Merge pull request #14048 from r-devulap/transcendental-accuracy-tests

BUG, TEST: Adding validation test suite to validate float32 exp

7 files changed, 1787 insertions, 8 deletions

diff --git a/numpy/core/src/umath/simd.inc.src b/numpy/core/src/umath/simd.inc.src
index ecf2a7951..6b07a9d88 100644
--- a/numpy/core/src/umath/simd.inc.src
+++ b/numpy/core/src/umath/simd.inc.src
@@ -1223,6 +1223,46 @@ avx2_get_mantissa(__m256 x)
                     _mm256_and_si256(
                         _mm256_castps_si256(x), mantissa_bits), exp_126_bits));
 }
+
+NPY_INLINE NPY_GCC_OPT_3 NPY_GCC_TARGET_AVX2 __m256
+avx2_scalef_ps(__m256 poly, __m256 quadrant)
+{
+    /*
+     * Handle denormals (which occur when quadrant <= -125):
+     * 1) This function computes poly*(2^quad) by adding the exponent of
+     poly to quad
+     * 2) When quad <= -125, the output is a denormal and the above logic
+     breaks down
+     * 3) To handle such cases, we split quadrant: -125 + (quadrant + 125)
+     * 4) poly*(2^-125) is computed the usual way
+     * 5) 2^(quad-125) can be computed by: 2 << abs(quad-125)
+     * 6) The final div operation generates the denormal
+     */
+     __m256 minquadrant = _mm256_set1_ps(-125.0f);
+     __m256 denormal_mask = _mm256_cmp_ps(quadrant, minquadrant, _CMP_LE_OQ);
+     if (_mm256_movemask_ps(denormal_mask) != 0x0000) {
+        __m256 quad_diff = _mm256_sub_ps(quadrant, minquadrant);
+        quad_diff = _mm256_sub_ps(_mm256_setzero_ps(), quad_diff);
+        quad_diff = _mm256_blendv_ps(_mm256_setzero_ps(), quad_diff, denormal_mask);
+        __m256i two_power_diff = _mm256_sllv_epi32(
+                                   _mm256_set1_epi32(1), _mm256_cvtps_epi32(quad_diff));
+        quadrant = _mm256_max_ps(quadrant, minquadrant); //keep quadrant >= -126
+        __m256i exponent = _mm256_slli_epi32(_mm256_cvtps_epi32(quadrant), 23);
+        poly = _mm256_castsi256_ps(
+                   _mm256_add_epi32(
+                       _mm256_castps_si256(poly), exponent));
+        __m256 denorm_poly = _mm256_div_ps(poly, _mm256_cvtepi32_ps(two_power_diff));
+        return _mm256_blendv_ps(poly, denorm_poly, denormal_mask);
+     }
+     else {
+        __m256i exponent = _mm256_slli_epi32(_mm256_cvtps_epi32(quadrant), 23);
+        poly = _mm256_castsi256_ps(
+                   _mm256_add_epi32(
+                       _mm256_castps_si256(poly), exponent));
+        return poly;
+     }
+}
+
 #endif
 
 #if defined HAVE_ATTRIBUTE_TARGET_AVX512F_WITH_INTRINSICS
@@ -1276,6 +1316,12 @@ avx512_get_mantissa(__m512 x)
 {
     return _mm512_getmant_ps(x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src);
 }
+
+static NPY_INLINE NPY_GCC_OPT_3 NPY_GCC_TARGET_AVX512F __m512
+avx512_scalef_ps(__m512 poly, __m512 quadrant)
+{
+    return _mm512_scalef_ps(poly, quadrant);
+}
 #endif
 
 /**begin repeat
@@ -1345,7 +1391,7 @@ static NPY_GCC_OPT_3 NPY_GCC_TARGET_@ISA@ void
     const npy_intp stride = steps/sizeof(npy_float);
     const npy_int num_lanes = @BYTES@/sizeof(npy_float);
     npy_float xmax = 88.72283935546875f;
-    npy_float xmin = -87.3365478515625f;
+    npy_float xmin = -103.97208404541015625f;
     npy_int indexarr[16];
     for (npy_int ii = 0; ii < 16; ii++) {
         indexarr[ii] = ii*stride;
@@ -1369,7 +1415,6 @@ static NPY_GCC_OPT_3 NPY_GCC_TARGET_@ISA@ void
     @vtype@ zeros_f = _mm@vsize@_set1_ps(0.0f);
     @vtype@ poly, num_poly, denom_poly, quadrant;
     @vtype@i vindex = _mm@vsize@_loadu_si@vsize@((@vtype@i*)&indexarr[0]);
-    @vtype@i exponent;
 
     @mask@ xmax_mask, xmin_mask, nan_mask, inf_mask;
     @mask@ overflow_mask = @isa@_get_partial_load_mask(0, num_lanes);
@@ -1426,10 +1471,7 @@ static NPY_GCC_OPT_3 NPY_GCC_TARGET_@ISA@ void
          * exponent of quadrant to the exponent of poly. quadrant is an int,
          * so extracting exponent is simply extracting 8 bits.
          */
-        exponent = _mm@vsize@_slli_epi32(_mm@vsize@_cvtps_epi32(quadrant), 23);
-        poly = _mm@vsize@_castsi@vsize@_ps(
-                    _mm@vsize@_add_epi32(
-                        _mm@vsize@_castps_si@vsize@(poly), exponent));
+        poly = @isa@_scalef_ps(poly, quadrant);
 
         /*
          * elem > xmax; return inf
@@ -1494,6 +1536,7 @@ static NPY_GCC_OPT_3 NPY_GCC_TARGET_@ISA@ void
     @vtype@ log_q5 = _mm@vsize@_set1_ps(NPY_COEFF_Q5_LOGf);
     @vtype@ loge2 = _mm@vsize@_set1_ps(NPY_LOGE2f);
     @vtype@ nan = _mm@vsize@_set1_ps(NPY_NANF);
+    @vtype@ neg_nan = _mm@vsize@_set1_ps(-NPY_NANF);
     @vtype@ neg_inf = _mm@vsize@_set1_ps(-NPY_INFINITYF);
     @vtype@ inf = _mm@vsize@_set1_ps(NPY_INFINITYF);
     @vtype@ zeros_f = _mm@vsize@_set1_ps(0.0f);
@@ -1560,11 +1603,12 @@ static NPY_GCC_OPT_3 NPY_GCC_TARGET_@ISA@ void
         poly = @fmadd@(exponent, loge2, poly);
 
         /*
-         * x < 0.0f; return NAN
+         * x < 0.0f; return -NAN
          * x = +/- NAN; return NAN
          * x = 0.0f; return -INF
          */
-        poly = @isa@_set_masked_lanes(poly, nan, @or_masks@(negx_mask, nan_mask));
+        poly = @isa@_set_masked_lanes(poly, nan, nan_mask);
+        poly = @isa@_set_masked_lanes(poly, neg_nan, negx_mask);
         poly = @isa@_set_masked_lanes(poly, neg_inf, zero_mask);
         poly = @isa@_set_masked_lanes(poly, inf, inf_mask);
 
diff --git a/numpy/core/tests/data/umath-validation-set-README b/numpy/core/tests/data/umath-validation-set-README
new file mode 100644
index 000000000..6561ca3b5
--- /dev/null
+++ b/numpy/core/tests/data/umath-validation-set-README
@@ -0,0 +1,15 @@
+Steps to validate transcendental functions:
+1) Add a file 'umath-validation-set-<ufuncname>', where ufuncname is name of
+   the function in NumPy you want to validate
+2) The file should contain 4 columns: dtype,input,expected output,ulperror
+    a. dtype: one of np.float16, np.float32, np.float64
+    b. input: floating point input to ufunc in hex. Example: 0x414570a4
+       represents 12.340000152587890625
+    c. expected output: floating point output for the corresponding input in hex.
