diff --git a/src/assign.c b/src/assign.c
index 9478c8745b..85979e2fb3 100644
--- a/src/assign.c
+++ b/src/assign.c
@@ -1,6 +1,4 @@
 #include "data.table.h"
-#include <Rdefines.h>
-#include <Rmath.h>
 
 static void finalizer(SEXP p)
 {
diff --git a/src/data.table.h b/src/data.table.h
index 062bbc8663..c7e4f0f7a9 100644
--- a/src/data.table.h
+++ b/src/data.table.h
@@ -1,10 +1,10 @@
+#include "dt_stdio.h"  // PRId64 and PRIu64
 #include <R.h>
 #define USE_RINTERNALS
 #include <Rinternals.h>
 // #include <signal.h> // the debugging machinery + breakpoint aidee
 // raise(SIGINT);
 #include <stdint.h>    // for uint64_t rather than unsigned long long
-#include <inttypes.h>  // for PRId64 and PRIu64
 #include <stdbool.h>
 #include "myomp.h"
 #include "types.h"
diff --git a/src/dt_stdio.h b/src/dt_stdio.h
new file mode 100644
index 0000000000..4e69e0d87e
--- /dev/null
+++ b/src/dt_stdio.h
@@ -0,0 +1,34 @@
+
+// It seems that latest min64-w64 compiler needs some help to avoid warnings; #4064
+// It appears that its inttypes.h defines PRId64 to be I64 on Windows but then warns that
+// I64 is not C99 too. Which is correct, but we know, and we don't want any warnings, and
+// we can't control settings on CRAN. So here we try and isolate ourselves from all scenarios.
+// There is a lot online about this, but these were a few that were most useful:
+// https://stackoverflow.com/questions/23718110/error-unknown-conversion-type-character-l-in-format-scanning-long-long
+// https://gitlab.freedesktop.org/nacho.garglez/cerbero/commit/4ec6bfdc1db1e4bc8d4278f53ad295af1efe89fb
+// https://github.com/GNOME/glib/commit/98a0ab929d8c59ee27e5f470f11d077bb6a56749#diff-969b60ad3d206fd45c208e266ccfed38
+// https://sourceforge.net/p/mingw-w64/wiki2/gnu%20printf/
+// Warning that __USE_MINGW_ANSI_STDIO could be deprecated:
+// https://mingw-w64-public.narkive.com/aQDJHqCv/how-to-printf-64-bit-integer-in-64-bit-compiler-in-strict-iso-mode-with-all-warnings-enabled
+// and then actual deprecation (with complaints) earlier in 2019 here:
+// https://osdn.net/projects/mingw/lists/archive/users/2019-January/000202.html
+// But I can't find _mingw.h. I can find mingw.h but not advice within it:
+// https://github.com/git/git/blob/master/compat/mingw.h#L448
+// The deprecation about I64 doesn't seem to take into account that lld throws the warning in MinGW:
+//   warning: unknown conversion type character 'l' in format [-Wformat=]
+// So let's see if the approach below works for now.
+// If we need to make changes in future, we can do it here in one place.
