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-rw-r--r--src/math/cosh.c73
-rw-r--r--src/math/coshf.c49
-rw-r--r--src/math/coshl.c69
3 files changed, 49 insertions, 142 deletions
diff --git a/src/math/cosh.c b/src/math/cosh.c
index 2fcdea8f..100f8231 100644
--- a/src/math/cosh.c
+++ b/src/math/cosh.c
@@ -1,71 +1,40 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_cosh.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunSoft, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* cosh(x)
- * Method :
- * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
- * 1. Replace x by |x| (cosh(x) = cosh(-x)).
- * 2.
- * [ exp(x) - 1 ]^2
- * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
- * 2*exp(x)
- *
- * exp(x) + 1/exp(x)
- * ln2/2 <= x <= 22 : cosh(x) := -------------------
- * 2
- * 22 <= x <= lnovft : cosh(x) := exp(x)/2
- * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
- * ln2ovft < x : cosh(x) := inf (overflow)
- *
- * Special cases:
- * cosh(x) is |x| if x is +INF, -INF, or NaN.
- * only cosh(0)=1 is exact for finite x.
- */
-
#include "libm.h"
+/* cosh(x) = (exp(x) + 1/exp(x))/2
+ * = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
+ * = 1 + x*x/2 + o(x^4)
+ */
double cosh(double x)
{
union {double f; uint64_t i;} u = {.f = x};
- uint32_t ix;
+ uint32_t w;
double t;
/* |x| */
u.i &= (uint64_t)-1/2;
x = u.f;
- ix = u.i >> 32;
+ w = u.i >> 32;
- /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
- if (ix < 0x3fd62e43) {
- t = expm1(x);
- if (ix < 0x3c800000)
+ /* |x| < log(2) */
+ if (w < 0x3fe62e42) {
+ if (w < 0x3ff00000 - (26<<20)) {
+ /* raise inexact if x!=0 */
+ FORCE_EVAL(x + 0x1p120f);
return 1;
+ }
+ t = expm1(x);
return 1 + t*t/(2*(1+t));
}
- /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */
- if (ix < 0x40360000) {
+ /* |x| < log(DBL_MAX) */
+ if (w < 0x40862e42) {
t = exp(x);
- return 0.5*t + 0.5/t;
+ /* note: if x>log(0x1p26) then the 1/t is not needed */
+ return 0.5*(t + 1/t);
}
- /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
- if (ix < 0x40862e42)
- return 0.5*exp(x);
-
- /* |x| in [log(maxdouble), overflowthresold] */
- if (ix <= 0x408633ce)
- return __expo2(x);
-
- /* overflow (or nan) */
- x *= 0x1p1023;
- return x;
+ /* |x| > log(DBL_MAX) or nan */
+ /* note: the result is stored to handle overflow */
+ t = __expo2(x);
+ return t;
}
diff --git a/src/math/coshf.c b/src/math/coshf.c
index 2bed1258..b09f2ee5 100644
--- a/src/math/coshf.c
+++ b/src/math/coshf.c
@@ -1,54 +1,33 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_coshf.c */
-/*
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-
#include "libm.h"
float coshf(float x)
{
union {float f; uint32_t i;} u = {.f = x};
- uint32_t ix;
+ uint32_t w;
float t;
/* |x| */
u.i &= 0x7fffffff;
x = u.f;
- ix = u.i;
+ w = u.i;
- /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
- if (ix < 0x3eb17218) {
- t = expm1f(x);
- if (ix < 0x39800000)
+ /* |x| < log(2) */
+ if (w < 0x3f317217) {
+ if (w < 0x3f800000 - (12<<23)) {
+ FORCE_EVAL(x + 0x1p120f);
return 1;
+ }
+ t = expm1f(x);
return 1 + t*t/(2*(1+t));
}
- /* |x| in [0.5*ln2,9], return (exp(|x|)+1/exp(|x|))/2; */
- if (ix < 0x41100000) {
+ /* |x| < log(FLT_MAX) */
+ if (w < 0x42b17217) {
t = expf(x);
- return 0.5f*t + 0.5f/t;
+ return 0.5f*(t + 1/t);
}
- /* |x| in [9, log(maxfloat)] return 0.5f*exp(|x|) */
- if (ix < 0x42b17217)
- return 0.5f*expf(x);
-
- /* |x| in [log(maxfloat), overflowthresold] */
- if (ix <= 0x42b2d4fc)
- return __expo2f(x);
-
- /* |x| > overflowthresold or nan */
- x *= 0x1p127f;
- return x;
+ /* |x| > log(FLT_MAX) or nan */
+ t = __expo2f(x);
+ return t;
}
diff --git a/src/math/coshl.c b/src/math/coshl.c
index 3ea56e00..d09070bb 100644
--- a/src/math/coshl.c
+++ b/src/math/coshl.c
@@ -1,35 +1,3 @@
-/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_coshl.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.