+       This should be computed using a high(er) precision library and then rounded to
+       same format as the input.
+    d. ulperror: expected maximum ulp error of the function. This
+       should be same across all rows of the same dtype. Otherwise, the function is
+       tested for the maximum ulp error among all entries of that dtype.
+3) Add file umath-validation-set-<ufuncname> to the test file test_umath_accuracy.py
+   which will then validate your ufunc.
diff --git a/numpy/core/tests/data/umath-validation-set-cos b/numpy/core/tests/data/umath-validation-set-cos
new file mode 100644
index 000000000..360ebcd6a
--- /dev/null
+++ b/numpy/core/tests/data/umath-validation-set-cos
@@ -0,0 +1,707 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0x3f800000,2
+np.float32,0x007b2490,0x3f800000,2
+np.float32,0x007c99fa,0x3f800000,2
+np.float32,0x00734a0c,0x3f800000,2
+np.float32,0x0070de24,0x3f800000,2
+np.float32,0x007fffff,0x3f800000,2
+np.float32,0x00000001,0x3f800000,2
+## -ve denormals ##
+np.float32,0x80495d65,0x3f800000,2
+np.float32,0x806894f6,0x3f800000,2
+np.float32,0x80555a76,0x3f800000,2
+np.float32,0x804e1fb8,0x3f800000,2
+np.float32,0x80687de9,0x3f800000,2
+np.float32,0x807fffff,0x3f800000,2
+np.float32,0x80000001,0x3f800000,2
+## +/-0.0f, +/-FLT_MIN +/-FLT_MAX ##
+np.float32,0x00000000,0x3f800000,2
+np.float32,0x80000000,0x3f800000,2
+np.float32,0x00800000,0x3f800000,2
+np.float32,0x7f7fffff,0x3f5a5f96,2
+np.float32,0x80800000,0x3f800000,2
+np.float32,0xff7fffff,0x3f5a5f96,2
+## 1.00f + 0x00000001 ##
+np.float32,0x3f800000,0x3f0a5140,2
+np.float32,0x3f800001,0x3f0a513f,2
+np.float32,0x3f800002,0x3f0a513d,2
+np.float32,0xc090a8b0,0xbe4332ce,2
+np.float32,0x41ce3184,0x3f4d1de1,2
+np.float32,0xc1d85848,0xbeaa8980,2
+np.float32,0x402b8820,0xbf653aa3,2
+np.float32,0x42b4e454,0xbf4a338b,2
+np.float32,0x42a67a60,0x3c58202e,2
+np.float32,0x41d92388,0xbed987c7,2
+np.float32,0x422dd66c,0x3f5dcab3,2
+np.float32,0xc28f5be6,0xbf5688d8,2
+np.float32,0x41ab2674,0xbf53aa3b,2
+np.float32,0xd0102756,0x3f45d12d,2
+np.float32,0xcf99405e,0xbe9cf281,2
+np.float32,0xcfd83a12,0x3eaae4ca,2
+np.float32,0x4fb54db0,0xbf7b2894,2
+np.float32,0xcfcca29d,0x3f752e4e,2
+np.float32,0xceec2ac0,0xbf745303,2
+np.float32,0xcfdca97f,0x3ef554a7,2
+np.float32,0xcfe92b0a,0x3f4618f2,2
+np.float32,0x5014b0eb,0x3ee933e6,2
+np.float32,0xcfa7ee96,0xbeedeeb2,2
+np.float32,0x754c09a0,0xbef298de,2
+np.float32,0x77a731fb,0x3f24599f,2
+np.float32,0x76de2494,0x3f79576c,2
+np.float32,0xf74920dc,0xbf4d196e,2
+np.float32,0x7707a312,0xbeb5cb8e,2
+np.float32,0x75bf9790,0xbf7fd7fe,2
+np.float32,0xf4ca7c40,0xbe15107d,2
+np.float32,0x77e91899,0xbe8a968b,2
+np.float32,0xf74c9820,0xbf7f9677,2
+np.float32,0x7785ca29,0xbe6ef93b,2
+np.float32,0x3f490fdb,0x3f3504f3,2
+np.float32,0xbf490fdb,0x3f3504f3,2
+np.float32,0x3fc90fdb,0xb33bbd2e,2
+np.float32,0xbfc90fdb,0xb33bbd2e,2
+np.float32,0x40490fdb,0xbf800000,2
+np.float32,0xc0490fdb,0xbf800000,2
+np.float32,0x3fc90fdb,0xb33bbd2e,2
+np.float32,0xbfc90fdb,0xb33bbd2e,2
+np.float32,0x40490fdb,0xbf800000,2
+np.float32,0xc0490fdb,0xbf800000,2
+np.float32,0x40c90fdb,0x3f800000,2
+np.float32,0xc0c90fdb,0x3f800000,2
+np.float32,0x4016cbe4,0xbf3504f3,2
+np.float32,0xc016cbe4,0xbf3504f3,2
+np.float32,0x4096cbe4,0x324cde2e,2
+np.float32,0xc096cbe4,0x324cde2e,2
+np.float32,0x4116cbe4,0xbf800000,2
+np.float32,0xc116cbe4,0xbf800000,2
+np.float32,0x40490fdb,0xbf800000,2
+np.float32,0xc0490fdb,0xbf800000,2
+np.float32,0x40c90fdb,0x3f800000,2
+np.float32,0xc0c90fdb,0x3f800000,2
+np.float32,0x41490fdb,0x3f800000,2
+np.float32,0xc1490fdb,0x3f800000,2
+np.float32,0x407b53d2,0xbf3504f1,2
+np.float32,0xc07b53d2,0xbf3504f1,2
+np.float32,0x40fb53d2,0xb4b5563d,2
+np.float32,0xc0fb53d2,0xb4b5563d,2
+np.float32,0x417b53d2,0xbf800000,2
+np.float32,0xc17b53d2,0xbf800000,2
+np.float32,0x4096cbe4,0x324cde2e,2
+np.float32,0xc096cbe4,0x324cde2e,2
+np.float32,0x4116cbe4,0xbf800000,2
+np.float32,0xc116cbe4,0xbf800000,2
+np.float32,0x4196cbe4,0x3f800000,2
+np.float32,0xc196cbe4,0x3f800000,2