+
+#ifndef DT_STDIO_H
+#define DT_STDIO_H
+#if defined(__MINGW32__) || (defined __MINGW64__)
+  #define __USE_MINGW_ANSI_STDIO 1
+  #include <stdio.h>
+  #define PRId64 "lld"
+  #define PRIu64 "llu"
+#else
+  #include <stdio.h>
+  #include <inttypes.h>
+  // let inttypes.h decide: lld on Linux/C99; I64 on Windows Visual Studio for example
+#endif
+#endif
diff --git a/src/fread.h b/src/fread.h
index e70dbbe42f..ec230c6986 100644
--- a/src/fread.h
+++ b/src/fread.h
@@ -1,9 +1,9 @@
 #ifndef dt_FREAD_H
 #define dt_FREAD_H
-#include <stdint.h>  // uint32_t
-#include <inttypes.h> // PRId64
-#include <stdlib.h>  // size_t
-#include <stdbool.h> // bool
+#include "dt_stdio.h"  // PRId64
+#include <stdint.h>    // uint32_t
+#include <stdlib.h>    // size_t
+#include <stdbool.h>   // bool
 #include "myomp.h"
 #ifdef DTPY
   #include "py_fread.h"
diff --git a/src/froll.c b/src/froll.c
index ef19255431..5116307393 100644
--- a/src/froll.c
+++ b/src/froll.c
@@ -1,7 +1,3 @@
-#include <stdio.h>
-#include <stdint.h>
-#include <stdbool.h>
-#include <Rdefines.h>
 #include "data.table.h"
 
 /* fast rolling mean - router
@@ -49,7 +45,7 @@ void frollmean(unsigned int algo, double *x, uint64_t nx, ans_t *ans, int k, int
  */
 void frollmeanFast(double *x, uint64_t nx, ans_t *ans, int k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running for input length %"PRIu64", window %d, hasna %d, narm %d\n", __func__, (uint64_t)nx, k, hasna, (int)narm);
+    snprintf(end(ans->message[0]), 500, "frollmeanFast: running for input length %"PRIu64", window %d, hasna %d, narm %d\n", (uint64_t)nx, k, hasna, (int)narm);
   long double w = 0.0;                                          // sliding window aggregate
   bool truehasna = hasna>0;                                     // flag to re-run with NA support if NAs detected
   if (!truehasna) {
@@ -138,7 +134,7 @@ void frollmeanFast(double *x, uint64_t nx, ans_t *ans, int k, double fill, bool
  */
 void frollmeanExact(double *x, uint64_t nx, ans_t *ans, int k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running in parallel for input length %"PRIu64", window %d, hasna %d, narm %d\n", __func__, (uint64_t)nx, k, hasna, (int)narm);
+    snprintf(end(ans->message[0]), 500, "frollmeanExact: running in parallel for input length %"PRIu64", window %d, hasna %d, narm %d\n", (uint64_t)nx, k, hasna, (int)narm);
   for (int i=0; i<k-1; i++) {                                   // fill partial window only
     ans->dbl_v[i] = fill;
   }
@@ -252,7 +248,7 @@ void frollsum(unsigned int algo, double *x, uint64_t nx, ans_t *ans, int k, int
 }
 void frollsumFast(double *x, uint64_t nx, ans_t *ans, int k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running for input length %"PRIu64", window %d, hasna %d, narm %d\n", __func__, (uint64_t)nx, k, hasna, (int)narm);
+    snprintf(end(ans->message[0]), 500, "frollsumFast: running for input length %"PRIu64", window %d, hasna %d, narm %d\n", (uint64_t)nx, k, hasna, (int)narm);
   long double w = 0.0;
   bool truehasna = hasna>0;
   if (!truehasna) {
@@ -336,7 +332,7 @@ void frollsumFast(double *x, uint64_t nx, ans_t *ans, int k, double fill, bool n
 }
 void frollsumExact(double *x, uint64_t nx, ans_t *ans, int k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running in parallel for input length %"PRIu64", window %d, hasna %d, narm %d\n", __func__, (uint64_t)nx, k, hasna, (int)narm);
+    snprintf(end(ans->message[0]), 500, "frollsumExact: running in parallel for input length %"PRIu64", window %d, hasna %d, narm %d\n", (uint64_t)nx, k, hasna, (int)narm);
   for (int i=0; i<k-1; i++) {
