ref: dcb29f7e9714e539ce32f0aa06287471c349892f
parent: 7a7012783c528091cb49dcc04028429daceab390
author: Sigrid Solveig Haflínudóttir <sigrid@ftrv.se>
date: Wed Aug 16 21:11:35 EDT 2023
npe: add acosh and log1p
--- a/include/npe/math.h
+++ b/include/npe/math.h
@@ -54,4 +54,7 @@
/* FIXME this is totally wrong */
#define signbit(x) (x == -0.0 || x < 0.0)
+double acosh(double x);
+double log1p(double x);
+
#endif
--- a/include/npe/stdlib.h
+++ b/include/npe/stdlib.h
@@ -9,5 +9,6 @@
int setenv(char *name, char *value, int overwrite);
char *realpath(char *path, char *buffer);
+int mkstemp(char *t);
#endif
--- /dev/null
+++ b/libnpe/acosh.c
@@ -1,0 +1,21 @@
+#include <math.h>
+/* taken from musl */
+
+/* acosh(x) = log(x + sqrt(x*x-1)) */
+double
+acosh(double x)
+{+ union {double f; u64int i;} u = {.f = x};+ unsigned e = u.i >> 52 & 0x7ff;
+
+ /* x < 1 domain error is handled in the called functions */
+
+ if (e < 0x3ff + 1)
+ /* |x| < 2, up to 2ulp error in [1,1.125] */
+ return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)));
+ if (e < 0x3ff + 26)
+ /* |x| < 0x1p26 */
+ return log(2*x - 1/(x+sqrt(x*x-1)));
+ /* |x| >= 0x1p26 or nan */
+ return log(x) + 0.693147180559945309417232121458176568;
+}
--- /dev/null
+++ b/libnpe/log1p.c
@@ -1,0 +1,125 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+/* double log1p(double x)
+ * Return the natural logarithm of 1+x.
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * 1+x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * Note. If k=0, then f=x is exact. However, if k!=0, then f
+ * may not be representable exactly. In that case, a correction
+ * term is need. Let u=1+x rounded. Let c = (1+x)-u, then
+ * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
+ * and add back the correction term c/u.
+ * (Note: when x > 2**53, one can simply return log(x))
+ *
+ * 2. Approximation of log(1+f): See log.c
+ *
+ * 3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c
+ *
+ * Special cases:
+ * log1p(x) is NaN with signal if x < -1 (including -INF) ;
+ * log1p(+INF) is +INF; log1p(-1) is -INF with signal;
+ * log1p(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * 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.
+ *
+ * Note: Assuming log() return accurate answer, the following
+ * algorithm can be used to compute log1p(x) to within a few ULP:
+ *
+ * u = 1+x;
+ * if(u==1.0) return x ; else
+ * return log(u)*(x/(u-1.0));
+ *
+ * See HP-15C Advanced Functions Handbook, p.193.
+ */
+
+#include <math.h>
+
+static const double
+ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
+ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
+Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+double
+log1p(double x)
+{+ union {double f; u64int i;} u = {x};+ double hfsq,f,c,s,z,R,w,t1,t2,dk;
+ u32int hx,hu;
+ int k;
+
+ hx = u.i>>32;
+ k = 1;
+ c = 0;
+ f = 0;
+ if (hx < 0x3fda827a || hx>>31) { /* 1+x < sqrt(2)+ */+ if (hx >= 0xbff00000) { /* x <= -1.0 */+ if (x == -1)
+ return Inf(-1); /* log1p(-1) = -inf */
+ return NaN(); /* log1p(x<-1) = NaN */
+ }
+ if (hx<<1 < 0x3ca00000<<1) { /* |x| < 2**-53 */+ /* underflow if subnormal */
+ if ((hx&0x7ff00000) == 0)
+ USED((float)x);
+ return x;
+ }
+ if (hx <= 0xbfd2bec4) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */+ k = 0;
+ c = 0;
+ f = x;
+ }
+ } else if (hx >= 0x7ff00000)
+ return x;
+ if (k) {+ u.f = 1 + x;
+ hu = u.i>>32;
+ hu += 0x3ff00000 - 0x3fe6a09e;
+ k = (int)(hu>>20) - 0x3ff;
+ /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
+ if (k < 54) {+ c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
+ c /= u.f;
+ } else
+ c = 0;
+ /* reduce u into [sqrt(2)/2, sqrt(2)] */
+ hu = (hu&0x000fffff) + 0x3fe6a09e;
+ u.i = (u64int)hu<<32 | (u.i&0xffffffff);
+ f = u.f - 1;
+ }
+ hfsq = 0.5*f*f;
+ s = f/(2.0+f);
+ z = s*s;
+ w = z*z;
+ t1 = w*(Lg2+w*(Lg4+w*Lg6));
+ t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+ R = t2 + t1;
+ dk = k;
+ return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
+}
--- a/libnpe/mkfile
+++ b/libnpe/mkfile
@@ -11,6 +11,7 @@
OFILES=\
_main.$O\
_npe.$O\
+ acosh.$O\
basename.$O\
closedir.$O\
dirfd.$O\
@@ -32,11 +33,13 @@
isatty.$O\
isinf.$O\
isnormal.$O\
+ log1p.$O\
localtime.$O\
log2.$O\
lrint.$O\
lrintf.$O\
mkdir.$O\
+ mkstemp.$O\
mktime.$O\
opendir.$O\
readdir.$O\