diff --git a/NEWS.md b/NEWS.md
index ac4b442ace..d53d5e514b 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -97,6 +97,8 @@ unit = "s")
 
 8. An `fwrite` error message could include a garbled number and cause test 1737.5 to fail, [#3492](https://github.com/Rdatatable/data.table/issues/3492). Thanks to @QuLogic for debugging the issue on ARMv7hl, and the PR fixing it.
 
+9. `fread` improves handling of very small (<1e-300) or very large (>1e+300) floating point numbers on non-x86 architectures (specifically ppc64le and armv7hl). Thanks to @QuLogic for reporting and fixing, [PR#4165](https://github.com/Rdatatable/data.table/pull/4165).
+
 ## NOTES
 
 1. `as.IDate`, `as.ITime`, `second`, `minute`, and `hour` now recognize UTC equivalents for speed: GMT, GMT-0, GMT+0, GMT0, Etc/GMT, and Etc/UTC, [#4116](https://github.com/Rdatatable/data.table/issues/4116).
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index b2ea9a3554..0ffe3f5bf5 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -2934,8 +2934,9 @@ if (test_bit64) test(1017.1, fread(f), copy(DT)[,A:=as.integer64(A)])
 test(1017.2, fread(f, integer64="character"), DT)
 unlink(f)
 
-# ERANGE errno handled, #106
-test(1018, identical(fread("1.46761e-313\n"), data.table(V1=1.46761e-313)))
+# ERANGE errno handled, #106 #4165
+test(1018.1, identical(fread("1.46761e-313\n"), data.table(V1=1.46761e-313)))
+test(1018.2, identical(fread("1.46761e+313\n"), data.table(V1=1.46761e+313)))
 test(1019, fread("A\n1.23456789123456789123456999\n"), data.table(A=1.234567891234568))
 
 # crash assigning to row 0, #2754
diff --git a/src/fread.c b/src/fread.c
index 69082c5d95..c94aeac069 100644
--- a/src/fread.c
+++ b/src/fread.c
@@ -648,9 +648,9 @@ static void StrtoI64(FieldParseContext *ctx)
 // TODO: review ERANGE checks and tests; that range outside [1.7e-308,1.7e+308] coerces to [0.0,Inf]
 /*
 f = "~/data.table/src/freadLookups.h"
-cat("const long double pow10lookup[701] = {\n", file=f, append=FALSE)
-for (i in (-350):(349)) cat("1.0E",i,"L,\n", sep="", file=f, append=TRUE)
-cat("1.0E350L\n};\n", file=f, append=TRUE)
+cat("const long double pow10lookup[601] = {\n", file=f, append=FALSE)
+for (i in (-300):(299)) cat("1.0E",i,"L,\n", sep="", file=f, append=TRUE)
+cat("1.0E300L\n};\n", file=f, append=TRUE)
 */
 
 
@@ -767,11 +767,23 @@ static void parse_double_regular(FieldParseContext *ctx)
     }
     e += Eneg? -E : E;
   }
-  e += 350; // lookup table is arranged from -350 (0) to +350 (700)
-  if (e<0 || e>700) goto fail;
+  if (e<-350 || e>350) goto fail;
 
-  double r = (double)((long double)acc * pow10lookup[e]);
-  *target = neg? -r : r;
+  long double r = (long double)acc;
+  if (e < -300 || e > 300) {
+    // Handle extra precision by pre-multiplying the result by pow(10, extra),
+    // and then remove extra from e.
+    // This avoids having to store very small or very large constants that may
+    // fail to be encoded by the compiler, even though the values can actually
+    // be stored correctly.
+    int_fast8_t extra = e < 0 ? e + 300 : e - 300;
+    r *= pow10lookup[extra + 300];
+    e -= extra;
+  }
+  e += 300; // lookup table is arranged from -300 (0) to +300 (600)
+
+  r *= pow10lookup[e];
+  *target = (double)(neg? -r : r);
   *(ctx->ch) = ch;
   return;
 
diff --git a/src/fread.h b/src/fread.h
index 91c084127b..60894a873f 100644
--- a/src/fread.h
+++ b/src/fread.h
@@ -30,7 +30,7 @@ typedef enum {
 
 extern int8_t typeSize[NUMTYPE];
 extern const char typeName[NUMTYPE][10];
-extern const long double pow10lookup[701];
+extern const long double pow10lookup[601];
 extern const uint8_t hexdigits[256];
 
 
diff --git a/src/freadLookups.h b/src/freadLookups.h
index faeb4ade54..bb736a60ac 100644
--- a/src/freadLookups.h
+++ b/src/freadLookups.h
@@ -27,57 +27,7 @@ const uint8_t hexdigits[256] = {
 };
 
 
-const long double pow10lookup[701] = {
-1.0E-350L,
-1.0E-349L,
-1.0E-348L,
-1.0E-347L,
-1.0E-346L,
-1.0E-345L,
-1.0E-344L,
-1.0E-343L,
-1.0E-342L,
-1.0E-341L,
-1.0E-340L,
-1.0E-339L,
-1.0E-338L,
-1.0E-337L,
-1.0E-336L,
-1.0E-335L,
-1.0E-334L,
-1.0E-333L,
-1.0E-332L,
-1.0E-331L,
-1.0E-330L,
-1.0E-329L,
-1.0E-328L,
-1.0E-327L,
-1.0E-326L,
-1.0E-325L,
-1.0E-324L,
-1.0E-323L,
-1.0E-322L,
-1.0E-321L,
-1.0E-320L,
-1.0E-319L,
-1.0E-318L,
-1.0E-317L,
-1.0E-316L,
-1.0E-315L,
-1.0E-314L,
-1.0E-313L,
-1.0E-312L,
-1.0E-311L,
-1.0E-310L,
-1.0E-309L,
-1.0E-308L,
-1.0E-307L,
-1.0E-306L,
-1.0E-305L,
-1.0E-304L,
-1.0E-303L,
-1.0E-302L,
-1.0E-301L,
+const long double pow10lookup[601] = {
 1.0E-300L,
 1.0E-299L,
 1.0E-298L,
@@ -678,57 +628,7 @@ const long double pow10lookup[701] = {
 1.0E297L,
 1.0E298L,
 1.0E299L,
-1.0E300L,
-1.0E301L,
-1.0E302L,
-1.0E303L,
-1.0E304L,
-1.0E305L,
-1.0E306L,
-1.0E307L,
-1.0E308L,
-1.0E309L,
-1.0E310L,
-1.0E311L,
-1.0E312L,
-1.0E313L,
-1.0E314L,
-1.0E315L,
-1.0E316L,
-1.0E317L,
-1.0E318L,
-1.0E319L,
-1.0E320L,
-1.0E321L,
-1.0E322L,
-1.0E323L,
-1.0E324L,
-1.0E325L,
-1.0E326L,
-1.0E327L,
-1.0E328L,
-1.0E329L,
-1.0E330L,
-1.0E331L,
-1.0E332L,
-1.0E333L,
-1.0E334L,
-1.0E335L,
-1.0E336L,
-1.0E337L,
-1.0E338L,
-1.0E339L,
-1.0E340L,
-1.0E341L,
-1.0E342L,
-1.0E343L,
-1.0E344L,
-1.0E345L,
-1.0E346L,
-1.0E347L,
-1.0E348L,
-1.0E349L,
-1.0E350L
+1.0E300L
 };
 
 #endif