e-05,
+	 1.687161999593914e-05,
+	 1.726617951652579e-05,
+	 1.766073222351063e-05,
+	 1.805527795459658e-05,
+	 1.844981657027173e-05,
+	 1.884434788899938e-05,
+	 1.923887178667568e-05,
+	 1.963338807543411e-05,
+	 2.002789662203610e-05,
+	 2.042239726350856e-05,
+	 2.081688984551045e-05,
+	 2.121137420731362e-05,
+	 2.160585020366140e-05,
+	 2.200031766471293e-05,
+	 2.239477644353030e-05,
+	 2.278922638862355e-05,
+	 2.318366733139895e-05,
+	 2.357809912616648e-05,
+	 2.397252161190611e-05,
+	 2.436693463850717e-05,
+	 2.476133804867249e-05,
+	 2.515573168735740e-05,
+	 2.555011539275585e-05,
+	 2.594448901262844e-05,
+	 2.633885239413270e-05,
+	 2.673320537848803e-05,
+	 2.712754781421039e-05,
+	 2.752187953377913e-05,
+	 2.791620040138838e-05,
+	 2.831051024050945e-05,
+	 2.870480891332929e-05,
+	 2.909909625655360e-05,
+	 2.949337210648327e-05,
+	 2.988763631923654e-05,
+	 3.028188873463122e-05,
+	 3.067612920327003e-05,
+	 3.107035755314027e-05,
+	 3.146457365118839e-05,
+	 3.185877731818632e-05,
+	 3.225296842167827e-05,
+	 3.264714678931476e-05,
+	 3.304131226628532e-05,
+	 3.343546470625303e-05,
+	 3.382960395220756e-05,
+	 3.422372984128839e-05,
+	 3.461784222625275e-05,
+	 3.501194094136184e-05,
+	 3.540602584001236e-05,
+	 3.580009676421725e-05,
+	 3.619415355896783e-05,
+	 3.658819606898828e-05,
+	 3.698222413256360e-05,
+	 3.737623759961558e-05,
+	 3.777023631558019e-05,
+	 3.816422012406606e-05,
+	 3.855818886796110e-05,
+	 3.895214239344983e-05,
+	 3.934608054482744e-05,
+	 3.974000316332509e-05,
+	 4.013391009880438e-05,
+	 4.052780119285966e-05,
+	 4.092167629402477e-05,
+	 4.131553523670950e-05,
+	 4.170937787334214e-05,
+	 4.210320405111855e-05,
+	 4.249701360853457e-05,
+	 4.289080638926642e-05,
+	 4.328458224262764e-05,
+	 4.367834101235882e-05,
+	 4.407208254216379e-05,
+	 4.446580667493457e-05,
+	 4.485951325743296e-05,
+	 4.525320213529415e-05,
+	 4.564687314707027e-05,
+	 4.604052614504553e-05,
+	 4.643416097316290e-05,
+	 4.682777746930432e-05,
+	 4.722137548202861e-05,
+	 4.761495485715089e-05,
+	 4.800851544198063e-05,
+	 4.840205707034650e-05,
+	 4.879557960053133e-05,
+	 4.918908286773508e-05,
+	 4.958256672101606e-05,
+	 4.997603100461701e-05,
+	 5.036947556272298e-05,
+	 5.076290023781856e-05,
+	 5.115630487646047e-05,
+	 5.154968932351106e-05,
+	 5.194305342337709e-05,
+	 5.233639701978578e-05,
+	 5.272971996186675e-05,
+	 5.312302209158545e-05,
+	 5.351630325096498e-05,
+	 5.390956328655539e-05,
+	 5.430280204568531e-05,
+	 5.469601937144993e-05,
+	 5.508921510788812e-05,
+	 5.548238910202844e-05,
+	 5.587554119254959e-05,
+	 5.626867123302761e-05,
+	 5.666177906026646e-05,
+	 5.705486452483136e-05,
+	 5.744792747176530e-05,
+	 5.784096774057170e-05,
+	 5.823398517928101e-05,
+	 5.862697963333669e-05,
+	 5.901995094921994e-05,
+	 5.941289896631685e-05,
+	 5.980582353508762e-05,
+	 6.019872449896147e-05,
+	 6.059160170043561e-05,
+	 6.098445498543843e-05,
+	 6.137728419841923e-05,
+	 6.177008918968614e-05,
+	 6.216286979746446e-05,
+	 6.255562586861984e-05,
+	 6.294835724790345e-05,
+	 6.334106378405790e-05,
+	 6.373374531646440e-05,
+	 6.412640169533940e-05,
+	 6.451903276031043e-05,
+	 6.491163836123763e-05,
+	 6.530421834041504e-05,
+	 6.569677254621874e-05,
+	 6.608930081907467e-05,
+	 6.648180300467884e-05,
+	 6.687427895012881e-05,
+	 6.726672850241030e-05,
+	 6.765915150244778e-05,
+	 6.805154779862556e-05,
+	 6.844391723306542e-05,
+	 6.883625965271705e-05,
+	 6.922857490098878e-05,
+	 6.962086282388699e-05,
+	 7.001312326963224e-05,
+	 7.040535607907874e-05,
+	 7.079756110056347e-05,
+	 7.118973817790561e-05,
+	 7.158188715570165e-05,
+	 7.197400787938955e-05,
+	 7.236610019440714e-05,
+	 7.275816394673754e-05,
+	 7.315019898155956e-05,
+	 7.354220514102986e-05,
+	 7.393418227496131e-05,
+	 7.432613022641832e-05,
+	 7.471804884252410e-05,
+	 7.510993796599932e-05,
+	 7.550179744326617e-05,
+	 7.589362711868172e-05,
+	 7.628542683887226e-05,
+	 7.667719644856037e-05,
+	 7.706893579445424e-05,
+	 7.746064471960257e-05,
+	 7.785232307213077e-05,
+	 7.824397069311407e-05,
+	 7.863558743319620e-05,
+	 7.902717313564044e-05,
+	 7.941872764421552e-05,
+	 7.981025080590855e-05,
+	 8.020174246764378e-05,
+	 8.059320247048232e-05,
+	 8.098463066597581e-05,
+	 8.137602689364404e-05,
+	 8.176739100288299e-05,
+	 8.215872283863294e-05,
+	 8.255002224671039e-05,
+	 8.294128907110016e-05,
+	 8.333252315822167e-05,
+	 8.372372435221428e-05,
+	 8.411489250183786e-05,
+	 8.450602744994464e-05,
+	 8.489712904126891e-05,
+	 8.528819712679954e-05,
+	 8.567923154545622e-05,
+	 8.607023214766979e-05,
+	 8.646119877855770e-05,
+	 8.685213128117572e-05,
+	 8.724302950290486e-05,
+	 8.763389328883085e-05,
+	 8.802472248730652e-05,
+	 8.841551694106225e-05,
+	 8.880627649659037e-05,
+	 8.919700099808029e-05,
+	 8.958769029518601e-05,
+	 8.997834423053302e-05,
+	 9.036896265139633e-05,
+	 9.075954540423977e-05,
+	 9.115009233260759e-05,
+	 9.154060328375660e-05,
+	 9.193107810317785e-05,
+	 9.232151663510942e-05,
+	 9.271191873096626e-05,
+	 9.310228423047216e-05,
+	 9.349261298256864e-05,
+	 9.388290483325177e-05,
+	 9.427315962767892e-05,
+	 9.466337720990975e-05,
+	 9.505355743155006e-05,
+	 9.544370013371267e-05,
+	 9.583380516169227e-05,
+	 9.622387236594623e-05,
+	 9.661390158929014e-05,
+	 9.700389267851904e-05,
+	 9.739384547955711e-05,
+	 9.778375983910324e-05,
+	 9.817363560451091e-05,
+	 9.856347261721133e-05,
+	 9.895327072912864e-05,
+	 9.934302978140069e-05,
+	 9.973274962318625e-05,
+	 1.001224301006458e-04,
+	 1.005120710586266e-04,
+	 1.009016723450495e-04,
+	 1.012912338038130e-04,
+	 1.016807552832619e-04,
+	 1.020702366292262e-04,
+	 1.024596776851532e-04,
+	 1.028490783019434e-04,
+	 1.032384383231154e-04,
+	 1.036277575949719e-04,
+	 1.040170359643481e-04,
+	 1.044062732778376e-04,
+	 1.047954693821035e-04,
+	 1.051846241232085e-04,
+	 1.055737373462861e-04,
+	 1.059628089016359e-04,
+	 1.063518386299136e-04,
+	 1.067408263821736e-04,
+	 1.071297720016758e-04,
+	 1.075186753370153e-04,
+	 1.079075362345124e-04,
+	 1.082963545415241e-04,
+	 1.086851301021314e-04,
+	 1.090738627650504e-04,
+	 1.094625523752495e-04,
+	 1.098511987793225e-04,
+	 1.102398018257169e-04,
+	 1.106283613580635e-04,
+	 1.110168772269773e-04,
+	 1.114053492757775e-04,
+	 1.117937773521273e-04,
+	 1.121821613036203e-04,
+	 1.125705009757695e-04,
+	 1.129587962173100e-04,
+	 1.133470468722491e-04,
+	 1.137352527873879e-04,
+	 1.141234138118102e-04,
+	 1.145115297909046e-04,
+	 1.148996005717352e-04,
+	 1.152876260011528e-04,
+	 1.156756059268026e-04,
+	 1.160635401935752e-04,
+	 1.164514286488634e-04,
+	 1.168392711417371e-04,
+	 1.172270675160659e-04,
+	 1.176148176204122e-04,
+	 1.180025213029248e-04,
+	 1.183901784088470e-04,
+	 1.187777887839013e-04,
+	 1.191653522795650e-04,
+	 1.195528687379955e-04,
+	 1.199403380084779e-04,
+	 1.203277599375793e-04,
+	 1.207151343736642e-04,
+	 1.211024611620411e-04,
+	 1.214897401516819e-04,
+	 1.218769711881080e-04,
+	 1.222641541188861e-04,
+	 1.226512887910341e-04,
+	 1.230383750522546e-04,
+	 1.234254127507875e-04,
+	 1.238124017313848e-04,
+	 1.241993418423605e-04,
+	 1.245862329330305e-04,
+	 1.249730748470151e-04,
+	 1.253598674337975e-04,
+	 1.257466105412958e-04,
+	 1.261333040142998e-04,
+	 1.265199477040235e-04,
+	 1.269065414545336e-04,
+	 1.272930851139742e-04,
+	 1.276795785295555e-04,
+	 1.280660215502940e-04,
+	 1.284524140235717e-04,
+	 1.288387557946632e-04,
+	 1.292250467133533e-04,
+	 1.296112866251243e-04,
+	 1.299974753790855e-04,
+	 1.303836128229531e-04,
+	 1.307696988042698e-04,
+	 1.311557331683816e-04,
+	 1.315417157664387e-04,
+	 1.319276464420403e-04,
+	 1.323135250471828e-04,
+	 1.326993514256334e-04,
+	 1.330851254289941e-04,
+	 1.334708469016801e-04,
+	 1.338565156937744e-04,
+	 1.342421316507116e-04,
+	 1.346276946213199e-04,
+	 1.350132044558853e-04,
+	 1.353986609976105e-04,
+	 1.357840640984470e-04,
+	 1.361694136045407e-04,
+	 1.365547093620471e-04,
+	 1.369399512219494e-04,
+	 1.373251390314144e-04,
+	 1.377102726370039e-04,
+	 1.380953518888432e-04,
+	 1.384803766325935e-04,
+	 1.388653467170688e-04,
+	 1.392502619920174e-04,
+	 1.396351223036889e-04,
+	 1.400199275002043e-04,
+	 1.404046774301298e-04,
+	 1.407893719417729e-04,
+	 1.411740108832741e-04,
+	 1.415585941035836e-04,
+	 1.419431214476940e-04,
+	 1.423275927683815e-04,
+	 1.427120079110142e-04,
+	 1.430963667233998e-04,
+	 1.434806690559252e-04,
+	 1.438649147549203e-04,
+	 1.442491036700635e-04,
+	 1.446332356494989e-04,
+	 1.450173105425354e-04,
+	 1.454013281948481e-04,
+	 1.457852884570325e-04,
+	 1.461691911771292e-04,
+	 1.465530362031210e-04,
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+	 1.473205525695710e-04,
+	 1.477042236058660e-04,
+	 1.480878363419589e-04,
+	 1.484713906268956e-04,
+	 1.488548863106759e-04,
+	 1.492383232398284e-04,
+	 1.496217012641095e-04,
+	 1.500050202306276e-04,
+	 1.503882799906289e-04,
+	 1.507714803919522e-04,
+	 1.511546212832247e-04,
+	 1.515377025120099e-04,
+	 1.519207239272822e-04,
+	 1.523036853806588e-04,
+	 1.526865867176077e-04,
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+	 1.755449541985493e-04,
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+	 1.763027836783566e-04,
+	 1.766815941113189e-04,
+	 1.770603348078628e-04,
+	 1.774390056168301e-04,
+	 1.778176063899672e-04,
+	 1.781961369780506e-04,
+	 1.785745972304970e-04,
+	 1.789529869986419e-04,
+	 1.793313061331756e-04,
+	 1.797095544849302e-04,
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+	 1.687161999593914e-05,
+	 1.647705380774646e-05,
+	 1.608248112171249e-05,
+	 1.568790209278624e-05,
+	 1.529331687261776e-05,
+	 1.489872561233522e-05,
+	 1.450412847643540e-05,
+	 1.410952559792103e-05,
+	 1.371491717226208e-05,
+	 1.332030331747572e-05,
+	 1.292568421694196e-05,
+	 1.253106000748985e-05,
+	 1.213643086235614e-05,
+	 1.174179691045990e-05,
+	 1.134715833669453e-05,
+	 1.095251528286557e-05,
+	 1.055786790041504e-05,
+	 1.016321635593315e-05,
+	 9.768560793783854e-06,
+	 9.373901382873813e-06,
+	 8.979238283446009e-06,
+	 8.584571627627556e-06,
+	 8.189901580852119e-06,
+	 7.795228314173757e-06,
+	 7.400551980805749e-06,
+	 7.005872720375008e-06,
+	 6.611190683273135e-06,
+	 6.216506078925673e-06,
+	 5.821818973682805e-06,
+	 5.427129630022263e-06,
+	 5.032438122689845e-06,
+	 4.637744673454331e-06,
+	 4.243049412429516e-06,
+	 3.848352564833629e-06,
+	 3.453654255165420e-06,
+	 3.058954680077266e-06,
+	 2.664254217133740e-06,
+	 2.269553150625779e-06,
+	 1.874852422670078e-06,
+	 1.480153958519865e-06,
+	 1.085465123675602e-06,
+	 6.908266104348143e-07,
+	 2.967708115050575e-07
+};
+constant double Gauss5000Z[5000]={
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+	 9.884882585479788e-01,
+	 9.885831170184199e-01,
+	 9.886775852899461e-01,
+	 9.887716633252704e-01,
+	 9.888653510872598e-01,
+	 9.889586485389351e-01,
+	 9.890515556434714e-01,
+	 9.891440723641978e-01,
+	 9.892361986645972e-01,
+	 9.893279345083072e-01,
+	 9.894192798591191e-01,
+	 9.895102346809784e-01,
+	 9.896007989379848e-01,
+	 9.896909725943920e-01,
+	 9.897807556146080e-01,
+	 9.898701479631951e-01,
+	 9.899591496048694e-01,
+	 9.900477605045018e-01,
+	 9.901359806271171e-01,
+	 9.902238099378942e-01,
+	 9.903112484021663e-01,
+	 9.903982959854213e-01,
+	 9.904849526533008e-01,
+	 9.905712183716012e-01,
+	 9.906570931062728e-01,
+	 9.907425768234204e-01,
+	 9.908276694893032e-01,
+	 9.909123710703346e-01,
+	 9.909966815330825e-01,
+	 9.910806008442692e-01,
+	 9.911641289707711e-01,
+	 9.912472658796194e-01,
+	 9.913300115379995e-01,
+	 9.914123659132512e-01,
+	 9.914943289728688e-01,
+	 9.915759006845011e-01,
+	 9.916570810159512e-01,
+	 9.917378699351770e-01,
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+	 9.918982734095585e-01,
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+	 9.920571108543973e-01,
+	 9.921359422372742e-01,
+	 9.922143820189177e-01,
+	 9.922924301683670e-01,
+	 9.923700866548164e-01,
+	 9.924473514476143e-01,
+	 9.925242245162640e-01,
+	 9.926007058304231e-01,
+	 9.926767953599043e-01,
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+	 9.928277989448553e-01,
+	 9.929027129407233e-01,
+	 9.929772350327095e-01,
+	 9.930513651913996e-01,
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+	 9.931984495920079e-01,
+	 9.932714037758712e-01,
+	 9.933439659103285e-01,
+	 9.934161359667391e-01,
+	 9.934879139166171e-01,
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+	 9.936302933836056e-01,
+	 9.937008948445183e-01,
+	 9.937711040865025e-01,
+	 9.938409210818464e-01,
+	 9.939103458029928e-01,
+	 9.939793782225393e-01,
+	 9.940480183132387e-01,
+	 9.941162660479983e-01,
+	 9.941841213998803e-01,
+	 9.942515843421018e-01,
+	 9.943186548480351e-01,
+	 9.943853328912067e-01,
+	 9.944516184452986e-01,
+	 9.945175114841477e-01,
+	 9.945830119817456e-01,
+	 9.946481199122388e-01,
+	 9.947128352499289e-01,
+	 9.947771579692725e-01,
+	 9.948410880448810e-01,
+	 9.949046254515209e-01,
+	 9.949677701641138e-01,
+	 9.950305221577358e-01,
+	 9.950928814076186e-01,
+	 9.951548478891488e-01,
+	 9.952164215778677e-01,
+	 9.952776024494718e-01,
+	 9.953383904798129e-01,
+	 9.953987856448975e-01,
+	 9.954587879208874e-01,
+	 9.955183972840993e-01,
+	 9.955776137110051e-01,
+	 9.956364371782318e-01,
+	 9.956948676625614e-01,
+	 9.957529051409312e-01,
+	 9.958105495904334e-01,
+	 9.958678009883155e-01,
+	 9.959246593119800e-01,
+	 9.959811245389847e-01,
+	 9.960371966470425e-01,
+	 9.960928756140213e-01,
+	 9.961481614179445e-01,
+	 9.962030540369904e-01,
+	 9.962575534494926e-01,
+	 9.963116596339400e-01,
+	 9.963653725689764e-01,
+	 9.964186922334012e-01,
+	 9.964716186061688e-01,
+	 9.965241516663890e-01,
+	 9.965762913933265e-01,
+	 9.966280377664015e-01,
+	 9.966793907651896e-01,
+	 9.967303503694215e-01,
+	 9.967809165589830e-01,
+	 9.968310893139156e-01,
+	 9.968808686144157e-01,
+	 9.969302544408352e-01,
+	 9.969792467736811e-01,
+	 9.970278455936161e-01,
+	 9.970760508814578e-01,
+	 9.971238626181795e-01,
+	 9.971712807849096e-01,
+	 9.972183053629318e-01,
+	 9.972649363336853e-01,
+	 9.973111736787648e-01,
+	 9.973570173799199e-01,
+	 9.974024674190559e-01,
+	 9.974475237782336e-01,
+	 9.974921864396690e-01,
+	 9.975364553857333e-01,
+	 9.975803305989536e-01,
+	 9.976238120620119e-01,
+	 9.976668997577459e-01,
+	 9.977095936691487e-01,
+	 9.977518937793688e-01,
+	 9.977938000717101e-01,
+	 9.978353125296320e-01,
+	 9.978764311367492e-01,
+	 9.979171558768322e-01,
+	 9.979574867338065e-01,
+	 9.979974236917534e-01,
+	 9.980369667349095e-01,
+	 9.980761158476671e-01,
+	 9.981148710145737e-01,
+	 9.981532322203326e-01,
+	 9.981911994498023e-01,
+	 9.982287726879969e-01,
+	 9.982659519200862e-01,
+	 9.983027371313952e-01,
+	 9.983391283074048e-01,
+	 9.983751254337510e-01,
+	 9.984107284962256e-01,
+	 9.984459374807759e-01,
+	 9.984807523735048e-01,
+	 9.985151731606706e-01,
+	 9.985491998286873e-01,
+	 9.985828323641244e-01,
+	 9.986160707537068e-01,
+	 9.986489149843153e-01,
+	 9.986813650429861e-01,
+	 9.987134209169111e-01,
+	 9.987450825934373e-01,
+	 9.987763500600682e-01,
+	 9.988072233044618e-01,
+	 9.988377023144328e-01,
+	 9.988677870779507e-01,
+	 9.988974775831408e-01,
+	 9.989267738182843e-01,
+	 9.989556757718179e-01,
+	 9.989841834323336e-01,
+	 9.990122967885794e-01,
+	 9.990400158294589e-01,
+	 9.990673405440310e-01,
+	 9.990942709215108e-01,
+	 9.991208069512686e-01,
+	 9.991469486228305e-01,
+	 9.991726959258782e-01,
+	 9.991980488502492e-01,
+	 9.992230073859366e-01,
+	 9.992475715230891e-01,
+	 9.992717412520110e-01,
+	 9.992955165631625e-01,
+	 9.993188974471594e-01,
+	 9.993418838947731e-01,
+	 9.993644758969308e-01,
+	 9.993866734447152e-01,
+	 9.994084765293649e-01,
+	 9.994298851422743e-01,
+	 9.994508992749930e-01,
+	 9.994715189192268e-01,
+	 9.994917440668371e-01,
+	 9.995115747098408e-01,
+	 9.995310108404106e-01,
+	 9.995500524508754e-01,
+	 9.995686995337189e-01,
+	 9.995869520815813e-01,
+	 9.996048100872582e-01,
+	 9.996222735437010e-01,
+	 9.996393424440169e-01,
+	 9.996560167814686e-01,
+	 9.996722965494749e-01,
+	 9.996881817416099e-01,
+	 9.997036723516038e-01,
+	 9.997187683733426e-01,
+	 9.997334698008677e-01,
+	 9.997477766283768e-01,
+	 9.997616888502225e-01,
+	 9.997752064609142e-01,
+	 9.997883294551163e-01,
+	 9.998010578276494e-01,
+	 9.998133915734896e-01,
+	 9.998253306877691e-01,
+	 9.998368751657757e-01,
+	 9.998480250029530e-01,
+	 9.998587801949006e-01,
+	 9.998691407373738e-01,
+	 9.998791066262838e-01,
+	 9.998886778576976e-01,
+	 9.998978544278384e-01,
+	 9.999066363330852e-01,
+	 9.999150235699730e-01,
+	 9.999230161351929e-01,
+	 9.999306140255922e-01,
+	 9.999378172381750e-01,
+	 9.999446257701015e-01,
+	 9.999510396186888e-01,
+	 9.999570587814121e-01,
+	 9.999626832559038e-01,
+	 9.999679130399564e-01,
+	 9.999727481315230e-01,
+	 9.999771885287215e-01,
+	 9.999812342298391e-01,
+	 9.999848852333429e-01,
+	 9.999881415378994e-01,
+	 9.999910031424144e-01,
+	 9.999934700461274e-01,
+	 9.999955422488499e-01,
+	 9.999972197516868e-01,
+	 9.999985025597460e-01,
+	 9.999993906966838e-01,
+	 9.999998843594127e-01
+};
+
+static int
+gauss_weights(double qr, double **w, double **z)
+{
+    if (qr < 100) {
+        *w = Gauss76Wt; *z = Gauss76Z; return 76;
+    } else if (qr < 750) {
+        *w = Gauss500Wt; *z = Gauss500Z; return 500;
+    } else {
+        *w = Gauss5000Wt; *z = Gauss5000Z; return 5000;
+    }
+}
\ No newline at end of file

