Update.

1998-04-03 23:38  Ulrich Drepper  <drepper@cygnus.com>

	* sysdeps/libm-ieee754/e_acos.c: Optimize by splitting large
	expressions and using array variables.
	* sysdeps/libm-ieee754/e_asin.c: Likewise.
	* sysdeps/libm-ieee754/e_j0.c: Likewise.
	* sysdeps/libm-ieee754/e_j1.c: Likewise.
	* sysdeps/libm-ieee754/e_log.c: Likewise.
	* sysdeps/libm-ieee754/e_pow.c: Likewise.
	* sysdeps/libm-ieee754/k_cos.c: Likewise.
	* sysdeps/libm-ieee754/k_sin.c: Likewise.
	* sysdeps/libm-ieee754/k_tan.c: Likewise.
	* sysdeps/libm-ieee754/s_atan.c: Likewise.
	* sysdeps/libm-ieee754/s_erf.c: Likewise.
	* sysdeps/libm-ieee754/s_expm1.c: Likewise.
	* sysdeps/libm-ieee754/s_log1p.c: Likewise.
	Patch by Naohiko Shimizu <nshimizu@et.u-tokai.ac.jp>.

1 files changed, 160 insertions, 53 deletions

diff --git a/sysdeps/libm-ieee754/s_erf.c b/sysdeps/libm-ieee754/s_erf.c
index f64f0fcefd..d8b6629a72 100644
--- a/sysdeps/libm-ieee754/s_erf.c
+++ b/sysdeps/libm-ieee754/s_erf.c
@@ -9,6 +9,9 @@
  * is preserved.
  * ====================================================
  */
+/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
+   for performance improvement on pipelined processors.
+*/
 
 #if defined(LIBM_SCCS) && !defined(lint)
 static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $";
@@ -128,68 +131,68 @@ erx =  8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
  */
 efx =  1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
 efx8=  1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
-pp0  =  1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
-pp1  = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
-pp2  = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
-pp3  = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
-pp4  = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
-qq1  =  3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
-qq2  =  6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
-qq3  =  5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
-qq4  =  1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
-qq5  = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
+pp[]  =  {1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
+ -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
+ -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
+ -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
+ -2.37630166566501626084e-05}, /* 0xBEF8EAD6, 0x120016AC */
+qq[]  =  {0.0, 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
+  6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
+  5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
+  1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
+ -3.96022827877536812320e-06}, /* 0xBED09C43, 0x42A26120 */
 /*
  * Coefficients for approximation to  erf  in [0.84375,1.25]
  */
-pa0  = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
-pa1  =  4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
-pa2  = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
-pa3  =  3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
-pa4  = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
-pa5  =  3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
-pa6  = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
-qa1  =  1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
-qa2  =  5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
-qa3  =  7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
-qa4  =  1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
-qa5  =  1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
-qa6  =  1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
+pa[]  = {-2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
+  4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
+ -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
+  3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
+ -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
+  3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
+ -2.16637559486879084300e-03}, /* 0xBF61BF38, 0x0A96073F */
+qa[]  =  {0.0, 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
+  5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
+  7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
+  1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
+  1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
+  1.19844998467991074170e-02}, /* 0x3F888B54, 0x5735151D */
 /*
  * Coefficients for approximation to  erfc in [1.25,1/0.35]
  */
-ra0  = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
-ra1  = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
-ra2  = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
-ra3  = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
-ra4  = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
-ra5  = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
-ra6  = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
-ra7  = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
-sa1  =  1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
-sa2  =  1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
-sa3  =  4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
-sa4  =  6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
-sa5  =  4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
-sa6  =  1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
-sa7  =  6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
-sa8  = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
+ra[]  = {-9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
+ -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
+ -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
+ -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
+ -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
+ -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
+ -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
+ -9.81432934416914548592e+00}, /* 0xC023A0EF, 0xC69AC25C */
+sa[]  =  {0.0,1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
+  1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
+  4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
+  6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
+  4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
+  1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
+  6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
+ -6.04244152148580987438e-02}, /* 0xBFAEEFF2, 0xEE749A62 */
 /*
  * Coefficients for approximation to  erfc in [1/.35,28]
  */
-rb0  = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
-rb1  = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
-rb2  = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
-rb3  = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
-rb4  = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
-rb5  = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
-rb6  = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
-sb1  =  3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
-sb2  =  3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
-sb3  =  1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
-sb4  =  3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
-sb5  =  2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
-sb6  =  4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
-sb7  = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
+rb[]  = {-9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
+ -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
+ -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
+ -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
+ -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
+ -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
+ -4.83519191608651397019e+02}, /* 0xC07E384E, 0x9BDC383F */
+sb[]  =  {0.0,3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
+  3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
+  1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
+  3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
+  2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
+  4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
+ -2.24409524465858183362e+01}; /* 0xC03670E2, 0x42712D62 */
 
