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@@ -1,4 +1,3 @@
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-/* @(#)e_pow.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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@@ -10,10 +9,6 @@
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* ====================================================
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*/
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-#if defined(LIBM_SCCS) && !defined(lint)
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-static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
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-#endif
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-
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/* __ieee754_pow(x,y) return x**y
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*
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* n
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@@ -26,25 +21,26 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
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* 3. Return x**y = 2**n*exp(y'*log2)
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*
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* Special cases:
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- * 1. (anything) ** 0 is 1
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- * 2. (anything) ** 1 is itself
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- * 3. (anything) ** NAN is NAN
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- * 4. NAN ** (anything except 0) is NAN
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- * 5. +-(|x| > 1) ** +INF is +INF
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- * 6. +-(|x| > 1) ** -INF is +0
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- * 7. +-(|x| < 1) ** +INF is +0
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- * 8. +-(|x| < 1) ** -INF is +INF
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- * 9. +-1 ** +-INF is NAN
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- * 10. +0 ** (+anything except 0, NAN) is +0
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- * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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- * 12. +0 ** (-anything except 0, NAN) is +INF
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- * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
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- * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
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- * 15. +INF ** (+anything except 0,NAN) is +INF
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- * 16. +INF ** (-anything except 0,NAN) is +0
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- * 17. -INF ** (anything) = -0 ** (-anything)
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- * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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- * 19. (-anything except 0 and inf) ** (non-integer) is NAN
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+ * 1. +-1 ** anything is 1.0
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+ * 2. +-1 ** +-INF is 1.0
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+ * 3. (anything) ** 0 is 1
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+ * 4. (anything) ** 1 is itself
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+ * 5. (anything) ** NAN is NAN
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+ * 6. NAN ** (anything except 0) is NAN
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+ * 7. +-(|x| > 1) ** +INF is +INF
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+ * 8. +-(|x| > 1) ** -INF is +0
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+ * 9. +-(|x| < 1) ** +INF is +0
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+ * 10 +-(|x| < 1) ** -INF is +INF
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+ * 11. +0 ** (+anything except 0, NAN) is +0
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+ * 12. -0 ** (+anything except 0, NAN, odd integer) is +0
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+ * 13. +0 ** (-anything except 0, NAN) is +INF
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+ * 14. -0 ** (-anything except 0, NAN, odd integer) is +INF
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+ * 15. -0 ** (odd integer) = -( +0 ** (odd integer) )
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+ * 16. +INF ** (+anything except 0,NAN) is +INF
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+ * 17. +INF ** (-anything except 0,NAN) is +0
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+ * 18. -INF ** (anything) = -0 ** (-anything)
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+ * 19. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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+ * 20. (-anything except 0 and inf) ** (non-integer) is NAN
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*
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* Accuracy:
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* pow(x,y) returns x**y nearly rounded. In particular
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@@ -62,281 +58,281 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
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#include "math_libm.h"
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#include "math_private.h"
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-libm_hidden_proto(scalbn)
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- libm_hidden_proto(fabs)
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-#ifdef __STDC__
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- static const double
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-#else
