diff --git a/example/simul_fit.py b/example/simul_fit.py
index 81de11709..783f86a92 100644
--- a/example/simul_fit.py
+++ b/example/simul_fit.py
@@ -8,21 +8,51 @@
 
 # latex data, same sample usans and sans
 # particles radius ~2300, uniform dispersity
-datasets = load_data(str(data_path / '1d_data' / 'latex_smeared.xml'), index='all')
+all_data = load_data(str(data_path / '1d_data' / 'latex_smeared.xml'), index='all')
 #[print(data) for data in datasets]
+datasets = all_data # Both SANS and USANS
+#datasets = all_data[0:1] # SANS
+#datasets = all_data[1:2] # USANS
 
-# A single sphere model to share between the datasets.  We will use
+# A single model to share between the datasets.  We will use
 # FreeVariables below to set the parameters that are independent between
 # the datasets.
-kernel = load_model('sphere')
-pars = dict(scale=0.01, background=0.0, sld=5.0, sld_solvent=0.0, radius=1500.,
-            #radius_pd=0.1, radius_pd_n=35,
-            )
+model_name = "ellipsoid"
+if model_name == "sphere":
+    kernel = load_model("sphere")
+    pars = dict(
+        scale=0.01, background=0.0, sld=5.0, sld_solvent=0.0, radius=1500.,
+        #radius_pd=0.1, radius_pd_n=35,
+        )
+elif model_name == "ellipsoid":
+    kernel = load_model("ellipsoid")
+    pars = dict(
+        scale=0.01, background=0.0, sld=5.0, sld_solvent=0.0,
+        radius_polar=1500., radius_equatorial=1500.,
+        )
+elif model_name == "triaxial_ellipsoid":
+    kernel = load_model("triaxial_ellipsoid", dtype="double!")
+    pars = dict(
+        scale=0.01, background=0.0, sld=5.0, sld_solvent=0.0,
+        radius_polar=1500., radius_equat_major=1500., radius_equat_minor=1500.,
+        )
+else:
+    raise ValueError("Use model_name in sphere, ellipsoid, triaxial_ellipsoid")
+
 model = Model(kernel, **pars)
 
 # radius and polydispersity (if any) are shared
-model.radius.range(0, 3000.)
-#model.radius_pd.range(0, 1)
+if model_name == "sphere":
+    model.radius.range(0, 3000.)
+    # model.radius_pd.range(0, 1)
+elif model_name == "ellipsoid":
+    model.radius_equatorial.range(0, 3000.)
+    model.radius_polar.range(0, 3000.)
+elif model_name == "triaxial_ellipsoid":
+    model.radius_equat_major.range(0, 3000.)
+    model.radius_equat_minor.range(0, 3000.)
+    model.radius_polar.range(0, 3000.)
+
 
