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asincos.c
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asincos.c
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/*
* Correctly rounded arcsine and arccosine
*
* Copyright (c) 2007 Christoph Lauter (ENS Lyon),
* with Sylvain Chevillard (ENS Lyon) for the polynomials
*
* This file is part of the crlibm library developed by the Arenaire
* project at Ecole Normale Superieure de Lyon
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
#include <stdio.h>
#include <stdlib.h>
#include "crlibm.h"
#include "crlibm_private.h"
#include "triple-double.h"
#include "asincos.h"
static inline void p0_quick(double *p_resh, double *p_resm, double x, int32_t xhi) {
double p_x_0_pow2h, p_x_0_pow2m;
double p_t_1_0h;
double p_t_2_0h;
double p_t_3_0h;
double p_t_4_0h;
double p_t_5_0h;
double p_t_6_0h;
double p_t_7_0h;
double p_t_8_0h;
double p_t_9_0h;
double p_t_10_0h;
double p_t_11_0h;
double p_t_12_0h;
double p_t_13_0h;
double p_t_14_0h;
double p_t_15_0h;
double p_t_16_0h;
double p_t_17_0h, p_t_17_0m;
double p_t_18_0h, p_t_18_0m;
double p_t_19_0h, p_t_19_0m;
double p_t_20_0h, p_t_20_0m;
if (xhi < EXTRABOUND2) {
double t1, t2, t3;
t2 = p0_quick_coeff_3h * x;
t1 = x * x;
t3 = t1 * t2;
Add12(*p_resh,*p_resm,x,t3);
return;
}
Mul12(&p_x_0_pow2h,&p_x_0_pow2m,x,x);
p_t_15_0h = p0_quick_coeff_5h;
if (xhi > EXTRABOUND) {
p_t_1_0h = p0_quick_coeff_19h;
p_t_2_0h = p_t_1_0h * p_x_0_pow2h;
p_t_3_0h = p0_quick_coeff_17h + p_t_2_0h;
p_t_4_0h = p_t_3_0h * p_x_0_pow2h;
p_t_5_0h = p0_quick_coeff_15h + p_t_4_0h;
p_t_6_0h = p_t_5_0h * p_x_0_pow2h;
p_t_7_0h = p0_quick_coeff_13h + p_t_6_0h;
p_t_8_0h = p_t_7_0h * p_x_0_pow2h;
p_t_9_0h = p0_quick_coeff_11h + p_t_8_0h;
p_t_10_0h = p_t_9_0h * p_x_0_pow2h;
p_t_11_0h = p0_quick_coeff_9h + p_t_10_0h;
p_t_12_0h = p_t_11_0h * p_x_0_pow2h;
p_t_13_0h = p0_quick_coeff_7h + p_t_12_0h;
p_t_14_0h = p_t_13_0h * p_x_0_pow2h;
p_t_15_0h = p_t_15_0h + p_t_14_0h;
}
p_t_16_0h = p_t_15_0h * p_x_0_pow2h;
Add12(p_t_17_0h,p_t_17_0m,p0_quick_coeff_3h,p_t_16_0h);
Mul122(&p_t_18_0h,&p_t_18_0m,x,p_x_0_pow2h,p_x_0_pow2m);
Mul22(&p_t_19_0h,&p_t_19_0m,p_t_17_0h,p_t_17_0m,p_t_18_0h,p_t_18_0m);
Add122(&p_t_20_0h,&p_t_20_0m,x,p_t_19_0h,p_t_19_0m);
*p_resh = p_t_20_0h; *p_resm = p_t_20_0m;
}
static inline void p_quick(double *p_resh, double *p_resm, double x, int index) {
double p_t_1_0h;
double p_t_2_0h;
double p_t_3_0h;
double p_t_4_0h;
double p_t_5_0h;
double p_t_6_0h;
double p_t_7_0h;
double p_t_8_0h;
double p_t_9_0h;
double p_t_10_0h;
double p_t_11_0h;
double p_t_12_0h;
double p_t_13_0h;
double p_t_14_0h;
double p_t_15_0h;
double p_t_16_0h;
double p_t_17_0h;
double p_t_18_0h;
double p_t_19_0h;
double p_t_20_0h;
double p_t_21_0h, p_t_21_0m;
double p_t_22_0h, p_t_22_0m;
double p_t_23_0h, p_t_23_0m;
