-/* s_atanf.c -- float version of s_atan.c.
- */
+/* Correctly-rounded arc-tangent of 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.
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $";
-#endif
+The original version of this file was copied from the CORE-MATH
+project (file src/binary32/atan/atanf.c, revision a8066a5).
-#include <float.h>
-#include <math.h>
-#include <math_private.h>
-#include <math-underflow.h>
-#include <libm-alias-float.h>
+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:
-static const float atanhi[] = {
- 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
- 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
- 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
- 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
-};
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
-static const float atanlo[] = {
- 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
- 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
- 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
- 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
-};
+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.
+*/
-static const float aT[] = {
- 3.3333334327e-01, /* 0x3eaaaaaa */
- -2.0000000298e-01, /* 0xbe4ccccd */
- 1.4285714924e-01, /* 0x3e124925 */
- -1.1111110449e-01, /* 0xbde38e38 */
- 9.0908870101e-02, /* 0x3dba2e6e */
- -7.6918758452e-02, /* 0xbd9d8795 */
- 6.6610731184e-02, /* 0x3d886b35 */
- -5.8335702866e-02, /* 0xbd6ef16b */
- 4.9768779427e-02, /* 0x3d4bda59 */
- -3.6531571299e-02, /* 0xbd15a221 */
- 1.6285819933e-02, /* 0x3c8569d7 */
-};
-
-static const float
-one = 1.0,
-huge = 1.0e30;
+#include <math.h>
+#include <stdint.h>
+#include <libm-alias-float.h>
+#include "math_config.h"
-float __atanf(float x)
+float
+__atanf (float x)
{
- float w,s1,s2,z;
- int32_t ix,hx,id;
-
- GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x4c000000) { /* if |x| >= 2^25 */
- if(ix>0x7f800000)
- return x+x; /* NaN */
- if(hx>0) return atanhi[3]+atanlo[3];
- else return -atanhi[3]-atanlo[3];
- } if (ix < 0x3ee00000) { /* |x| < 0.4375 */
- if (ix < 0x31000000) { /* |x| < 2^-29 */
- math_check_force_underflow (x);
- if(huge+x>one) return x; /* raise inexact */
- }
- id = -1;
- } else {
- x = fabsf(x);
- if (ix < 0x3f980000) { /* |x| < 1.1875 */
- if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
- id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
- } else { /* 11/16<=|x|< 19/16 */
- id = 1; x = (x-one)/(x+one);
- }
- } else {
- if (ix < 0x401c0000) { /* |x| < 2.4375 */
- id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
- } else { /* 2.4375 <= |x| < 2^66 */
- id = 3; x = -(float)1.0/x;
- }
- }}
- /* end of argument reduction */
- z = x*x;
- w = z*z;
- /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
- s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
- s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
- if (id<0) return x - x*(s1+s2);
- else {
- z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
- return (hx<0)? -z:z;
+ const double pi2 = 0x1.921fb54442d18p+0;
+ uint32_t t = asuint (x);
+ int e = (t >> 23) & 0xff;
+ bool gt = e >= 127;
+ uint32_t ta = t & 0x7fffffff;
+ if (__glibc_unlikely (ta >= 0x4c700518u)) /* |x| > 0x1.e00a3p+25 */
+ {
+ if (ta > 0x7f800000u)
+ return x + x; /* nan */
+ return copysign (pi2, (double) x);
+ }
+ if (__glibc_unlikely (e < 127 - 13))
+ {
+ if (__glibc_unlikely (e < 127 - 25))
+ {
+ if (!(t << 1))
+ return x;
+ return fmaf (-x, fabsf (x), x);
}
+ return fmaf (-0x1.5555555555555p-2f * x, x * x, x);
+ }
+ /* now |x| >= 0x1p-13 */
+ double z = x;
+ if (gt)
+ z = 1 / z; /* gt is non-zero for |x| >= 1 */
+ double z2 = z * z;
+ double z4 = z2 * z2;
+ double z8 = z4 * z4;
+ /* polynomials generated using rminimax
+ (https://gitlab.inria.fr/sfilip/rminimax) with the following command:
+ ./ratapprox --function="atan(x)" --dom=[0.000122070,1]
+ --num=[x,x^3,x^5,x^7,x^9,x^11,x^13] --den=[1,x^2,x^4,x^6,x^8,x^10,x^12]
+ --output=atanf.sollya --log (see output atanf.sollya) The coefficient
+ cd[0] was slightly reduced from the original value 0x1.51eccde075d67p-2 to
+ avoid an exceptional case for |x| = 0x1.1ad646p-4 and rounding to nearest.
+ */
+ static const double cn[] =
+ {
+ 0x1.51eccde075d67p-2, 0x1.a76bb5637f2f2p-1, 0x1.81e0eed20de88p-1,
+ 0x1.376c8ca67d11dp-2, 0x1.aec7b69202ac6p-5, 0x1.9561899acc73ep-9,
+ 0x1.bf9fa5b67e6p-16
+ };
+ static const double cd[] =
+ {
+ 0x1.51eccde075d66p-2, 0x1.dfbdd7b392d28p-1, 0x1p+0,
+ 0x1.fd22bf0e89b54p-2, 0x1.d91ff8b576282p-4, 0x1.653ea99fc9bbp-7,
+ 0x1.1e7fcc202340ap-12
+ };
+ double cn0 = cn[0] + z2 * cn[1];
+ double cn2 = cn[2] + z2 * cn[3];
+ double cn4 = cn[4] + z2 * cn[5];
+ double cn6 = cn[6];
+ cn0 += z4 * cn2;
+ cn4 += z4 * cn6;
+ cn0 += z8 * cn4;
+ cn0 *= z;
+ double cd0 = cd[0] + z2 * cd[1];
+ double cd2 = cd[2] + z2 * cd[3];
+ double cd4 = cd[4] + z2 * cd[5];
+ double cd6 = cd[6];
+ cd0 += z4 * cd2;
+ cd4 += z4 * cd6;
+ cd0 += z8 * cd4;
+ double r = cn0 / cd0;
+ if (!gt)
+ return r; /* for |x| < 1, (float) r is correctly rounded */
+
+#define PI_OVER2_H 0x1.9p0
+#define PI_OVER2_L 0x1.0fdaa22168c23p-7
+ /* now r approximates atan(1/x), we use atan(x) + atan(1/x) = sign(x)*pi/2,
+ where PI_OVER2_H + PI_OVER2_L approximates pi/2.
+ With sign(z)*L + (-r + sign(z)*H), it fails for x=0x1.98c252p+12 and
+ rounding upward.
+ With sign(z)*PI - r, where PI is a double approximation of pi to nearest,
+ it fails for x=0x1.ddf9f6p+0 and rounding upward. */
+ r = copysign (PI_OVER2_L, z) - r + copysign (PI_OVER2_H, z);
+ return r;
}
libm_alias_float (__atan, atan)
projects / thirdparty / glibc.git / commitdiff