+np.float32,0x40afede0,0x3f3504f7,2
+np.float32,0xc0afede0,0x3f3504f7,2
+np.float32,0x412fede0,0x353222c4,2
+np.float32,0xc12fede0,0x353222c4,2
+np.float32,0x41afede0,0xbf800000,2
+np.float32,0xc1afede0,0xbf800000,2
+np.float32,0x40c90fdb,0x3f800000,2
+np.float32,0xc0c90fdb,0x3f800000,2
+np.float32,0x41490fdb,0x3f800000,2
+np.float32,0xc1490fdb,0x3f800000,2
+np.float32,0x41c90fdb,0x3f800000,2
+np.float32,0xc1c90fdb,0x3f800000,2
+np.float32,0x40e231d6,0x3f3504f3,2
+np.float32,0xc0e231d6,0x3f3504f3,2
+np.float32,0x416231d6,0xb319a6a2,2
+np.float32,0xc16231d6,0xb319a6a2,2
+np.float32,0x41e231d6,0xbf800000,2
+np.float32,0xc1e231d6,0xbf800000,2
+np.float32,0x40fb53d2,0xb4b5563d,2
+np.float32,0xc0fb53d2,0xb4b5563d,2
+np.float32,0x417b53d2,0xbf800000,2
+np.float32,0xc17b53d2,0xbf800000,2
+np.float32,0x41fb53d2,0x3f800000,2
+np.float32,0xc1fb53d2,0x3f800000,2
+np.float32,0x410a3ae7,0xbf3504fb,2
+np.float32,0xc10a3ae7,0xbf3504fb,2
+np.float32,0x418a3ae7,0x35b08908,2
+np.float32,0xc18a3ae7,0x35b08908,2
+np.float32,0x420a3ae7,0xbf800000,2
+np.float32,0xc20a3ae7,0xbf800000,2
+np.float32,0x4116cbe4,0xbf800000,2
+np.float32,0xc116cbe4,0xbf800000,2
+np.float32,0x4196cbe4,0x3f800000,2
+np.float32,0xc196cbe4,0x3f800000,2
+np.float32,0x4216cbe4,0x3f800000,2
+np.float32,0xc216cbe4,0x3f800000,2
+np.float32,0x41235ce2,0xbf3504ef,2
+np.float32,0xc1235ce2,0xbf3504ef,2
+np.float32,0x41a35ce2,0xb53889b6,2
+np.float32,0xc1a35ce2,0xb53889b6,2
+np.float32,0x42235ce2,0xbf800000,2
+np.float32,0xc2235ce2,0xbf800000,2
+np.float32,0x412fede0,0x353222c4,2
+np.float32,0xc12fede0,0x353222c4,2
+np.float32,0x41afede0,0xbf800000,2
+np.float32,0xc1afede0,0xbf800000,2
+np.float32,0x422fede0,0x3f800000,2
+np.float32,0xc22fede0,0x3f800000,2
+np.float32,0x413c7edd,0x3f3504f4,2
+np.float32,0xc13c7edd,0x3f3504f4,2
+np.float32,0x41bc7edd,0x33800add,2
+np.float32,0xc1bc7edd,0x33800add,2
+np.float32,0x423c7edd,0xbf800000,2
+np.float32,0xc23c7edd,0xbf800000,2
+np.float32,0x41490fdb,0x3f800000,2
+np.float32,0xc1490fdb,0x3f800000,2
+np.float32,0x41c90fdb,0x3f800000,2
+np.float32,0xc1c90fdb,0x3f800000,2
+np.float32,0x42490fdb,0x3f800000,2
+np.float32,0xc2490fdb,0x3f800000,2
+np.float32,0x4155a0d9,0x3f3504eb,2
+np.float32,0xc155a0d9,0x3f3504eb,2
+np.float32,0x41d5a0d9,0xb5b3bc81,2
+np.float32,0xc1d5a0d9,0xb5b3bc81,2
+np.float32,0x4255a0d9,0xbf800000,2
+np.float32,0xc255a0d9,0xbf800000,2
+np.float32,0x416231d6,0xb319a6a2,2
+np.float32,0xc16231d6,0xb319a6a2,2
+np.float32,0x41e231d6,0xbf800000,2
+np.float32,0xc1e231d6,0xbf800000,2
+np.float32,0x426231d6,0x3f800000,2
+np.float32,0xc26231d6,0x3f800000,2
+np.float32,0x416ec2d4,0xbf3504f7,2
+np.float32,0xc16ec2d4,0xbf3504f7,2
+np.float32,0x41eec2d4,0x353ef0a7,2
+np.float32,0xc1eec2d4,0x353ef0a7,2
+np.float32,0x426ec2d4,0xbf800000,2
+np.float32,0xc26ec2d4,0xbf800000,2
+np.float32,0x417b53d2,0xbf800000,2
+np.float32,0xc17b53d2,0xbf800000,2
+np.float32,0x41fb53d2,0x3f800000,2
+np.float32,0xc1fb53d2,0x3f800000,2
+np.float32,0x427b53d2,0x3f800000,2
+np.float32,0xc27b53d2,0x3f800000,2
+np.float32,0x4183f268,0xbf3504e7,2
+np.float32,0xc183f268,0xbf3504e7,2
+np.float32,0x4203f268,0xb6059a13,2
+np.float32,0xc203f268,0xb6059a13,2
+np.float32,0x4283f268,0xbf800000,2
+np.float32,0xc283f268,0xbf800000,2
+np.float32,0x418a3ae7,0x35b08908,2
+np.float32,0xc18a3ae7,0x35b08908,2
+np.float32,0x420a3ae7,0xbf800000,2
+np.float32,0xc20a3ae7,0xbf800000,2
+np.float32,0x428a3ae7,0x3f800000,2
+np.float32,0xc28a3ae7,0x3f800000,2
+np.float32,0x41908365,0x3f3504f0,2
+np.float32,0xc1908365,0x3f3504f0,2
+np.float32,0x42108365,0xb512200d,2
+np.float32,0xc2108365,0xb512200d,2
+np.float32,0x42908365,0xbf800000,2
+np.float32,0xc2908365,0xbf800000,2
+np.float32,0x4196cbe4,0x3f800000,2
+np.float32,0xc196cbe4,0x3f800000,2
+np.float32,0x4216cbe4,0x3f800000,2
+np.float32,0xc216cbe4,0x3f800000,2
+np.float32,0x4296cbe4,0x3f800000,2
+np.float32,0xc296cbe4,0x3f800000,2
+np.float32,0x419d1463,0x3f3504ef,2
+np.float32,0xc19d1463,0x3f3504ef,2
+np.float32,0x421d1463,0xb5455799,2
+np.float32,0xc21d1463,0xb5455799,2
+np.float32,0x429d1463,0xbf800000,2