 # Contrast and dilution are the same for both measurements, but are not
 # separable with a single measurement (i.e., I(q) ~ F(q) contrast^2 Vf),
diff --git a/explore/check_adaptive.py b/explore/check_adaptive.py
new file mode 100644
index 000000000..6f1df3e4a
--- /dev/null
+++ b/explore/check_adaptive.py
@@ -0,0 +1,408 @@
+from math import sqrt
+
+from sasmodels import core, data, generate
+from sasmodels.compare import tic
+from sasmodels.direct_model import DirectModel
+
+# == Unnested ==
+
+MODELS = {}
+KERNELS = {}
+NESTED = {}
+UNNESTED = {}
+def register(loops):
+    def wrapper(par_fn):
+        model_name = par_fn.__name__
+        if loops == 1:
+            UNNESTED[model_name] = par_fn
+        else:
+            NESTED[model_name] = par_fn
+        return par_fn
+    return wrapper
+
+@register(1)
+def core_shell_bicelle(ab, c, shell=0.1, sld_core=0):
+    thick_rim = thick_face = ab*shell/2 if shell < 1 else shell
+    length = c - 2*thick_face
+    radius = ab/2 - thick_rim
+    pars = dict(
+        radius=radius, thick_rim=thick_rim, thick_face=thick_face, length=length,
+        sld_core=sld_core, sld_face=1, sld_rim=1, sld_solvent=0,
+    )
+    return pars
+
+@register(1)
+def core_shell_cylinder(ab, c, shell=0.1, sld_core=0):
+    thickness = ab*shell/2 if shell < 1 else shell
+    length = c - 2*thickness
+    radius = ab/2 - thickness
+    pars = dict(
+        radius=radius, thickness=thickness, length=length,
+        sld_core=sld_core, sld_shell=1, sld_solvent=0,
+    )
+    return pars
+
+@register(1)
+def core_shell_ellipsoid(ab, c, shell=0.1, sld_core=0):
+    thick_shell = ab*shell/2 if shell < 1 else shell
+    radius_equat_core = ab/2 - thick_shell
+    x_polar_shell = 1
+    x_core = (c/2 - thick_shell)/(ab/2 - thick_shell)
+    pars = dict(
+        radius_equat_core=radius_equat_core, x_core=x_core,
+        thick_shell=thick_shell, x_polar_shell=x_polar_shell,
+        sld_core=sld_core, sld_shell=1, sld_solvent=0,
+    )
+    return pars
+
+@register(1)
+def cylinder(ab, c):
+    pars = dict(sld=1, sld_solvent=0, radius=ab/2, length=c)
+    return pars
+
+@register(1)
+def ellipsoid(ab, c):
+    pars = dict(sld=1, sld_solvent=0, radius_equatorial=ab/2, radius_polar=c/2)
+    return pars
+
+@register(1)
+def flexible_cylinder(ab, c, n=10):
+    pars = dict(
+        length=c*n, kuhn_length=c,
+        radius=ab,
+        sld=1, sld_solvent=0,
+    )
+    return pars
+
+@register(1)
+def hollow_cylinder(ab, c, shell=0.1):
+    thickness = ab/2*shell
+    pars = dict(
+        radius=ab/2 - thickness,
+        thickness=thickness,
+        length=c,
+        sld=1, sld_solvent=0,
+    )
+    return pars
+
+@register(1)
+def stacked_disks(ab, c, shell=0.1, n=10, sld_core=0):
+    # Each stack (layer+core+layer) has total thickness length/n
+    # The shell is a portion of that total thickness, with the core being (1-portion)
+    # Therefore thick_core = length/n*(1-shell) and thick_layer = length/n*shell/2
+    jitter = 0.05
+    pars = dict(
+        thick_core=c/n*(1-shell),
+        thick_layer=c/n*shell/2,
+        radius=ab/2,
+        n_stacking=n,
+        sigma_d=jitter*(c/n),
+        sld_core=sld_core,
+        sld_layer=1,
+        sld_solvent=0,
+    )
+    return pars
+
+
+# == Nested ==
+
+@register(2)
+def barbell(a, b, c):
+    radius, radius_bell = a/2, b/2
+    h = sqrt(radius_bell**2 - radius**2)
+    # c/2 = length/2 + radius_bell + h
+    length = max(c - 2*(radius_bell + h), 0)  # "disk" fails because radius_bell > c
+    pars = dict(radius=radius, radius_bell=radius_bell, length=length, sld=1, sld_solvent=0)
+    return pars
+
+@register(2)
+def capped_cylinder(a, b, c):
+    radius, radius_cap = a/2, b/2
+    h = sqrt(radius_cap**2 - radius**2)
+    # c/2 = length/2 + radius_bell + h
+    length = max(c - 2*(radius_cap - h), 0)
+    pars = dict(radius=radius, radius_cap=radius_cap, length=length, sld=1, sld_solvent=0)
+    return pars
+
+@register(2)
+def core_shell_bicelle_elliptical_belt_rough(a, b, c, shell=0.1, sld_core=0, roughness=0.1):
+    thick_rim = thick_face = a*shell/2 if shell < 1 else shell
+    length = c - 2*thick_face
+    radius = a/2 - thick_rim
+    x_core = (b/2 - thick_rim) / (a/2 - thick_rim)
+    pars = dict(
+        radius=radius, x_core=x_core, thick_rim=thick_rim, thick_face=thick_face, length=length,
+        sld_core=sld_core, sld_face=1, sld_rim=1, sld_solvent=0,
+        sigma=thick_rim*roughness,
+    )
+    return pars
+
+@register(2)
+def core_shell_bicelle_elliptical(a, b, c, shell=0.1, sld_core=0):
+    thick_rim = thick_face = a*shell/2 if shell < 1 else shell
+    length = c - 2*thick_face
+    radius = a/2 - thick_rim
+    x_core = (b/2 - thick_rim) / (a/2 - thick_rim)
+    pars = dict(
+        radius=radius, x_core=x_core, thick_rim=thick_rim, thick_face=thick_face, length=length,
+        sld_core=sld_core, sld_face=1, sld_rim=1, sld_solvent=0,
+    )
+    return pars
+
+@register(2)
+def core_shell_parallelepiped(a, b, c, shell=0.1, sld_core=0):
+    thickness = a*shell/2 if shell < 1 else shell
+    length_a, length_b, length_c = a - 2*thickness, b - 2*thickness, c - 2*thickness
+    pars = dict(
+        sld_core=sld_core, sld_a=1, sld_b=1, sld_c=1, sld_solvent=0,
+        length_a=length_a, length_b=length_b, length_c=length_c,
+        thick_rim_a=thickness, thick_rim_b=thickness, thick_rim_c=thickness,
+    )
+    return pars
+
+@register(2)
+def elliptical_cylinder(a, b, c):
+    pars = dict(radius_minor=a/2, axis_ratio=b/c, length=c, sld=1, sld_solvent=0)
+    return pars
+
+@register(2)
+def flexible_cylinder_elliptical(a, b, c, n=10):
+    pars = dict(
+        length=c*n, kuhn_length=c,
+        radius=a, axis_ratio=b/a,
+        sld=1, sld_solvent=0,
+    )
+    return pars
+
+@register(2)
+def hollow_rectangular_prism_thin_walls(a, b, c):
+    pars = dict(
+        sld=1, sld_solvent=0,
+        length_a=a, b2a_ratio=b/a, c2a_ratio=c/a,
+    )
+    return pars
+
+@register(2)
+def hollow_rectangular_prism(a, b, c, shell=0.1):
+    thickness = a/2*shell
+    pars = dict(
+        sld=1, sld_solvent=0,
+        length_a=a, b2a_ratio=b/a, c2a_ratio=c/a,
+        thickness=thickness,
+    )
+    return pars
+
+@register(2)
+def parallelepiped(a, b, c):
+    pars = dict(
+        sld=1, sld_solvent=0,
+        length_a=a, length_b=b, length_c=c,
+    )
+    return pars
+
+@register(2)
+def pringle(a, b, c):
+    # It is nonsensical to have thickness >> radius, so c ought not be the "long" direction,
+    # however, this is how the loops are structured in the pringle model, so go with it.
+    # Let a be the radius of the disk under curvature (alpha==beta), and b be the uncurved radius.
+    alpha = beta = max(abs(1 - a/b), 0.001)
+    pars = dict(radius=b/2, thickness=c, alpha=alpha, beta=beta, sld=1, sld_solvent=0)
+    return pars
+
+@register(2)
+def rectangular_prism(a, b, c):
+    pars = dict(sld=1, sld_solvent=0, length_a=a, b2a_ratio=b/a, c2a_ratio=c/a)
+    return pars
+
+@register(2)
+def triaxial_ellipsoid(a, b, c):
+    pars = dict(
+        sld=1, sld_solvent=0,
+        radius_equat_minor=a, radius_equat_major=b, radius_polar=c,
+    )
+    return pars
+
+
+def check(models=[]):
+    import numpy as np
+
+    def longlines(fn):
+        def wrapped(*args, **kw):
+            with np.printoptions(
+                linewidth=1000,
+                formatter={'float': '{:.14e}'.format},
+            ):
+                return fn(*args, **kw)
+        return wrapped
+
+    def get_kernel(model_name, n_gauss=0, dtype="double", platform="dll"):
+        # print(f"{model_name=} {n_gauss=} {dtype=} {platform=}")
+        if model_name not in MODELS:
+            model_info = core.load_model_info(model_name)
+            MODELS[model_name] = model_info
+            # set_integration_size() below overwrites info. Cache the adaptive version immediately
+            KERNELS[(model_name, 0, dtype, platform)] = core.build_model(model_info, dtype=dtype, platform=platform)
+        if (model_name, n_gauss, dtype, platform) not in KERNELS:
+            model_info = MODELS[model_name]
+            if n_gauss:
+                # ocl adaptive... this had better be the first or second get_kernel since set_integration_size is stateful
+                generate.set_integration_size(model_info, n_gauss)
+            KERNELS[(model_name, n_gauss, dtype, platform)] = core.build_model(model_info, dtype=dtype, platform=platform)
+        return KERNELS[(model_name, n_gauss, dtype, platform)]
+
+    def timer(fn):
+        # Clear startup overhead
+        toc = tic()
+        fn()
+        dt = toc()
+        if dt > 1:
+            return dt
+        # loop
+        toc = tic()
+        fn()
+        dt = toc()
+        n = int(0.5 // dt)
+        for _ in range(n): fn()
+        return toc()/(n+1)
+
+    @longlines
+    def run_test(model_name, pars, speed_q, test_n_gauss, test_q, tol):
+
+        # Parameter string suitable for use with "python -m sasmodels.compare model par=value..."
+        par_str = " ".join(f"{k}={v}" for k, v in pars.items())
+        # print(f"{model_name} {par_str} -ngauss={test_n_gauss}")
+        k_adaptive = get_kernel(model_name, n_gauss=0, dtype="double", platform="dll")
+        speed_data = data.empty_data1D(speed_q)
+        test_data = data.empty_data1D(test_q)
+
+        Iq_test_adaptive = DirectModel(test_data, k_adaptive)(**pars) # clear startup overhead
+        dt_adaptive = timer(lambda: DirectModel(speed_data, k_adaptive)(**pars))
+
+        labelled = False
+        def print_label():
+            nonlocal labelled
+            if not labelled:
+                print(f"{model_name} {par_str}")
+                labelled = True
+
+        if dt_adaptive > speed_target:
+            print_label()
+            print(f"! ** {model_name} is slow: {dt_adaptive:.1f} s for {len(speed_q)} points in [{speed_q.min()}, {speed_q.max()}]")
+
+        if speed_check: # compare speed of adaptive with
+            if speed_check == "gpu":
+                k_speed = get_kernel(model_name, n_gauss=0, dtype="single", platform="ocl")
+            elif speed_check == "gauss-76":
+                k_speed = get_kernel(model_name, n_gauss=76)
+            else:
+                raise ValueError(f"Unknown speed check: {speed_check}. Use gpu or gauss-76")
+            dt_speed = timer(lambda: DirectModel(speed_data, k_speed)(**pars))
+
+            delta = dt_speed/dt_adaptive - 1
+            if delta >= 1 or delta <= -0.5 or dt_adaptive > 0.5:
+                print_label()
+                value = (
+                    f"{dt_speed/dt_adaptive:.1f}x slower" if delta >= 1
+                    else f"{dt_adaptive/dt_speed:.1f}x faster" if delta < -0.5
+                    else f"{int(delta*100)}% slower" if delta > 0.0
+                    else f"{int(-delta*100)}% faster"
+                )
+                if delta > 0.2:
+                    comment = f"  [{speed_check} {value}]" + (" ***" if speed_check != "gauss-76" else "")
+                elif delta < -0.2:
+                    comment = f"  [{speed_check} {value}]" + (" ***" if speed_check == "gauss-76" else "")
+                elif dt_adaptive > 0.2:
+                    comment = "  [slow]"
+                else:
+                    comment = ""
+                print(f"  cpu double: {dt_adaptive*1000:.1f} ms  {speed_check}: {dt_speed*1000:.1f} ms{comment}")
+
+        if speed_only: # speed_only test
+            return
+
+        k_accurate = get_kernel(model_name, n_gauss=test_n_gauss, dtype="double", platform="dll")
+        Iq_test_accurate = DirectModel(test_data, k_accurate)(**pars)
+        relerr = abs(Iq_test_adaptive - Iq_test_accurate)/Iq_test_accurate
+        index = relerr > tol
+        if index.any():
+            print_label()
+            print("  qvalue", test_q[index])
+            print("  target", Iq_test_accurate[index])
+            print("  actual", Iq_test_adaptive[index])
+            print("  relerr", relerr[index])
+
+        # Compare against 76-point gaussian
+        k_76 = get_kernel(model_name, n_gauss=76, dtype="double", platform="dll")
+        Iq_test_76 = DirectModel(test_data, k_76)(**pars)
+        relerr_76 = abs(Iq_test_76 - Iq_test_accurate)/Iq_test_accurate
+        index = (relerr_76 > tol) #& (relerr > tol) & (relerr > 10*relerr_76)
+        if index.any():
+            print_label()
+            #print("! ** gauss-76 is better than adaptive for {model_name} at some q values")
+            print("! ** gauss-76 is out of tolerance")
+            print("  qvalue", test_q[index])
+            print("  relerr", relerr[index])
+            print("  rel-76", relerr_76[index])
+
+    speed_target = 2
+    #speed_only = True
+    #speed_check = None
+    speed_only = False
+    speed_check = "gauss-76"  # None | "" | "gpu" | "gauss-76"
+    big_n = 5000
+    #small_n = 1000
+    small_n = big_n
+    n_per_decade = 1
+    print(f"""\
+== Speed and accuracy tests for all adaptive integration models ==
+* target evaluation time is {speed_target} s (running on a mac M2 chip)
+*     q in [1e-5, 1] with 40 points per decade for 201 points total
+* large models tested against {big_n} point gaussian integration
+*     q=[5e-4, 1e-3, 2e-3] with tol=1e-5 relative (measured q)
+*     q=[0.01, 0.1] with tol=0.2 relative (slit resolution limits)
+* small models tested against {small_n} point gaussian integration
+*     q in [1e-3, 1] with {n_per_decade} points per decade
+!!!! These tests run very slowly --- don't use as part of CI !!!!
+""")
+    def loop(aspect, a, b, c):
+        q = np.logspace(-5, 0, 201) # 5 decades, 40 points per decade
+        big = max(a, b, c) > 10000  # 1 μm
+        if big:
+            n_gauss = big_n
+            test_q = np.array([0.0005, 0.001, 0.002, 0.01, 0.1])
+            test_tol = np.array([5e-5, 5e-5, 5e-5, 2e-1, 2e-1])
+        else:
+            n_gauss = small_n
+            test_q = np.logspace(-3, 0, 3*n_per_decade + 1) # 3 decades, n points per decade
+            test_tol = np.full_like(test_q, 1e-10)
+
+        print(f"\n\n=== {'big' if big else 'small'} {aspect}: {a=} {b=} {c=} ===")
+        ab = max(a, b)
+        for name, fn in UNNESTED.items():
+            # skip models not listed
+            if models and name not in models:
+                continue
+            pars = dict(background=0, **fn(ab=ab, c=c))
+            run_test(name, pars, q, n_gauss, test_q, test_tol)
+
+        ab = max(a, b)
+        for name, fn in NESTED.items():
+            # skip models not listed
+            if models and name not in models:
+                continue
+            pars = dict(background=0, **fn(a=a, b=b, c=c))
+            run_test(name, pars, q, n_gauss, test_q, test_tol)
+
+    # small size (20 nm) tests
+    loop("rods", a=20, b=40, c=200)
+    loop("disks", a=180, b=200, c=40)
+    loop("cubes", a=200, b=200, c=200)
+
+    # large size (20 μm) tests
+    loop("rods", a=1_000, b=2000, c=200_000)
+    loop("disks", a=180_000, b=200_000, c=1_000)
+    loop("cubes", a=200_000, b=200_000, c=200_000)
+
+if __name__ == "__main__":
+    import sys
+    check(models=sys.argv[1:])
diff --git a/explore/precision.py b/explore/precision.py
index fdc009b78..05880f767 100755
--- a/explore/precision.py
+++ b/explore/precision.py
@@ -803,6 +803,21 @@ def np_2J1x_x(x):
     ocl_function=make_ocl("return sas_2J1x_x(q);", "sas_2J1x_x", ["lib/polevl.c", "lib/sas_J1.c"]),
 )
 