p_t_1_0h = p_quick_coeff_12h;
p_t_2_0h = p_t_1_0h * x;
p_t_3_0h = p_quick_coeff_11h + p_t_2_0h;
p_t_4_0h = p_t_3_0h * x;
p_t_5_0h = p_quick_coeff_10h + p_t_4_0h;
p_t_6_0h = p_t_5_0h * x;
p_t_7_0h = p_quick_coeff_9h + p_t_6_0h;
p_t_8_0h = p_t_7_0h * x;
p_t_9_0h = p_quick_coeff_8h + p_t_8_0h;
p_t_10_0h = p_t_9_0h * x;
p_t_11_0h = p_quick_coeff_7h + p_t_10_0h;
p_t_12_0h = p_t_11_0h * x;
p_t_13_0h = p_quick_coeff_6h + p_t_12_0h;
p_t_14_0h = p_t_13_0h * x;
p_t_15_0h = p_quick_coeff_5h + p_t_14_0h;
p_t_16_0h = p_t_15_0h * x;
p_t_17_0h = p_quick_coeff_4h + p_t_16_0h;
p_t_18_0h = p_t_17_0h * x;
p_t_19_0h = p_quick_coeff_3h + p_t_18_0h;
p_t_20_0h = p_t_19_0h * x;
Add12(p_t_21_0h,p_t_21_0m,p_quick_coeff_2h,p_t_20_0h);
MulAdd212(&p_t_22_0h,&p_t_22_0m,p_quick_coeff_1h,p_quick_coeff_1m,x,p_t_21_0h,p_t_21_0m);
MulAdd212(&p_t_23_0h,&p_t_23_0m,p_quick_coeff_0h,p_quick_coeff_0m,x,p_t_22_0h,p_t_22_0m);
*p_resh = p_t_23_0h; *p_resm = p_t_23_0m;
}
static inline void p9_quick(double *p_resh, double *p_resm, double x) {
double p_t_1_0h;
double p_t_2_0h;
double p_t_3_0h;
double p_t_4_0h;
double p_t_5_0h;
double p_t_6_0h;
double p_t_7_0h;
double p_t_8_0h;
double p_t_9_0h;
double p_t_10_0h;
double p_t_11_0h;
double p_t_12_0h;
double p_t_13_0h;
double p_t_14_0h;
double p_t_15_0h;
double p_t_16_0h;
double p_t_17_0h;
double p_t_18_0h;
double p_t_19_0h;
double p_t_20_0h;
double p_t_21_0h, p_t_21_0m;
double p_t_22_0h, p_t_22_0m;
double p_t_23_0h, p_t_23_0m;
p_t_1_0h = p9_quick_coeff_11h;
p_t_2_0h = p_t_1_0h * x;
p_t_3_0h = p9_quick_coeff_10h + p_t_2_0h;
p_t_4_0h = p_t_3_0h * x;
p_t_5_0h = p9_quick_coeff_9h + p_t_4_0h;
p_t_6_0h = p_t_5_0h * x;
p_t_7_0h = p9_quick_coeff_8h + p_t_6_0h;
p_t_8_0h = p_t_7_0h * x;
p_t_9_0h = p9_quick_coeff_7h + p_t_8_0h;
p_t_10_0h = p_t_9_0h * x;
p_t_11_0h = p9_quick_coeff_6h + p_t_10_0h;
p_t_12_0h = p_t_11_0h * x;
p_t_13_0h = p9_quick_coeff_5h + p_t_12_0h;
p_t_14_0h = p_t_13_0h * x;
p_t_15_0h = p9_quick_coeff_4h + p_t_14_0h;
p_t_16_0h = p_t_15_0h * x;
p_t_17_0h = p9_quick_coeff_3h + p_t_16_0h;
p_t_18_0h = p_t_17_0h * x;
p_t_19_0h = p9_quick_coeff_2h + p_t_18_0h;
p_t_20_0h = p_t_19_0h * x;
Add12(p_t_21_0h,p_t_21_0m,p9_quick_coeff_1h,p_t_20_0h);
Mul122(&p_t_22_0h,&p_t_22_0m,x,p_t_21_0h,p_t_21_0m);
Add122(&p_t_23_0h,&p_t_23_0m,p9_quick_coeff_0h,p_t_22_0h,p_t_22_0m);
*p_resh = p_t_23_0h; *p_resm = p_t_23_0m;
}
static void p0_accu(double *p_resh, double *p_resm, double *p_resl, double x) {
double p_x_0_pow2h, p_x_0_pow2m;
Mul12(&p_x_0_pow2h,&p_x_0_pow2m,x,x);
double p_t_1_0h;
double p_t_2_0h;
double p_t_3_0h;
double p_t_4_0h;
double p_t_5_0h;
double p_t_6_0h;
double p_t_7_0h, p_t_7_0m;
double p_t_8_0h, p_t_8_0m;
double p_t_9_0h, p_t_9_0m;
double p_t_10_0h, p_t_10_0m;
double p_t_11_0h, p_t_11_0m;
double p_t_12_0h, p_t_12_0m;
double p_t_13_0h, p_t_13_0m;
