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authorBrian Jones <cbj@gnu.org>2001-11-05 02:56:46 +0000
committerBrian Jones <cbj@gnu.org>2001-11-05 02:56:46 +0000
commit936e6f9bd41e192e1ede500ef5aa26dd2a276ec0 (patch)
tree0c60a4db8f04045d08eb13e41dc8618931b68331 /native/fdlibm/e_exp.c
parentcd15a52840b278df0d1171d691cac036db373d28 (diff)
downloadclasspath-936e6f9bd41e192e1ede500ef5aa26dd2a276ec0.tar.gz
* native/jni/awt: renamed native/jni/gtk-peer
* native/jni/javaio.h: moved to native/jni/java-io * native/jni/javaio.c: moved to native/jni/java-io * native/jni/java_io_File.c: moved to native/jni/java-io * native/jni/java_io_FileDescriptor.c: moved to native/jni/java-io * native/jni/java_io_FileInputStream.c: moved to native/jni/java-io * native/jni/java_io_FileOutputStream.c: moved to native/jni/java-io * native/jni/java_io_ObjectInputStream.c: moved to native/jni/java-io * native/jni/java_io_ObjectOutputStream.c: moved to native/jni/java-io * native/jni/java_io_RandomAccessFile.c: moved to native/jni/java-io * native/jni/javalang.h: moved to native/jni/java-lang * native/jni/javalang.c: moved to native/jni/java-lang * native/jni/java_lang_Double.c: moved to native/jni/java-lang * native/jni/java_lang_Float.c: moved to native/jni/java-lang * native/jni/java_lang_Object.c: moved to native/jni/java-lang * native/jni/java_lang_System.c: moved to native/jni/java-lang * native/jni/java_lang_reflect_Array.c: moved to native/jni/java-lang * native/jni/javanet.h: moved to native/jni/java-net * native/jni/javanet.c: moved to native/jni/java-net * native/jni/java_net_InetAddress.c: moved to native/jni/java-net * native/jni/java_net_PlainDatagramSocketImpl.c: moved to native/jni/java-net * native/jni/java_net_PlainSocketImpl.c: moved to native/jni/java-net * native/jni/java_util_ResourceBundle.c: moved to native/jni/java-util * native/jni/java_util_TimeZone.c: moved to native/jni/java-util * native/jni/ieeefp.h: moved to native/jni/mprec * native/jni/java-assert.h: moved to native/jni/mprec * native/jni/mprec.c: moved to native/jni/mprec * native/jni/mprec.h: moved to native/jni/mprec * native/jni/acos.c: removed * native/jni/asin.c: removed * native/jni/atan2.c: removed * native/jni/atan.c: removed * native/jni/ceil.c: removed * native/jni/cos.c: removed * native/jni/dtoa.c: removed * native/jni/e_fmod.c: removed * native/jni/exp.c: removed * native/jni/floor.c: removed * native/jni/jcl.c: removed * native/jni/jcl.h: removed * native/jni/k_cos.c: removed * native/jni/k_rem_pio2.c: removed * native/jni/k_sin.c: removed * native/jni/k_tan.c: removed * native/jni/log.c: removed * native/jni/pow.c: removed * native/jni/remainder.c: removed * native/jni/rint.c: removed * native/jni/s_fabs.c: removed * native/jni/sin.c: removed * native/jni/sqrt.c: removed * native/jni/tan.c: removed * native/jni/fdlibm.h: removed * native/jni/java_math_BigInteger.c: no longer needed * native/fdlibm/dtoa.c: added from gcj to sync sources * native/fdlibm/e_acos.c: added from gcj to sync sources * native/fdlibm/e_asin.c: added from gcj to sync sources * native/fdlibm/e_atan2.c: added from gcj to sync sources * native/fdlibm/e_exp.c: added from gcj to sync sources * native/fdlibm/e_fmod.c: added from gcj to sync sources * native/fdlibm/e_log.c: added from gcj to sync sources * native/fdlibm/e_pow.c: added from gcj to sync sources * native/fdlibm/e_remainder.c: added from gcj to sync sources * native/fdlibm/e_rem_pio2.c: added from gcj to sync sources * native/fdlibm/e_scalb.c: added from gcj to sync sources * native/fdlibm/e_sqrt.c: added from gcj to sync sources * native/fdlibm/fdlibm.h: added from gcj to sync sources * native/fdlibm/ieeefp.h: added from gcj to sync sources * native/fdlibm/java-assert.h: added from gcj to sync sources * native/fdlibm/k_cos.c: added from gcj to sync sources * native/fdlibm/k_rem_pio2.c: added from gcj to sync sources * native/fdlibm/k_sin.c: added from gcj to sync sources * native/fdlibm/k_tan.c: added from gcj to sync sources * native/fdlibm/mprec.c: added from gcj to sync sources * native/fdlibm/mprec.h: added from gcj to sync sources * native/fdlibm/s_atan.c: added from gcj to sync sources * native/fdlibm/s_ceil.c: added from gcj to sync sources * native/fdlibm/s_copysign.c: added from gcj to sync sources * native/fdlibm/s_cos.c: added from gcj to sync sources * native/fdlibm/s_fabs.c: added from gcj to sync sources * native/fdlibm/sf_fabs.c: added from gcj to sync sources * native/fdlibm/s_floor.c: added from gcj to sync sources * native/fdlibm/sf_rint.c: added from gcj to sync sources * native/fdlibm/s_rint.c: added from gcj to sync sources * native/fdlibm/s_scalbn.c: added from gcj to sync sources * native/fdlibm/s_sin.c: added from gcj to sync sources * native/fdlibm/s_tan.c: added from gcj to sync sources * native/fdlibm/strtod.c: added from gcj to sync sources * native/fdlibm/w_acos.c: added from gcj to sync sources * native/fdlibm/w_asin.c: added from gcj to sync sources * native/fdlibm/w_atan2.c: added from gcj to sync sources * native/fdlibm/w_exp.c: added from gcj to sync sources * native/fdlibm/w_fmod.c: added from gcj to sync sources * native/fdlibm/w_log.c: added from gcj to sync sources * native/fdlibm/w_pow.c: added from gcj to sync sources * native/fdlibm/w_remainder.c: added from gcj to sync sources * native/fdlibm/w_sqrt.c: added from gcj to sync sources * native/fdlibm/.cvsignore: new file * native/jni/gtk-peer/Makefile.am: added -module to LDFLAGS * native/jni/java-io/Makefile.am: added -module to LDFLAGS * native/jni/java-io/.cvsignore: new file * native/jni/java-lang/Makefile.am: added -module to LDFLAGS * native/jni/java-lang/.cvsignore: new file * native/jni/java-net/Makefile.am: added -module to LDFLAGS * native/jni/java-net/.cvsignore: new file * native/jni/java-util/Makefile.am: added -module to LDFLAGS * native/jni/java-util/.cvsignore: new file * native/fdlibm/Makefile.am: added -module to LDFLAGS * native/jni/Makefile.am: removed rules, SUBDIRS equals java-io, java-lang, java-net, java-util, gtk-peer * native/Makefile.am: prepended fdlibm to SUBDIRS * java/lang/Math.java static(): load libjavalang.so instead of libjavalangmath.so * java/math/BigInteger.java: replaced our native version with pure Java implementation from gcj * gnu/classpath/math: new directory * gnu/classpath/math/MPN.java: new file from gcj, which came from Kawa, and is included with permission from Per Bothner, the author. * README: updated with current information about CVS and the project * THANKYOU: added Per Bothner * TODO: updated with current information as I know it * NEWS: updated with information about a 0.03 release * HACKING: updated with new information * INSTALL: updated with new information * BUGS: added link to Savannah bug reporting page for the project * ltconfig: removed due to upgrade of libtool to 1.4.2 * ltmain.sh: updated with libtool 1.4.2 * depcomp: new file from automake 1.5 upgrade * configure.in: added to OUTPUT native/fdlibm/Makefile, native/jni/java-io/Makefile, native/jni/java-lang/Makefile, native/jni/java-net/Makefile, native/jni/java-util/Makefile, native/jni/gtk-peer/Makefile * install.sh: updated * missing: updated * mkinstalldirs: updated * native/lib/Makefile.am: INCLUDES += changed to just INCLUDES = to avoid automake warning * native/lib/jcl.h: removed TRUE/FALSE #defines, added DBG * native/nsa/: removed, files native_state.* moved to native/lib * native/lib: renamed native/jni/classpath * native/cni/Makefile.am: new file * native/cni/.cvsignore: new file * native/jni/gtk-peer/Makefile.am: LIBADD used to get native_state from a common location * native/jni/java-io/Makefile.am: LIBADD used to get jcl from a common location, source modified to use relevant JCL_* functions * native/jni/java-lang/Makefile.am: LIBADD used to get jcl from a common location * native/jni/java-net/Makefile.am: LIBADD used to get jcl from a common location, source modified to use relevant JCL_* functions * vm/reference/java/lang/Thread.java (Thread): wrongly marked private constructor Thread (ThreadGroup, String) now public * native/jni/java-util/java_util_ResourceBundle.c: removed file * native/jni/java-util/Makefile.am: removed java_util_ResourceBundle.c from library
Diffstat (limited to 'native/fdlibm/e_exp.c')
-rw-r--r--native/fdlibm/e_exp.c167
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diff --git a/native/fdlibm/e_exp.c b/native/fdlibm/e_exp.c
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+
+/* @(#)e_exp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* __ieee754_exp(x)
+ * Returns the exponential of x.