+add_function(
+    name="sin_arccos",
+    mp_function=lambda x: (mp.sin(mp.acos(x))),
+    np_function=lambda x: (np.sin(np.arccos(x))),
+    ocl_function=make_ocl("return sin(acos(q));", "sas_sin_arccos"),
+    limits=(0, 1),
+)
+add_function(
+    name="sin_from_cos",
+    mp_function=lambda x: (mp.sqrt(1 - x*x)),
+    np_function=lambda x: (np.sqrt(1-x*x)),
+    ocl_function=make_ocl("return sqrt(1.-q*q);", "sas_sin_from_cos"),
+    limits=(0, 1),
+)
+
 ALL_FUNCTIONS = set(FUNCTIONS.keys())
 ALL_FUNCTIONS.discard("loggamma")  # use cephes-based gammaln instead
 ALL_FUNCTIONS.discard("3j1/x:taylor")
diff --git a/sasmodels/compare.py b/sasmodels/compare.py
index 26b67ada8..847135d44 100755
--- a/sasmodels/compare.py
+++ b/sasmodels/compare.py
@@ -74,8 +74,8 @@ def __call__(self, **par: float) -> np.ndarray: ...
     -zero indicates that q=0 should be included
 
     === model parameters ===
-    -preset*/-random[=seed] preset or random parameters
-    -sets=n generates n random datasets with the seed given by -random=seed
+    -preset*/-random/-seed=k preset or random parameters
+    -sets=n generates n random datasets
     -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
@@ -89,9 +89,9 @@ def __call__(self, **par: float) -> np.ndarray: ...
     -ngauss=0 overrides the number of points in the 1-D gaussian quadrature
 
     === precision options ===
-    -engine=default uses the default calcution precision
-    -single/-double/-half/-fast sets an OpenCL calculation engine
-    -single!/-double!/-quad! sets an OpenMP calculation engine
+    -single/-double/-half/-fast sets a GPU calculation engine
+    -single!/-double!/-quad! sets a CPU calculation engine
+    -engine=a,b compare I(q) calculated with engine a and b
 
     === plotting ===
     -plot*/-noplot plots or suppress the plot of the model
@@ -1049,7 +1049,7 @@ 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',
@@ -1253,6 +1253,7 @@ 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:]
@@ -1330,6 +1331,10 @@ def parse_opts(argv):
 
     if PAR_SPLIT in opts['ngauss']:
         opts['ngauss'] = [int(k) for k in opts['ngauss'].split(PAR_SPLIT, 2)]
+        # TODO: change set_integration to be non-stateful so we can put adaptive after fixed
+        if opts['ngauss'][1] == 0:
+            a, b = opts['ngauss']
+            raise ValueError(f"Use -ngauss={b},{a} rather than -ngauss={a},{b}")
         comparison = True
     else:
         opts['ngauss'] = [int(opts['ngauss'])]*2
diff --git a/sasmodels/direct_model.py b/sasmodels/direct_model.py
index 7c1004ff2..e9c133c6b 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 0ae362d69..e0c32ea2a 100644
--- a/sasmodels/generate.py
+++ b/sasmodels/generate.py
@@ -281,7 +281,13 @@ def get_data_path(external_dir, target_file):
 %(docs)s
 """
 
-
+# TODO: set_integration_size should return a copy of info
+# For now it is set up so that the first call converts adaptive to non-adaptive
+# and subsequent calls convert number of gauss points for the non-adaptive.
+# There is currently no way to go back to adaptive after call set_integration_size.
+# If model_info is cached this will cause problems for a GUI or a notebook where the
+# user specifies n_gauss=0 for adaptive. This shows up with sasmodels.compare where
+# -n_gauss=0,76 shows differences but -n_gauss=76,0 shows none.
 def set_integration_size(info, n):
     # type: (ModelInfo, int) -> None
     """
@@ -291,13 +297,27 @@ 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 a9ce027f4..2ef063133 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 390df7454..80fec08ef 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("  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 87f1553e3..e8463fed0 100644
--- a/sasmodels/models/barbell.c
+++ b/sasmodels/models/barbell.c
@@ -1,7 +1,7 @@
 //barbell kernel - same as dumbbell
 static double
 _bell_kernel(double qab, double qc, double h, double radius_bell,
-             double half_length)
+             double half_length, int outer_n)
 {
     // translate a point in [-1,1] to a point in [lower,upper]
     const double upper = 1.0;
@@ -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+b);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, outer_n, &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;
@@ -35,9 +40,9 @@ _bell_kernel(double qab, double qc, double h, double radius_bell,
 
 static double
 _fq(double qab, double qc, double h,
-    double radius_bell, double radius, double half_length)
+    double radius_bell, double radius, double half_length, int n_outer)
 {
-    const double bell_fq = _bell_kernel(qab, qc, h, radius_bell, half_length);
+    const double bell_fq = _bell_kernel(qab, qc, h, radius_bell, half_length, n_outer);
     const double bj = sas_2J1x_x(radius*qab);
     const double si = sas_sinx_x(half_length*qc);
     const double cyl_fq = 2.0*M_PI*radius*radius*half_length*bj*si;
@@ -110,21 +115,32 @@ 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;
 
+    // The term h comes from solving the right triangle with diagonal
+    // equal to the bell radius and horizontal equal to the bar radius.
+    // The result is the height of the equator above the end of the rod.
+    // To get the total length of bar+bell use bar length + 2*(bell radius + h).
+    // We want the radius, so divide that by two.
+    const double qr_max = q*(half_length + radius_bell + h);
+    constant double *w_outer, *z_outer;
+    // Keep outer loop to 76 or less
+    int n_outer = gauss_weights(qr_max, ADAPTIVE_MAX_76, &w_outer, &z_outer);
+
     // 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_outer; i++){
+        const double theta = z_outer[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);
+        // Don't constrain size of inner loop to n_outer
+        const double Aq = _fq(qab, qc, h, radius_bell, radius, half_length, 1);
         // 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_outer[i] * Aq * sin_theta;
+        total_F2 += w_outer[i] * Aq * Aq * sin_theta;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     const double form_avg = total_F1 * zm;
@@ -141,8 +157,10 @@ Iqac(double qab, double qc,
     double sld, double solvent_sld,
     double radius_bell, double radius, double length)
 {
+    // TODO: For 2D data we may also want to limit the size of the integral at each (qx, qy)
+    const int n_outer = 1; // No limits on inner integral
     const double h = sqrt(square(radius_bell) - square(radius));
-    const double Aq = _fq(qab, qc, h, radius_bell, radius, 0.5*length);
+    const double Aq = _fq(qab, qc, h, radius_bell, radius, 0.5*length, n_outer);
 
     // Multiply by contrast^2 and convert to cm-1
     const double s = (sld - solvent_sld);
diff --git a/sasmodels/models/barbell.py b/sasmodels/models/barbell.py
index c29b7954d..13b4be74e 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 c792574cb..0132fc716 100644
--- a/sasmodels/models/capped_cylinder.c
+++ b/sasmodels/models/capped_cylinder.c
@@ -7,8 +7,8 @@
 //   length is the cylinder length, or the separation between the lens halves
 //   theta is the angle of the cylinder wrt q.
 static double
-_cap_kernel(double qab, double qc, double h, double radius_cap,
-    double half_length)
+_cap_kernel(double qab, double qc, double h, double radius_cap, double radius,
+    double half_length, int outer_n)
 {
     // translate a point in [-1,1] to a point in [lower,upper]
     const double upper = 1.0;
@@ -26,13 +26,25 @@ _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)
+
+    // m+b = qc*(half_length + radius_cap + h). With h in [-radius_cap, 0] depending
+    // on cylinder radius, that means m+b is in qc*[length/2, length_2 + radius_cap].
+    // The qab_r term will be very large for mostly flat caps. Since the bj term will
+    // oscillate at this frequency, it seems like we should increase the number of
+    // gauss points to accomodate. However, if we use the radius of the cylinder
+    // we seem to get good results, so use that to set the number of integration points.
+    //const double qr_max = fmax(qab_r, m+b);
+    const double qr_max = fmax(qab*radius, m+b);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, outer_n, &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;
@@ -41,9 +53,9 @@ _cap_kernel(double qab, double qc, double h, double radius_cap,
 }
 
 static double
-_fq(double qab, double qc, double h, double radius_cap, double radius, double half_length)
+_fq(double qab, double qc, double h, double radius_cap, double radius, double half_length, int n_outer)
 {
-    const double cap_Fq = _cap_kernel(qab, qc, h, radius_cap, half_length);
+    const double cap_Fq = _cap_kernel(qab, qc, h, radius_cap, radius, half_length, n_outer);
     const double bj = sas_2J1x_x(radius*qab);
     const double si = sas_sinx_x(half_length*qc);
     const double cyl_Fq = 2.0*M_PI*radius*radius*half_length*bj*si;
@@ -114,21 +126,36 @@ 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;
 
+    // The term h comes from solving the right triangle with diagonal
+    // equal to the cap radius and horizontal equal to the bar radius.
+    // The result is the (negative) height of the equator above the end of the rod.
+    // To get the total length of bar+cap use bar length + 2*(cap radius + h).
+    // We want the radius, so divide that by two.
+    // For a lentil with length=0, the radius will be the dominant term, hence
+    // the fmax in the calculation below. This isn't needed for the barbell shape
+    // since the bell length is always greater than the bar radius.
+    const double qr_max = q*fmax(half_length + radius_cap + h, radius);
+    //const double qr_max = q*(half_length + radius_cap + h);
+    constant double *w_outer, *z_outer;
+    // Keep outer loop to 76 or less
+    int n_outer = gauss_weights(qr_max, ADAPTIVE_MAX_76, &w_outer, &z_outer);
+
     // 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_outer ;i++) {
+        const double theta = z_outer[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);
+        // Don't constrain size of inner loop to n_outer
+        const double Aq = _fq(qab, qc, h, radius_cap, radius, half_length, 1);
         // 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_outer[i] * Aq * sin_theta;
+        total_F2 += w_outer[i] * Aq * Aq * sin_theta;
     }
     // translate dx in [-1,1] to dx in [lower,upper]
     const double form_avg = total_F1 * zm;
@@ -146,8 +173,10 @@ Iqac(double qab, double qc,
     double sld, double solvent_sld, double radius,
     double radius_cap, double length)
 {
+    // TODO: For 2D data we may also want to limit the size of the integral at each (qx, qy)
+    const int n_outer = 1; // No limits on inner integral
     const double h = -sqrt(square(radius_cap) - square(radius));
-    const double Aq = _fq(qab, qc, h, radius_cap, radius, 0.5*length);
+    const double Aq = _fq(qab, qc, h, radius_cap, radius, 0.5*length, n_outer);
 
