diff --git a/lib/msun/src/e_rem_pio2.c b/lib/msun/src/e_rem_pio2.c
index 96fc5c48361e..faf3a4659086 100644
--- a/lib/msun/src/e_rem_pio2.c
+++ b/lib/msun/src/e_rem_pio2.c
@@ -182,7 +182,7 @@ __ieee754_rem_pio2(double x, double *y)
 	tx[2] = z;
 	nx = 3;
 	while(tx[nx-1]==zero) nx--;	/* skip zero term */
-	n  =  __kernel_rem_pio2(tx,y,e0,nx,2);
+	n  =  __kernel_rem_pio2(tx,y,e0,nx,1);
 	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 	return n;
 }
diff --git a/lib/msun/src/e_rem_pio2f.c b/lib/msun/src/e_rem_pio2f.c
index 60f8256eed42..2cc466964d93 100644
--- a/lib/msun/src/e_rem_pio2f.c
+++ b/lib/msun/src/e_rem_pio2f.c
@@ -45,7 +45,7 @@ int
 __ieee754_rem_pio2f(float x, float *y)
 {
 	double w,r,fn;
-	double tx[1],ty[2];
+	double tx[1],ty[1];
 	float z;
 	int32_t e0,n,ix,hx;
 
@@ -77,7 +77,7 @@ __ieee754_rem_pio2f(float x, float *y)
 	e0 = (ix>>23)-150;		/* e0 = ilogb(|x|)-23; */
 	SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
 	tx[0] = z;
-	n  =  __kernel_rem_pio2(tx,ty,e0,1,1);
+	n  =  __kernel_rem_pio2(tx,ty,e0,1,0);
 	y[0] = ty[0];
 	y[1] = ty[0] - y[0];
 	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
diff --git a/lib/msun/src/k_rem_pio2.c b/lib/msun/src/k_rem_pio2.c
index 8abe6f8eadab..a2ffca60767a 100644
--- a/lib/msun/src/k_rem_pio2.c
+++ b/lib/msun/src/k_rem_pio2.c
@@ -78,8 +78,13 @@ __FBSDID("$FreeBSD$");
  * Here is the description of some local variables:
  *
  * 	jk	jk+1 is the initial number of terms of ipio2[] needed
- *		in the computation. The recommended value is 2,3,4,
- *		6 for single, double, extended,and quad.
+ *		in the computation. The minimum and recommended value
+ *		for jk is 3,4,4,6 for single, double, extended, and quad.
+ *		jk+1 must be 2 larger than you might expect so that our
+ *		recomputation test works. (Up to 24 bits in the integer
+ *		part (the 24 bits of it that we compute) and 23 bits in
+ *		the fraction part may be lost to cancelation before we
+ *		recompute.)
  *
  * 	jz	local integer variable indicating the number of 
  *		terms of ipio2[] used. 
@@ -129,7 +134,7 @@ __FBSDID("$FreeBSD$");
 #include "math.h"
 #include "math_private.h"
 
-static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
+static const int init_jk[] = {3,4,4,6}; /* initial value for jk */
 
 /*
  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi