diff --git a/src/math/cosh.c b/src/math/cosh.c
index 2fcdea8f8e24cec0ddd34802837482d3bb619b6d..100f8231d8829604b9e293491a9abb1774b4b29a 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 2bed1258a2ca9a87c88d4973c75dbb65c92499af..b09f2ee5751f4341cfb6cc759055279deda1d7cb 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 3ea56e00bfd5f8be949787119fcef32b90a2f20b..d09070bbf7a4962d7f1f66826ef58cbaafce6158 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