double p_t_14_0h, p_t_14_0m;
double p_t_15_0h, p_t_15_0m;
double p_t_16_0h, p_t_16_0m;
double p_t_17_0h, p_t_17_0m;
double p_t_18_0h, p_t_18_0m;
double p_t_19_0h, p_t_19_0m;
double p_t_20_0h, p_t_20_0m;
double p_t_21_0h, p_t_21_0m;
double p_t_22_0h, p_t_22_0m;
double p_t_23_0h, p_t_23_0m;
double p_t_24_0h, p_t_24_0m;
double p_t_25_0h, p_t_25_0m;
double p_t_26_0h, p_t_26_0m;
double p_t_27_0h, p_t_27_0m;
double p_t_28_0h, p_t_28_0m, p_t_28_0l;
double p_t_29_0h, p_t_29_0m, p_t_29_0l;
double p_t_30_0h, p_t_30_0m, p_t_30_0l;
double p_t_31_0h, p_t_31_0m, p_t_31_0l;
double p_t_32_0h, p_t_32_0m, p_t_32_0l;
double p_t_33_0h, p_t_33_0m, p_t_33_0l;
double p_t_34_0h, p_t_34_0m, p_t_34_0l;
double p_t_35_0h, p_t_35_0m, p_t_35_0l;
p_t_1_0h = p0_accu_coeff_37h;
p_t_2_0h = p_t_1_0h * p_x_0_pow2h;
p_t_3_0h = p0_accu_coeff_35h + p_t_2_0h;
p_t_4_0h = p_t_3_0h * p_x_0_pow2h;
p_t_5_0h = p0_accu_coeff_33h + p_t_4_0h;
p_t_6_0h = p_t_5_0h * p_x_0_pow2h;
Add12(p_t_7_0h,p_t_7_0m,p0_accu_coeff_31h,p_t_6_0h);
Mul22(&p_t_8_0h,&p_t_8_0m,p_t_7_0h,p_t_7_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_9_0h,&p_t_9_0m,p0_accu_coeff_29h,p_t_8_0h,p_t_8_0m);
Mul22(&p_t_10_0h,&p_t_10_0m,p_t_9_0h,p_t_9_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_11_0h,&p_t_11_0m,p0_accu_coeff_27h,p_t_10_0h,p_t_10_0m);
Mul22(&p_t_12_0h,&p_t_12_0m,p_t_11_0h,p_t_11_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_13_0h,&p_t_13_0m,p0_accu_coeff_25h,p_t_12_0h,p_t_12_0m);
Mul22(&p_t_14_0h,&p_t_14_0m,p_t_13_0h,p_t_13_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_15_0h,&p_t_15_0m,p0_accu_coeff_23h,p_t_14_0h,p_t_14_0m);
Mul22(&p_t_16_0h,&p_t_16_0m,p_t_15_0h,p_t_15_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_17_0h,&p_t_17_0m,p0_accu_coeff_21h,p_t_16_0h,p_t_16_0m);
Mul22(&p_t_18_0h,&p_t_18_0m,p_t_17_0h,p_t_17_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_19_0h,&p_t_19_0m,p0_accu_coeff_19h,p_t_18_0h,p_t_18_0m);
Mul22(&p_t_20_0h,&p_t_20_0m,p_t_19_0h,p_t_19_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_21_0h,&p_t_21_0m,p0_accu_coeff_17h,p_t_20_0h,p_t_20_0m);
Mul22(&p_t_22_0h,&p_t_22_0m,p_t_21_0h,p_t_21_0m,p_x_0_pow2h,p_x_0_pow2m);
Add122(&p_t_23_0h,&p_t_23_0m,p0_accu_coeff_15h,p_t_22_0h,p_t_22_0m);
MulAdd22(&p_t_24_0h,&p_t_24_0m,p0_accu_coeff_13h,p0_accu_coeff_13m,p_x_0_pow2h,p_x_0_pow2m,p_t_23_0h,p_t_23_0m);
MulAdd22(&p_t_25_0h,&p_t_25_0m,p0_accu_coeff_11h,p0_accu_coeff_11m,p_x_0_pow2h,p_x_0_pow2m,p_t_24_0h,p_t_24_0m);
MulAdd22(&p_t_26_0h,&p_t_26_0m,p0_accu_coeff_9h,p0_accu_coeff_9m,p_x_0_pow2h,p_x_0_pow2m,p_t_25_0h,p_t_25_0m);
Mul22(&p_t_27_0h,&p_t_27_0m,p_t_26_0h,p_t_26_0m,p_x_0_pow2h,p_x_0_pow2m);
Add23(&p_t_28_0h,&p_t_28_0m,&p_t_28_0l,p0_accu_coeff_7h,p0_accu_coeff_7m,p_t_27_0h,p_t_27_0m);
Mul233(&p_t_29_0h,&p_t_29_0m,&p_t_29_0l,p_x_0_pow2h,p_x_0_pow2m,p_t_28_0h,p_t_28_0m,p_t_28_0l);
