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authorSzabolcs Nagy <nsz@port70.net>2012-12-16 19:49:55 +0100
committerSzabolcs Nagy <nsz@port70.net>2012-12-16 19:49:55 +0100
commitf143458223f90262a9c2d929f9e815a74e3aa139 (patch)
tree0fa8e36f892fb0481977366226d1c42eae5a5b95
parent1aec620f9366c29d761fe42b3e02bd8024685db3 (diff)
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math: sinh.c cleanup similar to the cosh one
comments are kept in the double version of the function
-rw-r--r--src/math/sinh.c90
-rw-r--r--src/math/sinhf.c66
-rw-r--r--src/math/sinhl.c87
3 files changed, 72 insertions, 171 deletions
diff --git a/src/math/sinh.c b/src/math/sinh.c
index 0c67ba39..47e36bfa 100644
--- a/src/math/sinh.c
+++ b/src/math/sinh.c
@@ -1,71 +1,39 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_sinh.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.
- * ====================================================
- */
-/* sinh(x)
- * Method :
- * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
- * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
- * 2.
- * E + E/(E+1)
- * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
- * 2
- *
- * 22 <= x <= lnovft : sinh(x) := exp(x)/2
- * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
- * ln2ovft < x : sinh(x) := x*shuge (overflow)
- *
- * Special cases:
- * sinh(x) is |x| if x is +INF, -INF, or NaN.
- * only sinh(0)=0 is exact for finite x.
- */
-
#include "libm.h"
-static const double huge = 1.0e307;
-
+/* sinh(x) = (exp(x) - 1/exp(x))/2
+ * = (exp(x)-1 + (exp(x)-1)/exp(x))/2
+ * = x + x^3/6 + o(x^5)
+ */
double sinh(double x)
{
- double t, h;
- int32_t ix, jx;
-
- /* High word of |x|. */
- GET_HIGH_WORD(jx, x);
- ix = jx & 0x7fffffff;
-
- /* x is INF or NaN */
- if (ix >= 0x7ff00000)
- return x + x;
+ union {double f; uint64_t i;} u = {.f = x};
+ uint32_t w;
+ double t, h, absx;
h = 0.5;
- if (jx < 0) h = -h;
- /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
- if (ix < 0x40360000) { /* |x|<22 */
- if (ix < 0x3e300000) /* |x|<2**-28 */
- /* raise inexact, return x */
- if (huge+x > 1.0)
+ if (u.i >> 63)
+ h = -h;
+ /* |x| */
+ u.i &= (uint64_t)-1/2;
+ absx = u.f;
+ w = u.i >> 32;
+
+ /* |x| < log(DBL_MAX) */
+ if (w < 0x40862e42) {
+ t = expm1(absx);
+ if (w < 0x3ff00000) {
+ if (w < 0x3ff00000 - (26<<20))
+ /* note: inexact is raised by expm1 */
+ /* note: this branch avoids underflow */
return x;
- t = expm1(fabs(x));
- if (ix < 0x3ff00000)
- return h*(2.0*t - t*t/(t+1.0));
- return h*(t + t/(t+1.0));
+ return h*(2*t - t*t/(t+1));
+ }
+ /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
+ return h*(t + t/(t+1));
}
- /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
- if (ix < 0x40862E42)
- return h*exp(fabs(x));
-
- /* |x| in [log(maxdouble), overflowthresold] */
- if (ix <= 0x408633CE)
- return h * 2.0 * __expo2(fabs(x)); /* h is for sign only */
-
- /* |x| > overflowthresold, sinh(x) overflow */
- return x*huge;
+ /* |x| > log(DBL_MAX) or nan */
+ /* note: the result is stored to handle overflow */
+ t = 2*h*__expo2(absx);
+ return t;
}
diff --git a/src/math/sinhf.c b/src/math/sinhf.c
index b8d88224..6ad19ea2 100644
--- a/src/math/sinhf.c
+++ b/src/math/sinhf.c
@@ -1,57 +1,31 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_sinhf.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"
-static const float huge = 1.0e37;
-
float sinhf(float x)
{
- float t, h;
- int32_t ix, jx;
-
- GET_FLOAT_WORD(jx, x);
- ix = jx & 0x7fffffff;
-
- /* x is INF or NaN */
- if (ix >= 0x7f800000)
- return x + x;
+ union {float f; uint32_t i;} u = {.f = x};
+ uint32_t w;
+ float t, h, absx;