From 56630af2897f4de491f6b492dfbef48f6196a65d Mon Sep 17 00:00:00 2001
From: Paul Kienzle <pkienzle@nist.gov>
Date: Tue, 29 Jul 2025 09:49:57 -0400
Subject: [PATCH 2/5] add core shell bicelle; fix gpu build errors (mac)

---
 sasmodels/models/core_shell_bicelle.c  | 11 +++++++----
 sasmodels/models/core_shell_bicelle.py |  2 +-
 sasmodels/models/cylinderp.c           |  2 +-
 sasmodels/models/lib/adaptive.c        |  2 +-
 4 files changed, 10 insertions(+), 7 deletions(-)

diff --git a/sasmodels/models/core_shell_bicelle.c b/sasmodels/models/core_shell_bicelle.c
index bddb8d2e..b5d7df9b 100644
--- a/sasmodels/models/core_shell_bicelle.c
+++ b/sasmodels/models/core_shell_bicelle.c
@@ -93,16 +93,19 @@ Fq(double q,
     const double uplim = M_PI_4;
     const double halflength = 0.5*length;
 
+    double qr = q*fmax(radius+thick_radius, 2*halflength+thick_face);
+    constant double *w, *z;
+    int n = gauss_weights(qr, &w, &z);
     double total_F1 = 0.0;
     double total_F2 = 0.0;
-    for(int i=0;i<GAUSS_N;i++) {
-        double theta = (GAUSS_Z[i] + 1.0)*uplim;
+    for(int i=0;i<n;i++) {
+        double theta = (z[i] + 1.0)*uplim;
         double sin_theta, cos_theta; // slots to hold sincos function output
         SINCOS(theta, sin_theta, cos_theta);
         double form = bicelle_kernel(q*sin_theta, q*cos_theta, radius, thick_radius, thick_face,
                                    halflength, sld_core, sld_face, sld_rim, sld_solvent);
-        total_F1 += GAUSS_W[i]*form*sin_theta;
-        total_F2 += GAUSS_W[i]*form*form*sin_theta;
+        total_F1 += w[i]*form*sin_theta;
+        total_F2 += w[i]*form*form*sin_theta;
     }
     // Correct for integration range
     total_F1 *= uplim;
diff --git a/sasmodels/models/core_shell_bicelle.py b/sasmodels/models/core_shell_bicelle.py
index bca30229..a8f42200 100644
--- a/sasmodels/models/core_shell_bicelle.py
+++ b/sasmodels/models/core_shell_bicelle.py
@@ -152,7 +152,7 @@
 
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c",
+source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c",
           "core_shell_bicelle.c"]
 have_Fq = True
 radius_effective_modes = [
diff --git a/sasmodels/models/cylinderp.c b/sasmodels/models/cylinderp.c
index e47ca2c9..862be5d0 100644
--- a/sasmodels/models/cylinderp.c
+++ b/sasmodels/models/cylinderp.c
@@ -69,7 +69,7 @@ Fq(double q,
     double total_F2 = 0.0;
 
     double qr = q*(radius > length ? radius : length);
-    double *w, *z;
+    constant double *w, *z;
     int n = gauss_weights(qr, &w, &z);
     for (int i=0; i<n ;i++) {
         const double theta = z[i]*zm + zb;
diff --git a/sasmodels/models/lib/adaptive.c b/sasmodels/models/lib/adaptive.c
index bd4a0f50..0f0179da 100644
--- a/sasmodels/models/lib/adaptive.c
+++ b/sasmodels/models/lib/adaptive.c
@@ -11201,7 +11201,7 @@ constant double Gauss5000Z[5000]={
 };
 
 static int
-gauss_weights(double qr, double **w, double **z)
+gauss_weights(double qr, constant double **w, constant double **z)
 {
     if (qr < 100) {
         *w = Gauss76Wt; *z = Gauss76Z; return 76;

From 9bb7d2cea12451c6938dbc07160fa00afc880e8f Mon Sep 17 00:00:00 2001
From: Paul Kienzle <pkienzle@nist.gov>
Date: Wed, 30 Jul 2025 10:19:16 -0400
Subject: [PATCH 3/5] adaptive integration for most shape models

---
 sasmodels/direct_model.py                     |  20 +-
 sasmodels/generate.py                         |  28 +-
 sasmodels/gengauss.py                         |  13 +-
 sasmodels/model_test.py                       |  40 ++-
 sasmodels/models/barbell.c                    |  23 +-
 sasmodels/models/barbell.py                   |   2 +-
 sasmodels/models/capped_cylinder.c            |  23 +-
 sasmodels/models/capped_cylinder.py           |   2 +-
 sasmodels/models/core_shell_bicelle.c         |   5 +-
 .../models/core_shell_bicelle_elliptical.c    |  29 +-
 .../models/core_shell_bicelle_elliptical.py   |   2 +-
 ...core_shell_bicelle_elliptical_belt_rough.c |  29 +-
 ...ore_shell_bicelle_elliptical_belt_rough.py |   2 +-
 sasmodels/models/core_shell_cylinder.c        |  15 +-
 sasmodels/models/core_shell_cylinder.py       |   2 +-
 sasmodels/models/core_shell_ellipsoid.c       |  12 +-
 sasmodels/models/core_shell_ellipsoid.py      |  12 +-
 sasmodels/models/core_shell_parallelepiped.c  |  24 +-
 sasmodels/models/core_shell_parallelepiped.py |   2 +-
 sasmodels/models/cylinder.c                   |  14 +-
 sasmodels/models/cylinder.py                  |   2 +-
 sasmodels/models/cylinderp.c                  | 104 --------
 sasmodels/models/cylinderp.py                 | 251 ------------------
 sasmodels/models/ellipsoid.c                  |  15 +-
 sasmodels/models/ellipsoid.py                 |   2 +-
 sasmodels/models/elliptical_cylinder.c        |  24 +-
 sasmodels/models/elliptical_cylinder.py       |   2 +-
 .../models/flexible_cylinder_elliptical.c     |  11 +-
 .../models/flexible_cylinder_elliptical.py    |  11 +-
 sasmodels/models/hollow_cylinder.c            |  13 +-
 sasmodels/models/hollow_cylinder.py           |   2 +-
 sasmodels/models/hollow_rectangular_prism.c   |  24 +-
 sasmodels/models/hollow_rectangular_prism.py  |   2 +-
 .../hollow_rectangular_prism_thin_walls.c     |  24 +-
 .../hollow_rectangular_prism_thin_walls.py    |   2 +-
 sasmodels/models/lib/adaptive.c               |  82 +++---
 sasmodels/models/parallelepiped.c             |  24 +-
 sasmodels/models/parallelepiped.py            |   2 +-
 sasmodels/models/pringle.c                    |  20 +-
 sasmodels/models/pringle.py                   |   2 +-
 sasmodels/models/rectangular_prism.c          |  27 +-
 sasmodels/models/rectangular_prism.py         |   2 +-
 sasmodels/models/spherical_sld.c              |   3 +
 sasmodels/models/stacked_disks.c              |  13 +-
 sasmodels/models/stacked_disks.py             |  18 +-
 sasmodels/models/triaxial_ellipsoid.c         |  29 +-
 sasmodels/models/triaxial_ellipsoid.py        |   2 +-
 47 files changed, 434 insertions(+), 578 deletions(-)
 delete mode 100644 sasmodels/models/cylinderp.c
 delete mode 100644 sasmodels/models/cylinderp.py

diff --git a/sasmodels/direct_model.py b/sasmodels/direct_model.py
index 7662e17a..2fad3406 100644
--- a/sasmodels/direct_model.py
+++ b/sasmodels/direct_model.py
@@ -453,14 +453,18 @@ def test_reparameterize():
     except Exception:
         pass
 