 #ifdef __STDC__
 	double __erf(double x)
@@ -208,21 +211,46 @@ sb7  = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
 	}
 
 	if(ix < 0x3feb0000) {		/* |x|<0.84375 */
+	    double r1,r2,s1,s2,s3,z2,z4;
 	    if(ix < 0x3e300000) { 	/* |x|<2**-28 */
 	        if (ix < 0x00800000)
 		    return 0.125*(8.0*x+efx8*x);  /*avoid underflow */
 		return x + efx*x;
 	    }
 	    z = x*x;
+#ifdef DO_NOT_USE_THIS
 	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+#else
+	    r1 = pp[0]+z*pp[1]; z2=z*z;
+	    r2 = pp[2]+z*pp[3]; z4=z2*z2;
+	    s1 = one+z*qq[1];
+	    s2 = qq[2]+z*qq[3];
+	    s3 = qq[4]+z*qq[5];
+            r = r1 + z2*r2 + z4*pp[4];
+	    s  = s1 + z2*s2 + z4*s3;
+#endif
 	    y = r/s;
 	    return x + x*y;
 	}
 	if(ix < 0x3ff40000) {		/* 0.84375 <= |x| < 1.25 */
+	    double s2,s4,s6,P1,P2,P3,P4,Q1,Q2,Q3,Q4;
 	    s = fabs(x)-one;
+#ifdef DO_NOT_USE_THIS
 	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
+#else
+	    P1 = pa[0]+s*pa[1]; s2=s*s;
+	    Q1 = one+s*qa[1];   s4=s2*s2;
+	    P2 = pa[2]+s*pa[3]; s6=s4*s2;
+	    Q2 = qa[2]+s*qa[3];
+	    P3 = pa[4]+s*pa[5];
+	    Q3 = qa[4]+s*qa[5];
+	    P4 = s6*pa[6];
+	    Q4 = s6*qa[6];
+	    P = P1 + s2*P2 + s4*P3 + s6*P4;
+	    Q = Q1 + s2*Q2 + s4*Q3 + s6*Q4;
+#endif
 	    if(hx>=0) return erx + P/Q; else return -erx - P/Q;
 	}
 	if (ix >= 0x40180000) {		/* inf>|x|>=6 */
@@ -231,15 +259,42 @@ sb7  = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
 	x = fabs(x);
  	s = one/(x*x);
 	if(ix< 0x4006DB6E) {	/* |x| < 1/0.35 */
+#ifdef DO_NOT_USE_THIS
 	    R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 				ra5+s*(ra6+s*ra7))))));
 	    S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 				sa5+s*(sa6+s*(sa7+s*sa8)))))));
+#else
+	    double R1,R2,R3,R4,S1,S2,S3,S4,s2,s4,s6,s8;
+	    R1 = ra[0]+s*ra[1];s2 = s*s;
+	    S1 = one+s*sa[1];  s4 = s2*s2;
+	    R2 = ra[2]+s*ra[3];s6 = s4*s2;
+	    S2 = sa[2]+s*sa[3];s8 = s4*s4;
+	    R3 = ra[4]+s*ra[5];
+	    S3 = sa[4]+s*sa[5];
+	    R4 = ra[6]+s*ra[7];
+	    S4 = sa[6]+s*sa[7];
+	    R = R1 + s2*R2 + s4*R3 + s6*R4;
+	    S = S1 + s2*S2 + s4*S3 + s6*S4 + s8*sa[8];
+#endif
 	} else {	/* |x| >= 1/0.35 */
+#ifdef DO_NOT_USE_THIS
 	    R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 				rb5+s*rb6)))));
 	    S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 				sb5+s*(sb6+s*sb7))))));
+#else
+	    double R1,R2,R3,S1,S2,S3,S4,s2,s4,s6;
+	    R1 = rb[0]+s*rb[1];s2 = s*s;
+	    S1 = one+s*sb[1];  s4 = s2*s2;
+	    R2 = rb[2]+s*rb[3];s6 = s4*s2;
+	    S2 = sb[2]+s*sb[3];
+	    R3 = rb[4]+s*rb[5];
+	    S3 = sb[4]+s*sb[5];
+	    S4 = sb[6]+s*sb[7];
+	    R = R1 + s2*R2 + s4*R3 + s6*rb[6];
+	    S = S1 + s2*S2 + s4*S3 + s6*S4;
+#endif
 	}
 	z  = x;
 	SET_LOW_WORD(z,0);
@@ -269,11 +324,22 @@ weak_alias (__erf, erfl)
 	}
 