     // Multiply by contrast^2 and convert to cm-1
     const double s = (sld - solvent_sld);
diff --git a/sasmodels/models/capped_cylinder.py b/sasmodels/models/capped_cylinder.py
index 0bacdd7c2..30a000598 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 bddb8d2ea..fb3db0f64 100644
--- a/sasmodels/models/core_shell_bicelle.c
+++ b/sasmodels/models/core_shell_bicelle.c
@@ -93,16 +93,20 @@ Fq(double q,
     const double uplim = M_PI_4;
     const double halflength = 0.5*length;
 
+    const double qr_max = q*fmax(radius+thick_radius, 2*halflength+thick_face);
+    constant double *w, *z;
+    int n = gauss_weights(qr_max, 1, &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 e20125621..e62b60032 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/core_shell_bicelle_elliptical.c b/sasmodels/models/core_shell_bicelle_elliptical.c
index 0264c7dc3..7d74daa2f 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_outer = q*fmax(halfheight+thick_face, fmax(r_minor, r_major)+thick_rim);
+    constant double *w_outer, *z_outer;
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
     //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_outer;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_outer[i]*(vb-va) + va + vb )/2.0;
+        const double cos_theta = ( z_outer[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)+thick_rim);
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max_inner, n_outer, &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_outer[i] * inner_total_F1;
+        outer_total_F2 += w_outer[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 17c6e3878..fa81f0804 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 83b89b589..519c66b39 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_outer = q*fmax(halfheight+thick_face, fmax(r_minor, r_major)+thick_rim);
+    constant double *w_outer, *z_outer;
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
     //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_outer;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_outer[i]*(vb-va) + va + vb )/2.0;
+        const double cos_theta = ( z_outer[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)+thick_rim);
+        constant double *w_inner, *z_inner;
+        int n_inner = gauss_weights(qr_max_inner, n_outer, &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_outer[i] * inner_total_F1;
+        outer_total_F2 += w_outer[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 9d8df416c..7911a0ebc 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 38ab439ab..d6affa3da 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, 1, &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 89d3e2a23..162b4f1c6 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 bfc5248ab..64dc6d581 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, 1, &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 279053c10..56f793c74 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 00295d361..e1e0755ee 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_outer = q*fmax(sqrt(tA*tA + tB*tB), tC)/2;
+    constant double *w_outer, *z_outer;
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
     // 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_outer; i++) {
+        const double cos_alpha = 0.5 * ( z_outer[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_inner, n_outer, &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_outer[i] * inner_sum_F1 * 0.5;
+        outer_sum_F2 += w_outer[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 40cab8986..be0fa9151 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 2744e467f..335850eaa 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, 1, &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 0684dd125..a40535fb9 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/ellipsoid.c b/sasmodels/models/ellipsoid.c
index b91b0b511..584b97419 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, 1, &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 29f9fdf1b..34e67ecb7 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 2ab87e117..3214e8457 100644
--- a/sasmodels/models/elliptical_cylinder.c
+++ b/sasmodels/models/elliptical_cylinder.c
@@ -82,22 +82,31 @@ 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));
 
+    constant double *w_outer, *z_outer;
+    const double qr_max_outer = q*fmax(0.5*length, fmax(radius_minor, radius_minor*r_ratio));
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
+    constant double *w_inner, *z_inner;
+    const double qr_max_inner = q*fmax(radius_minor, radius_major);
+    int n_inner = gauss_weights(qr_max_inner, n_outer, &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_outer;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_outer[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 +114,8 @@ 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_outer[i] * inner_sum_F1 * si;
+        outer_sum_F2 += w_outer[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 b6cbc91bd..d2288e3b9 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 e4fff8dc4..79bfd13b6 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, 1, &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 ae72622de..924585d91 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 409b504f0..f1a4229a2 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, 1, &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 cd00dd8bd..294bcc9c7 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 4fc4bc4d9..ecd11befe 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_outer = q*fmax(sqrt(length_a*length_a + length_b*length_b), length_c)/2;
+    constant double *w_outer, *z_outer;
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
     //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_outer; i++) {
 