Add233(&p_t_30_0h,&p_t_30_0m,&p_t_30_0l,p0_accu_coeff_5h,p0_accu_coeff_5m,p_t_29_0h,p_t_29_0m,p_t_29_0l);
Mul233(&p_t_31_0h,&p_t_31_0m,&p_t_31_0l,p_x_0_pow2h,p_x_0_pow2m,p_t_30_0h,p_t_30_0m,p_t_30_0l);
Add233(&p_t_32_0h,&p_t_32_0m,&p_t_32_0l,p0_accu_coeff_3h,p0_accu_coeff_3m,p_t_31_0h,p_t_31_0m,p_t_31_0l);
Mul233(&p_t_33_0h,&p_t_33_0m,&p_t_33_0l,p_x_0_pow2h,p_x_0_pow2m,p_t_32_0h,p_t_32_0m,p_t_32_0l);
Add133(&p_t_34_0h,&p_t_34_0m,&p_t_34_0l,p0_accu_coeff_1h,p_t_33_0h,p_t_33_0m,p_t_33_0l);
Mul133(&p_t_35_0h,&p_t_35_0m,&p_t_35_0l,x,p_t_34_0h,p_t_34_0m,p_t_34_0l);
Renormalize3(p_resh,p_resm,p_resl,p_t_35_0h,p_t_35_0m,p_t_35_0l);
}
static void p_accu(double *p_resh, double *p_resm, double *p_resl, double x, int index) {
double p_t_1_0h;
double p_t_2_0h;
double p_t_3_0h;
double p_t_4_0h;
double p_t_5_0h;
double p_t_6_0h;
double p_t_7_0h;
double p_t_8_0h;
double p_t_9_0h;
double p_t_10_0h;
double p_t_11_0h;
double p_t_12_0h;
double p_t_13_0h;
double p_t_14_0h;
double p_t_15_0h;
double p_t_16_0h;
double p_t_17_0h, p_t_17_0m;
double p_t_18_0h, p_t_18_0m;
double p_t_19_0h, p_t_19_0m;
double p_t_20_0h, p_t_20_0m;
double p_t_21_0h, p_t_21_0m;
double p_t_22_0h, p_t_22_0m;
double p_t_23_0h, p_t_23_0m;
double p_t_24_0h, p_t_24_0m;
double p_t_25_0h, p_t_25_0m;
double p_t_26_0h, p_t_26_0m;
double p_t_27_0h, p_t_27_0m;
double p_t_28_0h, p_t_28_0m;
double p_t_29_0h, p_t_29_0m;
double p_t_30_0h, p_t_30_0m;
double p_t_31_0h, p_t_31_0m;
double p_t_32_0h, p_t_32_0m;
double p_t_33_0h, p_t_33_0m;
double p_t_34_0h, p_t_34_0m;
double p_t_35_0h, p_t_35_0m, p_t_35_0l;
double p_t_36_0h, p_t_36_0m, p_t_36_0l;
double p_t_37_0h, p_t_37_0m, p_t_37_0l;
double p_t_38_0h, p_t_38_0m, p_t_38_0l;
double p_t_39_0h, p_t_39_0m, p_t_39_0l;
p_t_1_0h = p_accu_coeff_22h;
p_t_2_0h = p_t_1_0h * x;
p_t_3_0h = p_accu_coeff_21h + p_t_2_0h;
p_t_4_0h = p_t_3_0h * x;
p_t_5_0h = p_accu_coeff_20h + p_t_4_0h;
p_t_6_0h = p_t_5_0h * x;
p_t_7_0h = p_accu_coeff_19h + p_t_6_0h;
p_t_8_0h = p_t_7_0h * x;
p_t_9_0h = p_accu_coeff_18h + p_t_8_0h;
p_t_10_0h = p_t_9_0h * x;
p_t_11_0h = p_accu_coeff_17h + p_t_10_0h;
p_t_12_0h = p_t_11_0h * x;
p_t_13_0h = p_accu_coeff_16h + p_t_12_0h;
p_t_14_0h = p_t_13_0h * x;
p_t_15_0h = p_accu_coeff_15h + p_t_14_0h;
p_t_16_0h = p_t_15_0h * x;
Add12(p_t_17_0h,p_t_17_0m,p_accu_coeff_14h,p_t_16_0h);
Mul122(&p_t_18_0h,&p_t_18_0m,x,p_t_17_0h,p_t_17_0m);
Add122(&p_t_19_0h,&p_t_19_0m,p_accu_coeff_13h,p_t_18_0h,p_t_18_0m);
Mul122(&p_t_20_0h,&p_t_20_0m,x,p_t_19_0h,p_t_19_0m);
Add122(&p_t_21_0h,&p_t_21_0m,p_accu_coeff_12h,p_t_20_0h,p_t_20_0m);
Mul122(&p_t_22_0h,&p_t_22_0m,x,p_t_21_0h,p_t_21_0m);
Add122(&p_t_23_0h,&p_t_23_0m,p_accu_coeff_11h,p_t_22_0h,p_t_22_0m);
Mul122(&p_t_24_0h,&p_t_24_0m,x,p_t_23_0h,p_t_23_0m);
Add122(&p_t_25_0h,&p_t_25_0m,p_accu_coeff_10h,p_t_24_0h,p_t_24_0m);
Mul122(&p_t_26_0h,&p_t_26_0m,x,p_t_25_0h,p_t_25_0m);
Add122(&p_t_27_0h,&p_t_27_0m,p_accu_coeff_9h,p_t_26_0h,p_t_26_0m);
MulAdd212(&p_t_28_0h,&p_t_28_0m,p_accu_coeff_8h,p_accu_coeff_8m,x,p_t_27_0h,p_t_27_0m);
MulAdd212(&p_t_29_0h,&p_t_29_0m,p_accu_coeff_7h,p_accu_coeff_7m,x,p_t_28_0h,p_t_28_0m);
MulAdd212(&p_t_30_0h,&p_t_30_0m,p_accu_coeff_6h,p_accu_coeff_6m,x,p_t_29_0h,p_t_29_0m);
MulAdd212(&p_t_31_0h,&p_t_31_0m,p_accu_coeff_5h,p_accu_coeff_5m,x,p_t_30_0h,p_t_30_0m);
MulAdd212(&p_t_32_0h,&p_t_32_0m,p_accu_coeff_4h,p_accu_coeff_4m,x,p_t_31_0h,p_t_31_0m);
MulAdd212(&p_t_33_0h,&p_t_33_0m,p_accu_coeff_3h,p_accu_coeff_3m,x,p_t_32_0h,p_t_32_0m);
Mul122(&p_t_34_0h,&p_t_34_0m,x,p_t_33_0h,p_t_33_0m);
Add23(&p_t_35_0h,&p_t_35_0m,&p_t_35_0l,p_accu_coeff_2h,p_accu_coeff_2m,p_t_34_0h,p_t_34_0m);
Mul133(&p_t_36_0h,&p_t_36_0m,&p_t_36_0l,x,p_t_35_0h,p_t_35_0m,p_t_35_0l);
Add233(&p_t_37_0h,&p_t_37_0m,&p_t_37_0l,p_accu_coeff_1h,p_accu_coeff_1m,p_t_36_0h,p_t_36_0m,p_t_36_0l);
Mul133(&p_t_38_0h,&p_t_38_0m,&p_t_38_0l,x,p_t_37_0h,p_t_37_0m,p_t_37_0l);
Add233(&p_t_39_0h,&p_t_39_0m,&p_t_39_0l,p_accu_coeff_0h,p_accu_coeff_0m,p_t_38_0h,p_t_38_0m,p_t_38_0l);
Renormalize3(p_resh,p_resm,p_resl,p_t_39_0h,p_t_39_0m,p_t_39_0l);
}
static void p9_accu(double *p_resh, double *p_resm, double *p_resl, double x) {
double p_t_1_0h;
double p_t_2_0h;
double p_t_3_0h;
double p_t_4_0h;
double p_t_5_0h;
double p_t_6_0h;
double p_t_7_0h;
double p_t_8_0h;
double p_t_9_0h;
double p_t_10_0h;
double p_t_11_0h;
double p_t_12_0h;
double p_t_13_0h;
double p_t_14_0h;
double p_t_15_0h;
double p_t_16_0h;
double p_t_17_0h, p_t_17_0m;
double p_t_18_0h, p_t_18_0m;
double p_t_19_0h, p_t_19_0m;
double p_t_20_0h, p_t_20_0m;
double p_t_21_0h, p_t_21_0m;
double p_t_22_0h, p_t_22_0m;
double p_t_23_0h, p_t_23_0m;
double p_t_24_0h, p_t_24_0m;
double p_t_25_0h, p_t_25_0m;
double p_t_26_0h, p_t_26_0m;
double p_t_27_0h, p_t_27_0m;
double p_t_28_0h, p_t_28_0m;
double p_t_29_0h, p_t_29_0m;
double p_t_30_0h, p_t_30_0m;
double p_t_31_0h, p_t_31_0m;
double p_t_32_0h, p_t_32_0m;
double p_t_33_0h, p_t_33_0m, p_t_33_0l;
double p_t_34_0h, p_t_34_0m, p_t_34_0l;
double p_t_35_0h, p_t_35_0m, p_t_35_0l;
p_t_1_0h = p9_accu_coeff_20h;
p_t_2_0h = p_t_1_0h * x;
p_t_3_0h = p9_accu_coeff_19h + p_t_2_0h;
p_t_4_0h = p_t_3_0h * x;
p_t_5_0h = p9_accu_coeff_18h + p_t_4_0h;
p_t_6_0h = p_t_5_0h * x;
p_t_7_0h = p9_accu_coeff_17h + p_t_6_0h;
p_t_8_0h = p_t_7_0h * x;
p_t_9_0h = p9_accu_coeff_16h + p_t_8_0h;
p_t_10_0h = p_t_9_0h * x;
p_t_11_0h = p9_accu_coeff_15h + p_t_10_0h;
p_t_12_0h = p_t_11_0h * x;
p_t_13_0h = p9_accu_coeff_14h + p_t_12_0h;
p_t_14_0h = p_t_13_0h * x;
p_t_15_0h = p9_accu_coeff_13h + p_t_14_0h;
p_t_16_0h = p_t_15_0h * x;
Add12(p_t_17_0h,p_t_17_0m,p9_accu_coeff_12h,p_t_16_0h);
Mul122(&p_t_18_0h,&p_t_18_0m,x,p_t_17_0h,p_t_17_0m);