 	if(ix < 0x3feb0000) {		/* |x|<0.84375 */
+	    double r1,r2,s1,s2,s3,z2,z4;
 	    if(ix < 0x3c700000)  	/* |x|<2**-56 */
 		return one-x;
 	    z = x*x;
+#ifdef DO_NOT_USE_THIS
 	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
 	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
+#else
+	    r1 = pp[0]+z*pp[1]; z2=z*z;
+	    r2 = pp[2]+z*pp[3]; z4=z2*z2;
+	    s1 = one+z*qq[1];
+	    s2 = qq[2]+z*qq[3];
+	    s3 = qq[4]+z*qq[5];
+            r = r1 + z2*r2 + z4*pp[4];
+	    s  = s1 + z2*s2 + z4*s3;
+#endif
 	    y = r/s;
 	    if(hx < 0x3fd00000) {  	/* x<1/4 */
 		return one-(x+x*y);
@@ -284,9 +350,23 @@ weak_alias (__erf, erfl)
 	    }
 	}
 	if(ix < 0x3ff40000) {		/* 0.84375 <= |x| < 1.25 */
+	    double s2,s4,s6,P1,P2,P3,P4,Q1,Q2,Q3,Q4;
 	    s = fabs(x)-one;
+#ifdef DO_NOT_USE_THIS
 	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
 	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
+#else
+	    P1 = pa[0]+s*pa[1]; s2=s*s;
+	    Q1 = one+s*qa[1];   s4=s2*s2;
+	    P2 = pa[2]+s*pa[3]; s6=s4*s2;
+	    Q2 = qa[2]+s*qa[3];
+	    P3 = pa[4]+s*pa[5];
+	    Q3 = qa[4]+s*qa[5];
+	    P4 = s6*pa[6];
+	    Q4 = s6*qa[6];
+	    P = P1 + s2*P2 + s4*P3 + s6*P4;
+	    Q = Q1 + s2*Q2 + s4*Q3 + s6*Q4;
+#endif
 	    if(hx>=0) {
 	        z  = one-erx; return z - P/Q;
 	    } else {
@@ -297,16 +377,43 @@ weak_alias (__erf, erfl)
 	    x = fabs(x);
  	    s = one/(x*x);
 	    if(ix< 0x4006DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
+#ifdef DO_NOT_USE_THIS
 	        R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
 				ra5+s*(ra6+s*ra7))))));
 	        S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
 				sa5+s*(sa6+s*(sa7+s*sa8)))))));
+#else
+		double R1,R2,R3,R4,S1,S2,S3,S4,s2,s4,s6,s8;
+	    R1 = ra[0]+s*ra[1];s2 = s*s;
+	    S1 = one+s*sa[1];  s4 = s2*s2;
+	    R2 = ra[2]+s*ra[3];s6 = s4*s2;
+	    S2 = sa[2]+s*sa[3];s8 = s4*s4;
+	    R3 = ra[4]+s*ra[5];
+	    S3 = sa[4]+s*sa[5];
+	    R4 = ra[6]+s*ra[7];
+	    S4 = sa[6]+s*sa[7];
+	    R = R1 + s2*R2 + s4*R3 + s6*R4;
+	    S = S1 + s2*S2 + s4*S3 + s6*S4 + s8*sa[8];
+#endif
 	    } else {			/* |x| >= 1/.35 ~ 2.857143 */
+		double R1,R2,R3,S1,S2,S3,S4,s2,s4,s6;
 		if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
+#ifdef DO_NOT_USE_THIS
 	        R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
 				rb5+s*rb6)))));
 	        S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
 				sb5+s*(sb6+s*sb7))))));
+#else
+		R1 = rb[0]+s*rb[1];s2 = s*s;
+		S1 = one+s*sb[1];  s4 = s2*s2;
+		R2 = rb[2]+s*rb[3];s6 = s4*s2;
+		S2 = sb[2]+s*sb[3];
+		R3 = rb[4]+s*rb[5];
+		S3 = sb[4]+s*sb[5];
+		S4 = sb[6]+s*sb[7];
+		R = R1 + s2*R2 + s4*R3 + s6*rb[6];
+		S = S1 + s2*S2 + s4*S3 + s6*S4;
+#endif
 	    }
 	    z  = x;
 	    SET_LOW_WORD(z,0);