-def _direct_calculate(model, data, pars):
+def _direct_calculate(model, data, pars, ngauss=0):
     from .core import build_model, load_model_info
+    from .generate import set_integration_size
+
     model_info = load_model_info(model)
+    if ngauss != 0:
+        set_integration_size(model_info, ngauss)
     kernel = build_model(model_info)
     calculator = DirectModel(data, kernel)
     return calculator(**pars)
 
-def Iq(model, q, dq=None, ql=None, qw=None, **pars):
+def Iq(model, q, dq=None, ql=None, qw=None, ngauss=0, **pars):
     """
     Compute I(q) for *model*. Resolution is *dq* for pinhole or *ql* and *qw*
     for slit geometry. Use 0 or None for infinite slits.
@@ -498,16 +502,16 @@ def broadcast(v):
             else np.full(len(q), v) if np.isscalar(v)
             else _as_numpy(v))
     data.dxl, data.dxw = broadcast(ql), broadcast(qw)
-    return _direct_calculate(model, data, pars)
+    return _direct_calculate(model, data, pars, ngauss=ngauss)
 
-def Iqxy(model, qx, qy, dqx=None, dqy=None, **pars):
+def Iqxy(model, qx, qy, dqx=None, dqy=None, ngauss=0, **pars):
     """
     Compute I(qx, qy) for *model*. Resolution is *dqx* and *dqy*.
     See :func:`Iq` for details on model and parameters.
     """
     from .data import Data2D
     data = Data2D(x=qx, y=qy, dx=dqx, dy=dqy)
-    return _direct_calculate(model, data, pars)
+    return _direct_calculate(model, data, pars, ngauss=ngauss)
 
 def Gxi(model, xi, **pars):
     """
@@ -528,6 +532,8 @@ def main():
     if len(sys.argv) < 3:
         print("usage: python -m sasmodels.direct_model modelname (q|qx,qy) par=val ...")
         sys.exit(1)
+
+    ngauss = 0
     model = sys.argv[1]
     call = sys.argv[2].upper()
     pars = dict((k, (float(v) if not k.endswith("_pd_type") else v))
@@ -542,13 +548,13 @@ def main():
         dq = dqw = dql = None
         #dq = [q*0.05] # 5% pinhole resolution
         #dqw, dql = [q*0.05], [1.0] # 5% horizontal slit resolution
-        print(Iq(model, [q], dq=dq, qw=dqw, ql=dql, **pars)[0])
+        print(Iq(model, [q], dq=dq, qw=dqw, ql=dql, ngauss=ngauss, **pars)[0])
         #print(Gxi(model, [q], **pars)[0])
     elif len(values) == 2:
         qx, qy = values
         dq = None
         #dq = [0.005] # 5% pinhole resolution at q = 0.1
-        print(Iqxy(model, [qx], [qy], dqx=dq, dqy=dq, **pars)[0])
+        print(Iqxy(model, [qx], [qy], dqx=dq, dqy=dq, ngauss=ngauss, **pars)[0])
     else:
         print("use q or qx,qy")
         sys.exit(1)
diff --git a/sasmodels/generate.py b/sasmodels/generate.py
index 7db1c3ec..55f395c6 100644
--- a/sasmodels/generate.py
+++ b/sasmodels/generate.py
@@ -291,13 +291,27 @@ def set_integration_size(info, n):
     Note: this really ought to be a method in modelinfo, but that leads to
     import loops.
     """
-    if info.source and any(lib.startswith('lib/gauss') for lib in info.source):
-        from .gengauss import gengauss
-        path = joinpath(MODEL_PATH, "lib", "gauss%d.c"%n)
-        if not exists(path):
-            gengauss(n, path)
-        info.source = ["lib/gauss%d.c"%n if lib.startswith('lib/gauss')
-                       else lib for lib in info.source]
+    from .gengauss import gengauss
+
+    if not info.source:
+        return
+
+    # Generate the integration points
+    path = joinpath(MODEL_PATH, "lib", f"gauss{n}.c")
+    if not exists(path):
+        # print(f"building Gaussian integration points of size {n} in {str(path)}")
+        gengauss(n, path)
+
+    # Replace adaptive.c or lib/gauss<n>.c
+    try:
+        index = info.source.index("lib/adaptive.c")
+        info.source[index:index+1] = [f"lib/gauss{n}.c", "lib/nonadaptive.c"]
+    except ValueError:
+        for index in range(len(info.source)-1, -1, -1):
+            if info.source[index].startswith("lib/gauss"):
+                info.source[index] = f"lib/gauss{n}.c"
+                break
+    # print("info.source is now", info.source)
 
 def format_units(units):
     # type: (str) -> str
diff --git a/sasmodels/gengauss.py b/sasmodels/gengauss.py
index a9ce027f..2ef06313 100755
--- a/sasmodels/gengauss.py
+++ b/sasmodels/gengauss.py
@@ -21,19 +21,18 @@ def gengauss(n, path):
         array_size = n
 
     with open(path, "w") as fid:
-        fid.write("""\
-// Generated by sasmodels.gengauss.gengauss(%d)
+        fid.write(f"""\
+// Generated by sasmodels.gengauss.gengauss({n})
 
 #ifdef GAUSS_N
 # undef GAUSS_N
 # undef GAUSS_Z
 # undef GAUSS_W
 #endif
-#define GAUSS_N %d
-#define GAUSS_Z Gauss%dZ
-#define GAUSS_W Gauss%dWt
-
-"""%(n, n, n, n))
+#define GAUSS_N {n}
+#define GAUSS_Z Gauss{n}Z
+#define GAUSS_W Gauss{n}Wt
+""")
 
         if array_size != n:
             fid.write("// Note: using array size %d so that it is a multiple of 4\n\n"%array_size)
diff --git a/sasmodels/model_test.py b/sasmodels/model_test.py
index ef9b079b..2a67c9ef 100755
--- a/sasmodels/model_test.py
+++ b/sasmodels/model_test.py
@@ -579,6 +579,31 @@ def _build_test(test):
     for test in tests:
         yield _build_test(test)
 
+def _generate_target_values(modelname, ngauss=0):
+    from .generate import set_integration_size
+
+    model_info = load_model_info(modelname)
+    if ngauss != 0:
+        set_integration_size(model_info, ngauss)
+    model = build_model(model_info, platform="dll", dtype="d")
+
+    for pars, q, Iq in model_info.tests:
+        qin = q
+        if isinstance(Iq, float):
+            q, Iq = [q], [Iq]
+        if isinstance(q[0], tuple):
+            qx, qy = zip(*q)
+            q_vectors = [np.array(qx), np.array(qy)]
+        else:
+            q_vectors = [np.array(q)]
+        kernel = model.make_kernel(q_vectors)
+        target = np.array(Iq)
+        actual = call_kernel(kernel, pars)
+        if True or (actual != target).any():
+            print("Test:", modelname, pars)
+            print(f"  q = ", qin)
+            print(f"  current => [{', '.join(f'{v:.15g}' for v in target)}]")
+            print(f"  ngauss={ngauss} => [{', '.join(f'{v:.15g}' for v in actual)}]")
 
 def main():
     # type: () -> int
@@ -601,6 +626,11 @@ def main():
                         help="Engines on which to run the test.  "
                         "Valid values are opencl, cuda, dll, and all. "
                         "Defaults to all if no value is given")
+    parser.add_argument("-t", "--targets", action="store_true",
+                        help="Generate target values for test.")
+    parser.add_argument("--ngauss", type=int, default=10000,
+                        help="Number of gauss points to use in integration for "
+                        "target values. Warning: this is very slow the first time.")
     parser.add_argument("models", nargs="*",
                         help="The names of the models to be tested.  "
                         "If the first model is 'all', then all but the listed "
@@ -630,9 +660,13 @@ def main():
         print("unknown engine " + opts.engine)
         return 1
 
-    runner = TestRunner(verbosity=opts.verbose, **test_args)
-    result = runner.run(make_suite(loaders, opts.models))
-    return 1 if result.failures or result.errors else 0
+    if opts.targets:
+        for model in opts.models:
+            _generate_target_values(model, ngauss=opts.ngauss)
+    else:
+        runner = TestRunner(verbosity=opts.verbose, **test_args)
+        result = runner.run(make_suite(loaders, opts.models))
+        return 1 if result.failures or result.errors else 0
 
 
 if __name__ == "__main__":
diff --git a/sasmodels/models/barbell.c b/sasmodels/models/barbell.c
index 87f1553e..c1344d0f 100644
--- a/sasmodels/models/barbell.c
+++ b/sasmodels/models/barbell.c
@@ -19,13 +19,18 @@ _bell_kernel(double qab, double qc, double h, double radius_bell,
     const double m = radius_bell*qc; // cos argument slope
     const double b = (half_length+h)*qc; // cos argument intercept
     const double qab_r = radius_bell*qab; // Q*R*sin(theta)
+
+    const double qr_max = fmax(qab_r, m);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     double total = 0.0;
-    for (int i = 0; i < GAUSS_N; i++){
-        const double t = GAUSS_Z[i]*zm + zb;
+    for (int i = 0; i < n; i++){
+        const double t = z[i]*zm + zb;
         const double radical = 1.0 - t*t;
         const double bj = sas_2J1x_x(qab_r*sqrt(radical));
         const double Fq = cos(m*t + b) * radical * bj;
-        total += GAUSS_W[i] * Fq;
+        total += w[i] * Fq;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     const double integral = total*zm;
@@ -110,21 +115,25 @@ Fq(double q,double *F1, double *F2, double sld, double solvent_sld,
     const double h = sqrt(square(radius_bell) - square(radius));
     const double half_length = 0.5*length;
 
+    const double qr_max = q*fmax(radius, half_length);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // translate a point in [-1,1] to a point in [0, pi/2]
     const double zm = M_PI_4;
     const double zb = M_PI_4;
     double total_F1 = 0.0;
     double total_F2 = 0.0;
-    for (int i = 0; i < GAUSS_N; i++){
-        const double theta = GAUSS_Z[i]*zm + zb;
+    for (int i = 0; i < n; i++){
+        const double theta = z[i]*zm + zb;
         double sin_theta, cos_theta; // slots to hold sincos function output
         SINCOS(theta, sin_theta, cos_theta);
         const double qab = q*sin_theta;
         const double qc = q*cos_theta;
         const double Aq = _fq(qab, qc, h, radius_bell, radius, half_length);
         // scale by sin_theta for spherical coord integration
-        total_F1 += GAUSS_W[i] * Aq * sin_theta;
-        total_F2 += GAUSS_W[i] * Aq * Aq * sin_theta;
+        total_F1 += w[i] * Aq * sin_theta;
+        total_F2 += w[i] * Aq * Aq * sin_theta;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     const double form_avg = total_F1 * zm;
diff --git a/sasmodels/models/barbell.py b/sasmodels/models/barbell.py
index d7f3d307..4f3fbcb7 100644
--- a/sasmodels/models/barbell.py
+++ b/sasmodels/models/barbell.py
@@ -117,7 +117,7 @@
     ]
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "barbell.c"]
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "barbell.c"]
 valid = "radius_bell >= radius"
 have_Fq = True
 radius_effective_modes = [
diff --git a/sasmodels/models/capped_cylinder.c b/sasmodels/models/capped_cylinder.c
index c792574c..80c23a18 100644
--- a/sasmodels/models/capped_cylinder.c
+++ b/sasmodels/models/capped_cylinder.c
@@ -26,13 +26,18 @@ _cap_kernel(double qab, double qc, double h, double radius_cap,
     const double m = radius_cap*qc; // cos argument slope
     const double b = (half_length+h)*qc; // cos argument intercept
     const double qab_r = radius_cap*qab; // Q*R*sin(theta)
+
+    const double qr_max = fmax(qab_r, m);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     double total = 0.0;
-    for (int i=0; i<GAUSS_N; i++) {
-        const double t = GAUSS_Z[i]*zm + zb;
+    for (int i=0; i<n; i++) {
+        const double t = z[i]*zm + zb;
         const double radical = 1.0 - t*t;
         const double bj = sas_2J1x_x(qab_r*sqrt(radical));
         const double Fq = cos(m*t + b) * radical * bj;
-        total += GAUSS_W[i] * Fq;
+        total += w[i] * Fq;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     const double integral = total*zm;
@@ -114,21 +119,25 @@ Fq(double q,double *F1, double *F2, double sld, double solvent_sld,
     const double h = -sqrt(square(radius_cap) - square(radius));
     const double half_length = 0.5*length;
 
+    const double qr_max = q*fmax(radius_cap, half_length);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // translate a point in [-1,1] to a point in [0, pi/2]
     const double zm = M_PI_4;
     const double zb = M_PI_4;
     double total_F1 = 0.0;
     double total_F2 = 0.0;
-    for (int i=0; i<GAUSS_N ;i++) {
-        const double theta = GAUSS_Z[i]*zm + zb;
+    for (int i=0; i<n ;i++) {
+        const double theta = z[i]*zm + zb;
         double sin_theta, cos_theta; // slots to hold sincos function output
         SINCOS(theta, sin_theta, cos_theta);
         const double qab = q*sin_theta;
         const double qc = q*cos_theta;
         const double Aq = _fq(qab, qc, h, radius_cap, radius, half_length);
         // scale by sin_theta for spherical coord integration
-        total_F1 += GAUSS_W[i] * Aq * sin_theta;
-        total_F2 += GAUSS_W[i] * Aq * Aq * sin_theta;
+        total_F1 += w[i] * Aq * sin_theta;
+        total_F2 += w[i] * Aq * Aq * sin_theta;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     const double form_avg = total_F1 * zm;
diff --git a/sasmodels/models/capped_cylinder.py b/sasmodels/models/capped_cylinder.py
index a0a3e498..d3a14336 100644
--- a/sasmodels/models/capped_cylinder.py
+++ b/sasmodels/models/capped_cylinder.py
@@ -137,7 +137,7 @@
              ]
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "capped_cylinder.c"]
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "capped_cylinder.c"]
 valid = "radius_cap >= radius"
 have_Fq = True
 radius_effective_modes = [
diff --git a/sasmodels/models/core_shell_bicelle.c b/sasmodels/models/core_shell_bicelle.c
index b5d7df9b..3517c41f 100644
--- a/sasmodels/models/core_shell_bicelle.c
+++ b/sasmodels/models/core_shell_bicelle.c
@@ -93,9 +93,10 @@ Fq(double q,
     const double uplim = M_PI_4;
     const double halflength = 0.5*length;
 
