/* * 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. */ #ifdef __RESTRICT #define restrict _Restrict #else #define restrict #endif void __vatanf(int n, float * restrict x, int stridex, float * restrict y, int stridey) { extern const double __vlibm_TBL_atan1[]; double conup0, conup1, conup2; float dummy, ansf = 0.0; float f0, f1, f2; float ans0, ans1, ans2; float poly0, poly1, poly2; float sign0, sign1, sign2; int intf, intz, argcount; int index0, index1, index2; float z,*yaddr0,*yaddr1,*yaddr2; int *pz = (int *) &z; #ifdef UNROLL4 double conup3; int index3; float f3, ans3, poly3, sign3, *yaddr3; #endif /* Power series atan(x) = x + p1*x**3 + p2*x**5 + p3*x**7 * Error = -3.08254E-18 On the interval |x| < 1/64 */ static const float p1 = -0.33329644f /* -3.333333333329292858E-01f */ ; static const float pone = 1.0f; if (n <= 0) return; /* if no. of elements is 0 or neg, do nothing */ do { LOOP0: intf = *(int *) x; /* upper half of x, as integer */ f0 = *x; sign0 = pone; if (intf < 0) { intf = intf & ~0x80000000; /* abs(upper argument) */ f0 = -f0; sign0 = -sign0; } if ((intf > 0x5B000000) || (intf < 0x31800000)) /* filter out special cases */ { if (intf > 0x7f800000) { ansf = f0- f0; /* return NaN if x=NaN*/ } else if (intf < 0x31800000) /* avoid underflow for small arg */ { dummy = 1.0e37 + f0; dummy = dummy; ansf = f0; } else if (intf > 0x5B000000) /* avoid underflow for big arg */ { index0= 2; ansf = __vlibm_TBL_atan1[index0];/* pi/2 up */ } *y = sign0*ansf; /* store answer, with sign bit */ x += stridex; y += stridey; argcount = 0; /* initialize argcount */ if (--n <=0) break; /* we are done */ goto LOOP0; /* otherwise, examine next arg */ } if (intf > 0x42800000) /* if (|x| > 64 */ { f0 = -pone/f0; index0 = 2; /* point to pi/2 upper, lower */ } else if (intf >= 0x3C800000) /* if |x| >= (1/64)... */ { intz = (intf + 0x00040000) & 0x7ff80000;/* round arg, keep upper */ pz[0] = intz; /* store as a float (z) */ f0 = (f0 - z)/(pone + f0*z); index0 = (intz - 0x3C800000) >> 18; /* (index >> 19) << 1) */ index0 = index0+ 4; /* skip over 0,0,pi/2,pi/2 */ } else /* |x| < 1/64 */ { index0 = 0; /* points to 0,0 in table */ } yaddr0 = y; /* address to store this answer */ x += stridex; /* point to next arg */ y += stridey; /* point to next result */ argcount = 1; /* we now have 1 good argument */ if (--n <=0) { goto UNROLL; /* finish up with 1 good arg */ } /*--------------------------------------------------------------------------*/ /*--------------------------------------------------------------------------*/ /*--------------------------------------------------------------------------*/ LOOP1: intf = *(int *) x; /* upper half of x, as integer */ f1 = *x; sign1 = pone; if (intf < 0) { intf = intf & ~0x80000000; /* abs(upper argument) */ f1 = -f1; sign1 = -sign1; } if ((intf > 0x5B000000) || (intf < 0x31800000)) /* filter out special cases */ { if (intf > 0x7f800000) { ansf = f1 - f1; /* return NaN if x=NaN*/ } else if (intf < 0x31800000) /* avoid underflow for small arg */ { dummy = 1.0e37 + f1; dummy = dummy; ansf = f1; } else if (intf > 0x5B000000) /* avoid underflow for big arg */ { index1 = 2; ansf = __vlibm_TBL_atan1[index1] ;/* pi/2 up */ } *y = sign1 * ansf; /* store answer, with sign bit */ x += stridex; y += stridey; argcount = 1; /* we still have 1 good arg */ if (--n <=0) { goto UNROLL; /* finish up with 1 good arg */ } goto LOOP1; /* otherwise, examine next arg */ } if (intf > 0x42800000) /* if (|x| > 64 */ { f1 = -pone/f1; index1 = 2; /* point to pi/2 upper, lower */ } else if (intf >= 0x3C800000) /* if |x| >= (1/64)... */ { intz = (intf + 0x00040000) & 0x7ff80000;/* round arg, keep upper */ pz[0] = intz; /* store as a float (z) */ f1 = (f1 - z)/(pone + f1*z); index1 = (intz - 0x3C800000) >> 18; /* (index >> 19) << 1) */ index1 = index1 + 4; /* skip over 0,0,pi/2,pi/2 */ } else { index1 = 0; /* points to 0,0 in table */ } yaddr1 = y; /* address to store this answer */ x += stridex; /* point to next arg */ y += stridey; /* point to next result */ argcount = 2; /* we now have 2 good arguments */ if (--n <=0) { goto UNROLL; /* finish up with 2 good args */ } /*--------------------------------------------------------------------------*/ /*--------------------------------------------------------------------------*/ /*--------------------------------------------------------------------------*/ LOOP2: intf = *(int *) x; /* upper half of x, as integer */ f2 = *x; sign2 = pone; if (intf < 0) { intf = intf & ~0x80000000; /* abs(upper argument) */ f2 = -f2; sign2 = -sign2; } if ((intf > 0x5B000000) || (intf < 0x31800000)) /* filter out special cases */ { if (intf > 0x7f800000) { ansf = f2 - f2; /* return NaN if x=NaN*/ } else if (intf < 0x31800000) /* avoid underflow for small arg */ { dummy = 1.0e37 + f2; dummy = dummy; ansf = f2; } else if (intf > 0x5B000000) /* avoid underflow for big arg */ { index2 = 2; ansf = __vlibm_TBL_atan1[index2] ;/* pi/2 up */ } *y = sign2 * ansf; /* store answer, with sign bit */ x += stridex; y += stridey; argcount = 2; /* we still have 2 good args */ if (--n <=0) { goto UNROLL; /* finish up with 2 good args */ } goto LOOP2; /* otherwise, examine next arg */ } if (intf > 0x42800000) /* if (|x| > 64 */ { f2 = -pone/f2; index2 = 2; /* point to pi/2 upper, lower */ } else if (intf >= 0x3C800000) /* if |x| >= (1/64)... */ { intz = (intf + 0x00040000) & 0x7ff80000;/* round arg, keep upper */ pz[0] = intz; /* store as a float (z) */ f2 = (f2 - z)/(pone + f2*z); index2 = (intz - 0x3C800000) >> 18; /* (index >> 19) << 1) */ index2 = index2 + 4; /* skip over 0,0,pi/2,pi/2 */ } else { index2 = 0; /* points to 0,0 in table */ } yaddr2 = y; /* address to store this answer */ x += stridex; /* point to next arg */ y += stridey; /* point to next result */ argcount = 3; /* we now have 3 good arguments */ if (--n <=0) { goto UNROLL; /* finish up with 2 good args */ } /*--------------------------------------------------------------------------*/ /*--------------------------------------------------------------------------*/ /*--------------------------------------------------------------------------*/ #ifdef UNROLL4 LOOP3: intf = *(int *) x; /* upper half of x, as integer */ f3 = *x; sign3 = pone; if (intf < 0) { intf = intf & ~0x80000000; /* abs(upper argument) */ f3 = -f3; sign3 = -sign3; } if ((intf > 0x5B000000) || (intf < 0x31800000)) /* filter out special cases */ { if (intf > 0x7f800000) { ansf = f3 - f3; /* return NaN if x=NaN*/ } else if (intf < 0x31800000) /* avoid underflow for small arg */ { dummy = 1.0e37 + f3; dummy = dummy; ansf = f3; } else if (intf > 0x5B000000) /* avoid underflow for big arg */ { index3 = 2; ansf = __vlibm_TBL_atan1[index3] ;/* pi/2 up */ } *y = sign3 * ansf; /* store answer, with sign bit */ x += stridex; y += stridey; argcount = 3; /* we still have 3 good args */ if (--n <=0) { goto UNROLL; /* finish up with 3 good args */ } goto LOOP3; /* otherwise, examine next arg */ } if (intf > 0x42800000) /* if (|x| > 64 */ { n3 = -pone; d3 = f3; f3 = n3/d3; index3 = 2; /* point to pi/2 upper, lower */ } else if (intf >= 0x3C800000) /* if |x| >= (1/64)... */ { intz = (intf + 0x00040000) & 0x7ff80000;/* round arg, keep upper */ pz[0] = intz; /* store as a float (z) */ n3 = (f3 - z); d3 = (pone + f3*z); /* get reduced argument */ f3 = n3/d3; index3 = (intz - 0x3C800000) >> 18; /* (index >> 19) << 1) */ index3 = index3 + 4; /* skip over 0,0,pi/2,pi/2 */ } else { n3 = f3; d3 = pone; index3 = 0; /* points to 0,0 in table */ } yaddr3 = y; /* address to store this answer */ x += stridex; /* point to next arg */ y += stridey; /* point to next result */ argcount = 4; /* we now have 4 good arguments */ if (--n <=0) { goto UNROLL; /* finish up with 3 good args */ } #endif /* UNROLL4 */ /* here is the n-way unrolled section, but we may actually have less than n arguments at this point */ UNROLL: #ifdef UNROLL4 if (argcount == 4) { conup0 = __vlibm_TBL_atan1[index0]; conup1 = __vlibm_TBL_atan1[index1]; conup2 = __vlibm_TBL_atan1[index2]; conup3 = __vlibm_TBL_atan1[index3]; poly0 = p1*f0*f0*f0 + f0; ans0 = sign0 * (float)(conup0 + poly0); poly1 = p1*f1*f1*f1 + f1; ans1 = sign1 * (float)(conup1 + poly1); poly2 = p1*f2*f2*f2 + f2; ans2 = sign2 * (float)(conup2 + poly2); poly3 = p1*f3*f3*f3 + f3; ans3 = sign3 * (float)(conup3 + poly3); *yaddr0 = ans0; *yaddr1 = ans1; *yaddr2 = ans2; *yaddr3 = ans3; } else #endif if (argcount == 3) { conup0 = __vlibm_TBL_atan1[index0]; conup1 = __vlibm_TBL_atan1[index1]; conup2 = __vlibm_TBL_atan1[index2]; poly0 = p1*f0*f0*f0 + f0; poly1 = p1*f1*f1*f1 + f1; poly2 = p1*f2*f2*f2 + f2; ans0 = sign0 * (float)(conup0 + poly0); ans1 = sign1 * (float)(conup1 + poly1); ans2 = sign2 * (float)(conup2 + poly2); *yaddr0 = ans0; *yaddr1 = ans1; *yaddr2 = ans2; } else if (argcount == 2) { conup0 = __vlibm_TBL_atan1[index0]; conup1 = __vlibm_TBL_atan1[index1]; poly0 = p1*f0*f0*f0 + f0; poly1 = p1*f1*f1*f1 + f1; ans0 = sign0 * (float)(conup0 + poly0); ans1 = sign1 * (float)(conup1 + poly1); *yaddr0 = ans0; *yaddr1 = ans1; } else if (argcount == 1) { conup0 = __vlibm_TBL_atan1[index0]; poly0 = p1*f0*f0*f0 + f0; ans0 = sign0 * (float)(conup0 + poly0); *yaddr0 = ans0; } } while (n > 0); }