-        const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
+        const double theta = 0.5 * ( z_outer[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_inner, n_outer, &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_outer[i] * inner_sum_F1 * sin(theta);
+        outer_sum_F2 += w_outer[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 44ac17bb5..786d15c38 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 2d5956dee..bc116f275 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_outer = q*fmax(sqrt(length_a*length_a + length_b*length_b), length_c)/2;
+    constant double *w_outer, *z_outer;
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
    //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_outer; i++) {
+        const double theta = 0.5 * ( z_outer[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_inner, n_outer, &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_outer[i] * inner_sum_F1 * sin_theta;
+        outer_sum_F2 += w_outer[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 b26283315..352c09eb9 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
new file mode 100644
index 000000000..d0140cc69
--- /dev/null
+++ b/sasmodels/models/lib/adaptive.c
@@ -0,0 +1,11299 @@
+// 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
+};
+
+constant double Gauss20Z[20]={
+	-.993128599185095,
+	-.963971927277914,
+	-.912234428251326,
+	-.839116971822219,
+	-.746331906460151,
+	-.636053680726515,
+	-.510867001950827,
+	-.37370608871542,
+	-.227785851141645,
+	-.076526521133497,
+	.0765265211334973,
+	.227785851141645,
+	.37370608871542,
+	.510867001950827,
+	.636053680726515,
+	.746331906460151,
+	.839116971822219,
+	.912234428251326,
+	.963971927277914,
+	.993128599185095
+};
+
+// From gauss76.c created by Andrew Jackson on 4/23/07
+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)
+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,
+	 1.165336479880733e-03,
+	 1.204027869149601e-03,
+	 1.242671820408409e-03,
+	 1.281266811103701e-03,
+	 1.319811320611454e-03,
+	 1.358303830294452e-03,
+	 1.396742823568952e-03,
+	 1.435126785955841e-03,
+	 1.473454205149692e-03,
+	 1.511723571066077e-03,
+	 1.549933375914893e-03,
+	 1.588082114248213e-03,
+	 1.626168283026832e-03,
+	 1.664190381676313e-03,
+	 1.702146912144630e-03,
+	 1.740036378965917e-03,
+	 1.777857289316139e-03,
+	 1.815608153070388e-03,
+	 1.853287482865413e-03,
+	 1.890893794157173e-03,
+	 1.928425605276330e-03,
+	 1.965881437489817e-03,
+	 2.003259815059579e-03,
+	 2.040559265296571e-03,
+	 2.077778318622784e-03,
+	 2.114915508628630e-03,
+	 2.151969372128613e-03,
+	 2.188938449220948e-03,
+	 2.225821283344425e-03,
+	 2.262616421335232e-03,
+	 2.299322413484867e-03,
+	 2.335937813598022e-03,
+	 2.372461179047613e-03,
+	 2.408891070833094e-03,
+	 2.445226053636986e-03,
+	 2.481464695880025e-03,
+	 2.517605569780848e-03,
+	 2.553647251408908e-03,
+	 2.589588320740147e-03,
+	 2.625427361717589e-03,
+	 2.661162962301745e-03,
+	 2.696793714530561e-03,
+	 2.732318214571477e-03,
+	 2.767735062778413e-03,
+	 2.803042863747321e-03,
+	 2.838240226370725e-03,
+	 2.873325763891207e-03,
+	 2.908298093958407e-03,
+	 2.943155838680763e-03,
+	 2.977897624683573e-03,
+	 3.012522083158995e-03,
+	 3.047027849921952e-03,
+	 3.081413565465073e-03,
+	 3.115677875009653e-03,
+	 3.149819428560841e-03,
+	 3.183836880959549e-03,
+	 3.217728891937877e-03,
+	 3.251494126168971e-03,
+	 3.285131253320412e-03,
+	 3.318638948108751e-03,
+	 3.352015890349086e-03,
+	 3.385260765007777e-03,
+	 3.418372262255511e-03,
+	 3.451349077517390e-03,
+	 3.484189911525201e-03,
+	 3.516893470368361e-03,
+	 3.549458465543619e-03,
+	 3.581883614008788e-03,
+	 3.614167638231078e-03,
+	 3.646309266237678e-03,
+	 3.678307231665397e-03,
+	 3.710160273812769e-03,
+	 3.741867137686732e-03,
+	 3.773426574055379e-03,
+	 3.804837339493179e-03,
+	 3.836098196433846e-03,
+	 3.867207913216764e-03,
+	 3.898165264136193e-03,
+	 3.928969029489244e-03,
+	 3.959617995624711e-03,
+	 3.990110954990701e-03,
+	 4.020446706180265e-03,
+	 4.050624053982856e-03,
+	 4.080641809426477e-03,
+	 4.110498789828263e-03,
+	 4.140193818840021e-03,
+	 4.169725726493931e-03,
+	 4.199093349248971e-03,
+	 4.228295530036851e-03,
+	 4.257331118307538e-03,
+	 4.286198970075190e-03,
+	 4.314897947962091e-03,
+	 4.343426921244611e-03,
+	 4.371784765896547e-03,
+	 4.399970364634929e-03,
+	 4.427982606961833e-03,
+	 4.455820389211089e-03,
+	 4.483482614589342e-03,
+	 4.510968193219581e-03,
+	 4.538276042185702e-03,
+	 4.565405085572943e-03,
+	 4.592354254512663e-03,
+	 4.619122487221627e-03,
+	 4.645708729046676e-03,
+	 4.672111932504496e-03,
+	 4.698331057323412e-03,
+	 4.724365070483955e-03,
+	 4.750212946261104e-03,
+	 4.775873666261901e-03,
+	 4.801346219468445e-03,
+	 4.826629602276532e-03,
+	 4.851722818534243e-03,
+	 4.876624879582988e-03,
+	 4.901334804294905e-03,
+	 4.925851619113115e-03,
+	 4.950174358088128e-03,
+	 4.974302062917732e-03,
+	 4.998233782983469e-03,
+	 5.021968575388614e-03,
+	 5.045505504995736e-03,
+	 5.068843644462437e-03,
+	 5.091982074279180e-03,
+	 5.114919882804157e-03,
+	 5.137656166300713e-03,
+	 5.160190028971708e-03,
+	 5.182520582995286e-03,
+	 5.204646948559915e-03,
+	 5.226568253898841e-03,
+	 5.248283635325014e-03,
+	 5.269792237264006e-03,
+	 5.291093212288944e-03,
+	 5.312185721152960e-03,
+	 5.333068932823244e-03,
+	 5.353742024512316e-03,
+	 5.374204181711735e-03,
+	 5.394454598223924e-03,
+	 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,
+	 5.814995123554692e-03,
+	 5.829714935036091e-03,
+	 5.844205058957268e-03,
+	 5.858464924415277e-03,
+	 5.872493969579269e-03,
+	 5.886291641712590e-03,
+	 5.899857397194484e-03,
+	 5.913190701541724e-03,
+	 5.926291029429509e-03,
+	 5.939157864711998e-03,
+	 5.951790700443030e-03,
+	 5.964189038895774e-03,
+	 5.976352391582588e-03,
+	 5.988280279274060e-03,
+	 5.999972232017961e-03,
+	 6.011427789157825e-03,
+	 6.022646499350923e-03,
+	 6.033627920586314e-03,
+	 6.044371620201973e-03,
+	 6.054877174902156e-03,
+	 6.065144170773754e-03,
+	 6.075172203302702e-03,
+	 6.084960877390098e-03,
+	 6.094509807367612e-03,
+	 6.103818617012588e-03,
+	 6.112886939563049e-03,
+	 6.121714417732096e-03,
+	 6.130300703721983e-03,
+	 6.138645459237716e-03,
+	 6.146748355500533e-03,
+	 6.154609073260798e-03,
+	 6.162227302810542e-03,
+	 6.169602743995691e-03,
+	 6.176735106227958e-03,
+	 6.183624108496229e-03,
+	 6.190269479377512e-03,
+	 6.196670957047917e-03,
+	 6.202828289292718e-03,
+	 6.208741233516422e-03,
+	 6.214409556752295e-03,
+	 6.219833035671504e-03,
+	 6.225011456591986e-03,
+	 6.229944615486780e-03,
+	 6.234632317992122e-03,
+	 6.239074379415144e-03,
+	 6.243270624741109e-03,
+	 6.247220888640188e-03,
+	 6.250925015474188e-03,
+	 6.254382859302541e-03,
+	 6.257594283888150e-03,
+	 6.260559162702589e-03,
+	 6.263277378931292e-03,
+	 6.265748825478042e-03,
+	 6.267973404969181e-03,
+	 6.269951029757533e-03,
+	 6.271681621925740e-03,
+	 6.273165113289455e-03,
+	 6.274401445399912e-03,
+	 6.275390569546285e-03,
+	 6.276132446757681e-03,
+	 6.276627047804537e-03,
+	 6.276874353199784e-03,
+	 6.276874353199784e-03,
+	 6.276627047804537e-03,
+	 6.276132446757681e-03,
+	 6.275390569546285e-03,
+	 6.274401445399912e-03,
+	 6.273165113289455e-03,
+	 6.271681621925740e-03,
+	 6.269951029757533e-03,
+	 6.267973404969181e-03,
+	 6.265748825478042e-03,
+	 6.263277378931292e-03,
+	 6.260559162702589e-03,
+	 6.257594283888150e-03,
+	 6.254382859302541e-03,
+	 6.250925015474188e-03,
+	 6.247220888640188e-03,
+	 6.243270624741109e-03,
+	 6.239074379415144e-03,
+	 6.234632317992122e-03,
+	 6.229944615486780e-03,
+	 6.225011456591986e-03,
+	 6.219833035671504e-03,
+	 6.214409556752295e-03,
+	 6.208741233516422e-03,
+	 6.202828289292718e-03,
+	 6.196670957047917e-03,
+	 6.190269479377512e-03,
+	 6.183624108496229e-03,
+	 6.176735106227958e-03,
+	 6.169602743995691e-03,
+	 6.162227302810542e-03,
+	 6.154609073260798e-03,
+	 6.146748355500533e-03,
+	 6.138645459237716e-03,
+	 6.130300703721983e-03,
+	 6.121714417732096e-03,
+	 6.112886939563049e-03,
+	 6.103818617012588e-03,
+	 6.094509807367612e-03,
+	 6.084960877390098e-03,
+	 6.075172203302702e-03,
+	 6.065144170773754e-03,
+	 6.054877174902156e-03,
+	 6.044371620201973e-03,
+	 6.033627920586314e-03,
+	 6.022646499350923e-03,
+	 6.011427789157825e-03,
+	 5.999972232017961e-03,
+	 5.988280279274060e-03,
+	 5.976352391582588e-03,
+	 5.964189038895774e-03,
+	 5.951790700443030e-03,
+	 5.939157864711998e-03,
+	 5.926291029429509e-03,
+	 5.913190701541724e-03,
+	 5.899857397194484e-03,
+	 5.886291641712590e-03,
+	 5.872493969579269e-03,
+	 5.858464924415277e-03,
+	 5.844205058957268e-03,
+	 5.829714935036091e-03,
+	 5.814995123554692e-03,
+	 5.800046204465426e-03,
+	 5.784868766747535e-03,
+	 5.769463408383798e-03,
+	 5.753830736336734e-03,
+	 5.737971366525110e-03,
+	 5.721885923799350e-03,
+	 5.705575041916975e-03,
+	 5.689039363517862e-03,
+	 5.672279540098574e-03,
+	 5.655296231986907e-03,
+	 5.638090108315933e-03,
+	 5.620661846997404e-03,
+	 5.603012134695263e-03,
+	 5.585141666798417e-03,
+	 5.567051147393411e-03,
+	 5.548741289236909e-03,
+	 5.530212813727135e-03,
+	 5.511466450875843e-03,
+	 5.492502939279533e-03,
+	 5.473323026089901e-03,
+	 5.453927466985097e-03,
+	 5.434317026139552e-03,
+	 5.414492476193605e-03,
+	 5.394454598223924e-03,
+	 5.374204181711735e-03,
+	 5.353742024512316e-03,
+	 5.333068932823244e-03,
+	 5.312185721152960e-03,
+	 5.291093212288944e-03,
+	 5.269792237264006e-03,
+	 5.248283635325014e-03,
+	 5.226568253898841e-03,
+	 5.204646948559915e-03,
+	 5.182520582995286e-03,
+	 5.160190028971708e-03,
+	 5.137656166300713e-03,
+	 5.114919882804157e-03,
+	 5.091982074279180e-03,
+	 5.068843644462437e-03,
+	 5.045505504995736e-03,
+	 5.021968575388614e-03,
+	 4.998233782983469e-03,
+	 4.974302062917732e-03,
+	 4.950174358088128e-03,
+	 4.925851619113115e-03,
+	 4.901334804294905e-03,
+	 4.876624879582988e-03,
+	 4.851722818534243e-03,
+	 4.826629602276532e-03,
+	 4.801346219468445e-03,
+	 4.775873666261901e-03,
+	 4.750212946261104e-03,
+	 4.724365070483955e-03,
+	 4.698331057323412e-03,
+	 4.672111932504496e-03,
+	 4.645708729046676e-03,
+	 4.619122487221627e-03,
+	 4.592354254512663e-03,
+	 4.565405085572943e-03,
+	 4.538276042185702e-03,
+	 4.510968193219581e-03,
+	 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,
+	 3.581883614008788e-03,
+	 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,
+	-9.923251917373580e-01,
+	-9.915294985827499e-01,
+	-9.906947397125084e-01,
+	-9.898209480155092e-01,
+	-9.889081579185339e-01,
+	-9.879564053849051e-01,
+	-9.869657279130641e-01,
+	-9.859361645350886e-01,
+	-9.848677558151522e-01,
+	-9.837605438479229e-01,
+	-9.826145722569035e-01,
+	-9.814298861927109e-01,
+	-9.802065323312958e-01,
+	-9.789445588721034e-01,
+	-9.776440155361730e-01,
+	-9.763049535641788e-01,
+	-9.749274257144106e-01,
+	-9.735114862606945e-01,
+	-9.720571909902542e-01,
+	-9.705645972015134e-01,
+	-9.690337637018371e-01,
+	-9.674647508052152e-01,
+	-9.658576203298855e-01,
+	-9.642124355958984e-01,
+	-9.625292614226219e-01,
+	-9.608081641261872e-01,
+	-9.590492115168765e-01,
+	-9.572524728964510e-01,
+	-9.554180190554201e-01,
+	-9.535459222702526e-01,
+	-9.516362563005288e-01,
+	-9.496890963860347e-01,
+	-9.477045192437970e-01,
+	-9.456826030650609e-01,
+	-9.436234275122095e-01,
+	-9.415270737156246e-01,
+	-9.393936242704907e-01,
+	-9.372231632335404e-01,
+	-9.350157761197427e-01,
+	-9.327715498989343e-01,
+	-9.304905729923920e-01,
+	-9.281729352693497e-01,
+	-9.258187280434574e-01,
+	-9.234280440691834e-01,
+	-9.210009775381599e-01,
+	-9.185376240754719e-01,
+	-9.160380807358894e-01,
+	-9.135024460000439e-01,
+	-9.109308197705482e-01,
+	-9.083233033680599e-01,
+	-9.056799995272898e-01,
+	-9.030010123929542e-01,
+	-9.002864475156713e-01,
+	-8.975364118478033e-01,
+	-8.947510137392416e-01,
+	-8.919303629331384e-01,
+	-8.890745705615831e-01,
+	-8.861837491412231e-01,
+	-8.832580125688314e-01,
+	-8.802974761168184e-01,
+	-8.773022564286910e-01,
+	-8.742724715144563e-01,
+	-8.712082407459724e-01,
+	-8.681096848522449e-01,
+	-8.649769259146710e-01,
+	-8.618100873622285e-01,
+	-8.586092939666133e-01,
+	-8.553746718373237e-01,
+	-8.521063484166915e-01,
+	-8.488044524748606e-01,
+	-8.454691141047138e-01,
+	-8.421004647167475e-01,
+	-8.386986370338935e-01,
+	-8.352637650862903e-01,
+	-8.317959842060023e-01,
+	-8.282954310216877e-01,
+	-8.247622434532156e-01,
+	-8.211965607062316e-01,
+	-8.175985232666736e-01,
+	-8.139682728952365e-01,
+	-8.103059526217874e-01,
+	-8.066117067397293e-01,
+	-8.028856808003170e-01,
+	-7.991280216069218e-01,
+	-7.953388772092481e-01,
+	-7.915183968974999e-01,
+	-7.876667311964989e-01,
+	-7.837840318597541e-01,
+	-7.798704518634826e-01,
+	-7.759261454005825e-01,
+	-7.719512678745576e-01,
+	-7.679459758933953e-01,
+	-7.639104272633951e-01,
+	-7.598447809829524e-01,
+	-7.557491972362932e-01,
+	-7.516238373871631e-01,
+	-7.474688639724699e-01,
+	-7.432844406958796e-01,
+	-7.390707324213666e-01,
+	-7.348279051667179e-01,
+	-7.305561260969925e-01,
+	-7.262555635179349e-01,
+	-7.219263868693439e-01,
+	-7.175687667183971e-01,
+	-7.131828747529303e-01,
+	-7.087688837746735e-01,
+	-7.043269676924420e-01,
+	-6.998573015152848e-01,
+	-6.953600613455899e-01,
+	-6.908354243721447e-01,
+	-6.862835688631563e-01,
+	-6.817046741592265e-01,
+	-6.770989206662871e-01,
+	-6.724664898484908e-01,
+	-6.678075642210626e-01,
+	-6.631223273431083e-01,
+	-6.584109638103827e-01,
+	-6.536736592480159e-01,
+	-6.489106003032010e-01,
+	-6.441219746378392e-01,
+	-6.393079709211461e-01,
+	-6.344687788222193e-01,
+	-6.296045890025642e-01,
+	-6.247155931085830e-01,
+	-6.198019837640233e-01,
+	-6.148639545623893e-01,
+	-6.099017000593140e-01,
+	-6.049154157648940e-01,
+	-5.999052981359867e-01,
+	-5.948715445684692e-01,
+	-5.898143533894622e-01,
+	-5.847339238495148e-01,
+	-5.796304561147554e-01,
+	-5.745041512590039e-01,
+	-5.693552112558506e-01,
+	-5.641838389706982e-01,
+	-5.589902381527688e-01,
+	-5.537746134270766e-01,
+	-5.485371702863653e-01,
+	-5.432781150830126e-01,
+	-5.379976550208994e-01,
+	-5.326959981472461e-01,
+	-5.273733533444159e-01,
+	-5.220299303216851e-01,
+	-5.166659396069802e-01,
+	-5.112815925385833e-01,
+	-5.058771012568060e-01,
+	-5.004526786956304e-01,
+	-4.950085385743205e-01,
+	-4.895448953890009e-01,
+	-4.840619644042066e-01,
+	-4.785599616444009e-01,
+	-4.730391038854647e-01,
+	-4.674996086461556e-01,
+	-4.619416941795375e-01,
+	-4.563655794643817e-01,
+	-4.507714841965395e-01,
+	-4.451596287802858e-01,
+	-4.395302343196359e-01,
+	-4.338835226096335e-01,
+	-4.282197161276124e-01,
+	-4.225390380244314e-01,
+	-4.168417121156813e-01,
+	-4.111279628728678e-01,
+	-4.053980154145666e-01,
+	-3.996520954975543e-01,
+	-3.938904295079136e-01,
+	-3.881132444521138e-01,
+	-3.823207679480666e-01,
+	-3.765132282161589e-01,
+	-3.706908540702600e-01,
+	-3.648538749087071e-01,
+	-3.590025207052671e-01,
+	-3.531370220000754e-01,
+	-3.472576098905531e-01,
+	-3.413645160223019e-01,
+	-3.354579725799772e-01,
+	-3.295382122781400e-01,
+	-3.236054683520885e-01,
+	-3.176599745486687e-01,
+	-3.117019651170644e-01,
+	-3.057316747995684e-01,
+	-2.997493388223338e-01,
+	-2.937551928861058e-01,
+	-2.877494731569357e-01,
+	-2.817324162568758e-01,
+	-2.757042592546567e-01,
+	-2.696652396563470e-01,
+	-2.636155953959953e-01,
+	-2.575555648262563e-01,
+	-2.514853867089997e-01,
+	-2.454053002059026e-01,
+	-2.393155448690274e-01,
+	-2.332163606313831e-01,
+	-2.271079877974721e-01,
+	-2.209906670338226e-01,
+	-2.148646393595063e-01,
+	-2.087301461366422e-01,
+	-2.025874290608875e-01,
+	-1.964367301519144e-01,
+	-1.902782917438753e-01,
+	-1.841123564758542e-01,
+	-1.779391672823076e-01,
+	-1.717589673834925e-01,
+	-1.655720002758839e-01,
+	-1.593785097225810e-01,
+	-1.531787397437032e-01,
+	-1.469729346067760e-01,
+	-1.407613388171065e-01,
+	-1.345441971081505e-01,
+	-1.283217544318700e-01,
+	-1.220942559490822e-01,
+	-1.158619470198002e-01,
+	-1.096250731935660e-01,
+	-1.033838801997762e-01,
+	-9.713861393800015e-02,
+	-9.088952046829167e-02,
+	-8.463684600149451e-02,
+	-7.838083688954174e-02,
+	-7.212173961574959e-02,
+	-6.585980078510620e-02,
+	-5.959526711455542e-02,
+	-5.332838542327645e-02,
+	-4.705940262295916e-02,
+	-4.078856570807596e-02,
+	-3.451612174615040e-02,
+	-2.824231786802273e-02,
+	-2.196740125811321e-02,
+	-1.569161914468308e-02,
+	-9.415218790093976e-03,
+	-3.138447481065866e-03,
+	 3.138447481065866e-03,
+	 9.415218790093976e-03,
+	 1.569161914468308e-02,
+	 2.196740125811321e-02,
+	 2.824231786802273e-02,
+	 3.451612174615040e-02,