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- static double
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-#endif
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- bp[] = { 1.0, 1.5, }, dp_h[] = {
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- 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
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+static const double
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+bp[] = {1.0, 1.5,},
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+dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
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+dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
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+zero = 0.0,
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+one = 1.0,
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+two = 2.0,
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+two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
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+huge = 1.0e300,
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+tiny = 1.0e-300,
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+ /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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+L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
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+L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
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+L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
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+L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
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+L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
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+L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
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+P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
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+P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
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+P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
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+P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
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+P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
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+lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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+lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
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+lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
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+ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
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+cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
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+cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
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+cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
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+ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
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+ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
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+ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
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- dp_l[] = {
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- 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
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+double attribute_hidden __ieee754_pow(double x, double y)
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+{
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+ double z,ax,z_h,z_l,p_h,p_l;
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+ double y1,t1,t2,r,s,t,u,v,w;
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+ int32_t i,j,k,yisint,n;
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+ int32_t hx,hy,ix,iy;
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+ u_int32_t lx,ly;
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- zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
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- huge_val = 1.0e300, tiny = 1.0e-300,
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- /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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- L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
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- L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
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- L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
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- L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
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- L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
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- L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
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- P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
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- P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
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- P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
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- P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
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- P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
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- lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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- lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
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- lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
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- ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
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- cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
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- cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
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- cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */
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- ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
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- ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */
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- ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */
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+ EXTRACT_WORDS(hx,lx,x);
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+ /* x==1: 1**y = 1 (even if y is NaN) */
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+ if (hx==0x3ff00000 && lx==0) {
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+ return x;
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+ }
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+ ix = hx&0x7fffffff;
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-#ifdef __STDC__
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- double attribute_hidden __ieee754_pow(double x, double y)
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-#else
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- double attribute_hidden __ieee754_pow(x, y)
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- double x, y;
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-#endif
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- {
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- double z, ax, z_h, z_l, p_h, p_l;
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- double y1, t1, t2, r, s, t, u, v, w;
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- int32_t i, j, k, yisint, n;
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- int32_t hx, hy, ix, iy;
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- u_int32_t lx, ly;
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+ EXTRACT_WORDS(hy,ly,y);
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+ iy = hy&0x7fffffff;
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- EXTRACT_WORDS(hx, lx, x);
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- EXTRACT_WORDS(hy, ly, y);
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- ix = hx & 0x7fffffff;
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- iy = hy & 0x7fffffff;
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+ /* y==zero: x**0 = 1 */
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+ if((iy|ly)==0) return one;
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- /* y==zero: x**0 = 1 */
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- if ((iy | ly) == 0)
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- return one;
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+ /* +-NaN return x+y */
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+ if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
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+ iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
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+ return x+y;
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- /* +-NaN return x+y */
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- if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
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- iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
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- return x + y;
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+ /* determine if y is an odd int when x < 0
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+ * yisint = 0 ... y is not an integer
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+ * yisint = 1 ... y is an odd int
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+ * yisint = 2 ... y is an even int
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+ */
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+ yisint = 0;
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+ if(hx<0) {
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+ if(iy>=0x43400000) yisint = 2; /* even integer y */
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+ else if(iy>=0x3ff00000) {
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+ k = (iy>>20)-0x3ff; /* exponent */
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+ if(k>20) {
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+ j = ly>>(52-k);
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+ if((j<<(52-k))==ly) yisint = 2-(j&1);
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+ } else if(ly==0) {
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+ j = iy>>(20-k);
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+ if((j<<(20-k))==iy) yisint = 2-(j&1);
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+ }
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+ }
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+ }
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- /* determine if y is an odd int when x < 0
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- * yisint = 0 ... y is not an integer
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- * yisint = 1 ... y is an odd int
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- * yisint = 2 ... y is an even int
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- */
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- yisint = 0;
