Submitted by: J.T. Conklin <jtc@wimsey.com>

Second part of update to fdlibm 5.2: speed up argument reduction for trig
functions in the case pi/4 < |x| < 3pi/4.

Remove unused static constants ("one").

6 files changed, 56 insertions, 10 deletions

diff --git a/lib/msun/src/e_log10.c b/lib/msun/src/e_log10.c
index 3e27b1c..69a2356 100644
--- a/lib/msun/src/e_log10.c
+++ b/lib/msun/src/e_log10.c
@@ -11,7 +11,7 @@
  */
 
 #ifndef lint
-static char rcsid[] = "$Id: e_log10.c,v 1.6 1994/08/18 23:05:44 jtc Exp $";
+static char rcsid[] = "$Id: e_log10.c,v 1.1.1.1 1994/08/19 09:39:44 jkh Exp $";
 #endif
 
 /* __ieee754_log10(x)
@@ -55,7 +55,6 @@ static const double
 #else
 static double
 #endif
-one	  = 1.0,
 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
diff --git a/lib/msun/src/e_log10f.c b/lib/msun/src/e_log10f.c
index 9ac22b5..d493ad8 100644
--- a/lib/msun/src/e_log10f.c
+++ b/lib/msun/src/e_log10f.c
@@ -14,7 +14,7 @@
  */
 
 #ifndef lint
-static char rcsid[] = "$Id: e_log10f.c,v 1.2 1994/08/18 23:05:46 jtc Exp $";
+static char rcsid[] = "$Id: e_log10f.c,v 1.1.1.1 1994/08/19 09:39:56 jkh Exp $";
 #endif
 
 #include "math.h"
@@ -25,7 +25,6 @@ static const float
 #else
 static float
 #endif
-one	  = 1.0,
 two25      =  3.3554432000e+07, /* 0x4c000000 */
 ivln10     =  4.3429449201e-01, /* 0x3ede5bd9 */
 log10_2hi  =  3.0102920532e-01, /* 0x3e9a2080 */
diff --git a/lib/msun/src/e_rem_pio2.c b/lib/msun/src/e_rem_pio2.c
index bf8bfe1..be7cd50 100644
--- a/lib/msun/src/e_rem_pio2.c
+++ b/lib/msun/src/e_rem_pio2.c
@@ -11,7 +11,7 @@
  */
 
 #ifndef lint
-static char rcsid[] = "$Id: e_rem_pio2.c,v 1.5 1994/08/18 23:05:56 jtc Exp $";
+static char rcsid[] = "$Id: e_rem_pio2.c,v 1.1.1.1 1994/08/19 09:39:44 jkh Exp $";
 #endif
 
 /* __ieee754_rem_pio2(x,y)
@@ -99,6 +99,31 @@ pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
 	ix = hx&0x7fffffff;
 	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
 	    {y[0] = x; y[1] = 0; return 0;}
+	if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
+	    if(hx>0) { 
+		z = x - pio2_1;
+		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
+		    y[0] = z - pio2_1t;
+		    y[1] = (z-y[0])-pio2_1t;
+		} else {		/* near pi/2, use 33+33+53 bit pi */
+		    z -= pio2_2;
+		    y[0] = z - pio2_2t;
+		    y[1] = (z-y[0])-pio2_2t;
+		}
+		return 1;
+	    } else {	/* negative x */
+		z = x + pio2_1;
+		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
+		    y[0] = z + pio2_1t;
+		    y[1] = (z-y[0])+pio2_1t;
+		} else {		/* near pi/2, use 33+33+53 bit pi */
+		    z += pio2_2;
+		    y[0] = z + pio2_2t;
+		    y[1] = (z-y[0])+pio2_2t;
+		}
+		return -1;
+	    }
+	}
 	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
 	    t  = fabs(x);
 	    n  = (int32_t) (t*invpio2+half);
diff --git a/lib/msun/src/e_rem_pio2f.c b/lib/msun/src/e_rem_pio2f.c
index eae6473..153a8c4 100644
--- a/lib/msun/src/e_rem_pio2f.c
+++ b/lib/msun/src/e_rem_pio2f.c
@@ -14,7 +14,7 @@
  */
 
 #ifndef lint
-static char rcsid[] = "$Id: e_rem_pio2f.c,v 1.2 1994/08/18 23:05:58 jtc Exp $";
+static char rcsid[] = "$Id: e_rem_pio2f.c,v 1.1.1.1 1994/08/19 09:39:57 jkh Exp $";
 #endif
 
 /* __ieee754_rem_pio2f(x,y)
@@ -114,6 +114,31 @@ pio2_3t =  6.1232342629e-17; /* 0x248d3132 */
 	ix = hx&0x7fffffff;
 	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
 	    {y[0] = x; y[1] = 0; return 0;}
+	if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */
+	    if(hx>0) { 
+		z = x - pio2_1;
+		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
+		    y[0] = z - pio2_1t;
+		    y[1] = (z-y[0])-pio2_1t;
+		} else {		/* near pi/2, use 24+24+24 bit pi */
+		    z -= pio2_2;
+		    y[0] = z - pio2_2t;
+		    y[1] = (z-y[0])-pio2_2t;
+		}
+		return 1;
+	    } else {	/* negative x */
+		z = x + pio2_1;
+		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
+		    y[0] = z + pio2_1t;
+		    y[1] = (z-y[0])+pio2_1t;
+		} else {		/* near pi/2, use 24+24+24 bit pi */
+		    z += pio2_2;
+		    y[0] = z + pio2_2t;
+		    y[1] = (z-y[0])+pio2_2t;
+		}
+		return -1;
+	    }
+	}
 	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
 	    t  = fabsf(x);
 	    n  = (int32_t) (t*invpio2+half);
diff --git a/lib/msun/src/s_frexp.c b/lib/msun/src/s_frexp.c
index 6bbec50..00d344f 100644
--- a/lib/msun/src/s_frexp.c
+++ b/lib/msun/src/s_frexp.c
@@ -11,7 +11,7 @@
  */
 
 #ifndef lint
-static char rcsid[] = "$Id: s_frexp.c,v 1.6 1994/08/18 23:06:49 jtc Exp $";
+static char rcsid[] = "$Id: s_frexp.c,v 1.1.1.1 1994/08/19 09:39:51 jkh Exp $";
 #endif
 
 /*
@@ -32,7 +32,6 @@ static const double
 #else
 static double
 #endif
-one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
 two54 =  1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
 
 #ifdef __STDC__
diff --git a/lib/msun/src/s_frexpf.c b/lib/msun/src/s_frexpf.c
index 6e341fd..6988cbe 100644
--- a/lib/msun/src/s_frexpf.c
+++ b/lib/msun/src/s_frexpf.c
@@ -14,7 +14,7 @@
  */
 
 #ifndef lint
-static char rcsid[] = "$Id: s_frexpf.c,v 1.2 1994/08/18 23:06:51 jtc Exp $";
+static char rcsid[] = "$Id: s_frexpf.c,v 1.1.1.1 1994/08/19 09:39:58 jkh Exp $";
 #endif
 
 #include "math.h"
@@ -25,7 +25,6 @@ static const float
 #else
 static float
 #endif
-one   =  1.0000000000e+00, /* 0x3F800000 */
 two25 =  3.3554432000e+07; /* 0x4c000000 */
 
 #ifdef __STDC__