+np.float32,0xc29d1463,0xbf800000,2
+np.float32,0x41a35ce2,0xb53889b6,2
+np.float32,0xc1a35ce2,0xb53889b6,2
+np.float32,0x42235ce2,0xbf800000,2
+np.float32,0xc2235ce2,0xbf800000,2
+np.float32,0x42a35ce2,0x3f800000,2
+np.float32,0xc2a35ce2,0x3f800000,2
+np.float32,0x41a9a561,0xbf3504ff,2
+np.float32,0xc1a9a561,0xbf3504ff,2
+np.float32,0x4229a561,0x360733d0,2
+np.float32,0xc229a561,0x360733d0,2
+np.float32,0x42a9a561,0xbf800000,2
+np.float32,0xc2a9a561,0xbf800000,2
+np.float32,0x41afede0,0xbf800000,2
+np.float32,0xc1afede0,0xbf800000,2
+np.float32,0x422fede0,0x3f800000,2
+np.float32,0xc22fede0,0x3f800000,2
+np.float32,0x42afede0,0x3f800000,2
+np.float32,0xc2afede0,0x3f800000,2
+np.float32,0x41b6365e,0xbf3504f6,2
+np.float32,0xc1b6365e,0xbf3504f6,2
+np.float32,0x4236365e,0x350bb91c,2
+np.float32,0xc236365e,0x350bb91c,2
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+np.float32,0xc28a3ae7,0x3f800000,2
+np.float32,0x430a3ae7,0x3f800000,2
+np.float32,0xc30a3ae7,0x3f800000,2
+np.float32,0x438a3ae7,0x3f800000,2
+np.float32,0xc38a3ae7,0x3f800000,2
+np.float32,0x428bcd06,0x3f3504f5,2
+np.float32,0xc28bcd06,0x3f3504f5,2
+np.float32,0x430bcd06,0x3497675b,2
+np.float32,0xc30bcd06,0x3497675b,2
+np.float32,0x438bcd06,0xbf800000,2
+np.float32,0xc38bcd06,0xbf800000,2
+np.float32,0x428d5f26,0xb60c0105,2
+np.float32,0xc28d5f26,0xb60c0105,2
+np.float32,0x430d5f26,0xbf800000,2
+np.float32,0xc30d5f26,0xbf800000,2
+np.float32,0x438d5f26,0x3f800000,2
+np.float32,0xc38d5f26,0x3f800000,2
+np.float32,0x428ef146,0xbf350526,2
+np.float32,0xc28ef146,0xbf350526,2
+np.float32,0x430ef146,0x3710bc40,2
+np.float32,0xc30ef146,0x3710bc40,2
+np.float32,0x438ef146,0xbf800000,2
+np.float32,0xc38ef146,0xbf800000,2
+np.float32,0x42908365,0xbf800000,2
+np.float32,0xc2908365,0xbf800000,2
+np.float32,0x43108365,0x3f800000,2
+np.float32,0xc3108365,0x3f800000,2
+np.float32,0x43908365,0x3f800000,2
+np.float32,0xc3908365,0x3f800000,2
+np.float32,0x42921585,0xbf3504e6,2
+np.float32,0xc2921585,0xbf3504e6,2
+np.float32,0x43121585,0xb618cee8,2
+np.float32,0xc3121585,0xb618cee8,2
+np.float32,0x43921585,0xbf800000,2
+np.float32,0xc3921585,0xbf800000,2
+np.float32,0x4293a7a5,0x3661deee,2
+np.float32,0xc293a7a5,0x3661deee,2
+np.float32,0x4313a7a5,0xbf800000,2
+np.float32,0xc313a7a5,0xbf800000,2
+np.float32,0x4393a7a5,0x3f800000,2
+np.float32,0xc393a7a5,0x3f800000,2
+np.float32,0x429539c5,0x3f350536,2
+np.float32,0xc29539c5,0x3f350536,2
+np.float32,0x431539c5,0x373bab34,2
+np.float32,0xc31539c5,0x373bab34,2
+np.float32,0x439539c5,0xbf800000,2
+np.float32,0xc39539c5,0xbf800000,2
+np.float32,0x4296cbe4,0x3f800000,2
+np.float32,0xc296cbe4,0x3f800000,2
+np.float32,0x4316cbe4,0x3f800000,2
+np.float32,0xc316cbe4,0x3f800000,2
+np.float32,0x4396cbe4,0x3f800000,2
+np.float32,0xc396cbe4,0x3f800000,2
+np.float32,0x42985e04,0x3f3504d7,2
+np.float32,0xc2985e04,0x3f3504d7,2
+np.float32,0x43185e04,0xb6a2455d,2
+np.float32,0xc3185e04,0xb6a2455d,2
+np.float32,0x43985e04,0xbf800000,2
+np.float32,0xc3985e04,0xbf800000,2
+np.float32,0x4299f024,0xb69bde6c,2
+np.float32,0xc299f024,0xb69bde6c,2
+np.float32,0x4319f024,0xbf800000,2
+np.float32,0xc319f024,0xbf800000,2
+np.float32,0x4399f024,0x3f800000,2
+np.float32,0xc399f024,0x3f800000,2
+np.float32,0x429b8243,0xbf3504ea,2
+np.float32,0xc29b8243,0xbf3504ea,2
+np.float32,0x431b8243,0xb5cb2eb8,2
+np.float32,0xc31b8243,0xb5cb2eb8,2
+np.float32,0x439b8243,0xbf800000,2
+np.float32,0xc39b8243,0xbf800000,2
+np.float32,0x435b2047,0x3f3504c1,2
+np.float32,0x42a038a2,0xb5e4ca7e,2
+np.float32,0x432038a2,0xbf800000,2
+np.float32,0x4345eb9b,0xbf800000,2
+np.float32,0x42c5eb9b,0xb5de638c,2
+np.float32,0x42eb9e94,0xb5d7fc9b,2
+np.float32,0x4350ea79,0x3631dadb,2
+np.float32,0x42dbe957,0xbf800000,2
+np.float32,0x425be957,0xb505522a,2
+np.float32,0x435be957,0x3f800000,2
+np.float32,0x487fe5ab,0xba140185,2
+np.float32,0x497fe5ab,0x3f7fffd5,2
+np.float32,0x49ffe5ab,0x3f7fff55,2
+np.float32,0x49ffeb37,0x3b9382f5,2
+np.float32,0x497ff0c3,0x3b13049f,2
+np.float32,0x49fff0c3,0xbf7fff57,2
+np.float32,0x49fff64f,0xbb928618,2