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- if (hx < 0) {
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- if (iy >= 0x43400000)
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- yisint = 2; /* even integer y */
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- else if (iy >= 0x3ff00000) {
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- k = (iy >> 20) - 0x3ff; /* exponent */
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- if (k > 20) {
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- j = ly >> (52 - k);
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- if ((j << (52 - k)) == ly)
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- yisint = 2 - (j & 1);
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- } else if (ly == 0) {
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- j = iy >> (20 - k);
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- if ((j << (20 - k)) == iy)
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- yisint = 2 - (j & 1);
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- }
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- }
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- }
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+ /* special value of y */
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+ if(ly==0) {
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+ if (iy==0x7ff00000) { /* y is +-inf */
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+ if (((ix-0x3ff00000)|lx)==0)
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+ return one; /* +-1**+-inf is 1 (yes, weird rule) */
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+ if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
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+ return (hy>=0) ? y : zero;
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+ /* (|x|<1)**-,+inf = inf,0 */
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+ return (hy<0) ? -y : zero;
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+ }
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+ if(iy==0x3ff00000) { /* y is +-1 */
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+ if(hy<0) return one/x; else return x;
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+ }
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+ if(hy==0x40000000) return x*x; /* y is 2 */
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+ if(hy==0x3fe00000) { /* y is 0.5 */
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+ if(hx>=0) /* x >= +0 */
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+ return __ieee754_sqrt(x);
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+ }
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+ }
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- /* special value of y */
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- if (ly == 0) {
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- if (iy == 0x7ff00000) { /* y is +-inf */
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- if (((ix - 0x3ff00000) | lx) == 0)
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- return y - y; /* inf**+-1 is NaN */
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- else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
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- return (hy >= 0) ? y : zero;
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- else /* (|x|<1)**-,+inf = inf,0 */
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- return (hy < 0) ? -y : zero;
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- }
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- if (iy == 0x3ff00000) { /* y is +-1 */
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- if (hy < 0)
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- return one / x;
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- else
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- return x;
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- }
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- if (hy == 0x40000000)
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- return x * x; /* y is 2 */
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- if (hy == 0x3fe00000) { /* y is 0.5 */
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- if (hx >= 0) /* x >= +0 */
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- return __ieee754_sqrt(x);
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- }
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- }
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+ ax = fabs(x);
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+ /* special value of x */
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+ if(lx==0) {
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+ if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
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+ z = ax; /*x is +-0,+-inf,+-1*/
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+ if(hy<0) z = one/z; /* z = (1/|x|) */
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+ if(hx<0) {
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+ if(((ix-0x3ff00000)|yisint)==0) {
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+ z = (z-z)/(z-z); /* (-1)**non-int is NaN */
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+ } else if(yisint==1)
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+ z = -z; /* (x<0)**odd = -(|x|**odd) */
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+ }
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+ return z;
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+ }
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+ }
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- ax = fabs(x);
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- /* special value of x */
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- if (lx == 0) {
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- if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
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- z = ax; /* x is +-0,+-inf,+-1 */
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- if (hy < 0)
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- z = one / z; /* z = (1/|x|) */
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- if (hx < 0) {
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- if (((ix - 0x3ff00000) | yisint) == 0) {
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- z = (z - z) / (z - z); /* (-1)**non-int is NaN */
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- } else if (yisint == 1)
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- z = -z; /* (x<0)**odd = -(|x|**odd) */
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- }
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- return z;
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- }
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- }
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+ /* (x<0)**(non-int) is NaN */
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+ if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
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- /* (x<0)**(non-int) is NaN */
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|
- if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0)
|
|
|
- return (x - x) / (x - x);
|
|
|
+ /* |y| is huge */
|
|
|
+ if(iy>0x41e00000) { /* if |y| > 2**31 */
|
|
|
+ if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
|
|
|
+ if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
|
|
+ if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
|
|
+ }
|
|
|
+ /* over/underflow if x is not close to one */
|
|
|
+ if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
|
|
+ if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
|
|
+ /* now |1-x| is tiny <= 2**-20, suffice to compute
|
|
|
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
|
|
|
+ t = x-1; /* t has 20 trailing zeros */
|
|
|
+ w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
|
|
|
+ u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
|
|
|
+ v = t*ivln2_l-w*ivln2;
|
|
|
+ t1 = u+v;
|
|
|
+ SET_LOW_WORD(t1,0);
|
|
|
+ t2 = v-(t1-u);
|
|
|
+ } else {
|
|
|
+ double s2,s_h,s_l,t_h,t_l;
|
|
|
+ n = 0;
|
|
|
+ /* take care subnormal number */
|
|
|
+ if(ix<0x00100000)
|
|
|
+ {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
|
|
|
+ n += ((ix)>>20)-0x3ff;
|
|
|
+ j = ix&0x000fffff;
|
|
|
+ /* determine interval */
|
|
|
+ ix = j|0x3ff00000; /* normalize ix */
|
|
|
+ if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
|
|
|
+ else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
|
|
|
+ else {k=0;n+=1;ix -= 0x00100000;}
|
|
|
+ SET_HIGH_WORD(ax,ix);
|
|
|
|
|
|
- /* |y| is huge */
|
|
|
- if (iy > 0x41e00000) { /* if |y| > 2**31 */
|
|
|
- if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
|
|
|
- if (ix <= 0x3fefffff)
|
|
|
- return (hy < 0) ? huge_val * huge_val : tiny * tiny;
|
|
|
- if (ix >= 0x3ff00000)
|
|
|
- return (hy > 0) ? huge_val * huge_val : tiny * tiny;
|
|
|
- }
|
|
|
- /* over/underflow if x is not close to one */
|
|
|
- if (ix < 0x3fefffff)
|
|
|
- return (hy < 0) ? huge_val * huge_val : tiny * tiny;
|
|
|
- if (ix > 0x3ff00000)
|
|
|
- return (hy > 0) ? huge_val * huge_val : tiny * tiny;
|
|
|
- /* now |1-x| is tiny <= 2**-20, suffice to compute
|
|
|
- log(x) by x-x^2/2+x^3/3-x^4/4 */
|
|
|
- t = x - 1; /* t has 20 trailing zeros */
|
|
|
- w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
|
|
|
- u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
|
|
|
- v = t * ivln2_l - w * ivln2;
|
|
|
- t1 = u + v;
|
|
|
- SET_LOW_WORD(t1, 0);
|
|
|
- t2 = v - (t1 - u);
|
|
|
- } else {
|
|
|
- double s2, s_h, s_l, t_h, t_l;
|
|
|
- n = 0;
|
|
|
- /* take care subnormal number */
|
|
|
- if (ix < 0x00100000) {
|
|
|
- ax *= two53;
|
|
|
- n -= 53;
|
|
|
- GET_HIGH_WORD(ix, ax);
|
|
|
- }
|
|
|
- n += ((ix) >> 20) - 0x3ff;
|
|
|
- j = ix & 0x000fffff;
|
|
|
- /* determine interval */
|
|
|
- ix = j | 0x3ff00000; /* normalize ix */
|
|
|
- if (j <= 0x3988E)
|
|
|
- k = 0; /* |x|<sqrt(3/2) */
|
|
|
- else if (j < 0xBB67A)
|
|
|
- k = 1; /* |x|<sqrt(3) */
|
|
|
- else {
|
|
|
- k = 0;
|
|
|
- n += 1;
|
|
|
- ix -= 0x00100000;
|
|
|
- }
|
|
|
- SET_HIGH_WORD(ax, ix);
|
|
|
+ /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
|
|
+ u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
|
|
+ v = one/(ax+bp[k]);
|
|
|
+ s = u*v;
|
|
|
+ s_h = s;
|
|
|
+ SET_LOW_WORD(s_h,0);
|
|
|
+ /* t_h=ax+bp[k] High */
|
|
|
+ t_h = zero;
|
|
|
+ SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
|
|
|
+ t_l = ax - (t_h-bp[k]);
|
|
|
+ s_l = v*((u-s_h*t_h)-s_h*t_l);
|
|
|
+ /* compute log(ax) */
|
|
|
+ s2 = s*s;
|
|
|
+ r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
|
|
+ r += s_l*(s_h+s);
|
|
|
+ s2 = s_h*s_h;
|
|
|
+ t_h = 3.0+s2+r;
|
|
|
+ SET_LOW_WORD(t_h,0);
|
|
|
+ t_l = r-((t_h-3.0)-s2);
|
|
|
+ /* u+v = s*(1+...) */
|
|
|
+ u = s_h*t_h;
|
|
|
+ v = s_l*t_h+t_l*s;
|
|
|
+ /* 2/(3log2)*(s+...) */
|
|
|
+ p_h = u+v;
|
|
|
+ SET_LOW_WORD(p_h,0);
|
|
|
+ p_l = v-(p_h-u);
|
|
|
+ z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
|
|
+ z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
|
|
+ /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
|
|
+ t = (double)n;
|
|
|
+ t1 = (((z_h+z_l)+dp_h[k])+t);
|
|
|
+ SET_LOW_WORD(t1,0);
|
|
|
+ t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
|
|
+ }
|
|
|
|
|
|
- /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
|
|
- u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
|
|
- v = one / (ax + bp[k]);
|
|
|
- s = u * v;
|
|
|
- s_h = s;
|
|
|
- SET_LOW_WORD(s_h, 0);
|
|
|
- /* t_h=ax+bp[k] High */
|
|
|
- t_h = zero;
|
|
|
- SET_HIGH_WORD(t_h,
|
|
|
- ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
|
|
|
- t_l = ax - (t_h - bp[k]);
|
|
|
- s_l = v * ((u - s_h * t_h) - s_h * t_l);
|
|
|
- /* compute log(ax) */
|
|
|
- s2 = s * s;
|
|
|
- r = s2 * s2 * (L1 +
|
|
|
- s2 * (L2 +
|
|
|
- s2 * (L3 +
|
|
|
- s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
|
|
- r += s_l * (s_h + s);
|
|
|
- s2 = s_h * s_h;
|
|
|
- t_h = 3.0 + s2 + r;
|
|
|
- SET_LOW_WORD(t_h, 0);
|
|
|
- t_l = r - ((t_h - 3.0) - s2);
|
|
|
- /* u+v = s*(1+...) */
|
|
|
- u = s_h * t_h;
|
|
|
- v = s_l * t_h + t_l * s;
|
|
|
- /* 2/(3log2)*(s+...) */
|
|
|
- p_h = u + v;
|
|
|
- SET_LOW_WORD(p_h, 0);
|
|
|
- p_l = v - (p_h - u);
|
|
|
- z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
|
|
|
- z_l = cp_l * p_h + p_l * cp + dp_l[k];
|
|
|
- /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
|
|
- t = (double) n;
|
|
|
- t1 = (((z_h + z_l) + dp_h[k]) + t);
|
|
|
- SET_LOW_WORD(t1, 0);
|
|
|
- t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
|
|
|
- }
|
|
|
+ s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
|
|
+ if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
|
|
|
+ s = -one;/* (-ve)**(odd int) */
|
|
|
|
|
|
- s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
|
|
- if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
|
|
|
- s = -one; /* (-ve)**(odd int) */
|
|
|
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
|
|
+ y1 = y;
|
|
|
+ SET_LOW_WORD(y1,0);
|
|
|
+ p_l = (y-y1)*t1+y*t2;
|
|
|
+ p_h = y1*t1;
|
|
|
+ z = p_l+p_h;
|
|
|
+ EXTRACT_WORDS(j,i,z);
|
|
|
+ if (j>=0x40900000) { /* z >= 1024 */
|
|
|
+ if(((j-0x40900000)|i)!=0) /* if z > 1024 */
|
|
|
+ return s*huge*huge; /* overflow */
|
|
|
+ else {
|
|
|
+ if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
|
|
+ }
|
|
|
+ } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
|
|
|
+ if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
|
|
|
+ return s*tiny*tiny; /* underflow */
|
|
|
+ else {
|
|
|
+ if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
|
|
+ }
|
|
|
+ }
|
|
|
+ /*
|
|
|
+ * compute 2**(p_h+p_l)
|
|
|
+ */
|
|
|
+ i = j&0x7fffffff;
|
|
|
+ k = (i>>20)-0x3ff;
|
|
|
+ n = 0;
|
|
|
+ if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
|
|
+ n = j+(0x00100000>>(k+1));
|
|
|
+ k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
|
|
|
+ t = zero;
|
|
|
+ SET_HIGH_WORD(t,n&~(0x000fffff>>k));
|
|
|
+ n = ((n&0x000fffff)|0x00100000)>>(20-k);
|
|
|
+ if(j<0) n = -n;
|
|
|
+ p_h -= t;
|
|
|
+ }
|
|
|
+ t = p_l+p_h;
|
|
|
+ SET_LOW_WORD(t,0);
|
|
|
+ u = t*lg2_h;
|
|
|
+ v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
|
|
+ z = u+v;
|
|
|
+ w = v-(z-u);
|
|
|
+ t = z*z;
|
|
|
+ t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
|
|
+ r = (z*t1)/(t1-two)-(w+z*w);
|
|
|
+ z = one-(r-z);
|
|
|
+ GET_HIGH_WORD(j,z);
|
|
|
+ j += (n<<20);
|
|
|
+ if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
|
|
|
+ else SET_HIGH_WORD(z,j);
|
|
|
+ return s*z;
|
|
|
+}
|
|
|
|
|
|
- /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
|
|
- y1 = y;
|
|
|
- SET_LOW_WORD(y1, 0);
|
|
|
- p_l = (y - y1) * t1 + y * t2;
|
|
|
- p_h = y1 * t1;
|
|
|
- z = p_l + p_h;
|
|
|
- EXTRACT_WORDS(j, i, z);
|
|
|
- if (j >= 0x40900000) { /* z >= 1024 */
|
|
|
- if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
|
|
|
- return s * huge_val * huge_val; /* overflow */
|
|
|
- else {
|
|
|
- if (p_l + ovt > z - p_h)
|
|
|
- return s * huge_val * huge_val; /* overflow */
|
|
|
- }
|
|
|
- } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
|
|
|
- if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */
|
|
|
- return s * tiny * tiny; /* underflow */
|
|
|
- else {
|
|
|
- if (p_l <= z - p_h)
|
|
|
- return s * tiny * tiny; /* underflow */
|
|
|
- }
|
|
|
- }
|
|
|
- /*
|
|
|
- * compute 2**(p_h+p_l)
|
|
|
- */
|
|
|
- i = j & 0x7fffffff;
|
|
|
- k = (i >> 20) - 0x3ff;
|
|
|
- n = 0;
|
|
|
- if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
|
|
- n = j + (0x00100000 >> (k + 1));
|
|
|
- k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
|
|
|
- t = zero;
|
|
|
- SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
|
|
|
- n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
|
|
|
- if (j < 0)
|
|
|
- n = -n;
|
|
|
- p_h -= t;
|
|
|
- }
|
|
|
- t = p_l + p_h;
|
|
|
- SET_LOW_WORD(t, 0);
|
|
|
- u = t * lg2_h;
|
|
|
- v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
|
|
|
- z = u + v;
|
|
|
- w = v - (z - u);
|
|
|
- t = z * z;
|
|
|
- t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
|
|
- r = (z * t1) / (t1 - two) - (w + z * w);
|
|
|
- z = one - (r - z);
|
|
|
- GET_HIGH_WORD(j, z);
|
|
|
- j += (n << 20);
|
|
|
- if ((j >> 20) <= 0)
|
|
|
- z = scalbn(z, n); /* subnormal output */
|
|
|
- else
|
|
|
- SET_HIGH_WORD(z, j);
|
|
|
- return s * z;
|
|
|
- }
|
|
|
+/*
|
|
|
+ * wrapper pow(x,y) return x**y
|
|
|
+ */
|
|
|
+#ifndef _IEEE_LIBM
|
|
|
+double pow(double x, double y)
|
|
|
+{
|
|
|
+ double z = __ieee754_pow(x, y);
|
|
|
+ if (_LIB_VERSION == _IEEE_|| isnan(y))
|
|
|
+ return z;
|
|
|
+ if (isnan(x)) {
|
|
|
+ if (y == 0.0)
|
|
|
+ return __kernel_standard(x, y, 42); /* pow(NaN,0.0) */
|
|
|
+ return z;
|
|
|
+ }
|
|
|
+ if (x == 0.0) {
|
|
|
+ if (y == 0.0)
|
|
|
+ return __kernel_standard(x, y, 20); /* pow(0.0,0.0) */
|
|
|
+ if (isfinite(y) && y < 0.0)
|
|
|
+ return __kernel_standard(x,y,23); /* pow(0.0,negative) */
|
|
|
+ return z;
|
|
|
+ }
|
|
|
+ if (!isfinite(z)) {
|
|
|
+ if (isfinite(x) && isfinite(y)) {
|
|
|
+ if (isnan(z))
|
|
|
+ return __kernel_standard(x, y, 24); /* pow neg**non-int */
|
|
|
+ return __kernel_standard(x, y, 21); /* pow overflow */
|
|
|
+ }
|
|
|
+ }
|
|
|
+ if (z == 0.0 && isfinite(x) && isfinite(y))
|
|
|
+ return __kernel_standard(x, y, 22); /* pow underflow */
|
|
|
+ return z;
|
|
|
+}
|
|
|
+#else
|
|
|
+strong_alias(__ieee754_pow, pow)
|
|
|
+#endif
|
|
|
+libm_hidden_def(pow)
|