+	 4.078856570807596e-02,
+	 4.705940262295916e-02,
+	 5.332838542327645e-02,
+	 5.959526711455542e-02,
+	 6.585980078510620e-02,
+	 7.212173961574959e-02,
+	 7.838083688954174e-02,
+	 8.463684600149451e-02,
+	 9.088952046829167e-02,
+	 9.713861393800015e-02,
+	 1.033838801997762e-01,
+	 1.096250731935660e-01,
+	 1.158619470198002e-01,
+	 1.220942559490822e-01,
+	 1.283217544318700e-01,
+	 1.345441971081505e-01,
+	 1.407613388171065e-01,
+	 1.469729346067760e-01,
+	 1.531787397437032e-01,
+	 1.593785097225810e-01,
+	 1.655720002758839e-01,
+	 1.717589673834925e-01,
+	 1.779391672823076e-01,
+	 1.841123564758542e-01,
+	 1.902782917438753e-01,
+	 1.964367301519144e-01,
+	 2.025874290608875e-01,
+	 2.087301461366422e-01,
+	 2.148646393595063e-01,
+	 2.209906670338226e-01,
+	 2.271079877974721e-01,
+	 2.332163606313831e-01,
+	 2.393155448690274e-01,
+	 2.454053002059026e-01,
+	 2.514853867089997e-01,
+	 2.575555648262563e-01,
+	 2.636155953959953e-01,
+	 2.696652396563470e-01,
+	 2.757042592546567e-01,
+	 2.817324162568758e-01,
+	 2.877494731569357e-01,
+	 2.937551928861058e-01,
+	 2.997493388223338e-01,
+	 3.057316747995684e-01,
+	 3.117019651170644e-01,
+	 3.176599745486687e-01,
+	 3.236054683520885e-01,
+	 3.295382122781400e-01,
+	 3.354579725799772e-01,
+	 3.413645160223019e-01,
+	 3.472576098905531e-01,
+	 3.531370220000754e-01,
+	 3.590025207052671e-01,
+	 3.648538749087071e-01,
+	 3.706908540702600e-01,
+	 3.765132282161589e-01,
+	 3.823207679480666e-01,
+	 3.881132444521138e-01,
+	 3.938904295079136e-01,
+	 3.996520954975543e-01,
+	 4.053980154145666e-01,
+	 4.111279628728678e-01,
+	 4.168417121156813e-01,
+	 4.225390380244314e-01,
+	 4.282197161276124e-01,
+	 4.338835226096335e-01,
+	 4.395302343196359e-01,
+	 4.451596287802858e-01,
+	 4.507714841965395e-01,
+	 4.563655794643817e-01,
+	 4.619416941795375e-01,
+	 4.674996086461556e-01,
+	 4.730391038854647e-01,
+	 4.785599616444009e-01,
+	 4.840619644042066e-01,
+	 4.895448953890009e-01,
+	 4.950085385743205e-01,
+	 5.004526786956304e-01,
+	 5.058771012568060e-01,
+	 5.112815925385833e-01,
+	 5.166659396069802e-01,
+	 5.220299303216851e-01,
+	 5.273733533444159e-01,
+	 5.326959981472461e-01,
+	 5.379976550208994e-01,
+	 5.432781150830126e-01,
+	 5.485371702863653e-01,
+	 5.537746134270766e-01,
+	 5.589902381527688e-01,
+	 5.641838389706982e-01,
+	 5.693552112558506e-01,
+	 5.745041512590039e-01,
+	 5.796304561147554e-01,
+	 5.847339238495148e-01,
+	 5.898143533894622e-01,
+	 5.948715445684692e-01,
+	 5.999052981359867e-01,
+	 6.049154157648940e-01,
+	 6.099017000593140e-01,
+	 6.148639545623893e-01,
+	 6.198019837640233e-01,
+	 6.247155931085830e-01,
+	 6.296045890025642e-01,
+	 6.344687788222193e-01,
+	 6.393079709211461e-01,
+	 6.441219746378392e-01,
+	 6.489106003032010e-01,
+	 6.536736592480159e-01,
+	 6.584109638103827e-01,
+	 6.631223273431083e-01,
+	 6.678075642210626e-01,
+	 6.724664898484908e-01,
+	 6.770989206662871e-01,
+	 6.817046741592265e-01,
+	 6.862835688631563e-01,
+	 6.908354243721447e-01,
+	 6.953600613455899e-01,
+	 6.998573015152848e-01,
+	 7.043269676924420e-01,
+	 7.087688837746735e-01,
+	 7.131828747529303e-01,
+	 7.175687667183971e-01,
+	 7.219263868693439e-01,
+	 7.262555635179349e-01,
+	 7.305561260969925e-01,
+	 7.348279051667179e-01,
+	 7.390707324213666e-01,
+	 7.432844406958796e-01,
+	 7.474688639724699e-01,
+	 7.516238373871631e-01,
+	 7.557491972362932e-01,
+	 7.598447809829524e-01,
+	 7.639104272633951e-01,
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+	 9.998505288592006e-01,
+	 9.999391798145371e-01,
+	 9.999884567522129e-01
+};
+
+// Generated by sasmodels.gengauss.gengauss(5000)
+constant double Gauss5000Wt[5000]={
+	 2.967708115050575e-07,
+	 6.908266104348143e-07,
+	 1.085465123675602e-06,
+	 1.480153958519865e-06,
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+	 2.664254217133740e-06,
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+	 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,
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+	 1.292568421694196e-05,
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+	 1.410952559792103e-05,
+	 1.450412847643540e-05,
+	 1.489872561233522e-05,
+	 1.529331687261776e-05,
+	 1.568790209278624e-05,
+	 1.608248112171249e-05,
+	 1.647705380774646e-05,
+	 1.687161999593914e-05,
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+	 6.059160170043561e-05,
+	 6.019872449896147e-05,
+	 5.980582353508762e-05,
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+	 5.272971996186675e-05,
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+	 4.997603100461701e-05,
+	 4.958256672101606e-05,
+	 4.918908286773508e-05,
+	 4.879557960053133e-05,
+	 4.840205707034650e-05,
+	 4.800851544198063e-05,
+	 4.761495485715089e-05,
+	 4.722137548202861e-05,
+	 4.682777746930432e-05,
+	 4.643416097316290e-05,
+	 4.604052614504553e-05,
+	 4.564687314707027e-05,
+	 4.525320213529415e-05,
+	 4.485951325743296e-05,
+	 4.446580667493457e-05,
+	 4.407208254216379e-05,
+	 4.367834101235882e-05,
+	 4.328458224262764e-05,
+	 4.289080638926642e-05,
+	 4.249701360853457e-05,
+	 4.210320405111855e-05,
+	 4.170937787334214e-05,
+	 4.131553523670950e-05,
+	 4.092167629402477e-05,
+	 4.052780119285966e-05,
+	 4.013391009880438e-05,
+	 3.974000316332509e-05,
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+	 3.658819606898828e-05,
+	 3.619415355896783e-05,
+	 3.580009676421725e-05,
+	 3.540602584001236e-05,
+	 3.501194094136184e-05,
+	 3.461784222625275e-05,
+	 3.422372984128839e-05,
+	 3.382960395220756e-05,
+	 3.343546470625303e-05,
+	 3.304131226628532e-05,
+	 3.264714678931476e-05,
+	 3.225296842167827e-05,
+	 3.185877731818632e-05,
+	 3.146457365118839e-05,
+	 3.107035755314027e-05,
+	 3.067612920327003e-05,
+	 3.028188873463122e-05,
+	 2.988763631923654e-05,
+	 2.949337210648327e-05,
+	 2.909909625655360e-05,
+	 2.870480891332929e-05,
+	 2.831051024050945e-05,
+	 2.791620040138838e-05,
+	 2.752187953377913e-05,
+	 2.712754781421039e-05,
+	 2.673320537848803e-05,
+	 2.633885239413270e-05,
+	 2.594448901262844e-05,
+	 2.555011539275585e-05,
+	 2.515573168735740e-05,
+	 2.476133804867249e-05,
+	 2.436693463850717e-05,
+	 2.397252161190611e-05,
+	 2.357809912616648e-05,
+	 2.318366733139895e-05,
+	 2.278922638862355e-05,
+	 2.239477644353030e-05,
+	 2.200031766471293e-05,
+	 2.160585020366140e-05,
+	 2.121137420731362e-05,
+	 2.081688984551045e-05,
+	 2.042239726350856e-05,
+	 2.002789662203610e-05,
+	 1.963338807543411e-05,
+	 1.923887178667568e-05,
+	 1.884434788899938e-05,
+	 1.844981657027173e-05,
+	 1.805527795459658e-05,
+	 1.766073222351063e-05,
+	 1.726617951652579e-05,
+	 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]={
+	-9.999998843594127e-01,
+	-9.999993906966838e-01,
+	-9.999985025597460e-01,
+	-9.999972197516868e-01,
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+	-9.999910031424144e-01,
+	-9.999881415378994e-01,
+	-9.999848852333429e-01,
+	-9.999812342298391e-01,
+	-9.999771885287215e-01,
+	-9.999727481315230e-01,
+	-9.999679130399564e-01,
+	-9.999626832559038e-01,
+	-9.999570587814121e-01,
+	-9.999510396186888e-01,
+	-9.999446257701015e-01,
+	-9.999378172381750e-01,
+	-9.999306140255922e-01,
+	-9.999230161351929e-01,
+	-9.999150235699730e-01,
+	-9.999066363330852e-01,
+	-9.998978544278384e-01,
+	-9.998886778576976e-01,
+	-9.998791066262838e-01,
+	-9.998691407373738e-01,
+	-9.998587801949006e-01,
+	-9.998480250029530e-01,
+	-9.998368751657757e-01,
+	-9.998253306877691e-01,
+	-9.998133915734896e-01,
+	-9.998010578276494e-01,
+	-9.997883294551163e-01,
+	-9.997752064609142e-01,
+	-9.997616888502225e-01,
+	-9.997477766283768e-01,
+	-9.997334698008677e-01,
+	-9.997187683733426e-01,
+	-9.997036723516038e-01,
+	-9.996881817416099e-01,
+	-9.996722965494749e-01,
+	-9.996560167814686e-01,
+	-9.996393424440169e-01,
+	-9.996222735437010e-01,
+	-9.996048100872582e-01,
+	-9.995869520815813e-01,
+	-9.995686995337189e-01,
+	-9.995500524508754e-01,
+	-9.995310108404106e-01,
+	-9.995115747098408e-01,
+	-9.994917440668371e-01,
+	-9.994715189192268e-01,
+	-9.994508992749930e-01,
+	-9.994298851422743e-01,
+	-9.994084765293649e-01,
+	-9.993866734447152e-01,
+	-9.993644758969308e-01,
+	-9.993418838947731e-01,
+	-9.993188974471594e-01,
+	-9.992955165631625e-01,
+	-9.992717412520110e-01,
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+	-9.992230073859366e-01,
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+	-9.991208069512686e-01,
+	-9.990942709215108e-01,
+	-9.990673405440310e-01,
+	-9.990400158294589e-01,
+	-9.990122967885794e-01,
+	-9.989841834323336e-01,
+	-9.989556757718179e-01,
+	-9.989267738182843e-01,
+	-9.988974775831408e-01,
+	-9.988677870779507e-01,
+	-9.988377023144328e-01,
+	-9.988072233044618e-01,
+	-9.987763500600682e-01,
+	-9.987450825934373e-01,
+	-9.987134209169111e-01,
+	-9.986813650429861e-01,
+	-9.986489149843153e-01,
+	-9.986160707537068e-01,
+	-9.985828323641244e-01,
+	-9.985491998286873e-01,
+	-9.985151731606706e-01,
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+	-9.984107284962256e-01,
+	-9.983751254337510e-01,
+	-9.983391283074048e-01,
+	-9.983027371313952e-01,
+	-9.982659519200862e-01,
+	-9.982287726879969e-01,
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+	-9.981532322203326e-01,
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+	-9.980369667349095e-01,
+	-9.979974236917534e-01,
+	-9.979574867338065e-01,
+	-9.979171558768322e-01,
+	-9.978764311367492e-01,
+	-9.978353125296320e-01,
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+	-9.976238120620119e-01,
+	-9.975803305989536e-01,
+	-9.975364553857333e-01,
+	-9.974921864396690e-01,
+	-9.974475237782336e-01,
+	-9.974024674190559e-01,
+	-9.973570173799199e-01,
+	-9.973111736787648e-01,
+	-9.972649363336853e-01,
+	-9.972183053629318e-01,
+	-9.971712807849096e-01,
+	-9.971238626181795e-01,
+	-9.970760508814578e-01,
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+	-9.948410880448810e-01,
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+	-9.947128352499289e-01,
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+	 9.999985025597460e-01,
+	 9.999993906966838e-01,
+	 9.999998843594127e-01
+};
+
+// Adaptive integration uses nested gaussian integration with order determined by the
+// length scale qr, which drives the oscillation frequency of the scattering amplitude.
+// Using polar coordinates, the oscillation with longitude appears to be independent of
+// of latitude, so efficient spherical integration methods that sample roughly uniformly
+// in solid angle don't perform as well as expected. The theta-phi uniform grid only
+// uses 2x more points than the efficient grids, so the improvements from using
+// Gauss-Legendre integration outweigh the increase in the number of integration points.
+//
+// The qr for the loop over phi may be different from that over theta. This is particularly
+// the case for long rods, where the loop over phi depends on the cross section of the
+// rod, so you can use far fewer phi points than the max dimension of the shape would
+// suggest. Models such as the triaxial ellipsoid can relabel their axis so that c the
+// long axis of the shape, allowing a smaller number of total evaluation points.
+//
+// If size of the grid is too large even after relabeling then the evaluation will be
+// very slow. To prevent this, we pass the number of elements in the outer loop to
+// limit the size of the inner loop, giving n_outer*n_inner < _ADAPTIVE_MAX_N. This works
+// well enough for existing models, giving high accuracy results even for 20 micro shapes
+// at q=1e-3 (the upper limit of qr for USANS). Even out to q=1e-1 the calculations are
+// mostly within 10% of the full grid value (good enough to estimate slit resolution for
+// USANS measurements) without being exceedingly slow.
+//
+//     qr_outer = max dimension
+//     qr_inner = max cross section
+//     n_outer = gauss_weights(qr_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+//     n_inner = gauss_weights(qr_inner, n_outer, &w_inner, &z_inner);
+//
+// For a standard integral over a hemisphere ∫∫ F(θ,φ) sin θ dφ dθ with θ in [0, π/2]
+// and φ in [0, 2π], we do a u-substitution ∫∫ F(u,φ) du with u=cos θ in [0, 1]. Then
+// the loops will look like:
+//
+//    const double *w_outer, *z_outer;
+//    const int n_outer = gauss_weights(qr_outer, 1, &w_outer, &z_outer);
+//    double total_outer = 0.;
+//    for (int j=0; j < n_outer; j++) {
+//        cos_theta = 0.5*z_outer[j] + 0.5; // [-1, 1] => [0, 1]
+//        ...
+//        const double *w_inner, *z_inner;
+//        const int n_inner = gauss_weights(qr_inner, n_outer, &w_inner, &z_inner);
+//        double total_inner = 0.;
+//        for (int k=0; k < n_inner; k++) {
+//            phi = M_PI*(z_inner[k] + 1.0);  // [-1, 1] => [0, 2 pi]
+//            ...
+//            total_inner += w_inner[k]*Fq;
+//        }
+//        total_outer += w_outer[k]*total_inner;
+//     }
+//     total_outer /= 2.0*M_PI; // correct for dφ = 2πw/2, du = w/2
+//
+// Some models (barbell, capped cylinder, pringle) are not using spherical integration.
+// Instead we find that limiting the outer integral to 76 points leads to okay results:
+//
+//     n_outer = gauss_weights(qr_outer, ADAPTIVE_MAX_76, &w_outer, &z_outer);
+//
+#define _ADAPTIVE_MAX_N 100000
+#define ADAPTIVE_MAX_76 (_ADAPTIVE_MAX_N / 76)
+#define ADAPTIVE_MAX_OUTER (_ADAPTIVE_MAX_N / 500)
+static int
+gauss_weights(double qr, int outer_n, constant double **w, constant double **z)
+{
+	// TODO: add more stages (150, 1500) so the n^2 model slowdown is a little less brutal
+	// TODO: adjust cutoff for n=500
+	//     For the pringle model I get npoints = 0.365 qr_max + 43
+	//     and empirical values 14 => 20, 120 => 76, 1200 => 500, 14500 => 5000
+	//     The error threshhold is abrupt: if n is too low the result is bad, but
+	//     there is little benefit for having too large an n.
+	//     These results are specific to the pringle inner integral and may not hold in general.
+	//     Check that all models have reasonable cutoff.
+	// *w = Gauss5000Wt; *z = Gauss5000Z; return 5000; // max precision
+	// *w = Gauss76Wt; *z = Gauss76Z; return 76; // default
+
+	if (qr < 10 || outer_n > _ADAPTIVE_MAX_N / 76) {
+        *w = Gauss20Wt; *z = Gauss20Z; return 20;
+	} else if (qr < 100 || outer_n > _ADAPTIVE_MAX_N / 500) {
+        *w = Gauss76Wt; *z = Gauss76Z; return 76;
+    } else if (qr < 750 || outer_n > _ADAPTIVE_MAX_N / 5000) {
+        *w = Gauss500Wt; *z = Gauss500Z; return 500;
+    } else {
+        *w = Gauss5000Wt; *z = Gauss5000Z; return 5000;
+    }
+}
\ No newline at end of file
diff --git a/sasmodels/models/lib/nonadaptive.c b/sasmodels/models/lib/nonadaptive.c
new file mode 100644
index 000000000..8c1715ba8
--- /dev/null
+++ b/sasmodels/models/lib/nonadaptive.c
@@ -0,0 +1,13 @@
+// To force a fixed rather than adaptive integration scheme, replace [..., "lib/adaptive.c", ...]
+// with [..., "lib/gauss<n>.c", "lib/nonadaptive.c", ...] in your source lists.
+
+// Hack for barbell and capped cylinder keeps the outer integral to 76 points or fewer
+// by calling gauss_weights with n_outer=ADAPTIVE_MAX_76
+#define ADAPTIVE_MAX_76 1 // Doesn't matter since n_outer is ignored
+#define ADAPTIVE_MAX_OUTER 1 // Doesn't matter since n_outer is ignored
+
+static int
+gauss_weights(double qr, int n_outer, constant double **w, constant double **z)
+{
+    *w = GAUSS_W; *z = GAUSS_Z; return GAUSS_N;
+}
\ No newline at end of file
diff --git a/sasmodels/models/parallelepiped.c b/sasmodels/models/parallelepiped.c
index 7b5262b6d..d3f041c78 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_outer = q*fmax(sqrt(length_a*length_a + length_b*length_b), length_c)/2;
+    constant double *w_outer, *z_outer;
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
     // 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_outer; i++) {
+        const double sigma = 0.5 * ( z_outer[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_inner, n_outer, &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_outer[i] * inner_total_F1 * si;
+        outer_total_F2 += w_outer[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 257759785..4f8066aba 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 802ca0668..081cdace5 100644
--- a/sasmodels/models/pringle.c
+++ b/sasmodels/models/pringle.c
@@ -18,23 +18,28 @@ void _integrate_bessel(
     double q_cos_psi,
     double n,
     double *Sn,
-    double *Cn)
+    double *Cn,
+    int n_outer)
 {
     // translate gauss point z in [-1,1] to a point in [0, radius]
     const double zm = 0.5*radius;
     const double zb = 0.5*radius;
 