-    double qr = q*fmax(radius+thick_radius, 2*halflength+thick_face);
+    const double qr_max = q*fmax(radius+thick_radius, 2*halflength+thick_face);
     constant double *w, *z;
-    int n = gauss_weights(qr, &w, &z);
+    int n = gauss_weights(qr_max, &w, &z);
+
     double total_F1 = 0.0;
     double total_F2 = 0.0;
     for(int i=0;i<n;i++) {
diff --git a/sasmodels/models/core_shell_bicelle_elliptical.c b/sasmodels/models/core_shell_bicelle_elliptical.c
index 0264c7dc..29282565 100644
--- a/sasmodels/models/core_shell_bicelle_elliptical.c
+++ b/sasmodels/models/core_shell_bicelle_elliptical.c
@@ -82,35 +82,44 @@ Fq(double q,
     const double dr2 = vol2*(sld_rim-sld_solvent);
     const double dr3 = vol3*(sld_face-sld_rim);
 
+    const double qr_max = q*(halfheight+thick_face);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     //initialize integral
     double outer_total_F1 = 0.0;
     double outer_total_F2 = 0.0;
-    for(int i=0;i<GAUSS_N;i++) {
+    for(int i=0;i<n;i++) {
         //setup inner integral over the ellipsoidal cross-section
-        //const double cos_theta = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0;
-        const double cos_theta = ( GAUSS_Z[i] + 1.0 )/2.0;
+        //const double cos_theta = ( z[i]*(vb-va) + va + vb )/2.0;
+        const double cos_theta = ( z[i] + 1.0 )/2.0;
         const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
         const double qab = q*sin_theta;
         const double qc = q*cos_theta;
         const double si1 = sas_sinx_x(halfheight*qc);
         const double si2 = sas_sinx_x((halfheight+thick_face)*qc);
+
+        const double qr_max_inner = qab*fmax(r_minor, r_major);
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max_inner, &w_inner, &z_inner);
+
         double inner_total_F1 = 0;
         double inner_total_F2 = 0;
-        for(int j=0;j<GAUSS_N;j++) {
+        for(int j=0;j<n_inner;j++) {
             //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe)
-            //const double beta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0;
-            const double beta = ( GAUSS_Z[j] +1.0)*M_PI_2;
+            //const double beta = ( z_inner[j]*(vbj-vaj) + vaj + vbj )/2.0;
+            const double beta = ( z_inner[j] +1.0)*M_PI_2;
             const double rr = sqrt(r2A - r2B*cos(beta));
             const double be1 = sas_2J1x_x(rr*qab);
             const double be2 = sas_2J1x_x((rr+thick_rim)*qab);
             const double f = dr1*si1*be1 + dr2*si2*be2 + dr3*si2*be1;
 
-            inner_total_F1 += GAUSS_W[j] * f;
-            inner_total_F2 += GAUSS_W[j] * f * f;
+            inner_total_F1 += w_inner[j] * f;
+            inner_total_F2 += w_inner[j] * f * f;
         }
         //now calculate outer integral
-        outer_total_F1 += GAUSS_W[i] * inner_total_F1;
-        outer_total_F2 += GAUSS_W[i] * inner_total_F2;
+        outer_total_F1 += w[i] * inner_total_F1;
+        outer_total_F2 += w[i] * inner_total_F2;
     }
     // now complete change of integration variables (1-0)/(1-(-1))= 0.5
     outer_total_F1 *= 0.25;
diff --git a/sasmodels/models/core_shell_bicelle_elliptical.py b/sasmodels/models/core_shell_bicelle_elliptical.py
index ad780d86..51b48542 100644
--- a/sasmodels/models/core_shell_bicelle_elliptical.py
+++ b/sasmodels/models/core_shell_bicelle_elliptical.py
@@ -144,7 +144,7 @@
 
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c",
+source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c",
           "core_shell_bicelle_elliptical.c"]
 have_Fq = True
 radius_effective_modes = [
diff --git a/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.c b/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.c
index 83b89b58..cbe57c1b 100644
--- a/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.c
+++ b/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.c
@@ -93,36 +93,45 @@ Fq(double q,
     const double dr2 = vol2*(rhor-rhosolv);
     const double dr3 = vol3*(rhoh-rhosolv);
 
+    const double qr_max = q*(halfheight+thick_face);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     //initialize integral
     double outer_total_F1 = 0.0;
     double outer_total_F2 = 0.0;
-    for(int i=0;i<GAUSS_N;i++) {
+    for(int i=0;i<n;i++) {
         //setup inner integral over the ellipsoidal cross-section
         // since we generate these lots of times, why not store them somewhere?
-        //const double cos_theta = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0;
-        const double cos_theta = ( GAUSS_Z[i] + 1.0 )/2.0;
+        //const double cos_theta = ( z[i]*(vb-va) + va + vb )/2.0;
+        const double cos_theta = ( z[i] + 1.0 )/2.0;
         const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
         const double qab = q*sin_theta;
         const double qc = q*cos_theta;
         const double si1 = sas_sinx_x(halfheight*qc);
         const double si2 = sas_sinx_x((halfheight+thick_face)*qc);
+
+        const double qr_max_inner = qab*fmax(r_minor, r_major);
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max_inner, &w_inner, &z_inner);
+
         double inner_total_F1 = 0;
         double inner_total_F2 = 0;
-        for(int j=0;j<GAUSS_N;j++) {
+        for(int j=0;j<n_inner;j++) {
             //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe)
-            //const double beta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0;
-            const double beta = ( GAUSS_Z[j] +1.0)*M_PI_2;
+            //const double beta = ( z_inner[j]*(vbj-vaj) + vaj + vbj )/2.0;
+            const double beta = ( z_inner[j] +1.0)*M_PI_2;
             const double rr = sqrt(r2A - r2B*cos(beta));
             const double be1 = sas_2J1x_x(rr*qab);
             const double be2 = sas_2J1x_x((rr+thick_rim)*qab);
             const double f = dr1*si1*be1 + dr2*si1*be2 + dr3*si2*be1;
 
-            inner_total_F1 += GAUSS_W[j] * f;
-            inner_total_F2 += GAUSS_W[j] * f * f;
+            inner_total_F1 += w_inner[j] * f;
+            inner_total_F2 += w_inner[j] * f * f;
         }
         //now calculate outer integral
-        outer_total_F1 += GAUSS_W[i] * inner_total_F1;
-        outer_total_F2 += GAUSS_W[i] * inner_total_F2;
+        outer_total_F1 += w[i] * inner_total_F1;
+        outer_total_F2 += w[i] * inner_total_F2;
     }
     // now complete change of integration variables (1-0)/(1-(-1))= 0.5
     outer_total_F1 *= 0.25;
diff --git a/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.py b/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.py
index 002e8879..1b180b20 100644
--- a/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.py
+++ b/sasmodels/models/core_shell_bicelle_elliptical_belt_rough.py
@@ -157,7 +157,7 @@
 
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c",
+source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c",
           "core_shell_bicelle_elliptical_belt_rough.c"]
 have_Fq = True
 radius_effective_modes = [
diff --git a/sasmodels/models/core_shell_cylinder.c b/sasmodels/models/core_shell_cylinder.c
index 38ab439a..84c76fcf 100644
--- a/sasmodels/models/core_shell_cylinder.c
+++ b/sasmodels/models/core_shell_cylinder.c
@@ -75,20 +75,25 @@ Fq(double q,
     const double shell_r = (radius + thickness);
     const double shell_h = (0.5*length + thickness);
     const double shell_vd = form_volume(radius,thickness,length) * (shell_sld-solvent_sld);
+
+    const double qr_max = q*fmax(shell_r, shell_h);
+    constant double *z, *w;
+    int n = gauss_weights(qr_max, &w, &z);
+
     double total_F1 = 0.0;
     double total_F2 = 0.0;
-    for (int i=0; i<GAUSS_N ;i++) {
+    for (int i=0; i<n ;i++) {
         // translate a point in [-1,1] to a point in [0, pi/2]
-        //const double theta = ( GAUSS_Z[i]*(upper-lower) + upper + lower )/2.0;
+        //const double theta = ( z[i]*(upper-lower) + upper + lower )/2.0;
         double sin_theta, cos_theta;
-        const double theta = GAUSS_Z[i]*M_PI_4 + M_PI_4;
+        const double theta = z[i]*M_PI_4 + M_PI_4;
         SINCOS(theta, sin_theta,  cos_theta);
         const double qab = q*sin_theta;
         const double qc = q*cos_theta;
         const double fq = _cyl(core_vd, core_r*qab, core_h*qc)
             + _cyl(shell_vd, shell_r*qab, shell_h*qc);
-        total_F1 += GAUSS_W[i] * fq * sin_theta;
-        total_F2 += GAUSS_W[i] * fq * fq * sin_theta;
+        total_F1 += w[i] * fq * sin_theta;
+        total_F2 += w[i] * fq * fq * sin_theta;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     //const double form = (upper-lower)/2.0*total;
diff --git a/sasmodels/models/core_shell_cylinder.py b/sasmodels/models/core_shell_cylinder.py
index 84d08cc6..938a0bcb 100644
--- a/sasmodels/models/core_shell_cylinder.py
+++ b/sasmodels/models/core_shell_cylinder.py
@@ -133,7 +133,7 @@
                "rotation about beam"],
              ]
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "core_shell_cylinder.c"]
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "core_shell_cylinder.c"]
 have_Fq = True
 radius_effective_modes = [
     "excluded volume", "equivalent volume sphere", "outer radius", "half outer length",
diff --git a/sasmodels/models/core_shell_ellipsoid.c b/sasmodels/models/core_shell_ellipsoid.c
index bfc5248a..7c2356d0 100644
--- a/sasmodels/models/core_shell_ellipsoid.c
+++ b/sasmodels/models/core_shell_ellipsoid.c
@@ -104,20 +104,24 @@ Fq(double q,
     const double equat_shell = radius_equat_core + thick_shell;
     const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell;
 
+    const double qr_max = q*fmax(equat_shell, polar_shell);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // translate from [-1, 1] => [0, 1]
     const double m = 0.5;
     const double b = 0.5;
     double total_F1 = 0.0;     //initialize intergral
     double total_F2 = 0.0;     //initialize intergral
-    for(int i=0;i<GAUSS_N;i++) {
-        const double cos_theta = GAUSS_Z[i]*m + b;
+    for(int i=0;i<n;i++) {
+        const double cos_theta = z[i]*m + b;
         const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
         double fq = _cs_ellipsoid_kernel(q*sin_theta, q*cos_theta,
             radius_equat_core, polar_core,
             equat_shell, polar_shell,
             sld_core_shell, sld_shell_solvent);
-        total_F1 += GAUSS_W[i] * fq;
-        total_F2 += GAUSS_W[i] * fq * fq;
+        total_F1 += w[i] * fq;
+        total_F2 += w[i] * fq * fq;
     }
     total_F1 *= m;
     total_F2 *= m;
diff --git a/sasmodels/models/core_shell_ellipsoid.py b/sasmodels/models/core_shell_ellipsoid.py
index 7f0415a9..5ab10cce 100644
--- a/sasmodels/models/core_shell_ellipsoid.py
+++ b/sasmodels/models/core_shell_ellipsoid.py
@@ -149,7 +149,7 @@
     ]
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/sas_3j1x_x.c", "lib/gauss76.c", "core_shell_ellipsoid.c"]
+source = ["lib/sas_3j1x_x.c", "lib/adaptive.c", "core_shell_ellipsoid.c"]
 have_Fq = True
 radius_effective_modes = [
     "average outer curvature", "equivalent volume sphere",
@@ -194,10 +194,10 @@ def random():
       'sld_solvent': 6.3,
       'background': 0.001,
       'scale': 1.0,
-     }, 1.0, 0.00189402],
+     }, 1.0, 0.00199393783025264],
 
     # Additional tests with larger range of parameters
-    [{'background': 0.01}, 0.1, 11.6915],
+    [{'background': 0.01}, 0.1, 11.6915291814002],
 
     [{'radius_equat_core': 20.0,
       'x_core': 200.0,
@@ -208,13 +208,13 @@ def random():
       'sld_solvent': 6.0,
       'background': 0.0,
       'scale': 1.0,
-     }, 0.01, 8688.53],
+     }, 0.01, 8688.52423647087],
 
     # 2D tests
     [{'background': 0.001,
       'theta': 90.0,
       'phi': 0.0,
-     }, (0.4, 0.5), 0.00690673],
+     }, (0.4, 0.5), 0.00690673646263621],
 
     [{'radius_equat_core': 20.0,
       'x_core': 200.0,
@@ -227,5 +227,5 @@ def random():
       'scale': 0.01,
       'theta': 90.0,
       'phi': 0.0,
-     }, (qx, qy), 0.01000025],
+     }, (qx, qy), 0.010000250020321],
 ]
diff --git a/sasmodels/models/core_shell_parallelepiped.c b/sasmodels/models/core_shell_parallelepiped.c
index 00295d36..12b5ee28 100644
--- a/sasmodels/models/core_shell_parallelepiped.c
+++ b/sasmodels/models/core_shell_parallelepiped.c
@@ -131,22 +131,30 @@ Fq(double q,
     const double drB = (brim_sld-solvent_sld);
     const double drC = (crim_sld-solvent_sld);
 
+    const double qr_max = q*0.5*tC;
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // outer integral (with gauss points), integration limits = 0, 1
     // substitute d_cos_alpha for sin_alpha d_alpha
     double outer_sum_F1 = 0; //initialize integral
     double outer_sum_F2 = 0; //initialize integral
-    for( int i=0; i<GAUSS_N; i++) {
-        const double cos_alpha = 0.5 * ( GAUSS_Z[i] + 1.0 );
+    for( int i=0; i<n; i++) {
+        const double cos_alpha = 0.5 * ( z[i] + 1.0 );
         const double mu = half_q * sqrt(1.0-cos_alpha*cos_alpha);
         const double siC = length_c * sas_sinx_x(length_c * cos_alpha * half_q);
         const double siCt = tC * sas_sinx_x(tC * cos_alpha * half_q);
 
+        const double qr_max_inner = mu*fmax(tA, tB);  // = qab*max(len)/2
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max, &w_inner, &z_inner);
+
         // inner integral (with gauss points), integration limits = 0, 1
         // substitute beta = PI/2 u (so 2/PI * d_(PI/2 * beta) = d_beta)
         double inner_sum_F1 = 0.0;
         double inner_sum_F2 = 0.0;
-        for(int j=0; j<GAUSS_N; j++) {
-            const double u = 0.5 * ( GAUSS_Z[j] + 1.0 );
+        for(int j=0; j<n_inner; j++) {
+            const double u = 0.5 * ( z_inner[j] + 1.0 );
             double sin_beta, cos_beta;
             SINCOS(M_PI_2*u, sin_beta, cos_beta);
             const double siA = length_a * sas_sinx_x(length_a * mu * sin_beta);
@@ -166,13 +174,13 @@ Fq(double q,
                 + drC*siA*siB*(siCt-siC);
 #endif
 