+np.float32,0x497ffbdb,0xbf7fffd6,2
+np.float32,0x49fffbdb,0x3f7fff59,2
+np.float32,0x48fffbdb,0xba9207c6,2
+np.float32,0x4e736e56,0xbf800000,2
+np.float32,0x4d4da377,0xbf800000,2
+np.float32,0x4ece58c3,0xbf800000,2
+np.float32,0x4ee0db9c,0xbf800000,2
+np.float32,0x4dee7002,0x3f800000,2
+np.float32,0x4ee86afc,0x38857a23,2
+np.float32,0x4dca4f3f,0xbf800000,2
+np.float32,0x4ecb48af,0xb95d1e10,2
+np.float32,0x4e51e33f,0xbf800000,2
+np.float32,0x4ef5f421,0xbf800000,2
+np.float32,0x46027eb2,0x3e7d94c9,2
+np.float32,0x4477baed,0xbe7f1824,2
+np.float32,0x454b8024,0x3e7f5268,2
+np.float32,0x455d2c09,0x3e7f40cb,2
+np.float32,0x4768d3de,0xba14b4af,2
+np.float32,0x46c1e7cd,0x3e7fb102,2
+np.float32,0x44a52949,0xbe7dc9d5,2
+np.float32,0x4454633a,0x3e7dbc7d,2
+np.float32,0x4689810b,0x3e7eb02b,2
+np.float32,0x473473cd,0xbe7eef6f,2
+np.float32,0x44a5193f,0x3e7e1b1f,2
+np.float32,0x46004b36,0x3e7dac59,2
+np.float32,0x467f604b,0x3d7ffd3a,2
+np.float32,0x45ea1805,0x3dffd2e0,2
+np.float32,0x457b6af3,0x3dff7831,2
+np.float32,0x44996159,0xbe7d85f4,2
+np.float32,0x47883553,0xbb80584e,2
+np.float32,0x44e19f0c,0xbdffcfe6,2
+np.float32,0x472b3bf6,0xbe7f7a82,2
+np.float32,0x4600bb4e,0x3a135e33,2
+np.float32,0x449f4556,0x3e7e42e5,2
+np.float32,0x474e9420,0x3dff77b2,2
+np.float32,0x45cbdb23,0x3dff7240,2
+np.float32,0x44222747,0x3dffb039,2
+np.float32,0x4772e419,0xbdff74b8,2
diff --git a/numpy/core/tests/data/umath-validation-set-exp b/numpy/core/tests/data/umath-validation-set-exp
new file mode 100644
index 000000000..1b2cc9ce4
--- /dev/null
+++ b/numpy/core/tests/data/umath-validation-set-exp
@@ -0,0 +1,135 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0x3f800000,3
+np.float32,0x007b2490,0x3f800000,3
+np.float32,0x007c99fa,0x3f800000,3
+np.float32,0x00734a0c,0x3f800000,3
+np.float32,0x0070de24,0x3f800000,3
+np.float32,0x00495d65,0x3f800000,3
+np.float32,0x006894f6,0x3f800000,3
+np.float32,0x00555a76,0x3f800000,3
+np.float32,0x004e1fb8,0x3f800000,3
+np.float32,0x00687de9,0x3f800000,3
+## -ve denormals ##
+np.float32,0x805b59af,0x3f800000,3
+np.float32,0x807ed8ed,0x3f800000,3
+np.float32,0x807142ad,0x3f800000,3
+np.float32,0x80772002,0x3f800000,3
+np.float32,0x8062abcb,0x3f800000,3
+np.float32,0x8045e31c,0x3f800000,3
+np.float32,0x805f01c2,0x3f800000,3
+np.float32,0x80506432,0x3f800000,3
+np.float32,0x8060089d,0x3f800000,3
+np.float32,0x8071292f,0x3f800000,3
+## floats that output a denormal ##
+np.float32,0xc2cf3fc1,0x00000001,3
+np.float32,0xc2c79726,0x00000021,3
+np.float32,0xc2cb295d,0x00000005,3
+np.float32,0xc2b49e6b,0x00068c4c,3
+np.float32,0xc2ca8116,0x00000008,3
+np.float32,0xc2c23f82,0x000001d7,3
+np.float32,0xc2cb69c0,0x00000005,3
+np.float32,0xc2cc1f4d,0x00000003,3
+np.float32,0xc2ae094e,0x00affc4c,3
+np.float32,0xc2c86c44,0x00000015,3
+## random floats between -87.0f and 88.0f ##
+np.float32,0x4030d7e0,0x417d9a05,3
+np.float32,0x426f60e8,0x6aa1be2c,3
+np.float32,0x41a1b220,0x4e0efc11,3
+np.float32,0xc20cc722,0x26159da7,3
+np.float32,0x41c492bc,0x512ec79d,3
+np.float32,0x40980210,0x42e73a0e,3
+np.float32,0xbf1f7b80,0x3f094de3,3
+np.float32,0x42a678a4,0x7b87a383,3
+np.float32,0xc20f3cfd,0x25a1c304,3
+np.float32,0x423ff34c,0x6216467f,3
+np.float32,0x00000000,0x3f800000,3
+## floats that cause an overflow ##
+np.float32,0x7f06d8c1,0x7f800000,3
+np.float32,0x7f451912,0x7f800000,3
+np.float32,0x7ecceac3,0x7f800000,3
+np.float32,0x7f643b45,0x7f800000,3
+np.float32,0x7e910ea0,0x7f800000,3
+np.float32,0x7eb4756b,0x7f800000,3
+np.float32,0x7f4ec708,0x7f800000,3
+np.float32,0x7f6b4551,0x7f800000,3
+np.float32,0x7d8edbda,0x7f800000,3
+np.float32,0x7f730718,0x7f800000,3
+np.float32,0x42b17217,0x7f7fff84,3
+np.float32,0x42b17218,0x7f800000,3
+np.float32,0x42b17219,0x7f800000,3
+np.float32,0xfef2b0bc,0x00000000,3
+np.float32,0xff69f83e,0x00000000,3
+np.float32,0xff4ecb12,0x00000000,3
+np.float32,0xfeac6d86,0x00000000,3
+np.float32,0xfde0cdb8,0x00000000,3
+np.float32,0xff26aef4,0x00000000,3
+np.float32,0xff6f9277,0x00000000,3
+np.float32,0xff7adfc4,0x00000000,3
+np.float32,0xff0ad40e,0x00000000,3