Add122(&p_t_19_0h,&p_t_19_0m,p9_accu_coeff_11h,p_t_18_0h,p_t_18_0m);
Mul122(&p_t_20_0h,&p_t_20_0m,x,p_t_19_0h,p_t_19_0m);
Add122(&p_t_21_0h,&p_t_21_0m,p9_accu_coeff_10h,p_t_20_0h,p_t_20_0m);
Mul122(&p_t_22_0h,&p_t_22_0m,x,p_t_21_0h,p_t_21_0m);
Add122(&p_t_23_0h,&p_t_23_0m,p9_accu_coeff_9h,p_t_22_0h,p_t_22_0m);
Mul122(&p_t_24_0h,&p_t_24_0m,x,p_t_23_0h,p_t_23_0m);
Add122(&p_t_25_0h,&p_t_25_0m,p9_accu_coeff_8h,p_t_24_0h,p_t_24_0m);
MulAdd212(&p_t_26_0h,&p_t_26_0m,p9_accu_coeff_7h,p9_accu_coeff_7m,x,p_t_25_0h,p_t_25_0m);
MulAdd212(&p_t_27_0h,&p_t_27_0m,p9_accu_coeff_6h,p9_accu_coeff_6m,x,p_t_26_0h,p_t_26_0m);
MulAdd212(&p_t_28_0h,&p_t_28_0m,p9_accu_coeff_5h,p9_accu_coeff_5m,x,p_t_27_0h,p_t_27_0m);
MulAdd212(&p_t_29_0h,&p_t_29_0m,p9_accu_coeff_4h,p9_accu_coeff_4m,x,p_t_28_0h,p_t_28_0m);
MulAdd212(&p_t_30_0h,&p_t_30_0m,p9_accu_coeff_3h,p9_accu_coeff_3m,x,p_t_29_0h,p_t_29_0m);
MulAdd212(&p_t_31_0h,&p_t_31_0m,p9_accu_coeff_2h,p9_accu_coeff_2m,x,p_t_30_0h,p_t_30_0m);
Mul122(&p_t_32_0h,&p_t_32_0m,x,p_t_31_0h,p_t_31_0m);
Add23(&p_t_33_0h,&p_t_33_0m,&p_t_33_0l,p9_accu_coeff_1h,p9_accu_coeff_1m,p_t_32_0h,p_t_32_0m);
Mul133(&p_t_34_0h,&p_t_34_0m,&p_t_34_0l,x,p_t_33_0h,p_t_33_0m,p_t_33_0l);
Add233(&p_t_35_0h,&p_t_35_0m,&p_t_35_0l,p9_accu_coeff_0h,p9_accu_coeff_0m,p_t_34_0h,p_t_34_0m,p_t_34_0l);
Renormalize3(p_resh,p_resm,p_resl,p_t_35_0h,p_t_35_0m,p_t_35_0l);
}
double asin_rn(double x) {
db_number xdb, zdb;
double sign, z, zp;
int index;
double asinh, asinm, asinl;
double asinhover, asinmover, asinlover;
double p9h, p9m, p9l, sqrh, sqrm, sqrl;
double t1h, t1m, t1l;
double asin;
double xabs;
/* Start already computations for argument reduction */
zdb.d = 1.0 + x * x;
xdb.d = x;
/* Special case handling */
/* Remove sign of x in floating-point */
xabs = ABS(x);
xdb.i[HI] &= 0x7fffffff;
/* If |x| < 2^(-28) we have
arcsin(x) = x * ( 1 + xi )
with 0 <= xi < 2^(-55)
So we can decide the rounding without any computation
*/
if (xdb.i[HI] < ASINSIMPLEBOUND) {
return x;
}
/* asin is defined on -1 <= x <= 1, elsewhere it is NaN */
if (xdb.i[HI] >= 0x3ff00000) {
if (x == 1.0) {
return PIHALFH;
}
if (x == -1.0) {
return - PIHALFH;
}
return (x-x)/0.0; /* return NaN */
}
/* Argument reduction:
We have 10 intervals and 3 paths:
- interval 0 => path 1 using p0
- interval 1-8 => path 2 using p
- interval 9 => path 3 using p9
*/
index = (0x000f0000 & zdb.i[HI]) >> 16;
/* 0 <= index <= 15
index approximates roughly x^2
Map indexes to intervals as follows:
0 -> 0
1 -> 1
...
8 -> 8
9 -> 9
...
15 -> 9
For this mapping, filter first the case 0 -> 0
In consequence, 1 <= index <= 15, i.e.
0 <= index - 1 <= 14 with the mapping index - 1 -> interval as
0 -> 1
...
7 -> 8
8 -> 9
...
15 -> 9
Thus it suffices to check the 3rd bit of index - 1 after the first filter.