+    const double qr_max = fmax(q_cos_psi*radius*radius*fmax(alpha, beta), q_sin_psi*radius);
+    constant double *w, *z;
+    int n_inner = gauss_weights(qr_max, n_outer, &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_inner; 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;
@@ -51,7 +56,8 @@ double _sum_bessel_orders(
     double alpha,
     double beta,
     double q_sin_psi,
-    double q_cos_psi)
+    double q_cos_psi,
+    int n_outer)
 {
     //calculate sum term from n = -3 to 3
     //Note 1:
@@ -64,10 +70,10 @@ double _sum_bessel_orders(
     double Sn, Cn, sum;
     sum = 0.0;
     for (int n=3; n>0; n--) {
-      _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, n, &Sn, &Cn);
+      _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, n, &Sn, &Cn, n_outer);
       sum += 2.0*(Sn*Sn + Cn*Cn);
     }
-    _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, 0, &Sn, &Cn);
+    _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, 0, &Sn, &Cn, n_outer);
     sum += Sn*Sn+ Cn*Cn;
     return sum;
 }
@@ -80,19 +86,26 @@ double _integrate_psi(
     double alpha,
     double beta)
 {
+    const double qhalf_thickness = q*0.5*thickness;
+    const double qr_max = fmax(qhalf_thickness, q*radius);
+    constant double *w_outer, *z_outer;
+    // Keep outer loop to 76 or less
+    int n_outer = gauss_weights(qr_max, ADAPTIVE_MAX_76, &w_outer, &z_outer);
+    // printf("qr_max=%.1f n=%d\n", qr_max, n_outer);
+
     // 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_outer; i++) {
+        double psi = z_outer[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 bessel_term = _sum_bessel_orders(radius, alpha, beta, q*sin_psi, q*cos_psi, n_outer);
+        double sinc_term = square(sas_sinx_x(qhalf_thickness * cos_psi));
         double pringle_kernel = 4.0 * sin_psi * bessel_term * sinc_term;
-        sum += GAUSS_W[i] * pringle_kernel;
+        sum += w_outer[i] * pringle_kernel;
     }
 