+np.float32,0xff6fd8f3,0x00000000,3
+np.float32,0xc2cff1b4,0x00000001,3
+np.float32,0xc2cff1b5,0x00000000,3
+np.float32,0xc2cff1b6,0x00000000,3
+np.float32,0x7f800000,0x7f800000,3
+np.float32,0xff800000,0x00000000,3
+np.float32,0x4292f27c,0x7480000a,3
+np.float32,0x42a920be,0x7c7fff94,3
+np.float32,0x41c214c9,0x50ffffd9,3
+np.float32,0x41abe686,0x4effffd9,3
+np.float32,0x4287db5a,0x707fffd3,3
+np.float32,0x41902cbb,0x4c800078,3
+np.float32,0x42609466,0x67ffffeb,3
+np.float32,0x41a65af5,0x4e7fffd1,3
+np.float32,0x417f13ff,0x4affffc9,3
+np.float32,0x426d0e6c,0x6a3504f2,3
+np.float32,0x41bc8934,0x507fff51,3
+np.float32,0x42a7bdde,0x7c0000d6,3
+np.float32,0x4120cf66,0x46b504f6,3
+np.float32,0x4244da8f,0x62ffff1a,3
+np.float32,0x41a0cf69,0x4e000034,3
+np.float32,0x41cd2bec,0x52000005,3
+np.float32,0x42893e41,0x7100009e,3
+np.float32,0x41b437e1,0x4fb50502,3
+np.float32,0x41d8430f,0x5300001d,3
+np.float32,0x4244da92,0x62ffffda,3
+np.float32,0x41a0cf63,0x4dffffa9,3
+np.float32,0x3eb17218,0x3fb504f3,3
+np.float32,0x428729e8,0x703504dc,3
+np.float32,0x41a0cf67,0x4e000014,3
+np.float32,0x4252b77d,0x65800011,3
+np.float32,0x41902cb9,0x4c800058,3
+np.float32,0x42a0cf67,0x79800052,3
+np.float32,0x4152b77b,0x48ffffe9,3
+np.float32,0x41265af3,0x46ffffc8,3
+np.float32,0x42187e0b,0x5affff9a,3
+np.float32,0xc0d2b77c,0x3ab504f6,3
+np.float32,0xc283b2ac,0x10000072,3
+np.float32,0xc1cff1b4,0x2cb504f5,3
+np.float32,0xc05dce9e,0x3d000000,3
+np.float32,0xc28ec9d2,0x0bfffea5,3
+np.float32,0xc23c893a,0x1d7fffde,3
+np.float32,0xc2a920c0,0x027fff6c,3
+np.float32,0xc1f9886f,0x2900002b,3
+np.float32,0xc2c42920,0x000000b5,3
+np.float32,0xc2893e41,0x0dfffec5,3
+np.float32,0xc2c4da93,0x00000080,3
+np.float32,0xc17f1401,0x3400000c,3
+np.float32,0xc1902cb6,0x327fffaf,3
+np.float32,0xc27c4e3b,0x11ffffc5,3
+np.float32,0xc268e5c5,0x157ffe9d,3
+np.float32,0xc2b4e953,0x0005a826,3
+np.float32,0xc287db5a,0x0e800016,3
+np.float32,0xc207db5a,0x2700000b,3
+np.float32,0xc2b2d4fe,0x000ffff1,3
+np.float32,0xc268e5c0,0x157fffdd,3
+np.float32,0xc22920bd,0x2100003b,3
+np.float32,0xc2902caf,0x0b80011e,3
+np.float32,0xc1902cba,0x327fff2f,3
+np.float32,0xc2ca6625,0x00000008,3
+np.float32,0xc280ece8,0x10fffeb5,3
+np.float32,0xc2918f94,0x0b0000ea,3
+np.float32,0xc29b43d5,0x077ffffc,3
+np.float32,0xc1e61ff7,0x2ab504f5,3
+np.float32,0xc2867878,0x0effff15,3
+np.float32,0xc2a2324a,0x04fffff4,3
diff --git a/numpy/core/tests/data/umath-validation-set-log b/numpy/core/tests/data/umath-validation-set-log
new file mode 100644
index 000000000..a7bd98481
--- /dev/null
+++ b/numpy/core/tests/data/umath-validation-set-log
@@ -0,0 +1,118 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0xc2afbc1b,4
+np.float32,0x007b2490,0xc2aec01e,4
+np.float32,0x007c99fa,0xc2aeba17,4
+np.float32,0x00734a0c,0xc2aee1dc,4
+np.float32,0x0070de24,0xc2aeecba,4
+np.float32,0x007fffff,0xc2aeac50,4
+np.float32,0x00000001,0xc2ce8ed0,4
+## -ve denormals ##
+np.float32,0x80495d65,0xffc00000,4
+np.float32,0x806894f6,0xffc00000,4
+np.float32,0x80555a76,0xffc00000,4
+np.float32,0x804e1fb8,0xffc00000,4
+np.float32,0x80687de9,0xffc00000,4
+np.float32,0x807fffff,0xffc00000,4
+np.float32,0x80000001,0xffc00000,4
+## +/-0.0f, +/-FLT_MIN +/-FLT_MAX ##
+np.float32,0x00000000,0xff800000,4
+np.float32,0x80000000,0xff800000,4
+np.float32,0x7f7fffff,0x42b17218,4
+np.float32,0x80800000,0xffc00000,4
+np.float32,0xff7fffff,0xffc00000,4
+## 1.00f + 0x00000001 ##
+np.float32,0x3f800000,0x00000000,4
+np.float32,0x3f800001,0x33ffffff,4
+np.float32,0x3f800002,0x347ffffe,4
+np.float32,0x3f7fffff,0xb3800000,4
+np.float32,0x3f7ffffe,0xb4000000,4
+np.float32,0x3f7ffffd,0xb4400001,4
+np.float32,0x402df853,0x3f7ffffe,4
+np.float32,0x402df854,0x3f7fffff,4
+np.float32,0x402df855,0x3f800000,4
+np.float32,0x402df856,0x3f800001,4
+np.float32,0x3ebc5ab0,0xbf800001,4
+np.float32,0x3ebc5ab1,0xbf800000,4
+np.float32,0x3ebc5ab2,0xbf800000,4
+np.float32,0x3ebc5ab3,0xbf7ffffe,4
+np.float32,0x423ef575,0x407768ab,4
+np.float32,0x427b8c61,0x408485dd,4
+np.float32,0x4211e9ee,0x406630b0,4