-            inner_sum_F1 += GAUSS_W[j] * f;
-            inner_sum_F2 += GAUSS_W[j] * f * f;
+            inner_sum_F1 += w_inner[j] * f;
+            inner_sum_F2 += w_inner[j] * f * f;
         }
         // now complete change of inner integration variable (1-0)/(1-(-1))= 0.5
         // and sum up the outer integral
-        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * 0.5;
-        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * 0.5;
+        outer_sum_F1 += w[i] * inner_sum_F1 * 0.5;
+        outer_sum_F2 += w[i] * inner_sum_F2 * 0.5;
     }
     // now complete change of outer integration variable (1-0)/(1-(-1))= 0.5
     outer_sum_F1 *= 0.5;
diff --git a/sasmodels/models/core_shell_parallelepiped.py b/sasmodels/models/core_shell_parallelepiped.py
index 22a59ec7..8f9655ac 100644
--- a/sasmodels/models/core_shell_parallelepiped.py
+++ b/sasmodels/models/core_shell_parallelepiped.py
@@ -224,7 +224,7 @@
                "rotation about c axis"],
              ]
 
-source = ["lib/gauss76.c", "core_shell_parallelepiped.c"]
+source = ["lib/adaptive.c", "core_shell_parallelepiped.c"]
 have_Fq = True
 radius_effective_modes = [
     "equivalent cylinder excluded volume",
diff --git a/sasmodels/models/cylinder.c b/sasmodels/models/cylinder.c
index 2744e467..8d060c5e 100644
--- a/sasmodels/models/cylinder.c
+++ b/sasmodels/models/cylinder.c
@@ -51,6 +51,7 @@ radius_effective(int mode, double radius, double length)
     }
 }
 
+
 static void
 Fq(double q,
     double *F1,
@@ -60,20 +61,23 @@ Fq(double q,
     double radius,
     double length)
 {
+    const double qr_max = q*fmax(radius, 0.5*length);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // translate a point in [-1,1] to a point in [0, pi/2]
     const double zm = M_PI_4;
     const double zb = M_PI_4;
-
     double total_F1 = 0.0;
     double total_F2 = 0.0;
-    for (int i=0; i<GAUSS_N ;i++) {
-        const double theta = GAUSS_Z[i]*zm + zb;
+    for (int i=0; i<n ;i++) {
+        const double theta = z[i]*zm + zb;
         double sin_theta, cos_theta; // slots to hold sincos function output
         // theta (theta,phi) the projection of the cylinder on the detector plane
         SINCOS(theta , sin_theta, cos_theta);
         const double form = _fq(q*sin_theta, q*cos_theta, radius, length);
-        total_F1 += GAUSS_W[i] * form * sin_theta;
-        total_F2 += GAUSS_W[i] * form * form * sin_theta;
+        total_F1 += w[i] * form * sin_theta;
+        total_F2 += w[i] * form * form * sin_theta;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     total_F1 *= zm;
diff --git a/sasmodels/models/cylinder.py b/sasmodels/models/cylinder.py
index 37a9d458..ae9ba4ff 100644
--- a/sasmodels/models/cylinder.py
+++ b/sasmodels/models/cylinder.py
@@ -142,7 +142,7 @@
     ]
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "cylinder.c"]
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "cylinder.c"]
 valid = "radius >= 0.0 && length >= 0.0"
 have_Fq = True
 radius_effective_modes = [
diff --git a/sasmodels/models/cylinderp.c b/sasmodels/models/cylinderp.c
deleted file mode 100644
index 862be5d0..00000000
--- a/sasmodels/models/cylinderp.c
+++ /dev/null
@@ -1,104 +0,0 @@
-static double
-form_volume(double radius, double length)
-{
-    return M_PI*radius*radius*length;
-}
-
-static double
-_fq(double qab, double qc, double radius, double length)
-{
-    return sas_2J1x_x(qab*radius) * sas_sinx_x(qc*0.5*length);
-}
-
-static double
-radius_from_excluded_volume(double radius, double length)
-{
-    return 0.5*cbrt(0.75*radius*(2.0*radius*length
-           + (radius + length)*(M_PI*radius + length)));
-}
-
-static double
-radius_from_volume(double radius, double length)
-{
-    return cbrt(M_PI*radius*radius*length/M_4PI_3);
-}
-
-static double
-radius_from_diagonal(double radius, double length)
-{
-    return sqrt(radius*radius + 0.25*length*length);
-}
-
-static double
-radius_effective(int mode, double radius, double length)
-{
-    switch (mode) {
-    default:
-    case 1:
-        return radius_from_excluded_volume(radius, length);
-    case 2:
-        return radius_from_volume(radius, length);
-    case 3:
-        return radius;
-    case 4:
-        return 0.5*length;
-    case 5:
-        return (radius < 0.5*length ? radius : 0.5*length);
-    case 6:
-        return (radius > 0.5*length ? radius : 0.5*length);
-    case 7:
-        return radius_from_diagonal(radius,length);
-    }
-}
-
-
-static void
-Fq(double q,
-    double *F1,
-    double *F2,
-    double sld,
-    double solvent_sld,
-    double radius,
-    double length)
-{
-    // translate a point in [-1,1] to a point in [0, pi/2]
-    const double zm = M_PI_4;
-    const double zb = M_PI_4;
-
-    double total_F1 = 0.0;
-    double total_F2 = 0.0;
-
-    double qr = q*(radius > length ? radius : length);
-    constant double *w, *z;
-    int n = gauss_weights(qr, &w, &z);
-    for (int i=0; i<n ;i++) {
-        const double theta = z[i]*zm + zb;
-        double sin_theta, cos_theta; // slots to hold sincos function output
-        // theta (theta,phi) the projection of the cylinder on the detector plane
-        SINCOS(theta , sin_theta, cos_theta);
-        const double form = _fq(q*sin_theta, q*cos_theta, radius, length);
-        total_F1 += w[i] * form * sin_theta;
-        total_F2 += w[i] * form * form * sin_theta;
-    }
-    // translate dx in [-1,1] to dx in [lower,upper]
-    total_F1 *= zm;
-    total_F2 *= zm;
-    const double s = (sld - solvent_sld) * form_volume(radius, length);
-    *F1 = 1e-2 * s * total_F1;
-    *F2 = 1e-4 * s * s * total_F2;
-}
-
-
-
-static double
-Iqac(double qab, double qc,
-    double sld,
-    double solvent_sld,
-    double radius,
-    double length)
-{
-    const double form = _fq(qab, qc, radius, length);
-    const double s = (sld-solvent_sld) * form_volume(radius, length);
-    return 1.0e-4 * square(s * form);
-}
-
diff --git a/sasmodels/models/cylinderp.py b/sasmodels/models/cylinderp.py
deleted file mode 100644
index 7f1ac3b5..00000000
--- a/sasmodels/models/cylinderp.py
+++ /dev/null
@@ -1,251 +0,0 @@
-# cylinder model
-# Note: model title and parameter table are inserted automatically
-r"""
-
-For information about polarised and magnetic scattering, see
-the :ref:`magnetism` documentation.
-
-Definition
-----------
-
-The output of the 2D scattering intensity function for oriented cylinders is
-given by (Guinier, 1955)
-
-.. math::
-
-    I(q,\alpha) = \frac{\text{scale}}{V} F^2(q,\alpha) + \text{background}
-
-where
-
-.. math::
-
-    F(q,\alpha) = 2 (\Delta \rho) V
-           \frac{\sin \left(\tfrac12 qL\cos\alpha \right)}
-                {\tfrac12 qL \cos \alpha}
-           \frac{J_1 \left(q R \sin \alpha\right)}{q R \sin \alpha}
-
-and $\alpha$ is the angle between the axis of the cylinder and $\vec q$,
-$V =\pi R^2L$ is the volume of the cylinder, $L$ is the length of the cylinder,
-$R$ is the radius of the cylinder, and $\Delta\rho$ (contrast) is the
-scattering length density difference between the scatterer and the solvent.
-$J_1$ is the first order Bessel function.
-
-For randomly oriented particles:
-
-.. math::
-
-    P(q)=F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha}
-
-
-The output of the 1D scattering intensity function for randomly oriented
-cylinders is thus given by
-
-.. math::
-
-    I(q) = \frac{\text{scale}}{V}
-        \int_0^{\pi/2} F^2(q,\alpha) \sin \alpha\ d\alpha + \text{background}
-
-
-NB: The 2nd virial coefficient of the cylinder is calculated based on the
-radius and length values, and used as the effective radius for $S(q)$
-when $P(q) \cdot S(q)$ is applied.
-
-For 2d scattering from oriented cylinders, we define the direction of the
-axis of the cylinder using two angles $\theta$ (note this is not the same as
-the scattering angle used in q) and $\phi$. Those angles are defined in
-:numref:`cylinder-angle-definition` , for further details see
-:ref:`orientation`.
-
-.. _cylinder-angle-definition:
-
-.. figure:: img/cylinder_angle_definition.png
-
-    Angles $\theta$ and $\phi$ orient the cylinder relative to the beam line
-    coordinates, where the beam is along the $z$ axis. Rotation $\theta$,
-    initially in the $xz$ plane, is carried out first, then rotation $\phi$
-    about the $z$ axis. Orientation distributions are described as rotations
-    about two perpendicular axes $\delta_1$ and $\delta_2$ in the frame of
-    the cylinder itself, which when $\theta = \phi = 0$ are parallel to the
-    $Y$ and $X$ axes.
-
-.. figure:: img/cylinder_angle_projection.png
-
-    Examples for oriented cylinders.
-
-The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the
-model when fitting 2d data.
-
-Validation
-----------
-
-Validation of the code was done by comparing the output of the 1D model
-to the output of the software provided by the NIST (Kline, 2006).
-The implementation of the intensity for fully oriented cylinders was done
-by averaging over a uniform distribution of orientations using
-
-.. math::
-
-    P(q) = \int_0^{\pi/2} d\phi
-        \int_0^\pi p(\theta) P_0(q,\theta) \sin \theta\ d\theta
-
-
-where $p(\theta,\phi) = 1$ is the probability distribution for the orientation
-and $P_0(q,\theta)$ is the scattering intensity for the fully oriented
-system, and then comparing to the 1D result.
-
-References
-----------
-
-#.  J. Pedersen, *Adv. Colloid Interface Sci.*, 70 (1997) 171-210
-#.  G. Fournet, *Bull. Soc. Fr. Mineral. Cristallogr.*, 74 (1951) 39-113
-#.  L. Onsager, *Ann. New York Acad. Sci.*, 51 (1949) 627-659
-
-Authorship and Verification
-----------------------------
-
-* **Author:**
-* **Last Modified by:** Paul Butler (docs only) November 10, 2022
-* **Last Reviewed by:**
-"""
-
-import numpy as np  # type: ignore
-from numpy import pi, inf  # type: ignore
-
-name = "cylinder"
-title = "Right circular cylinder with uniform scattering length density."
-description = """
-     f(q,alpha) = 2*(sld - sld_solvent)*V*sin(qLcos(alpha)/2))
-                /[qLcos(alpha)/2]*J1(qRsin(alpha))/[qRsin(alpha)]
-
-            P(q,alpha)= scale/V*f(q,alpha)^(2)+background
-            V: Volume of the cylinder
-            R: Radius of the cylinder
-            L: Length of the cylinder
-            J1: The Bessel function
-            alpha: angle between the axis of the
-            cylinder and the q-vector for 1D
-            :the ouput is P(q)=scale/V*integral
-            from pi/2 to zero of...
-            f(q,alpha)^(2)*sin(alpha)*dalpha + background
-"""
-category = "shape:cylinder"
-
-# pylint: disable=bad-whitespace, line-too-long
-#             [ "name", "units", default, [lower, upper], "type", "description"],
-parameters = [
-    ["sld",         "1e-6/Ang^2",   4, [-inf, inf], "sld",         "Cylinder scattering length density"],
-    ["sld_solvent", "1e-6/Ang^2",   1, [-inf, inf], "sld",         "Solvent scattering length density"],
-    ["radius",      "Ang",         20, [0, inf],    "volume",      "Cylinder radius"],
-    ["length",      "Ang",        400, [0, inf],    "volume",      "Cylinder length"],
-    ["theta",       "degrees",     60, [-360, 360], "orientation", "cylinder axis to beam angle"],
-    ["phi",         "degrees",     60, [-360, 360], "orientation", "rotation about beam"],
-    ]
-# pylint: enable=bad-whitespace, line-too-long
-
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "cylinderp.c"]
-valid = "radius >= 0.0 && length >= 0.0"
-have_Fq = True
-radius_effective_modes = [
-    "excluded volume", "equivalent volume sphere", "radius",
-    "half length", "half min dimension", "half max dimension", "half diagonal",
-    ]
-
-def random():
-    """Return a random parameter set for the model."""
-    volume = 10**np.random.uniform(5, 12)
-    length = 10**np.random.uniform(-2, 2)*volume**0.333
-    radius = np.sqrt(volume/length/np.pi)
-    pars = dict(
-        #scale=1,
-        #background=0,
-        length=length,
-        radius=radius,
-    )
-    return pars
-
-
-# Test 1-D and 2-D models
-qx, qy = 0.2 * np.cos(2.5), 0.2 * np.sin(2.5)
-theta, phi = 80.1534480601659, 10.1510817110481  # (10, 10) in sasview 3.x
-tests = [
-    [{}, 0.2, 0.042761386790780453],
-    [{}, [0.2], [0.042761386790780453]],
-    [{"scale": 1., "background": 0.}, [0.01, 0.05, 0.2],
-     # these numerical results NOT independently verified
-     [3.01823887e+02, 5.36661653e+01, 4.17613868e-02]],
-    [{"scale": 1., "background": 0.},
-     # the longer list here checks  F1, F2=I(Q)*V, R_eff, volume, volume_ratio
-     0.05, 2214.9614083, 26975556.88749548, 73.34013315261608,
-     502654.8245743669, 1.0],
-#2345678901234567890123456789012345678901234567890123456789012345678901234567890
-    [{"@S": "hardsphere",         # MONODISPERSE
-      "scale": 5., "background": 0., "volfraction": 0.2,
-      "structure_factor_mode": 0,  # normal decoupling approx
-      "radius_effective_mode": 1,  # Reff "excluded volume"
-     }, [0.01, 0.05, 0.2], [7.35571916e+01, 5.78147797e+01, 4.15623248e-2]
-     ],
-    [{"@S": "hardsphere",
-      "scale": 5., "background": 0., "volfraction": 0.2,
-      "structure_factor_mode": 1,  # beta approx
-      "radius_effective_mode": 1,  # Reff "excluded volume"
-     }, [0.01, 0.05, 0.2], [8.29729770e+01, 5.44206752e+01, 4.17598382e-2]
-     ],
-    [{"@S": "hardsphere",         # POLYDISPERSE
-      "scale": 5., "background": 0., "volfraction": 0.2,
-      "radius_pd": 0.2, "radius_pd_n": 15, "length_pd": 0.1,
-      "structure_factor_mode": 0,  # normal decoupling approx
-      "radius_effective_mode": 1,  # Reff "excluded volume"
-     }, [0.01, 0.05, 0.2], [87.50350037, 63.95202427, 0.27889988]
-     ],
-    [{"@S": "hardsphere",
-      "scale": 5., "background": 0., "volfraction": 0.2,
-      "radius_pd": 0.2, "radius_pd_n": 15, "length_pd": 0.1,
-      "structure_factor_mode": 1,  # beta approx
-      "radius_effective_mode": 1,  # Reff "excluded volume"
-     }, [0.01, 0.05, 0.2], [132.2101165, 59.89948174, 0.28048784]
-     ],
-    #
-    [{'theta': theta, 'phi': phi}, (qx, qy), 0.03514647218513852],
-    [{'theta': theta, 'phi': phi}, [(qx, qy)], [0.03514647218513852]],
-]
-del qx, qy, theta, phi  # not necessary to delete, but cleaner
-
-def _extend_with_reff_tests(radius, length):
-    """Test R_eff and form volume calculations"""
-    # V and Vr are the same for each R_eff mode
-    V = pi*radius**2*length  # shell volume = form volume for solid objects
-    Vr = 1.0  # form:shell volume ratio
-    # Use test value for I(0.2) from above to check Fsq value.  Need to
-    # remove scale and background before testing.
-    q = 0.2
-    scale, background = V, 0.001
-    Fsq = (0.042761386790780453 - background)*scale
-    F = None  # Need target value for <F>
-    # Various values for R_eff, depending on mode
-    r_effs = [
-        0.,
-        0.5*(0.75*radius*(2.0*radius*length
-                          + (radius + length)*(pi*radius + length)))**(1./3.),
-        (0.75*radius**2*length)**(1./3.),
-        radius,
-        length/2.,
-        min(radius, length/2.),
-        max(radius, length/2.),
-        np.sqrt(4*radius**2 + length**2)/2.,
-    ]
-    tests.extend([
-        ({'radius_effective_mode': 0}, q, F, Fsq, r_effs[0], V, Vr),
-        ({'radius_effective_mode': 1}, q, F, Fsq, r_effs[1], V, Vr),
-        ({'radius_effective_mode': 2}, q, F, Fsq, r_effs[2], V, Vr),
-        ({'radius_effective_mode': 3}, q, F, Fsq, r_effs[3], V, Vr),
-        ({'radius_effective_mode': 4}, q, F, Fsq, r_effs[4], V, Vr),
-        ({'radius_effective_mode': 5}, q, F, Fsq, r_effs[5], V, Vr),
-        ({'radius_effective_mode': 6}, q, F, Fsq, r_effs[6], V, Vr),
-        ({'radius_effective_mode': 7}, q, F, Fsq, r_effs[7], V, Vr),
-    ])
-
-# Test Reff and volume with default model parameters
-_extend_with_reff_tests(parameters[2][2], parameters[3][2])
-del _extend_with_reff_tests
-
-# ADDED by:  RKH  ON: 18Mar2016 renamed sld's etc
diff --git a/sasmodels/models/ellipsoid.c b/sasmodels/models/ellipsoid.c
index b91b0b51..6ac42a18 100644
--- a/sasmodels/models/ellipsoid.c
+++ b/sasmodels/models/ellipsoid.c
@@ -64,18 +64,23 @@ Fq(double q,
     //     u = sin, du = cos dT
     //     i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du
     const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0;
+
+    const double qr_max = q*fmax(radius_polar,radius_equatorial);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // translate a point in [-1,1] to a point in [0, 1]
-    // const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper+lower)/2;
+    // const double u = z[i]*(upper-lower)/2 + (upper+lower)/2;
     const double zm = 0.5;
     const double zb = 0.5;
     double total_F2 = 0.0;
     double total_F1 = 0.0;
-    for (int i=0;i<GAUSS_N;i++) {
-        const double u = GAUSS_Z[i]*zm + zb;
+    for (int i=0;i<n;i++) {
+        const double u = z[i]*zm + zb;
         const double r = radius_equatorial*sqrt(1.0 + u*u*v_square_minus_one);
         const double f = sas_3j1x_x(q*r);
-        total_F2 += GAUSS_W[i] * f * f;
-        total_F1 += GAUSS_W[i] * f;
+        total_F2 += w[i] * f * f;
+        total_F1 += w[i] * f;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     total_F1 *= zm;
diff --git a/sasmodels/models/ellipsoid.py b/sasmodels/models/ellipsoid.py
index 00969bcd..a8fc282e 100644
--- a/sasmodels/models/ellipsoid.py
+++ b/sasmodels/models/ellipsoid.py
@@ -153,7 +153,7 @@
 # pylint: enable=bad-whitespace, line-too-long
 
