/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2006 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #pragma weak __atanf = atanf /* INDENT OFF */ /* * float atanf(float x); * Table look-up algorithm * By K.C. Ng, March 9, 1989 * * Algorithm. * * The algorithm is based on atan(x)=atan(y)+atan((x-y)/(1+x*y)). * We use poly1(x) to approximate atan(x) for x in [0,1/8] with * error (relative) * |(atan(x)-poly1(x))/x|<= 2^-115.94 long double * |(atan(x)-poly1(x))/x|<= 2^-58.85 double * |(atan(x)-poly1(x))/x|<= 2^-25.53 float * and use poly2(x) to approximate atan(x) for x in [0,1/65] with * error (absolute) * |atan(x)-poly2(x)|<= 2^-122.15 long double * |atan(x)-poly2(x)|<= 2^-64.79 double * |atan(x)-poly2(x)|<= 2^-35.36 float * and use poly3(x) to approximate atan(x) for x in [1/8,7/16] with * error (relative, on for single precision) * |(atan(x)-poly1(x))/x|<= 2^-25.53 float * * Here poly1-3 are odd polynomial with the following form: * x + x^3*(a1+x^2*(a2+...)) * * (0). Purge off Inf and NaN and 0 * (1). Reduce x to positive by atan(x) = -atan(-x). * (2). For x <= 1/8, use * (2.1) if x < 2^(-prec/2-2), atan(x) = x with inexact * (2.2) Otherwise * atan(x) = poly1(x) * (3). For x >= 8 then * (3.1) if x >= 2^(prec+2), atan(x) = atan(inf) - pio2lo * (3.2) if x >= 2^(prec/3+2), atan(x) = atan(inf) - 1/x * (3.3) if x > 65, atan(x) = atan(inf) - poly2(1/x) * (3.4) Otherwise, atan(x) = atan(inf) - poly1(1/x) * * (4). Now x is in (0.125, 8) * Find y that match x to 4.5 bit after binary (easy). * If iy is the high word of y, then * single : j = (iy - 0x3e000000) >> 19 * (single is modified to (iy-0x3f000000)>>19) * double : j = (iy - 0x3fc00000) >> 16 * quad : j = (iy - 0x3ffc0000) >> 12 * * Let s = (x-y)/(1+x*y). Then * atan(x) = atan(y) + poly1(s) * = _TBL_r_atan_hi[j] + (_TBL_r_atan_lo[j] + poly2(s) ) * * Note. |s| <= 1.5384615385e-02 = 1/65. Maxium occurs at x = 1.03125 * */ #include "libm.h" extern const float _TBL_r_atan_hi[], _TBL_r_atan_lo[]; static const float big = 1.0e37F, one = 1.0F, p1 = -3.333185951111688247225368498733544672172e-0001F, p2 = 1.969352894213455405211341983203180636021e-0001F, q1 = -3.332921964095646819563419704110132937456e-0001F, a1 = -3.333323465223893614063523351509338934592e-0001F, a2 = 1.999425625935277805494082274808174062403e-0001F, a3 = -1.417547090509737780085769846290301788559e-0001F, a4 = 1.016250813871991983097273733227432685084e-0001F, a5 = -5.137023693688358515753093811791755221805e-0002F, pio2hi = 1.570796371e+0000F, pio2lo = -4.371139000e-0008F; /* INDENT ON */ float atanf(float xx) { float x, y, z, r, p, s; volatile double dummy __unused; int ix, iy, sign, j; x = xx; ix = *(int *) &x; sign = ix & 0x80000000; ix ^= sign; /* for |x| < 1/8 */ if (ix < 0x3e000000) { if (ix < 0x38800000) { /* if |x| < 2**(-prec/2-2) */ dummy = big + x; /* get inexact flag if x != 0 */ #ifdef lint dummy = dummy; #endif return (x); } z = x * x; if (ix < 0x3c000000) { /* if |x| < 2**(-prec/4-1) */ x = x + (x * z) * p1; return (x); } else { x = x + (x * z) * (p1 + z * p2); return (x); } } /* for |x| >= 8.0 */ if (ix >= 0x41000000) { *(int *) &x = ix; if (ix < 0x42820000) { /* x < 65 */ r = one / x; z = r * r; y = r * (one + z * (p1 + z * p2)); /* poly1 */ y -= pio2lo; } else if (ix < 0x44800000) { /* x < 2**(prec/3+2) */ r = one / x; z = r * r; y = r * (one + z * q1); /* poly2 */ y -= pio2lo; } else if (ix < 0x4c800000) { /* x < 2**(prec+2) */ y = one / x - pio2lo; } else if (ix < 0x7f800000) { /* x < inf */ y = -pio2lo; } else { /* x is inf or NaN */ if (ix > 0x7f800000) { return (x * x); /* - -> * for Cheetah */ } y = -pio2lo; } if (sign == 0) x = pio2hi - y; else x = y - pio2hi; return (x); } /* now x is between 1/8 and 8 */ if (ix < 0x3f000000) { /* between 1/8 and 1/2 */ z = x * x; x = x + (x * z) * (a1 + z * (a2 + z * (a3 + z * (a4 + z * a5)))); return (x); } *(int *) &x = ix; iy = (ix + 0x00040000) & 0x7ff80000; *(int *) &y = iy; j = (iy - 0x3f000000) >> 19; if (ix == iy) p = x - y; /* p=0.0 */ else { if (sign == 0) s = (x - y) / (one + x * y); else s = (y - x) / (one + x * y); z = s * s; p = s * (one + z * q1); } if (sign == 0) { r = p + _TBL_r_atan_lo[j]; x = r + _TBL_r_atan_hi[j]; } else { r = p - _TBL_r_atan_lo[j]; x = r - _TBL_r_atan_hi[j]; } return (x); }
