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280 lines
6.6 KiB
C
280 lines
6.6 KiB
C
/* $NetBSD: fpu_hyperb.c,v 1.16 2013/10/11 03:37:08 isaki Exp $ */
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/*
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* Copyright (c) 1995 Ken Nakata
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the author nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* @(#)fpu_hyperb.c 10/24/95
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*/
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/*
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* Copyright (c) 2011 Tetsuya Isaki. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
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* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include <sys/cdefs.h>
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__KERNEL_RCSID(0, "$NetBSD: fpu_hyperb.c,v 1.16 2013/10/11 03:37:08 isaki Exp $");
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#include <machine/ieee.h>
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#include "fpu_emulate.h"
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/* The number of items to terminate the Taylor expansion */
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#define MAX_ITEMS (2000)
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/*
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* fpu_hyperb.c: defines the following functions
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*
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* fpu_atanh(), fpu_cosh(), fpu_sinh(), and fpu_tanh()
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*/
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/*
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* 1 1 + x
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* atanh(x) = ---*log(-------)
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* 2 1 - x
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*/
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struct fpn *
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fpu_atanh(struct fpemu *fe)
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{
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struct fpn x;
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struct fpn t;
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struct fpn *r;
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if (ISNAN(&fe->fe_f2))
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return &fe->fe_f2;
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if (ISINF(&fe->fe_f2))
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return fpu_newnan(fe);
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/* if x is +0/-0, return +0/-0 */
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if (ISZERO(&fe->fe_f2))
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return &fe->fe_f2;
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/*
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* -INF if x == -1
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* +INF if x == 1
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*/
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r = &fe->fe_f2;
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if (r->fp_exp == 0 && r->fp_mant[0] == FP_1 &&
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r->fp_mant[1] == 0 && r->fp_mant[2] == 0) {
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r->fp_class = FPC_INF;
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return r;
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}
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/* NAN if |x| > 1 */
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if (fe->fe_f2.fp_exp >= 0)
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return fpu_newnan(fe);
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CPYFPN(&x, &fe->fe_f2);
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/* t := 1 - x */
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fpu_const(&fe->fe_f1, FPU_CONST_1);
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fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
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r = fpu_add(fe);
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CPYFPN(&t, r);
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/* r := 1 + x */
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fpu_const(&fe->fe_f1, FPU_CONST_1);
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CPYFPN(&fe->fe_f2, &x);
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r = fpu_add(fe);
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/* (1-x)/(1+x) */
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CPYFPN(&fe->fe_f1, r);
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CPYFPN(&fe->fe_f2, &t);
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r = fpu_div(fe);
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/* log((1-x)/(1+x)) */
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CPYFPN(&fe->fe_f2, r);
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r = fpu_logn(fe);
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/* r /= 2 */
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r->fp_exp--;
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return r;
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}
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/*
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* taylor expansion used by sinh(), cosh().
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*/
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static struct fpn *
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__fpu_sinhcosh_taylor(struct fpemu *fe, struct fpn *s0, uint32_t f)
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{
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struct fpn res;
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struct fpn x2;
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struct fpn *s1;
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struct fpn *r;
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int sign;
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uint32_t k;
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/* x2 := x * x */
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CPYFPN(&fe->fe_f1, &fe->fe_f2);
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r = fpu_mul(fe);
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CPYFPN(&x2, r);
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/* res := s0 */
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CPYFPN(&res, s0);
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sign = 1; /* sign := (-1)^n */
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for (; f < (2 * MAX_ITEMS); ) {
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/* (f1 :=) s0 * x^2 */
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CPYFPN(&fe->fe_f1, s0);
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CPYFPN(&fe->fe_f2, &x2);
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r = fpu_mul(fe);
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CPYFPN(&fe->fe_f1, r);
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/*
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* for sinh(), s1 := s0 * x^2 / (2n+1)2n
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* for cosh(), s1 := s0 * x^2 / 2n(2n-1)
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*/
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k = f * (f + 1);
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fpu_explode(fe, &fe->fe_f2, FTYPE_LNG, &k);
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s1 = fpu_div(fe);
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/* break if s1 is enough small */
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if (ISZERO(s1))
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break;
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if (res.fp_exp - s1->fp_exp >= EXT_FRACBITS)
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break;
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/* s0 := s1 for next loop */
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CPYFPN(s0, s1);
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/* res += s1 */
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CPYFPN(&fe->fe_f2, s1);
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CPYFPN(&fe->fe_f1, &res);
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r = fpu_add(fe);
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CPYFPN(&res, r);
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f += 2;
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sign ^= 1;
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}
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CPYFPN(&fe->fe_f2, &res);
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return &fe->fe_f2;
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}
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struct fpn *
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fpu_cosh(struct fpemu *fe)
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{
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struct fpn s0;
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struct fpn *r;
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if (ISNAN(&fe->fe_f2))
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return &fe->fe_f2;
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if (ISINF(&fe->fe_f2)) {
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fe->fe_f2.fp_sign = 0;
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return &fe->fe_f2;
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}
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fpu_const(&s0, FPU_CONST_1);
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r = __fpu_sinhcosh_taylor(fe, &s0, 1);
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return r;
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}
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struct fpn *
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fpu_sinh(struct fpemu *fe)
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{
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struct fpn s0;
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struct fpn *r;
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if (ISNAN(&fe->fe_f2))
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return &fe->fe_f2;
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if (ISINF(&fe->fe_f2))
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return &fe->fe_f2;
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/* if x is +0/-0, return +0/-0 */
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if (ISZERO(&fe->fe_f2))
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return &fe->fe_f2;
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CPYFPN(&s0, &fe->fe_f2);
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r = __fpu_sinhcosh_taylor(fe, &s0, 2);
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return r;
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}
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struct fpn *
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fpu_tanh(struct fpemu *fe)
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{
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struct fpn x;
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struct fpn s;
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struct fpn *r;
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int sign;
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if (ISNAN(&fe->fe_f2))
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return &fe->fe_f2;
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/* if x is +0/-0, return +0/-0 */
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if (ISZERO(&fe->fe_f2))
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return &fe->fe_f2;
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if (ISINF(&fe->fe_f2)) {
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sign = fe->fe_f2.fp_sign;
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fpu_const(&fe->fe_f2, FPU_CONST_1);
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fe->fe_f2.fp_sign = sign;
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return &fe->fe_f2;
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}
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CPYFPN(&x, &fe->fe_f2);
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/* sinh(x) */
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CPYFPN(&fe->fe_f2, &x);
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r = fpu_sinh(fe);
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CPYFPN(&s, r);
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/* cosh(x) */
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CPYFPN(&fe->fe_f2, &x);
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r = fpu_cosh(fe);
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CPYFPN(&fe->fe_f2, r);
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CPYFPN(&fe->fe_f1, &s);
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r = fpu_div(fe);
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return r;
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}
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