     return zm * sum;
diff --git a/sasmodels/models/pringle.py b/sasmodels/models/pringle.py
index d086245a4..d7207ef5a 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 b75a7470b..473def35c 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_outer = q*fmax(sqrt(length_a*length_a + length_b*length_b), length_c)/2;
+    constant double *w_outer, *z_outer;
+    int n_outer = gauss_weights(qr_max_outer, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
    //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_outer; i++) {
+        const double theta = 0.5 * ( z_outer[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_inner, n_outer, &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_outer[i] * inner_sum_F1 * sin_theta;
+        outer_sum_F2 += w_outer[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 9a281537b..2613b654a 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 696cf8e88..41cf2f6bd 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 25cb1ed22..57980a464 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, 1, &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 1487db029..dddee562a 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 075edf65c..19acbcb91 100644
--- a/sasmodels/models/triaxial_ellipsoid.c
+++ b/sasmodels/models/triaxial_ellipsoid.c
@@ -94,36 +94,55 @@ Fq(double q,
     double *F2,
     double sld,
     double sld_solvent,
-    double radius_equat_minor,
-    double radius_equat_major,
-    double radius_polar)
+    double Ra,
+    double Rb,
+    double Rc)
 {
+    // Because we are integrating over the entire surface, the orientation is arbitrary. Sort
+    // to Rc > (Ra, Rb) so that the integration will be more accurate.
+    const double maybe_min = fmin(Ra, Rb);
+    const double maybe_max = fmax(Ra, Rb);
+    const double maybe_mid = fmax(maybe_min, Rc);
+    const double radius_equat_minor = fmin(maybe_min, Rc);
+    const double radius_equat_major = fmin(maybe_max, maybe_mid);
+    const double radius_polar = fmax(maybe_max, maybe_mid);
+
     const double pa = square(radius_equat_minor/radius_equat_major) - 1.0;
     const double pc = square(radius_polar/radius_equat_major) - 1.0;
+
+    const double qr_max_inner = fmax(q*radius_equat_minor, q*radius_equat_major);
+    const double qr_max = fmax(qr_max_inner, q*radius_polar);
+    constant double *z_outer, *w_outer;
+    int n_outer = gauss_weights(qr_max, ADAPTIVE_MAX_OUTER, &w_outer, &z_outer);
+
+    constant double *z_inner, *w_inner;
+    int n_inner = gauss_weights(qr_max_inner, n_outer, &w_inner, &z_inner);
+    // printf("outer: qr=%g n=%d  inner: qr=%g n=%d\n", qr_max, n_outer, qr_max_inner, n_inner);
+
     // 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_outer;i++) {
+        //const double u = z[i]*(upper-lower)/2 + (upper + lower)/2;
+        const double phi = z_outer[i]*zm + zb;
         const double pa_sinsq_phi = pa*square(sin(phi));
 
         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_outer[i] * inner_sum_F1;  // correcting for dx later
+        outer_sum_F2 += w_outer[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 0de7349d5..0d5142420 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")
diff --git a/sasmodels/models/truncated_octahedron.c b/sasmodels/models/truncated_octahedron.c
index 45712adfb..0948000b1 100644
--- a/sasmodels/models/truncated_octahedron.c
+++ b/sasmodels/models/truncated_octahedron.c
@@ -1,5 +1,5 @@
-#include <math.h>
-#include <stdio.h>
+//#include <math.h>
+//#include <stdio.h>
 
 //truncated octahedron volume 
 // NOTE: needs to be called form_volume() for a shape category