- * ====================================================
- */
-/* coshl(x)
- * Method :
- * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
- * 1. Replace x by |x| (coshl(x) = coshl(-x)).
- * 2.
- * [ exp(x) - 1 ]^2
- * 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
- * 2*exp(x)
- *
- * exp(x) + 1/exp(x)
- * ln2/2 <= x <= 22 : coshl(x) := -------------------
- * 2
- * 22 <= x <= lnovft : coshl(x) := expl(x)/2
- * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
- * ln2ovft < x : coshl(x) := inf (overflow)
- *
- * Special cases:
- * coshl(x) is |x| if x is +INF, -INF, or NaN.
- * only coshl(0)=1 is exact for finite x.
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -45,41 +13,32 @@ long double coshl(long double x)
struct{uint64_t m; uint16_t se; uint16_t pad;} i;
} u = {.f = x};
unsigned ex = u.i.se & 0x7fff;
+ uint32_t w;
long double t;
- uint32_t mx,lx;
/* |x| */
u.i.se = ex;
x = u.f;
- mx = u.i.m >> 32;
- lx = u.i.m;
+ w = u.i.m >> 32;
- /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
- if (ex < 0x3fff-2 || (ex == 0x3fff-2 && mx < 0xb17217f7)) {
- t = expm1l(x);
- if (ex < 0x3fff-64)
+ /* |x| < log(2) */
+ if (ex < 0x3fff-1 || (ex == 0x3fff-1 && w < 0xb17217f7)) {
+ if (ex < 0x3fff-32) {
+ FORCE_EVAL(x + 0x1p120f);
return 1;
+ }
+ t = expm1l(x);
return 1 + t*t/(2*(1+t));
}
- /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
- if (ex < 0x3fff+4 || (ex == 0x3fff+4 && mx < 0xb0000000)) {
+ /* |x| < log(LDBL_MAX) */
+ if (ex < 0x3fff+13 || (ex == 0x3fff+13 && w < 0xb17217f7)) {
t = expl(x);
- return 0.5*t + 0.5/t;
- }
-
- /* |x| in [22, ln(maxdouble)] return 0.5*exp(|x|) */
- if (ex < 0x3fff+13 || (ex == 0x3fff+13 && mx < 0xb1700000))
- return 0.5*expl(x);
-
- /* |x| in [log(maxdouble), log(2*maxdouble)) */
- if (ex == 0x3fff+13 && (mx < 0xb174ddc0 ||
- (mx == 0xb174ddc0 && lx < 0x31aec0eb))) {
- t = expl(0.5*x);
- return 0.5*t*t;
+ return 0.5*(t + 1/t);
}
- /* |x| >= log(2*maxdouble) or nan */
- return x*0x1p16383L;
+ /* |x| > log(LDBL_MAX) or nan */
+ t = expl(0.5*x);
+ return 0.5*t*t;
}
#endif
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