+np.float32,0x424d5c41,0x407c0fed,4
+np.float32,0x42be722a,0x4091cc91,4
+np.float32,0x42b73d30,0x4090908b,4
+np.float32,0x427e48e2,0x4084de7f,4
+np.float32,0x428f759b,0x4088bba3,4
+np.float32,0x41629069,0x4029a0cc,4
+np.float32,0x4272c99d,0x40836379,4
+np.float32,0x4d1b7458,0x4197463d,4
+np.float32,0x4f10c594,0x41ace2b2,4
+np.float32,0x4ea397c2,0x41a85171,4
+np.float32,0x4fefa9d1,0x41b6769c,4
+np.float32,0x4ebac6ab,0x41a960dc,4
+np.float32,0x4f6efb42,0x41b0e535,4
+np.float32,0x4e9ab8e7,0x41a7df44,4
+np.float32,0x4e81b5d1,0x41a67625,4
+np.float32,0x5014d9f2,0x41b832bd,4
+np.float32,0x4f02175c,0x41ac07b8,4
+np.float32,0x7f034f89,0x42b01c47,4
+np.float32,0x7f56d00e,0x42b11849,4
+np.float32,0x7f1cd5f6,0x42b0773a,4
+np.float32,0x7e979174,0x42af02d7,4
+np.float32,0x7f23369f,0x42b08ba2,4
+np.float32,0x7f0637ae,0x42b0277d,4
+np.float32,0x7efcb6e8,0x42b00897,4
+np.float32,0x7f7907c8,0x42b163f6,4
+np.float32,0x7e95c4c2,0x42aefcba,4
+np.float32,0x7f4577b2,0x42b0ed2d,4
+np.float32,0x3f49c92e,0xbe73ae84,4
+np.float32,0x3f4a23d1,0xbe71e2f8,4
+np.float32,0x3f4abb67,0xbe6ee430,4
+np.float32,0x3f48169a,0xbe7c5532,4
+np.float32,0x3f47f5fa,0xbe7cfc37,4
+np.float32,0x3f488309,0xbe7a2ad8,4
+np.float32,0x3f479df4,0xbe7ebf5f,4
+np.float32,0x3f47cfff,0xbe7dbec9,4
+np.float32,0x3f496704,0xbe75a125,4
+np.float32,0x3f478ee8,0xbe7f0c92,4
+np.float32,0x3f4a763b,0xbe7041ce,4
+np.float32,0x3f47a108,0xbe7eaf94,4
+np.float32,0x3f48136c,0xbe7c6578,4
+np.float32,0x3f481c17,0xbe7c391c,4
+np.float32,0x3f47cd28,0xbe7dcd56,4
+np.float32,0x3f478be8,0xbe7f1bf7,4
+np.float32,0x3f4c1f8e,0xbe67e367,4
+np.float32,0x3f489b0c,0xbe79b03f,4
+np.float32,0x3f4934cf,0xbe76a08a,4
+np.float32,0x3f4954df,0xbe75fd6a,4
+np.float32,0x3f47a3f5,0xbe7ea093,4
+np.float32,0x3f4ba4fc,0xbe6a4b02,4
+np.float32,0x3f47a0e1,0xbe7eb05c,4
+np.float32,0x3f48c30a,0xbe78e42f,4
+np.float32,0x3f48cab8,0xbe78bd05,4
+np.float32,0x3f4b0569,0xbe6d6ea4,4
+np.float32,0x3f47de32,0xbe7d7607,4
+np.float32,0x3f477328,0xbe7f9b00,4
+np.float32,0x3f496dab,0xbe757f52,4
+np.float32,0x3f47662c,0xbe7fddac,4
+np.float32,0x3f48ddd8,0xbe785b80,4
+np.float32,0x3f481866,0xbe7c4bff,4
+np.float32,0x3f48b119,0xbe793fb6,4
+np.float32,0x3f48c7e8,0xbe78cb5c,4
+np.float32,0x3f4985f6,0xbe7503da,4
+np.float32,0x3f483fdf,0xbe7b8212,4
+np.float32,0x3f4b1c76,0xbe6cfa67,4
+np.float32,0x3f480b2e,0xbe7c8fa8,4
+np.float32,0x3f48745f,0xbe7a75bf,4
+np.float32,0x3f485bda,0xbe7af308,4
+np.float32,0x3f47a660,0xbe7e942c,4
+np.float32,0x3f47d4d5,0xbe7da600,4
+np.float32,0x3f4b0a26,0xbe6d56be,4
+np.float32,0x3f4a4883,0xbe712924,4
+np.float32,0x3f4769e7,0xbe7fca84,4
+np.float32,0x3f499702,0xbe74ad3f,4
+np.float32,0x3f494ab1,0xbe763131,4
+np.float32,0x3f476b69,0xbe7fc2c6,4
+np.float32,0x3f4884e8,0xbe7a214a,4
+np.float32,0x3f486945,0xbe7aae76,4
diff --git a/numpy/core/tests/data/umath-validation-set-sin b/numpy/core/tests/data/umath-validation-set-sin
new file mode 100644
index 000000000..a56273195
--- /dev/null
+++ b/numpy/core/tests/data/umath-validation-set-sin
@@ -0,0 +1,707 @@
+dtype,input,output,ulperrortol
+## +ve denormals ##
+np.float32,0x004b4716,0x004b4716,2
+np.float32,0x007b2490,0x007b2490,2
+np.float32,0x007c99fa,0x007c99fa,2
+np.float32,0x00734a0c,0x00734a0c,2
+np.float32,0x0070de24,0x0070de24,2
+np.float32,0x007fffff,0x007fffff,2
+np.float32,0x00000001,0x00000001,2
+## -ve denormals ##
+np.float32,0x80495d65,0x80495d65,2
+np.float32,0x806894f6,0x806894f6,2
+np.float32,0x80555a76,0x80555a76,2
+np.float32,0x804e1fb8,0x804e1fb8,2
+np.float32,0x80687de9,0x80687de9,2
+np.float32,0x807fffff,0x807fffff,2
+np.float32,0x80000001,0x80000001,2
+## +/-0.0f, +/-FLT_MIN +/-FLT_MAX ##
+np.float32,0x00000000,0x00000000,2
+np.float32,0x80000000,0x80000000,2
+np.float32,0x00800000,0x00800000,2
+np.float32,0x7f7fffff,0xbf0599b3,2
+np.float32,0x80800000,0x80800000,2
+np.float32,0xff7fffff,0x3f0599b3,2
+## 1.00f ##
+np.float32,0x3f800000,0x3f576aa4,2
+np.float32,0x3f800001,0x3f576aa6,2
+np.float32,0x3f800002,0x3f576aa7,2
+np.float32,0xc090a8b0,0x3f7b4e48,2
+np.float32,0x41ce3184,0x3f192d43,2
+np.float32,0xc1d85848,0xbf7161cb,2
