diff --git a/test/7_24_2_Associated_Legendre_Polynomials_and_Spherical_Harmonics.jl b/test/7_24_2_Associated_Legendre_Polynomials_and_Spherical_Harmonics.jl
index 7544365..ef1944a 100644
--- a/test/7_24_2_Associated_Legendre_Polynomials_and_Spherical_Harmonics.jl
+++ b/test/7_24_2_Associated_Legendre_Polynomials_and_Spherical_Harmonics.jl
@@ -6,14 +6,15 @@ let
     m = 2
     x = 0.5
 
-    @test sf_legendre_Plm_array(lmax, m, x)         == [2.25, 5.625, 4.21875, -4.921875]
-    @test sf_legendre_Plm_deriv_array(lmax, m, x)   == ([2.25,5.625,4.21875,-4.921875],
-                                                        [-3.0,3.75,33.75,55.78125])
-    @test sf_legendre_sphPlm_array(lmax, m, x)      == [0.2897056515173923, 0.38324455366248106, 
+    # these give subtly different answers on 32/64-bit.    
+    @test sf_legendre_Plm_array(lmax, m, x)         ≈ [2.25, 5.625, 4.21875, -4.921875]
+    @test sf_legendre_Plm_deriv_array(lmax, m, x)[1] ≈ [2.25,5.625,4.21875,-4.921875]
+    @test sf_legendre_Plm_deriv_array(lmax, m, x)[2] ≈ [-3.0,3.75,33.75,55.78125]
+    @test sf_legendre_sphPlm_array(lmax, m, x)      ≈ [0.2897056515173923, 0.38324455366248106, 
                                                         0.18816934037548766, -0.15888479843070935]
-    @test sf_legendre_sphPlm_deriv_array(lmax, m, x) ==     ([0.2897056515173923,0.38324455366248106,
-                                                            0.18816934037548766,-0.15888479843070935],
-                                                            [-0.38627420202318974,0.2554963691083207,
-                                                            1.5053547230039015,1.8006943822147061])
+    @test sf_legendre_sphPlm_deriv_array(lmax, m, x)[1]  ≈ [0.2897056515173923,0.38324455366248106,
+                                                            0.18816934037548766,-0.15888479843070935]
+    @test sf_legendre_sphPlm_deriv_array(lmax, m, x)[2]  ≈ [-0.38627420202318974,0.2554963691083207,
+                                                            1.5053547230039015,1.8006943822147061]
 
 end