Deterministic GPU histogram. (#5361)

* Use pre-rounding based method to obtain reproducible floating point
  summation.
* GPU Hist for regression and classification are bit-by-bit reproducible.
* Add doc.
* Switch to thrust reduce for `node_sum_gradient`.

tests/python-gpu/test_gpu_basic_models.py

@@ -1,6 +1,8 @@
 import sys
+import os
 import unittest
 import numpy as np
+import xgboost as xgb
 sys.path.append("tests/python")
 # Don't import the test class, otherwise they will run twice.
 import test_basic_models as test_bm  # noqa
@@ -12,3 +14,33 @@ class TestGPUBasicModels(unittest.TestCase):
 
     def test_eta_decay_gpu_hist(self):
         self.cputest.run_eta_decay('gpu_hist')
+
+    def test_deterministic_gpu_hist(self):
+        kRows = 1000
+        kCols = 64
+        kClasses = 4
+        # Create large values to force rounding.
+        X = np.random.randn(kRows, kCols) * 1e4
+        y = np.random.randint(0, kClasses, size=kRows)
+
+        cls = xgb.XGBClassifier(tree_method='gpu_hist',
+                                deterministic_histogram=True,
+                                single_precision_histogram=True)
+        cls.fit(X, y)
+        cls.get_booster().save_model('test_deterministic_gpu_hist-0.json')
+
+        cls = xgb.XGBClassifier(tree_method='gpu_hist',
+                                deterministic_histogram=True,
+                                single_precision_histogram=True)
+        cls.fit(X, y)
+        cls.get_booster().save_model('test_deterministic_gpu_hist-1.json')
+
+        with open('test_deterministic_gpu_hist-0.json', 'r') as fd:
+            model_0 = fd.read()
+        with open('test_deterministic_gpu_hist-1.json', 'r') as fd:
+            model_1 = fd.read()
+
+        assert hash(model_0) == hash(model_1)
+
+        os.remove('test_deterministic_gpu_hist-0.json')
+        os.remove('test_deterministic_gpu_hist-1.json')