 
-source = ["lib/sas_3j1x_x.c", "lib/gauss76.c", "ellipsoid.c"]
+source = ["lib/sas_3j1x_x.c", "lib/adaptive.c", "ellipsoid.c"]
 have_Fq = True
 radius_effective_modes = [
     "average curvature", "equivalent volume sphere", "min radius", "max radius",
diff --git a/sasmodels/models/elliptical_cylinder.c b/sasmodels/models/elliptical_cylinder.c
index 2ab87e11..22ae7824 100644
--- a/sasmodels/models/elliptical_cylinder.c
+++ b/sasmodels/models/elliptical_cylinder.c
@@ -82,22 +82,30 @@ Fq(double q, double *F1, double *F2, double radius_minor, double r_ratio, double
     const double rA = 0.5*(square(radius_major) + square(radius_minor));
     const double rB = 0.5*(square(radius_major) - square(radius_minor));
 
+    const double qr_max = q*0.5*length;
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
+    const double qr_max_inner = q*fmax(radius_minor, radius_major);
+    constant double *w_inner, *z_inner;
+    int n_inner = gauss_weights(qr_max, &w_inner, &z_inner);
+
     //initialize integral
     double outer_sum_F1 = 0.0;
     double outer_sum_F2 = 0.0;
-    for(int i=0;i<GAUSS_N;i++) {
+    for(int i=0;i<n;i++) {
         //setup inner integral over the ellipsoidal cross-section
-        const double cos_val = ( GAUSS_Z[i]*(vb-va) + va + vb )/2.0;
+        const double cos_val = ( z[i]*(vb-va) + va + vb )/2.0;
         const double sin_val = sqrt(1.0 - cos_val*cos_val);
         //const double arg = radius_minor*sin_val;
         double inner_sum_F1 = 0.0;
         double inner_sum_F2 = 0.0;
-        for(int j=0;j<GAUSS_N;j++) {
-            const double theta = ( GAUSS_Z[j]*(vbj-vaj) + vaj + vbj )/2.0;
+        for(int j=0;j<n_inner;j++) {
+            const double theta = ( z_inner[j]*(vbj-vaj) + vaj + vbj )/2.0;
             const double r = sin_val*sqrt(rA - rB*cos(theta));
             const double be = sas_2J1x_x(q*r);
-            inner_sum_F1 += GAUSS_W[j] * be;
-            inner_sum_F2 += GAUSS_W[j] * be * be;
+            inner_sum_F1 += w_inner[j] * be;
+            inner_sum_F2 += w_inner[j] * be * be;
         }
         //now calculate the value of the inner integral
         inner_sum_F1 *= 0.5*(vbj-vaj);
@@ -105,8 +113,8 @@ Fq(double q, double *F1, double *F2, double radius_minor, double r_ratio, double
 
         //now calculate outer integral
         const double si = sas_sinx_x(q*0.5*length*cos_val);
-        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * si;
-        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * si * si;
+        outer_sum_F1 += w[i] * inner_sum_F1 * si;
+        outer_sum_F2 += w[i] * inner_sum_F2 * si * si;
     }
     // correct limits and divide integral by pi
     outer_sum_F1 *= 0.5*(vb-va)/M_PI;
diff --git a/sasmodels/models/elliptical_cylinder.py b/sasmodels/models/elliptical_cylinder.py
index 87ec33bc..cad0370f 100644
--- a/sasmodels/models/elliptical_cylinder.py
+++ b/sasmodels/models/elliptical_cylinder.py
@@ -123,7 +123,7 @@
 
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "elliptical_cylinder.c"]
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "elliptical_cylinder.c"]
 have_Fq = True
 radius_effective_modes = [
     "equivalent cylinder excluded volume",
diff --git a/sasmodels/models/flexible_cylinder_elliptical.c b/sasmodels/models/flexible_cylinder_elliptical.c
index e4fff8dc..44167b0c 100644
--- a/sasmodels/models/flexible_cylinder_elliptical.c
+++ b/sasmodels/models/flexible_cylinder_elliptical.c
@@ -14,15 +14,18 @@ double form_volume(double length, double kuhn_length, double radius)
 double
 elliptical_crosssection(double q, double a, double b)
 {
-    double sum=0.0;
+    const double qr_max = q*fmax(a, b);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
 
-    for(int i=0;i<GAUSS_N;i++) {
-        const double zi = ( GAUSS_Z[i] + 1.0 )*M_PI_4;
+    double sum=0.0;
+    for(int i=0;i<n;i++) {
+        const double zi = ( z[i] + 1.0 )*M_PI_4;
         double sn, cn;
         SINCOS(zi, sn, cn);
         const double arg = q*sqrt(a*a*sn*sn + b*b*cn*cn);
         const double yyy = sas_2J1x_x(arg);
-        sum += GAUSS_W[i] * yyy * yyy;
+        sum += w[i] * yyy * yyy;
     }
     sum *= 0.5;
     return(sum);
diff --git a/sasmodels/models/flexible_cylinder_elliptical.py b/sasmodels/models/flexible_cylinder_elliptical.py
index ae72622d..924585d9 100644
--- a/sasmodels/models/flexible_cylinder_elliptical.py
+++ b/sasmodels/models/flexible_cylinder_elliptical.py
@@ -117,7 +117,7 @@
     ]
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "lib/wrc_cyl.c",
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "lib/wrc_cyl.c",
           "flexible_cylinder_elliptical.c"]
 
 def random():
@@ -146,7 +146,8 @@ def random():
     #  'background':    0.0001,
     # }, 0.001, 3509.2187],
 
-    # Additional tests with larger range of parameters
+    # Tests with a range of parameters
+    # Values computed with 10000 integration points
     [{'length':     1000.0,
       'kuhn_length': 100.0,
       'radius':       20.0,
@@ -154,7 +155,7 @@ def random():
       'sld':           1.0,
       'sld_solvent':   6.3,
       'background':    0.0001,
-     }, 1.0, 0.00223819],
+     }, 1.0, 0.002238188259406479],
     [{'length':        10.0,
       'kuhn_length': 800.0,
       'radius':        2.0,
@@ -162,7 +163,7 @@ def random():
       'sld':           6.0,
       'sld_solvent':  12.3,
       'background':    0.001,
-     }, 0.1, 0.390281],
+     }, 0.1, 0.39028135615503373],
     [{'length':        100.0,
       'kuhn_length': 800.0,
       'radius':       50.0,
@@ -170,5 +171,5 @@ def random():
       'sld':           0.1,
       'sld_solvent':   5.1,
       'background':    0.0,
-     }, 1.0, 0.0016338264790]
+     }, 1.0, 0.001848640535039348],
     ]
diff --git a/sasmodels/models/hollow_cylinder.c b/sasmodels/models/hollow_cylinder.c
index 409b504f..ed1dd98a 100644
--- a/sasmodels/models/hollow_cylinder.c
+++ b/sasmodels/models/hollow_cylinder.c
@@ -70,18 +70,21 @@ static void
 Fq(double q, double *F1, double *F2, double radius, double thickness, double length,
     double sld, double solvent_sld)
 {
+    const double qr_max= q * fmax(radius + thickness, 0.5*length);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     const double lower = 0.0;
     const double upper = 1.0;        //limits of numerical integral
-
     double total_F1 = 0.0;            //initialize intergral
     double total_F2 = 0.0;
-    for (int i=0;i<GAUSS_N;i++) {
-        const double cos_theta = 0.5*( GAUSS_Z[i] * (upper-lower) + lower + upper );
+    for (int i=0;i<n;i++) {
+        const double cos_theta = 0.5*( z[i] * (upper-lower) + lower + upper );
         const double sin_theta = sqrt(1.0 - cos_theta*cos_theta);
         const double form = _fq(q*sin_theta, q*cos_theta,
                                 radius, thickness, length);
-        total_F1 += GAUSS_W[i] * form;
-        total_F2 += GAUSS_W[i] * form * form;
+        total_F1 += w[i] * form;
+        total_F2 += w[i] * form * form;
     }
     total_F1 *= 0.5*(upper-lower);
     total_F2 *= 0.5*(upper-lower);
diff --git a/sasmodels/models/hollow_cylinder.py b/sasmodels/models/hollow_cylinder.py
index 27096f94..78903097 100644
--- a/sasmodels/models/hollow_cylinder.py
+++ b/sasmodels/models/hollow_cylinder.py
@@ -98,7 +98,7 @@
     ]
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "hollow_cylinder.c"]
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "hollow_cylinder.c"]
 have_Fq = True
 radius_effective_modes = [
     "excluded volume", "equivalent outer volume sphere",
diff --git a/sasmodels/models/hollow_rectangular_prism.c b/sasmodels/models/hollow_rectangular_prism.c
index 4fc4bc4d..d2727227 100644
--- a/sasmodels/models/hollow_rectangular_prism.c
+++ b/sasmodels/models/hollow_rectangular_prism.c
@@ -72,6 +72,10 @@ Fq(double q,
     const double vol_total = length_a * length_b * length_c;
     const double vol_core = 8.0 * (a_half-thickness) * (b_half-thickness) * (c_half-thickness);
 
+    const double qr_max = q*c_half;
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     //Integration limits to use in Gaussian quadrature
     const double v1a = 0.0;
     const double v1b = M_PI_2;  //theta integration limits
@@ -80,20 +84,24 @@ Fq(double q,
 
     double outer_sum_F1 = 0.0;
     double outer_sum_F2 = 0.0;
-    for(int i=0; i<GAUSS_N; i++) {
+    for(int i=0; i<n; i++) {
 
-        const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
+        const double theta = 0.5 * ( z[i]*(v1b-v1a) + v1a + v1b );
         double sin_theta, cos_theta;
         SINCOS(theta, sin_theta, cos_theta);
 
         const double termC1 = sas_sinx_x(q * c_half * cos(theta));
         const double termC2 = sas_sinx_x(q * (c_half-thickness)*cos(theta));
 
+        const double qr_max_inner = q*sin_theta*fmax(a_half, b_half);  // = qab*max(len)/2
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max, &w_inner, &z_inner);
+
         double inner_sum_F1 = 0.0;
         double inner_sum_F2 = 0.0;
-        for(int j=0; j<GAUSS_N; j++) {
+        for(int j=0; j<n_inner; j++) {
 
-            const double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
+            const double phi = 0.5 * ( z_inner[j]*(v2b-v2a) + v2a + v2b );
             double sin_phi, cos_phi;
             SINCOS(phi, sin_phi, cos_phi);
 
@@ -108,14 +116,14 @@ Fq(double q,
             const double AP1 = vol_total * termA1 * termB1 * termC1;
             const double AP2 = vol_core * termA2 * termB2 * termC2;
 
-            inner_sum_F1 += GAUSS_W[j] * (AP1-AP2);
-            inner_sum_F2 += GAUSS_W[j] * square(AP1-AP2);
+            inner_sum_F1 += w_inner[j] * (AP1-AP2);
+            inner_sum_F2 += w_inner[j] * square(AP1-AP2);
         }
         inner_sum_F1 *= 0.5 * (v2b-v2a);
         inner_sum_F2 *= 0.5 * (v2b-v2a);
 
-        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin(theta);
-        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin(theta);
+        outer_sum_F1 += w[i] * inner_sum_F1 * sin(theta);
+        outer_sum_F2 += w[i] * inner_sum_F2 * sin(theta);
     }
     outer_sum_F1 *= 0.5*(v1b-v1a);
     outer_sum_F2 *= 0.5*(v1b-v1a);
diff --git a/sasmodels/models/hollow_rectangular_prism.py b/sasmodels/models/hollow_rectangular_prism.py
index 31b65464..fc758b46 100644
--- a/sasmodels/models/hollow_rectangular_prism.py
+++ b/sasmodels/models/hollow_rectangular_prism.py
@@ -146,7 +146,7 @@
                "rotation about c axis"],
              ]
 