*/
if (index == 0) {
/* Path 1 using p0 */
p0_quick(&asinh, &asinm, x, xdb.i[HI]);
/* Rounding test */
if(asinh == (asinh + (asinm * RNROUNDCST)))
return asinh;
/* Rounding test failed, launch accurate phase */
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
p0_accu(&asinh, &asinm, &asinl, x);
/* Final rounding */
RoundToNearest3(&asin,asinh,asinm,asinl);
return asin;
}
/* Strip off the sign of argument x */
sign = 1.0;
if (x < 0.0) sign = -sign;
index--;
if ((index & 0x8) != 0) {
/* Path 3 using p9 */
/* Do argument reduction using a MI_9 as a midpoint value
for the polynomial and compute exactly zp = 2 * (1 - x)
for the asymptotical approximation using a square root.
*/
z = xabs - MI_9;
zp = 2.0 * (1.0 - xabs);
/* Polynomial approximation and square root extraction */
p9_quick(&p9h, &p9m, z);
p9h = -p9h;
p9m = -p9m;
sqrt12_64_unfiltered(&sqrh,&sqrm,zp);
/* Reconstruction */
Mul22(&t1h,&t1m,sqrh,sqrm,p9h,p9m);
Add22(&asinh,&asinm,PIHALFH,PIHALFM,t1h,t1m);
/* Rounding test */
if(asinh == (asinh + (asinm * RNROUNDCST)))
return sign * asinh;
/* Rounding test failed, launch accurate phase */
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
p9_accu(&p9h, &p9m, &p9l, z);
p9h = -p9h;
p9m = -p9m;
p9l = -p9l;
Sqrt13(&sqrh,&sqrm,&sqrl,zp);
/* Reconstruction */
Mul33(&t1h,&t1m,&t1l,sqrh,sqrm,sqrl,p9h,p9m,p9l);
Add33(&asinhover,&asinmover,&asinlover,PIHALFH,PIHALFM,PIHALFL,t1h,t1m,t1l);
Renormalize3(&asinh,&asinm,&asinl,asinhover,asinmover,asinlover);
/* Final rounding */
RoundToNearest3(&asin,asinh,asinm,asinl);
return sign * asin;
}
/* Path 2 using p */
/* Do argument reduction using a table value for
the midpoint value
*/
z = xabs - mi_i;
p_quick(&asinh, &asinm, z, index);
/* Rounding test */
if(asinh == (asinh + (asinm * RNROUNDCST)))
return sign * asinh;
/* Rounding test failed, launch accurate phase */
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
p_accu(&asinh, &asinm, &asinl, z, index);
/* Final rounding */
RoundToNearest3(&asin,asinh,asinm,asinl);
return sign * asin;
}
double asin_ru(double x) {
db_number xdb, zdb;
double sign, z, zp;
int index;
double asinh, asinm, asinl;
double asinhover, asinmover, asinlover;
double p9h, p9m, p9l, sqrh, sqrm, sqrl;
double t1h, t1m, t1l;
double xabs;
/* Start already computations for argument reduction */
zdb.d = 1.0 + x * x;
xdb.d = x;
/* Special case handling */
/* Remove sign of x in floating-point */
xabs = ABS(x);
xdb.i[HI] &= 0x7fffffff;
/* If |x| < 2^(-28) we have
arcsin(x) = x * ( 1 + xi )
with 0 <= xi < 2^(-55)
So we can decide the rounding without any computation
*/
if (xdb.i[HI] < ASINSIMPLEBOUND) {
/* If x == 0 then we got the algebraic result arcsin(0) = 0
If x < 0 then the truncation rest is negative but less than
1 ulp; we round upwards by returning x
*/
if (x <= 0.0) return x;
/* Otherwise the rest is positive, less than 1 ulp and the
image is not algebraic
We return x + 1ulp
*/
xdb.l++;
return xdb.d;
}
/* asin is defined on -1 <= x <= 1, elsewhere it is NaN */
if (xdb.i[HI] >= 0x3ff00000) {
if (x == 1.0) {
return PIHALFRU;
}
if (x == -1.0) {
return - PIHALFH;
}
return (x-x)/0.0; /* return NaN */
}
/* Argument reduction:
We have 10 intervals and 3 paths:
- interval 0 => path 1 using p0
- interval 1-8 => path 2 using p
- interval 9 => path 3 using p9
*/
index = (0x000f0000 & zdb.i[HI]) >> 16;
/* 0 <= index <= 15
index approximates roughly x^2
Map indexes to intervals as follows:
0 -> 0
1 -> 1
...
8 -> 8
9 -> 9
...
15 -> 9
For this mapping, filter first the case 0 -> 0
In consequence, 1 <= index <= 15, i.e.
0 <= index - 1 <= 14 with the mapping index - 1 -> interval as
0 -> 1
...
7 -> 8
8 -> 9
...
15 -> 9
Thus it suffices to check the 3rd bit of index - 1 after the first filter.
