1131852Sdas/* From: @(#)e_rem_pio2.c 1.4 95/01/18 */ 2131852Sdas/* 3131852Sdas * ==================================================== 4131852Sdas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5131852Sdas * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 6131852Sdas * 7131852Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 8131852Sdas * Permission to use, copy, modify, and distribute this 9131852Sdas * software is freely granted, provided that this notice 10131852Sdas * is preserved. 11131852Sdas * ==================================================== 12131852Sdas * 13131852Sdas * Optimized by Bruce D. Evans. 14131852Sdas */ 15131852Sdas 16131852Sdas#include <sys/cdefs.h> 17131852Sdas#if 0 18131852Sdas__FBSDID("$FreeBSD: head/lib/msun/ld128/e_rem_pio2l.h 336545 2018-07-20 12:42:24Z bde $"); 19131852Sdas#endif 20131852Sdas 21131852Sdas/* ld128 version of __ieee754_rem_pio2l(x,y) 22131852Sdas * 23131852Sdas * return the remainder of x rem pi/2 in y[0]+y[1] 24131852Sdas * use __kernel_rem_pio2() 25131852Sdas */ 26131852Sdas 27131852Sdas#include <float.h> 28131852Sdas#include <machine/ieee.h> 29131852Sdas 30131852Sdas#include "math.h" 31131852Sdas#include "math_private.h" 32131852Sdas 33131852Sdas#define BIAS (LDBL_MAX_EXP - 1) 34131852Sdas 35131852Sdas/* 36131852Sdas * XXX need to verify that nonzero integer multiples of pi/2 within the 37131852Sdas * range get no closer to a long double than 2**-140, or that 38131852Sdas * ilogb(x) + ilogb(min_delta) < 45 - -140. 39131852Sdas */ 40131852Sdas/* 41131852Sdas * invpio2: 113 bits of 2/pi 42131852Sdas * pio2_1: first 68 bits of pi/2 43131852Sdas * pio2_1t: pi/2 - pio2_1 44131852Sdas * pio2_2: second 68 bits of pi/2 45131852Sdas * pio2_2t: pi/2 - (pio2_1+pio2_2) 46131852Sdas * pio2_3: third 68 bits of pi/2 47131852Sdas * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 48131852Sdas */ 49131852Sdas 50131852Sdasstatic const double 51131852Sdaszero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 52131852Sdastwo24 = 1.67772160000000000000e+07; /* 0x41700000, 0x00000000 */ 53131852Sdas 54131852Sdasstatic const long double 55131852Sdasinvpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */ 56131852Sdaspio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */ 57131852Sdaspio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */ 58131852Sdaspio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */ 59pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */ 60pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */ 61pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */ 62 63static inline __always_inline int 64__ieee754_rem_pio2l(long double x, long double *y) 65{ 66 union ieee_ext_u u,u1; 67 long double z,w,t,r,fn; 68 double tx[5],ty[3]; 69 int64_t n; 70 int e0,ex,i,j,nx; 71 int16_t expsign, expsign1; 72 73 u.extu_ld = x; 74 ex = u.extu_exp; 75 expsign = u.extu_exp | (u.extu_sign << 15); 76 if (ex < BIAS + 45 || (ex == BIAS + 45 && 77 u.extu_frach < 0x921fb54442d1LL)) { 78 /* |x| ~< 2^45*(pi/2), medium size */ 79 /* TODO: use only double precision for fn, as in expl(). */ 80 fn = rnintl(x * invpio2); 81 n = i64rint(fn); 82 r = x-fn*pio2_1; 83 w = fn*pio2_1t; /* 1st round good to 180 bit */ 84 { 85 union ieee_ext_u u2; 86 int ex1; 87 j = ex; 88 y[0] = r-w; 89 u2.extu_ld = y[0]; 90 ex1 = u2.extu_exp; 91 i = j-ex1; 92 if(i>51) { /* 2nd iteration needed, good to 248 */ 93 t = r; 94 w = fn*pio2_2; 95 r = t-w; 96 w = fn*pio2_2t-((t-r)-w); 97 y[0] = r-w; 98 u2.extu_ld = y[0]; 99 ex1 = u2.extu_exp; 100 i = j-ex1; 101 if(i>119) { /* 3rd iteration need, 316 bits acc */ 102 t = r; /* will cover all possible cases */ 103 w = fn*pio2_3; 104 r = t-w; 105 w = fn*pio2_3t-((t-r)-w); 106 y[0] = r-w; 107 } 108 } 109 } 110 y[1] = (r-y[0])-w; 111 return n; 112 } 113 /* 114 * all other (large) arguments 115 */ 116 if(ex==0x7fff) { /* x is inf or NaN */ 117 y[0]=y[1]=x-x; return 0; 118 } 119 /* set z = scalbn(|x|,ilogb(x)-23) */ 120 u1.extu_ld = x; 121 e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */ 122 expsign1 = ex - e0; 123 u1.extu_exp = expsign1; 124 u1.extu_sign = expsign1 >> 15; 125 z = u1.extu_ld; 126 for(i=0;i<4;i++) { 127 tx[i] = (double)((int32_t)(z)); 128 z = (z-tx[i])*two24; 129 } 130 tx[4] = z; 131 nx = 5; 132 while(tx[nx-1]==zero) nx--; /* skip zero term */ 133 n = __kernel_rem_pio2(tx,ty,e0,nx,3); 134 t = (long double)ty[2] + ty[1]; 135 r = t + ty[0]; 136 w = ty[0] - (r - t); 137 if(expsign<0) {y[0] = -r; y[1] = -w; return -n;} 138 y[0] = r; y[1] = w; return n; 139} 140