-source = ["lib/gauss76.c", "hollow_rectangular_prism.c"]
+source = ["lib/adaptive.c", "hollow_rectangular_prism.c"]
 have_Fq = True
 radius_effective_modes = [
     "equivalent cylinder excluded volume", "equivalent outer volume sphere",
diff --git a/sasmodels/models/hollow_rectangular_prism_thin_walls.c b/sasmodels/models/hollow_rectangular_prism_thin_walls.c
index 2d5956de..17204b8c 100644
--- a/sasmodels/models/hollow_rectangular_prism_thin_walls.c
+++ b/sasmodels/models/hollow_rectangular_prism_thin_walls.c
@@ -64,6 +64,10 @@ Fq(double q,
     const double b_half = 0.5 * length_b;
     const double c_half = 0.5 * length_c;
 
+    const double qr_max = q*c_half;
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
    //Integration limits to use in Gaussian quadrature
     const double v1a = 0.0;
     const double v1b = M_PI_2;  //theta integration limits
@@ -72,8 +76,8 @@ Fq(double q,
 
     double outer_sum_F1 = 0.0;
     double outer_sum_F2 = 0.0;
-    for(int i=0; i<GAUSS_N; i++) {
-        const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
+    for(int i=0; i<n; i++) {
+        const double theta = 0.5 * ( z[i]*(v1b-v1a) + v1a + v1b );
 
         double sin_theta, cos_theta;
         double sin_c, cos_c;
@@ -84,10 +88,14 @@ Fq(double q,
         const double termAL_theta = 8.0 * cos_c / (q*q*sin_theta*sin_theta);
         const double termAT_theta = 8.0 * sin_c / (q*q*sin_theta*cos_theta);
 
+        const double qr_max_inner = q*sin_theta*fmax(a_half, b_half);  // = qab*max(len)/2
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max, &w_inner, &z_inner);
+
         double inner_sum_F1 = 0.0;
         double inner_sum_F2 = 0.0;
-        for(int j=0; j<GAUSS_N; j++) {
-            const double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
+        for(int j=0; j<n_inner; j++) {
+            const double phi = 0.5 * ( z_inner[j]*(v2b-v2a) + v2a + v2b );
 
             double sin_phi, cos_phi;
             double sin_a, cos_a;
@@ -104,14 +112,14 @@ Fq(double q,
             const double AT = termAT_theta
                 * ( cos_a*sin_b/cos_phi + cos_b*sin_a/sin_phi );
 
-            inner_sum_F1 += GAUSS_W[j] * (AL+AT);
-            inner_sum_F2 += GAUSS_W[j] * square(AL+AT);
+            inner_sum_F1 += w_inner[j] * (AL+AT);
+            inner_sum_F2 += w_inner[j] * square(AL+AT);
         }
 
         inner_sum_F1 *= 0.5 * (v2b-v2a);
         inner_sum_F2 *= 0.5 * (v2b-v2a);
-        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin_theta;
-        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin_theta;
+        outer_sum_F1 += w[i] * inner_sum_F1 * sin_theta;
+        outer_sum_F2 += w[i] * inner_sum_F2 * sin_theta;
     }
 
     outer_sum_F1 *= 0.5*(v1b-v1a);
diff --git a/sasmodels/models/hollow_rectangular_prism_thin_walls.py b/sasmodels/models/hollow_rectangular_prism_thin_walls.py
index b2628331..352c09eb 100644
--- a/sasmodels/models/hollow_rectangular_prism_thin_walls.py
+++ b/sasmodels/models/hollow_rectangular_prism_thin_walls.py
@@ -107,7 +107,7 @@
                "Ratio sides c/a"],
              ]
 
-source = ["lib/gauss76.c", "hollow_rectangular_prism_thin_walls.c"]
+source = ["lib/adaptive.c", "hollow_rectangular_prism_thin_walls.c"]
 have_Fq = True
 radius_effective_modes = [
     "equivalent cylinder excluded volume", "equivalent outer volume sphere",
diff --git a/sasmodels/models/lib/adaptive.c b/sasmodels/models/lib/adaptive.c
index 0f0179da..170afecb 100644
--- a/sasmodels/models/lib/adaptive.c
+++ b/sasmodels/models/lib/adaptive.c
@@ -1,15 +1,51 @@
-// Created by Andrew Jackson on 4/23/07
+// From gauss20.c created by Andrew Jackson on 4/23/07
+constant double Gauss20Wt[20]={
+	.0176140071391521,
+	.0406014298003869,
+	.0626720483341091,
+	.0832767415767047,
+	.10193011981724,
+	.118194531961518,
+	.131688638449177,
+	.142096109318382,
+	.149172986472604,
+	.152753387130726,
+	.152753387130726,
+	.149172986472604,
+	.142096109318382,
+	.131688638449177,
+	.118194531961518,
+	.10193011981724,
+	.0832767415767047,
+	.0626720483341091,
+	.0406014298003869,
+	.0176140071391521
+};
 
-#ifdef GAUSS_N
-# undef GAUSS_N
-# undef GAUSS_Z
-# undef GAUSS_W
-#endif
-#define GAUSS_N 76
-#define GAUSS_Z Gauss76Z
-#define GAUSS_W Gauss76Wt
+constant double Gauss20Z[20]={
+	-.993128599185095,
+	-.963971927277914,
+	-.912234428251326,
+	-.839116971822219,
+	-.746331906460151,
+	-.636053680726515,
+	-.510867001950827,
+	-.37370608871542,
+	-.227785851141645,
+	-.076526521133497,
+	.0765265211334973,
+	.227785851141645,
+	.37370608871542,
+	.510867001950827,
+	.636053680726515,
+	.746331906460151,
+	.839116971822219,
+	.912234428251326,
+	.963971927277914,
+	.993128599185095
+};
 
-// Gaussians
+// From gauss76.c created by Andrew Jackson on 4/23/07
 constant double Gauss76Wt[76] = {
    .00126779163408536,		//0
    .00294910295364247,
@@ -169,16 +205,6 @@ constant double Gauss76Z[76] = {
 };
 
 // Generated by sasmodels.gengauss.gengauss(500)
-
-#ifdef GAUSS_N
-# undef GAUSS_N
-# undef GAUSS_Z
-# undef GAUSS_W
-#endif
-#define GAUSS_N 500
-#define GAUSS_Z Gauss500Z
-#define GAUSS_W Gauss500Wt
-
 constant double Gauss500Wt[500]={
 	 2.962364450557860e-05,
 	 6.895707281791116e-05,
@@ -1185,16 +1211,6 @@ constant double Gauss500Z[500]={
 };
 
 // Generated by sasmodels.gengauss.gengauss(5000)
-
-#ifdef GAUSS_N
-# undef GAUSS_N
-# undef GAUSS_Z
-# undef GAUSS_W
-#endif
-#define GAUSS_N 5000
-#define GAUSS_Z Gauss5000Z
-#define GAUSS_W Gauss5000Wt
-
 constant double Gauss5000Wt[5000]={
 	 2.967708115050575e-07,
 	 6.908266104348143e-07,
@@ -11203,7 +11219,11 @@ constant double Gauss5000Z[5000]={
 static int
 gauss_weights(double qr, constant double **w, constant double **z)
 {
-    if (qr < 100) {
+	// *w = Gauss5000Wt; *z = Gauss5000Z; return 5000; // max precision
+	// *w = Gauss76Wt; *z = Gauss76Z; return 76; // default
+	if (qr < 10) {
+        *w = Gauss20Wt; *z = Gauss20Z; return 20;
+	} else if (qr < 100) {
         *w = Gauss76Wt; *z = Gauss76Z; return 76;
     } else if (qr < 750) {
         *w = Gauss500Wt; *z = Gauss500Z; return 500;
diff --git a/sasmodels/models/parallelepiped.c b/sasmodels/models/parallelepiped.c
index 7b5262b6..7ee90563 100644
--- a/sasmodels/models/parallelepiped.c
+++ b/sasmodels/models/parallelepiped.c
@@ -75,34 +75,42 @@ Fq(double q,
     const double a_scaled = length_a / length_b;
     const double c_scaled = length_c / length_b;
 
+    const double qr_max = mu*c_scaled;
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // outer integral (with gauss points), integration limits = 0, 1
     double outer_total_F1 = 0.0; //initialize integral
     double outer_total_F2 = 0.0; //initialize integral
-    for( int i=0; i<GAUSS_N; i++) {
-        const double sigma = 0.5 * ( GAUSS_Z[i] + 1.0 );
+    for( int i=0; i<n; i++) {
+        const double sigma = 0.5 * ( z[i] + 1.0 );
         const double mu_proj = mu * sqrt(1.0-sigma*sigma);
 
+        const double qr_max_inner = mu_proj*fmax(a_scaled, 1.0);  // = qab*max(len)/2
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max, &w_inner, &z_inner);
+
         // inner integral (with gauss points), integration limits = 0, 1
         // corresponding to angles from 0 to pi/2.
         double inner_total_F1 = 0.0;
         double inner_total_F2 = 0.0;
-        for(int j=0; j<GAUSS_N; j++) {
-            const double uu = 0.5 * ( GAUSS_Z[j] + 1.0 );
+        for(int j=0; j<n_inner; j++) {
+            const double uu = 0.5 * ( z_inner[j] + 1.0 );
             double sin_uu, cos_uu;
             SINCOS(M_PI_2*uu, sin_uu, cos_uu);
             const double si1 = sas_sinx_x(mu_proj * sin_uu * a_scaled);
             const double si2 = sas_sinx_x(mu_proj * cos_uu);
             const double fq = si1 * si2;
-            inner_total_F1 += GAUSS_W[j] * fq;
-            inner_total_F2 += GAUSS_W[j] * fq * fq;
+            inner_total_F1 += w_inner[j] * fq;
+            inner_total_F2 += w_inner[j] * fq * fq;
         }
         // now complete change of inner integration variable (1-0)/(1-(-1))= 0.5
         inner_total_F1 *= 0.5;
         inner_total_F2 *= 0.5;
 
         const double si = sas_sinx_x(mu * c_scaled * sigma);
-        outer_total_F1 += GAUSS_W[i] * inner_total_F1 * si;
-        outer_total_F2 += GAUSS_W[i] * inner_total_F2 * si * si;
+        outer_total_F1 += w[i] * inner_total_F1 * si;
+        outer_total_F2 += w[i] * inner_total_F2 * si * si;
     }
     // now complete change of outer integration variable (1-0)/(1-(-1))= 0.5
     outer_total_F1 *= 0.5;
diff --git a/sasmodels/models/parallelepiped.py b/sasmodels/models/parallelepiped.py
index 91a9ebf1..7a473986 100644
--- a/sasmodels/models/parallelepiped.py
+++ b/sasmodels/models/parallelepiped.py
@@ -231,7 +231,7 @@
                "rotation about c axis"],
              ]
 
-source = ["lib/gauss76.c", "parallelepiped.c"]
+source = ["lib/adaptive.c", "parallelepiped.c"]
 have_Fq = True
 radius_effective_modes = [
     "equivalent cylinder excluded volume", "equivalent volume sphere",
diff --git a/sasmodels/models/pringle.c b/sasmodels/models/pringle.c
index 802ca066..6607350a 100644
--- a/sasmodels/models/pringle.c
+++ b/sasmodels/models/pringle.c
@@ -24,17 +24,21 @@ void _integrate_bessel(
     const double zm = 0.5*radius;
     const double zb = 0.5*radius;
 
+    const double qr_max = fmax(q_sin_psi*beta*radius*radius, q_cos_psi*radius);
+    constant double *w, *z;
+    int n_outer = gauss_weights(qr_max, &w, &z);
+
     // evaluate at Gauss points
     double sumS = 0.0;		// initialize integral
     double sumC = 0.0;		// initialize integral
     double r;
-    for (int i=0; i < GAUSS_N; i++) {
-        r = GAUSS_Z[i]*zm + zb;
+    for (int i=0; i < n_outer; i++) {
+        r = z[i]*zm + zb;
 
         const double qrs = r*q_sin_psi;
         const double qrrc = r*r*q_cos_psi;
 
-        double y = GAUSS_W[i] * r * sas_JN(n, beta*qrrc) * sas_JN(2*n, qrs);
+        double y = w[i] * r * sas_JN(n, beta*qrrc) * sas_JN(2*n, qrs);
         double S, C;
         SINCOS(alpha*qrrc, S, C);
         sumS += y*S;
@@ -80,19 +84,23 @@ double _integrate_psi(
     double alpha,
     double beta)
 {
+    const double qr_max = q*0.5*thickness;
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // translate gauss point z in [-1,1] to a point in [0, pi/2]
     const double zm = M_PI_4;
     const double zb = M_PI_4;
 
     double sum = 0.0;
-    for (int i = 0; i < GAUSS_N; i++) {
-        double psi = GAUSS_Z[i]*zm + zb;
+    for (int i = 0; i < n; i++) {
+        double psi = z[i]*zm + zb;
         double sin_psi, cos_psi;
         SINCOS(psi, sin_psi, cos_psi);
         double bessel_term = _sum_bessel_orders(radius, alpha, beta, q*sin_psi, q*cos_psi);
         double sinc_term = square(sas_sinx_x(q * thickness * cos_psi / 2.0));
         double pringle_kernel = 4.0 * sin_psi * bessel_term * sinc_term;
-        sum += GAUSS_W[i] * pringle_kernel;
+        sum += w[i] * pringle_kernel;
     }
 
     return zm * sum;
diff --git a/sasmodels/models/pringle.py b/sasmodels/models/pringle.py
index d086245a..d7207ef5 100644
--- a/sasmodels/models/pringle.py
+++ b/sasmodels/models/pringle.py
@@ -76,7 +76,7 @@
 
 
 source = ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c",
-          "lib/sas_JN.c", "lib/gauss76.c", "pringle.c"]
+          "lib/sas_JN.c", "lib/adaptive.c", "pringle.c"]
 radius_effective_modes = [
     "equivalent cylinder excluded volume",
     "equivalent volume sphere",
diff --git a/sasmodels/models/rectangular_prism.c b/sasmodels/models/rectangular_prism.c
index b75a7470..140cb3ac 100644
--- a/sasmodels/models/rectangular_prism.c
+++ b/sasmodels/models/rectangular_prism.c
@@ -36,6 +36,8 @@ radius_effective(int mode, double length_a, double b2a_ratio, double c2a_ratio)
     }
 }
 
+// TODO: why is there a separate Iq and Fq?
+/*
 static double
 Iq(double q,
     double sld,
@@ -98,6 +100,7 @@ Iq(double q,
 
     return answer;
 }
+*/
 
 static void
 Fq(double q,
@@ -115,6 +118,10 @@ Fq(double q,
     const double b_half = 0.5 * length_b;
     const double c_half = 0.5 * length_c;
 