h = 0.5;
- if (jx < 0)
+ if (u.i >> 31)
h = -h;
- /* |x| in [0,9], return sign(x)*0.5*(E+E/(E+1))) */
- if (ix < 0x41100000) { /* |x|<9 */
- if (ix < 0x39800000) /* |x|<2**-12 */
- /* raise inexact, return x */
- if (huge+x > 1.0f)
+ /* |x| */
+ u.i &= 0x7fffffff;
+ absx = u.f;
+ w = u.i;
+
+ /* |x| < log(FLT_MAX) */
+ if (w < 0x42b17217) {
+ t = expm1f(absx);
+ if (w < 0x3f800000) {
+ if (w < 0x3f800000 - (12<<23))
return x;
- t = expm1f(fabsf(x));
- if (ix < 0x3f800000)
- return h*(2.0f*t - t*t/(t+1.0f));
- return h*(t + t/(t+1.0f));
+ return h*(2*t - t*t/(t+1));
+ }
+ return h*(t + t/(t+1));
}
- /* |x| in [9, logf(maxfloat)] return 0.5*exp(|x|) */
- if (ix < 0x42b17217)
- return h*expf(fabsf(x));
-
- /* |x| in [logf(maxfloat), overflowthresold] */
- if (ix <= 0x42b2d4fc)
- return h * 2.0f * __expo2f(fabsf(x)); /* h is for sign only */
-
- /* |x| > overflowthresold, sinh(x) overflow */
- return x*huge;
+ /* |x| > logf(FLT_MAX) or nan */
+ t = 2*h*__expo2f(absx);
+ return t;
}
diff --git a/src/math/sinhl.c b/src/math/sinhl.c
index 8a54677e..14e3371b 100644
--- a/src/math/sinhl.c
+++ b/src/math/sinhl.c
@@ -1,32 +1,3 @@
-/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.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.
- * ====================================================
- */
-/* sinhl(x)
- * Method :
- * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
- * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
- * 2.
- * E + E/(E+1)
- * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
- * 2
- *
- * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
- * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
- * ln2ovft < x : sinhl(x) := x*huge (overflow)
- *
- * Special cases:
- * sinhl(x) is |x| if x is +INF, -INF, or NaN.
- * only sinhl(0)=0 is exact for finite x.
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
@@ -35,47 +6,35 @@ long double sinhl(long double x)
return sinh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-static const long double huge = 1.0e4931L;
-
long double sinhl(long double x)
{
- long double t,w,h;
- uint32_t jx,ix,i0,i1;
-
- /* Words of |x|. */
- GET_LDOUBLE_WORDS(jx, i0, i1, x);
- ix = jx & 0x7fff;
-
- /* x is INF or NaN */
- if (ix == 0x7fff) return x + x;
+ union {
+ long double f;
+ struct{uint64_t m; uint16_t se; uint16_t pad;} i;
+ } u = {.f = x};
+ unsigned ex = u.i.se & 0x7fff;
+ long double h, t, absx;
h = 0.5;
- if (jx & 0x8000)
+ if (u.i.se & 0x8000)
h = -h;
- /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
- if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x| < 25 */
- if (ix < 0x3fdf) /* |x|<2**-32 */
- if (huge + x > 1.0)
- return x;/* sinh(tiny) = tiny with inexact */
- t = expm1l(fabsl(x));
- if (ix < 0x3fff)
- return h*(2.0*t - t*t/(t + 1.0));
- return h*(t + t/(t + 1.0));
- }
-
- /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
- if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
- return h*expl(fabsl(x));
-
- /* |x| in [log(maxdouble), overflowthreshold] */
- if (ix < 0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 ||
- (i0 == 0xb174ddc0 && i1 <= 0x31aec0ea)))) {
- w = expl(0.5*fabsl(x));
- t = h*w;
- return t*w;
+ /* |x| */
+ u.i.se = ex;
+ absx = u.f;
+
+ /* |x| < log(LDBL_MAX) */
+ if (ex < 0x3fff+13 || (ex == 0x3fff+13 && u.i.m>>32 < 0xb17217f7)) {
+ t = expm1l(absx);
+ if (ex < 0x3fff) {
+ if (ex < 0x3fff-32)
+ return x;
+ return h*(2*t - t*t/(1+t));
+ }
+ return h*(t + t/(t+1));
}
- /* |x| > overflowthreshold, sinhl(x) overflow */
- return x*huge;
+ /* |x| > log(LDBL_MAX) or nan */
+ t = expl(0.5*absx);
+ return h*t*t;
}
#endif