+ *
+ * Method
+ * 1. Argument reduction:
+ * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
+ * Given x, find r and integer k such that
+ *
+ * x = k*ln2 + r, |r| <= 0.5*ln2.
+ *
+ * Here r will be represented as r = hi-lo for better
+ * accuracy.
+ *
+ * 2. Approximation of exp(r) by a special rational function on
+ * the interval [0,0.34658]:
+ * Write
+ * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
+ * We use a special Reme algorithm on [0,0.34658] to generate
+ * a polynomial of degree 5 to approximate R. The maximum error
+ * of this polynomial approximation is bounded by 2**-59. In
+ * other words,
+ * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
+ * (where z=r*r, and the values of P1 to P5 are listed below)
+ * and
+ * | 5 | -59
+ * | 2.0+P1*z+...+P5*z - R(z) | <= 2
+ * | |
+ * The computation of exp(r) thus becomes
+ * 2*r
+ * exp(r) = 1 + -------
+ * R - r
+ * r*R1(r)
+ * = 1 + r + ----------- (for better accuracy)
+ * 2 - R1(r)
+ * where
+ * 2 4 10
+ * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
+ *
+ * 3. Scale back to obtain exp(x):
+ * From step 1, we have
+ * exp(x) = 2^k * exp(r)
+ *
+ * Special cases:
+ * exp(INF) is INF, exp(NaN) is NaN;
+ * exp(-INF) is 0, and
+ * for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ * For IEEE double
+ * if x > 7.09782712893383973096e+02 then exp(x) overflow
+ * if x < -7.45133219101941108420e+02 then exp(x) underflow
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "fdlibm.h"
+
+#ifndef _DOUBLE_IS_32BITS
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.0,
+halF[2] = {0.5,-0.5,},
+huge = 1.0e+300,
+twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
+o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
+ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
+ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
+invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
+
+
+#ifdef __STDC__
+ double __ieee754_exp(double x) /* default IEEE double exp */
+#else
+ double __ieee754_exp(x) /* default IEEE double exp */
+ double x;
+#endif
+{
+ double y,hi,lo,c,t;
+ int32_t k,xsb;
+ uint32_t hx;
+
+ GET_HIGH_WORD(hx,x);
+ xsb = (hx>>31)&1; /* sign bit of x */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out non-finite argument */
+ if(hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if(hx>=0x7ff00000) {
+ uint32_t lx;
+ GET_LOW_WORD(lx,x);
+ if(((hx&0xfffff)|lx)!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ if(x < u_threshold) return twom1000*twom1000; /* underflow */
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
+ } else {
+ k = invln2*x+halF[xsb];
+ t = k;
+ hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
+ lo = t*ln2LO[0];
+ }
+ x = hi - lo;
+ }
+ else if(hx < 0x3e300000) { /* when |x|<2**-28 */
+ if(huge+x>one) return one+x;/* trigger inexact */
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ t = x*x;
+ c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+ if(k==0) return one-((x*c)/(c-2.0)-x);
+ else y = one-((lo-(x*c)/(2.0-c))-hi);
+ if(k >= -1021) {
+ uint32_t hy;
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
+ return y;
+ } else {
+ uint32_t hy;
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
+ return y*twom1000;
+ }
+}
+
+#endif /* defined(_DOUBLE_IS_32BITS) */