+    const double qr_max = q*c_half;
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, &w, &z);
+
    //Integration limits to use in Gaussian quadrature
     const double v1a = 0.0;
     const double v1b = M_PI_2;  //theta integration limits
@@ -123,17 +130,21 @@ Fq(double q,
 
     double outer_sum_F1 = 0.0;
     double outer_sum_F2 = 0.0;
-    for(int i=0; i<GAUSS_N; i++) {
-        const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
+    for(int i=0; i<n; i++) {
+        const double theta = 0.5 * ( z[i]*(v1b-v1a) + v1a + v1b );
         double sin_theta, cos_theta;
         SINCOS(theta, sin_theta, cos_theta);
 
         const double termC = sas_sinx_x(q * c_half * cos_theta);
 
+        const double qr_max_inner = q*sin_theta*fmax(a_half, b_half);
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max, &w_inner, &z_inner);
+
         double inner_sum_F1 = 0.0;
         double inner_sum_F2 = 0.0;
-        for(int j=0; j<GAUSS_N; j++) {
-            double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
+        for(int j=0; j<n_inner; j++) {
+            double phi = 0.5 * ( z_inner[j]*(v2b-v2a) + v2a + v2b );
             double sin_phi, cos_phi;
             SINCOS(phi, sin_phi, cos_phi);
 
@@ -141,13 +152,13 @@ Fq(double q,
             const double termA = sas_sinx_x(q * a_half * sin_theta * sin_phi);
             const double termB = sas_sinx_x(q * b_half * sin_theta * cos_phi);
             const double AP = termA * termB * termC;
-            inner_sum_F1 += GAUSS_W[j] * AP;
-            inner_sum_F2 += GAUSS_W[j] * AP * AP;
+            inner_sum_F1 += w_inner[j] * AP;
+            inner_sum_F2 += w_inner[j] * AP * AP;
         }
         inner_sum_F1 = 0.5 * (v2b-v2a) * inner_sum_F1;
         inner_sum_F2 = 0.5 * (v2b-v2a) * inner_sum_F2;
-        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin_theta;
-        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin_theta;
+        outer_sum_F1 += w[i] * inner_sum_F1 * sin_theta;
+        outer_sum_F2 += w[i] * inner_sum_F2 * sin_theta;
     }
 
     outer_sum_F1 *= 0.5*(v1b-v1a);
diff --git a/sasmodels/models/rectangular_prism.py b/sasmodels/models/rectangular_prism.py
index 5ea236c4..05a6fd51 100644
--- a/sasmodels/models/rectangular_prism.py
+++ b/sasmodels/models/rectangular_prism.py
@@ -144,7 +144,7 @@
                "rotation about c axis"],
              ]
 
-source = ["lib/gauss76.c", "rectangular_prism.c"]
+source = ["lib/adaptive.c", "rectangular_prism.c"]
 have_Fq = True
 radius_effective_modes = [
     "equivalent cylinder excluded volume", "equivalent volume sphere",
diff --git a/sasmodels/models/spherical_sld.c b/sasmodels/models/spherical_sld.c
index 696cf8e8..41cf2f6b 100644
--- a/sasmodels/models/spherical_sld.c
+++ b/sasmodels/models/spherical_sld.c
@@ -57,6 +57,8 @@ static double f_linear(double q, double r, double contrast, double slope)
     return vol*(bes*contrast + fun*slope);
 }
 
+// TODO: why both Iq and Fq ?
+/*
 static double Iq(
     double q,
     double fp_n_shells,
@@ -114,6 +116,7 @@ static double Iq(
     const double f2 = f * f * 1.0e-4;
     return f2;
 }
+*/
 
 static void Fq(
     double q,
diff --git a/sasmodels/models/stacked_disks.c b/sasmodels/models/stacked_disks.c
index 25cb1ed2..a97bfa1b 100644
--- a/sasmodels/models/stacked_disks.c
+++ b/sasmodels/models/stacked_disks.c
@@ -75,13 +75,16 @@ stacked_disks_1d(
 /*    StackedDiscsX  :  calculates the form factor of a stacked "tactoid" of core shell disks
 like clay platelets that are not exfoliated
 */
-    double summ = 0.0;    //initialize integral
-
     double d = 2.0*thick_layer+thick_core;
     double halfheight = 0.5*thick_core;
 
-    for(int i=0; i<GAUSS_N; i++) {
-        double zi = (GAUSS_Z[i] + 1.0)*M_PI_4;
+    const double qr_max = fmax(halfheight+thick_layer, radius);
+    constant double *w, *z;
+    int n = gauss_weights(q*qr_max, &w, &z);
+
+    double summ = 0.0;    //initialize integral
+    for(int i=0; i<n; i++) {
+        double zi = (z[i] + 1.0)*M_PI_4;
         double sin_alpha, cos_alpha; // slots to hold sincos function output
         SINCOS(zi, sin_alpha, cos_alpha);
         double yyy = stacked_disks_kernel(q*sin_alpha, q*cos_alpha,
@@ -94,7 +97,7 @@ like clay platelets that are not exfoliated
                            layer_sld,
                            solvent_sld,
                            d);
-        summ += GAUSS_W[i] * yyy * sin_alpha;
+        summ += w[i] * yyy * sin_alpha;
     }
 
     double answer = M_PI_4*summ;
diff --git a/sasmodels/models/stacked_disks.py b/sasmodels/models/stacked_disks.py
index 036df24f..487d7828 100644
--- a/sasmodels/models/stacked_disks.py
+++ b/sasmodels/models/stacked_disks.py
@@ -146,7 +146,7 @@
     ]
 # pylint: enable=bad-whitespace, line-too-long
 
-source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "stacked_disks.c"]
+source = ["lib/polevl.c", "lib/sas_J1.c", "lib/adaptive.c", "stacked_disks.c"]
 
 def random():
     """Return a random parameter set for the model."""
@@ -173,7 +173,7 @@ def random():
 # april 6 2017, rkh added a 2d unit test, assume correct!
 qx = q*cos(pi/6.0)
 qy = q*sin(pi/6.0)
-# Accuracy tests based on content in test/utest_extra_models.py.
+# Test values based on stacked disk calculation with 10000 integration points.
 # Added 2 tests with n_stacked = 5 using SasView 3.1.2 - PDB;
 # for which alas q=0.001 values seem closer to n_stacked=1 not 5,
 # changed assuming my 4.1 code OK, RKH
@@ -190,7 +190,7 @@ def random():
       'phi': 0.0,
       'scale': 0.01,
       'background': 0.001,
-     }, 0.001, 5075.12],
+     }, 0.001, 5075.11570493149],
     [{'thick_core': 10.0,
       'thick_layer': 15.0,
       'radius': 3000.0,
@@ -207,7 +207,7 @@ def random():
       # check other cpu types
       #}, 0.001, 5065.12793824],
       #}, 0.001, 5075.11570493],
-     }, 0.001, 25325.635693],
+     }, 0.001, 25325.6356930102],
     [{'thick_core': 10.0,
       'thick_layer': 15.0,
       'radius': 100.0,
@@ -220,7 +220,7 @@ def random():
       'phi': 20.0,
       'scale': 0.01,
       'background': 0.001,
-     }, (qx, qy), 0.0491167089952],
+     }, (qx, qy), 0.0491167089952473],
     [{'thick_core': 10.0,
       'thick_layer': 15.0,
       'radius': 3000.0,
@@ -237,7 +237,7 @@ def random():
       # check other cpu types
       #}, 0.164, 0.0127673597265],
       #}, 0.164, 0.01480812968],
-     }, 0.164, 0.0598367986509],
+     }, 0.164, 0.0592213685787702],
 
     [{'thick_core': 10.0,
       'thick_layer': 15.0,
@@ -253,7 +253,7 @@ def random():
       'background': 0.001,
       # second test here was at q=90, changed it to q=5,
       # note I(q) is then just value of flat background
-     }, [0.001, 5.0], [5075.12, 0.001]],
+     }, [0.001, 5.0], [5075.11570493149, 0.00100000482962961]],
 
     [{'thick_core': 10.0,
       'thick_layer': 15.0,
@@ -267,7 +267,7 @@ def random():
       'phi': 0.0,
       'scale': 0.01,
       'background': 0.001,
-     }, ([0.4, 0.5]), [0.00105074, 0.00121761]],
+     }, ([0.4, 0.5]), [0.00104871450175645, 0.00131279870340243]],
     #[{'thick_core': 10.0,
     #  'thick_layer': 15.0,
     #  'radius': 3000.0,
@@ -297,6 +297,6 @@ def random():
       'phi': 0.0,
       'scale': 0.01,
       'background': 0.001,
-     }, ([1.3, 1.57]), [0.0010039, 0.0010038]],
+     }, ([1.3, 1.57]), [0.00100223756201264, 0.00100209845708764]],
     ]
 # 11Jan2017   RKH checking unit test again, note they are all 1D, no 2D
diff --git a/sasmodels/models/triaxial_ellipsoid.c b/sasmodels/models/triaxial_ellipsoid.c
index 075edf65..19b9cfcb 100644
--- a/sasmodels/models/triaxial_ellipsoid.c
+++ b/sasmodels/models/triaxial_ellipsoid.c
@@ -100,30 +100,41 @@ Fq(double q,
 {
     const double pa = square(radius_equat_minor/radius_equat_major) - 1.0;
     const double pc = square(radius_polar/radius_equat_major) - 1.0;
+
+    // TODO: check that c_length dominates the outer loop, and a_length, b_length inner
+    // const double qr_max = q*fmax(fmax(radius_equat_minor, radius_equat_major), radius_polar);
+    const double qr_max = q*radius_polar;
+    constant double *z, *w;
+    int n = gauss_weights(qr_max, &w, &z);
+
     // translate a point in [-1,1] to a point in [0, pi/2]
     const double zm = M_PI_4;
     const double zb = M_PI_4;
     double outer_sum_F1 = 0.0;
     double outer_sum_F2 = 0.0;
-    for (int i=0;i<GAUSS_N;i++) {
-        //const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper + lower)/2;
-        const double phi = GAUSS_Z[i]*zm + zb;
+    for (int i=0;i<n;i++) {
+        //const double u = z[i]*(upper-lower)/2 + (upper + lower)/2;
+        const double phi = z[i]*zm + zb;
         const double pa_sinsq_phi = pa*square(sin(phi));
 
+        const double qr_max_inner = q*fmax(radius_equat_major, radius_equat_minor);
+        constant double *z_inner, *w_inner;
+        int n_inner = gauss_weights(qr_max_inner, &w_inner, &z_inner);
+
         double inner_sum_F1 = 0.0;
         double inner_sum_F2 = 0.0;
         const double um = 0.5;
         const double ub = 0.5;
-        for (int j=0;j<GAUSS_N;j++) {
+        for (int j=0;j<n_inner;j++) {
             // translate a point in [-1,1] to a point in [0, 1]
-            const double usq = square(GAUSS_Z[j]*um + ub);
+            const double usq = square(z_inner[j]*um + ub);
             const double r = radius_equat_major*sqrt(pa_sinsq_phi*(1.0-usq) + 1.0 + pc*usq);
             const double fq = sas_3j1x_x(q*r);
-            inner_sum_F1 += GAUSS_W[j] * fq;
-            inner_sum_F2 += GAUSS_W[j] * fq * fq;
+            inner_sum_F1 += w_inner[j] * fq;
+            inner_sum_F2 += w_inner[j] * fq * fq;
         }
-        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1;  // correcting for dx later
-        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2;  // correcting for dx later
+        outer_sum_F1 += w[i] * inner_sum_F1;  // correcting for dx later
+        outer_sum_F2 += w[i] * inner_sum_F2;  // correcting for dx later
     }
     // translate integration ranges from [-1,1] to [lower,upper] and normalize by 4 pi
     outer_sum_F1 *= 0.25;  // = outer*um*zm*8.0/(4.0*M_PI);
diff --git a/sasmodels/models/triaxial_ellipsoid.py b/sasmodels/models/triaxial_ellipsoid.py
index 4919c8cf..464efe7b 100644
--- a/sasmodels/models/triaxial_ellipsoid.py
+++ b/sasmodels/models/triaxial_ellipsoid.py
@@ -158,7 +158,7 @@
                "rotation about polar axis"],
              ]
 
-source = ["lib/sas_3j1x_x.c", "lib/gauss76.c", "triaxial_ellipsoid.c"]
+source = ["lib/sas_3j1x_x.c", "lib/adaptive.c", "triaxial_ellipsoid.c"]
 # Equations do not require Ra <= Rb <= Rc so don't test for it.
 #valid = ("radius_equat_minor <= radius_equat_major"
 #         " && radius_equat_major <= radius_polar")

From c6d9666dccb27c5e02a099630e6f60d8fb8833d5 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci-lite[bot]"
 <117423508+pre-commit-ci-lite[bot]@users.noreply.github.com>
Date: Wed, 30 Jul 2025 16:19:23 +0000
Subject: [PATCH 4/5] [pre-commit.ci lite] apply automatic fixes for ruff
 linting errors

---
 sasmodels/model_test.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/sasmodels/model_test.py b/sasmodels/model_test.py
index 2a67c9ef..4d0ca340 100755
--- a/sasmodels/model_test.py
+++ b/sasmodels/model_test.py
@@ -601,7 +601,7 @@ def _generate_target_values(modelname, ngauss=0):
         actual = call_kernel(kernel, pars)
         if True or (actual != target).any():
             print("Test:", modelname, pars)
-            print(f"  q = ", qin)
+            print("  q = ", qin)
             print(f"  current => [{', '.join(f'{v:.15g}' for v in target)}]")
             print(f"  ngauss={ngauss} => [{', '.join(f'{v:.15g}' for v in actual)}]")
 

From 615df7145463540bd8a2e0f2958e8810dd5d3dd4 Mon Sep 17 00:00:00 2001
From: Paul Kienzle <pkienzle@nist.gov>
Date: Wed, 30 Jul 2025 14:54:04 -0400
Subject: [PATCH 5/5] use sasmodels.compare -seed=<n> for reproducibile -sets

---
 sasmodels/compare.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/sasmodels/compare.py b/sasmodels/compare.py
index 081e2589..57370c75 100755
--- a/sasmodels/compare.py
+++ b/sasmodels/compare.py
@@ -80,7 +80,7 @@ def __call__(self, **par: float) -> np.ndarray: ...
 
     === model parameters ===
     -preset*/-random[=seed] preset or random parameters
-    -sets=n generates n random datasets with the seed given by -random=seed
+    -sets=n generates n random datasets using -seed=seed
     -pars/-nopars* prints the parameter set or not
     -sphere[=150] set up spherical integration over theta/phi using n points
     -mono*/-poly suppress or allow polydispersity on generated parameters
@@ -1023,7 +1023,7 @@ def plot_models(opts, result, limits=None, setnum=0):
     '2d', '1d', 'sesans',
 
     # Parameter set
-    'preset', 'random', 'random=', 'sets=',
+    'preset', 'random', 'random=', 'sets=', 'seed=',
     'nopars', 'pars',
     'sphere', 'sphere=', # integrate over a sphere in 2d with n points
     'poly', 'mono',
@@ -1227,6 +1227,7 @@ def parse_opts(argv):
         elif arg.startswith('-res='):      opts['res'] = arg[5:]
         elif arg.startswith('-noise='):    opts['noise'] = float(arg[7:])
         elif arg.startswith('-sets='):     opts['sets'] = int(arg[6:])
+        elif arg.startswith('-seed='):     opts['seed'] = int(arg[6:])
         elif arg.startswith('-accuracy='): opts['accuracy'] = arg[10:]
         elif arg.startswith('-cutoff='):   opts['cutoff'] = arg[8:]
         elif arg.startswith('-title='):    opts['title'] = arg[7:]