1/* e_rem_pio2f.c -- float version of e_rem_pio2.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16#if defined(LIBM_SCCS) && !defined(lint)
17static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";
18#endif
19
20/* __ieee754_rem_pio2f(x,y)
21 *
22 * return the remainder of x rem pi/2 in y[0]+y[1]
23 * use __kernel_rem_pio2f()
24 */
25
26#include <math.h>
27#include <math_private.h>
28
29/*
30 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
31 */
32static const int32_t two_over_pi[] = {
330xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
340x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
350x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
360xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
370x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
380xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
390xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
400x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
410x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
420x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
430x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
440x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
450x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
460x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
470xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
480xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
490x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
500xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
510x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
520x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
530x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
540x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
55};
56
57/* This array is like the one in e_rem_pio2.c, but the numbers are
58 single precision and the last 8 bits are forced to 0. */
59static const int32_t npio2_hw[] = {
600x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
610x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
620x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
630x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
640x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
650x4242c700, 0x42490f00
66};
67
68/*
69 * invpio2: 24 bits of 2/pi
70 * pio2_1: first 17 bit of pi/2
71 * pio2_1t: pi/2 - pio2_1
72 * pio2_2: second 17 bit of pi/2
73 * pio2_2t: pi/2 - (pio2_1+pio2_2)
74 * pio2_3: third 17 bit of pi/2
75 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
76 */
77
78static const float
79zero = 0.0000000000e+00, /* 0x00000000 */
80half = 5.0000000000e-01, /* 0x3f000000 */
81two8 = 2.5600000000e+02, /* 0x43800000 */
82invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
83pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
84pio2_1t = 1.0804334124e-05, /* 0x37354443 */
85pio2_2 = 1.0804273188e-05, /* 0x37354400 */
86pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
87pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
88pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
89
90int32_t __ieee754_rem_pio2f(float x, float *y)
91{
92 float z,w,t,r,fn;
93 float tx[3];
94 int32_t e0,i,j,nx,n,ix,hx;
95
96 GET_FLOAT_WORD(hx,x);
97 ix = hx&0x7fffffff;
98 if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
99 {y[0] = x; y[1] = 0; return 0;}
100 if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
101 if(hx>0) {
102 z = x - pio2_1;
103 if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
104 y[0] = z - pio2_1t;
105 y[1] = (z-y[0])-pio2_1t;
106 } else { /* near pi/2, use 24+24+24 bit pi */
107 z -= pio2_2;
108 y[0] = z - pio2_2t;
109 y[1] = (z-y[0])-pio2_2t;
110 }
111 return 1;
112 } else { /* negative x */
113 z = x + pio2_1;
114 if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
115 y[0] = z + pio2_1t;
116 y[1] = (z-y[0])+pio2_1t;
117 } else { /* near pi/2, use 24+24+24 bit pi */
118 z += pio2_2;
119 y[0] = z + pio2_2t;
120 y[1] = (z-y[0])+pio2_2t;
121 }
122 return -1;
123 }
124 }
125 if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
126 t = fabsf(x);
127 n = (int32_t) (t*invpio2+half);
128 fn = (float)n;
129 r = t-fn*pio2_1;
130 w = fn*pio2_1t; /* 1st round good to 40 bit */
131 if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) {
132 y[0] = r-w; /* quick check no cancellation */
133 } else {
134 u_int32_t high;
135 j = ix>>23;
136 y[0] = r-w;
137 GET_FLOAT_WORD(high,y[0]);
138 i = j-((high>>23)&0xff);
139 if(i>8) { /* 2nd iteration needed, good to 57 */
140 t = r;
141 w = fn*pio2_2;
142 r = t-w;
143 w = fn*pio2_2t-((t-r)-w);
144 y[0] = r-w;
145 GET_FLOAT_WORD(high,y[0]);
146 i = j-((high>>23)&0xff);
147 if(i>25) { /* 3rd iteration need, 74 bits acc */
148 t = r; /* will cover all possible cases */
149 w = fn*pio2_3;
150 r = t-w;
151 w = fn*pio2_3t-((t-r)-w);
152 y[0] = r-w;
153 }
154 }
155 }
156 y[1] = (r-y[0])-w;
157 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
158 else return n;
159 }
160 /*
161 * all other (large) arguments
162 */
163 if(ix>=0x7f800000) { /* x is inf or NaN */
164 y[0]=y[1]=x-x; return 0;
165 }
166 /* set z = scalbn(|x|,ilogb(x)-7) */
167 e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */
168 SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
169 for(i=0;i<2;i++) {
170 tx[i] = (float)((int32_t)(z));
171 z = (z-tx[i])*two8;
172 }
173 tx[2] = z;
174 nx = 3;
175 while(tx[nx-1]==zero) nx--; /* skip zero term */
176 n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
177 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
178 return n;
179}
180