+np.float32,0x402b8820,0x3ee3f29f,2
+np.float32,0x42b4e454,0x3f1d0151,2
+np.float32,0x42a67a60,0x3f7ffa4c,2
+np.float32,0x41d92388,0x3f67beef,2
+np.float32,0x422dd66c,0xbeffb0c1,2
+np.float32,0xc28f5be6,0xbf0bae79,2
+np.float32,0x41ab2674,0x3f0ffe2b,2
+np.float32,0xd0102756,0x3f227e8a,2
+np.float32,0xcf99405e,0x3f73ad00,2
+np.float32,0xcfd83a12,0xbf7151a7,2
+np.float32,0x4fb54db0,0xbe46354b,2
+np.float32,0xcfcca29d,0xbe9345e6,2
+np.float32,0xceec2ac0,0x3e98dc89,2
+np.float32,0xcfdca97f,0xbf60b2b4,2
+np.float32,0xcfe92b0a,0xbf222705,2
+np.float32,0x5014b0eb,0x3f63e75c,2
+np.float32,0xcfa7ee96,0x3f62ada4,2
+np.float32,0x754c09a0,0xbf617056,2
+np.float32,0x77a731fb,0x3f44472b,2
+np.float32,0x76de2494,0xbe680739,2
+np.float32,0xf74920dc,0xbf193338,2
+np.float32,0x7707a312,0xbf6f51b1,2
+np.float32,0x75bf9790,0xbd0f1a47,2
+np.float32,0xf4ca7c40,0xbf7d45e7,2
+np.float32,0x77e91899,0x3f767181,2
+np.float32,0xf74c9820,0xbd685b75,2
+np.float32,0x7785ca29,0x3f78ee61,2
+np.float32,0x3f490fdb,0x3f3504f3,2
+np.float32,0xbf490fdb,0xbf3504f3,2
+np.float32,0x3fc90fdb,0x3f800000,2
+np.float32,0xbfc90fdb,0xbf800000,2
+np.float32,0x40490fdb,0xb3bbbd2e,2
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diff --git a/numpy/core/tests/test_umath_accuracy.py b/numpy/core/tests/test_umath_accuracy.py
new file mode 100644
index 000000000..6ea0c402c
--- /dev/null
+++ b/numpy/core/tests/test_umath_accuracy.py
@@ -0,0 +1,53 @@
+import numpy as np
+import platform
+from os import path
+import sys
+import pytest
+from ctypes import *
+from numpy.testing import assert_array_max_ulp
+
+runtest = sys.platform.startswith('linux') and (platform.machine() == 'x86_64')
+platform_skip = pytest.mark.skipif(not runtest,
+                                   reason="""
+                                   stick to x86_64 and linux platforms.
+                                   test seems to fail on some of ARM and power
+                                   architectures.
+                                   """)
+
+# convert string to hex function taken from:
+# https://stackoverflow.com/questions/1592158/convert-hex-to-float #
+def convert(s):
+    i = int(s, 16)                   # convert from hex to a Python int
+    cp = pointer(c_int(i))           # make this into a c integer
+    fp = cast(cp, POINTER(c_float))  # cast the int pointer to a float pointer
+    return fp.contents.value         # dereference the pointer, get the float
+
+str_to_float = np.vectorize(convert)
+files = ['umath-validation-set-exp',
+         'umath-validation-set-log',
+         'umath-validation-set-sin',
+         'umath-validation-set-cos']
+
+class TestAccuracy(object):
+    @platform_skip
+    def test_validate_transcendentals(self):
+        with np.errstate(all='ignore'):
+            for filename in files:
+                data_dir = path.join(path.dirname(__file__), 'data')
+                filepath = path.join(data_dir, filename)
+                file_without_comments = (r for r in open(filepath) if not r[0] in ('$', '#'))
+                data = np.genfromtxt(file_without_comments,
+                                     dtype=('|S39','|S39','|S39',np.int),
+                                     names=('type','input','output','ulperr'),
+                                     delimiter=',',
+                                     skip_header=1)
+                npfunc = getattr(np, filename.split('-')[3])
+                for datatype in np.unique(data['type']):
+                    data_subset = data[data['type'] == datatype]
+                    inval  = np.array(str_to_float(data_subset['input'].astype(str)), dtype=eval(datatype))
+                    outval = np.array(str_to_float(data_subset['output'].astype(str)), dtype=eval(datatype))
+                    perm = np.random.permutation(len(inval))
+                    inval = inval[perm]
+                    outval = outval[perm]
+                    maxulperr = data_subset['ulperr'].max()
+                    assert_array_max_ulp(npfunc(inval), outval, maxulperr)