     ans->dbl_v[i] = fill;
   }
diff --git a/src/frolladaptive.c b/src/frolladaptive.c
index 9451e70e22..9521217593 100644
--- a/src/frolladaptive.c
+++ b/src/frolladaptive.c
@@ -1,7 +1,3 @@
-#include <stdio.h>
-#include <stdint.h>
-#include <stdbool.h>
-#include <Rdefines.h>
 #include "data.table.h"
 
 /* fast adaptive rolling mean - router
@@ -30,7 +26,7 @@ void fadaptiverollmean(unsigned int algo, double *x, uint64_t nx, ans_t *ans, in
  */
 void fadaptiverollmeanFast(double *x, uint64_t nx, ans_t *ans, int *k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running for input length %"PRIu64", hasna %d, narm %d\n", __func__, (uint64_t)nx, hasna, (int) narm);
+    snprintf(end(ans->message[0]), 500, "fadaptiverollmeanFast: running for input length %"PRIu64", hasna %d, narm %d\n", (uint64_t)nx, hasna, (int) narm);
   bool truehasna = hasna>0;                                     // flag to re-run if NAs detected
   long double w = 0.0;
   double *cs = malloc(nx*sizeof(double));                       // cumsum vector, same as double cs[nx] but no segfault
@@ -115,7 +111,7 @@ void fadaptiverollmeanFast(double *x, uint64_t nx, ans_t *ans, int *k, double fi
  */
 void fadaptiverollmeanExact(double *x, uint64_t nx, ans_t *ans, int *k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running in parallel for input length %"PRIu64", hasna %d, narm %d\n", __func__, (uint64_t)nx, hasna, (int) narm);
+    snprintf(end(ans->message[0]), 500, "fadaptiverollmeanExact: running in parallel for input length %"PRIu64", hasna %d, narm %d\n", (uint64_t)nx, hasna, (int) narm);
   bool truehasna = hasna>0;                                     // flag to re-run if NAs detected
   if (!truehasna || !narm) {                                    // narm=FALSE handled here as NAs properly propagated in exact algo
     #pragma omp parallel for num_threads(getDTthreads())
@@ -219,7 +215,7 @@ void fadaptiverollsum(unsigned int algo, double *x, uint64_t nx, ans_t *ans, int
 }
 void fadaptiverollsumFast(double *x, uint64_t nx, ans_t *ans, int *k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running for input length %"PRIu64", hasna %d, narm %d\n", __func__, (uint64_t)nx, hasna, (int) narm);
+    snprintf(end(ans->message[0]), 500, "fadaptiverollsumFast: running for input length %"PRIu64", hasna %d, narm %d\n", (uint64_t)nx, hasna, (int) narm);
   bool truehasna = hasna>0;
   long double w = 0.0;
   double *cs = malloc(nx*sizeof(double));
@@ -299,7 +295,7 @@ void fadaptiverollsumFast(double *x, uint64_t nx, ans_t *ans, int *k, double fil
 }
 void fadaptiverollsumExact(double *x, uint64_t nx, ans_t *ans, int *k, double fill, bool narm, int hasna, bool verbose) {
   if (verbose)
-    snprintf(end(ans->message[0]), 500, "%s: running in parallel for input length %"PRIu64", hasna %d, narm %d\n", __func__, (uint64_t)nx, hasna, (int) narm);
+    snprintf(end(ans->message[0]), 500, "fadaptiverollsumExact: running in parallel for input length %"PRIu64", hasna %d, narm %d\n", (uint64_t)nx, hasna, (int) narm);
   bool truehasna = hasna>0;
   if (!truehasna || !narm) {
     #pragma omp parallel for num_threads(getDTthreads())
diff --git a/src/fwrite.c b/src/fwrite.c
index aa30ab8413..b5ff08cde6 100644
--- a/src/fwrite.c
+++ b/src/fwrite.c
@@ -1,9 +1,9 @@
+#include "dt_stdio.h"
 #include <errno.h>
 #include <unistd.h>    // for access()
 #include <fcntl.h>
 #include <stdbool.h>   // true and false
 #include <stdint.h>    // INT32_MIN
-#include <inttypes.h>  // PRId64
 #include <math.h>      // isfinite, isnan
 #include <stdlib.h>    // abs
 #include <string.h>    // strlen, strerror