*/
if (index == 0) {
/* Path 1 using p0 */
p0_quick(&asinh, &asinm, x, xdb.i[HI]);
/* Rounding test */
TEST_AND_RETURN_RU(asinh, asinm, RDROUNDCST);
/* Rounding test failed, launch accurate phase */
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
p0_accu(&asinh, &asinm, &asinl, x);
/* Final rounding */
ReturnRoundUpwards3(asinh,asinm,asinl);
}
/* Strip off the sign of argument x */
sign = 1.0;
if (x < 0.0) sign = -sign;
index--;
if ((index & 0x8) != 0) {
/* Path 3 using p9 */
/* Do argument reduction using a MI_9 as a midpoint value
for the polynomial and compute exactly zp = 2 * (1 - x)
for the asymptotical approximation using a square root.
*/
z = xabs - MI_9;
zp = 2.0 * (1.0 - xabs);
/* Polynomial approximation and square root extraction */
p9_quick(&p9h, &p9m, z);
p9h = -p9h;
p9m = -p9m;
sqrt12_64_unfiltered(&sqrh,&sqrm,zp);
/* Reconstruction */
Mul22(&t1h,&t1m,sqrh,sqrm,p9h,p9m);
Add22(&asinh,&asinm,PIHALFH,PIHALFM,t1h,t1m);
/* Rounding test */
asinh *= sign;
asinm *= sign;
TEST_AND_RETURN_RU(asinh, asinm, RDROUNDCST);
/* Rounding test failed, launch accurate phase */
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
p9_accu(&p9h, &p9m, &p9l, z);
p9h = -p9h;
p9m = -p9m;
p9l = -p9l;
Sqrt13(&sqrh,&sqrm,&sqrl,zp);
/* Reconstruction */
Mul33(&t1h,&t1m,&t1l,sqrh,sqrm,sqrl,p9h,p9m,p9l);
Add33(&asinhover,&asinmover,&asinlover,PIHALFH,PIHALFM,PIHALFL,t1h,t1m,t1l);
Renormalize3(&asinh,&asinm,&asinl,asinhover,asinmover,asinlover);
/* Final rounding */
asinh *= sign;
asinm *= sign;
asinl *= sign;
ReturnRoundUpwards3(asinh,asinm,asinl);
}
/* Path 2 using p */
/* Do argument reduction using a table value for
the midpoint value
*/
z = xabs - mi_i;
p_quick(&asinh, &asinm, z, index);
/* Rounding test */
asinh *= sign;
asinm *= sign;
TEST_AND_RETURN_RU(asinh, asinm, RDROUNDCST);
/* Rounding test failed, launch accurate phase */
#if EVAL_PERF
crlibm_second_step_taken++;
#endif
if (x == ASINBADCASEX) return ASINBADCASEYRU;
p_accu(&asinh, &asinm, &asinl, z, index);
/* Final rounding */
asinh *= sign;
asinm *= sign;
asinl *= sign;
ReturnRoundUpwards3(asinh,asinm,asinl);
}
double asin_rd(double x) {
db_number xdb, zdb;
double sign, z, zp;
int index;
double asinh, asinm, asinl;
double asinhover, asinmover, asinlover;
double p9h, p9m, p9l, sqrh, sqrm, sqrl;
double t1h, t1m, t1l;
double xabs;
/* Start already computations for argument reduction */
zdb.d = 1.0 + x * x;
xdb.d = x;
/* Special case handling */
/* Remove sign of x in floating-point */
xabs = ABS(x);
xdb.i[HI] &= 0x7fffffff;
/* If |x| < 2^(-28) we have
arcsin(x) = x * ( 1 + xi )
with 0 <= xi < 2^(-55)
So we can decide the rounding without any computation
*/
if (xdb.i[HI] < ASINSIMPLEBOUND) {
/* If x == 0 then we got the algebraic result arcsin(0) = 0
If x > 0 then the truncation rest is positive but less than
1 ulp; we round downwards by returning x
*/
if (x >= 0) return x;
/* Otherwise the rest is negative, less than 1 ulp and the
image is not algebraic
We return x - 1ulp
We stripped off the sign, so we add 1 ulp to -x (in xdb.d) and multiply by -1
*/
xdb.l++;
return -1 * xdb.d;
}
/* asin is defined on -1 <= x <= 1, elsewhere it is NaN */
if (xdb.i[HI] >= 0x3ff00000) {
if (x == 1.0) {
return PIHALFH;
}
if (x == -1.0) {
return - PIHALFRU;
}
return (x-x)/0.0; /* return NaN */
}
/* Argument reduction:
We have 10 intervals and 3 paths:
- interval 0 => path 1 using p0
- interval 1-8 => path 2 using p
- interval 9 => path 3 using p9
*/
index = (0x000f0000 & zdb.i[HI]) >> 16;
/* 0 <= index <= 15
index approximates roughly x^2
Map indexes to intervals as follows:
0 -> 0
1 -> 1
...
8 -> 8
9 -> 9
...
15 -> 9
For this mapping, filter first the case 0 -> 0