-/* e_coshf.c -- float version of e_cosh.c.
- */
+/* Correctly-rounded hyperbolic cosine function for binary32 value.
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
+Copyright (c) 2022-2024 Alexei Sibidanov.
+The original version of this file was copied from the CORE-MATH
+project (file src/binary32/cosh/coshf.c, revision 5c58ea1).
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+*/
+
+#include <stdint.h>
#include <math.h>
-#include <math-narrow-eval.h>
-#include <math_private.h>
#include <libm-alias-finite.h>
-
-static const float huge = 1.0e30;
-static const float one = 1.0, half=0.5;
+#include "math_config.h"
float
__ieee754_coshf (float x)
{
- float t,w;
- int32_t ix;
-
- GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff;
-
- /* |x| in [0,22] */
- if (ix < 0x41b00000) {
- /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
- if(ix<0x3eb17218) {
- if (ix<0x24000000) return one; /* cosh(tiny) = 1 */
- t = __expm1f(fabsf(x));
- w = one+t;
- return one+(t*t)/(w+w);
- }
-
- /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
- t = __ieee754_expf(fabsf(x));
- return half*t+half/t;
+ static const double c[] =
+ {
+ 1, 0x1.62e42fef4c4e7p-6, 0x1.ebfd1b232f475p-13, 0x1.c6b19384ecd93p-20
+ };
+ static const double ch[] =
+ {
+ 1, 0x1.62e42fefa39efp-6, 0x1.ebfbdff82c58fp-13,
+ 0x1.c6b08d702e0edp-20, 0x1.3b2ab6fb92e5ep-27, 0x1.5d886e6d54203p-35,
+ 0x1.430976b8ce6efp-43
+ };
+ static const uint64_t tb[] =
+ {
+ 0x3fe0000000000000, 0x3fe059b0d3158574, 0x3fe0b5586cf9890f,
+ 0x3fe11301d0125b51, 0x3fe172b83c7d517b, 0x3fe1d4873168b9aa,
+ 0x3fe2387a6e756238, 0x3fe29e9df51fdee1, 0x3fe306fe0a31b715,
+ 0x3fe371a7373aa9cb, 0x3fe3dea64c123422, 0x3fe44e086061892d,
+ 0x3fe4bfdad5362a27, 0x3fe5342b569d4f82, 0x3fe5ab07dd485429,
+ 0x3fe6247eb03a5585, 0x3fe6a09e667f3bcd, 0x3fe71f75e8ec5f74,
+ 0x3fe7a11473eb0187, 0x3fe82589994cce13, 0x3fe8ace5422aa0db,
+ 0x3fe93737b0cdc5e5, 0x3fe9c49182a3f090, 0x3fea5503b23e255d,
+ 0x3feae89f995ad3ad, 0x3feb7f76f2fb5e47, 0x3fec199bdd85529c,
+ 0x3fecb720dcef9069, 0x3fed5818dcfba487, 0x3fedfc97337b9b5f,
+ 0x3feea4afa2a490da, 0x3fef50765b6e4540
+ };
+ const double iln2 = 0x1.71547652b82fep+5;
+ double z = x;
+ uint32_t ax = asuint (x) << 1;
+ if (__glibc_unlikely (ax > 0x8565a9f8u))
+ { /* |x| >~ 89.4 */
+ if (ax >= 0xff000000u)
+ {
+ if (ax << 8)
+ return x + x; /* nan */
+ return INFINITY; /* +-inf */
}
-
- /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
- if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x));
-
- /* |x| in [log(maxdouble), overflowthresold] */
- if (ix<=0x42b2d4fc) {
- w = __ieee754_expf(half*fabsf(x));
- t = half*w;
- return t*w;
+ return __math_oflowf (0);
+ }
+ if (__glibc_unlikely (ax < 0x7c000000u))
+ { /* |x| < 0.125 */
+ if (__glibc_unlikely (ax < 0x74000000u))
+ { /* |x| < 0x1p-11 */
+ if (__glibc_unlikely (ax < 0x66000000u)) /* |x| < 0x1p-24 */
+ return fmaf (fabsf (x), 0x1p-25, 1.0f);
+ return (0.5f * x) * x + 1.0f;
}
-
- /* x is INF or NaN */
- if(ix>=0x7f800000) return x*x;
-
- /* |x| > overflowthresold, cosh(x) overflow */
- return math_narrow_eval (huge*huge);
+ static const double cp[] =
+ {
+ 0x1.fffffffffffe3p-2, 0x1.55555555723cfp-5,
+ 0x1.6c16bee4a5986p-10, 0x1.a0483fc0328f7p-16
+ };
+ double z2 = z * z;
+ double z4 = z2 * z2;
+ return 1.0 + z2 * ((cp[0] + z2 * cp[1]) + z4 * (cp[2] + z2 * (cp[3])));
+ }
+ double a = iln2 * z;
+ double ia = roundeven_finite (a);
+ double h = a - ia;
+ double h2 = h * h;
+ int64_t jp = asuint64 (ia + 0x1.8p52);
+ int64_t jm = -jp;
+ double sp = asdouble (tb[jp & 31] + ((jp >> 5) << 52));
+ double sm = asdouble (tb[jm & 31] + ((jm >> 5) << 52));
+ double te = c[0] + h2 * c[2];
+ double to = (c[1] + h2 * c[3]);
+ double rp = sp * (te + h * to);
+ double rm = sm * (te - h * to);
+ double r = rp + rm;
+ float ub = r;
+ double lb = r - 1.45e-10 * r;
+ if (__glibc_unlikely (ub != lb))
+ {
+ const double iln2h = 0x1.7154765p+5;
+ const double iln2l = 0x1.5c17f0bbbe88p-26;
+ h = (iln2h * z - ia) + iln2l * z;
+ h2 = h * h;
+ te = ch[0] + h2 * ch[2] + (h2 * h2) * (ch[4] + h2 * ch[6]);
+ to = ch[1] + h2 * (ch[3] + h2 * ch[5]);
+ r = sp * (te + h * to) + sm * (te - h * to);
+ ub = r;
+ }
+ return ub;
}
libm_alias_finite (__ieee754_coshf, __coshf)
projects / thirdparty / glibc.git / commitdiff
