e_rem_pio2f.c revision 2117 
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#ifndef lint
17static char rcsid[] = "$Id: e_rem_pio2f.c,v 1.2 1994/08/18 23:05:58 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 */
32#ifdef __STDC__
33static const int32_t two_over_pi[] = {
34#else
35static int32_t two_over_pi[] = {
36#endif
370xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
380x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
390x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
400xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
410x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
420xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
430xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
440x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
450x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
460x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
470x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
480x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
490x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
500x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
510xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
520xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
530x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
540xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
550x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
560x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
570x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
580x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
59};
60
61/* This array is like the one in e_rem_pio2.c, but the numbers are
62   single precision and the last 8 bits are forced to 0.  */
63#ifdef __STDC__
64static const int32_t npio2_hw[] = {
65#else
66static int32_t npio2_hw[] = {
67#endif
680x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
690x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
700x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
710x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
720x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
730x4242c700, 0x42490f00
74};
75
76/*
77 * invpio2:  24 bits of 2/pi
78 * pio2_1:   first  17 bit of pi/2
79 * pio2_1t:  pi/2 - pio2_1
80 * pio2_2:   second 17 bit of pi/2
81 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
82 * pio2_3:   third  17 bit of pi/2
83 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
84 */
85
86#ifdef __STDC__
87static const float
88#else
89static float
90#endif
91zero =  0.0000000000e+00, /* 0x00000000 */
92half =  5.0000000000e-01, /* 0x3f000000 */
93two8 =  2.5600000000e+02, /* 0x43800000 */
94invpio2 =  6.3661980629e-01, /* 0x3f22f984 */
95pio2_1  =  1.5707855225e+00, /* 0x3fc90f80 */
96pio2_1t =  1.0804334124e-05, /* 0x37354443 */
97pio2_2  =  1.0804273188e-05, /* 0x37354400 */
98pio2_2t =  6.0770999344e-11, /* 0x2e85a308 */
99pio2_3  =  6.0770943833e-11, /* 0x2e85a300 */
100pio2_3t =  6.1232342629e-17; /* 0x248d3132 */
101
102#ifdef __STDC__
103	int32_t __ieee754_rem_pio2f(float x, float *y)
104#else
105	int32_t __ieee754_rem_pio2f(x,y)
106	float x,y[];
107#endif
108{
109	float z,w,t,r,fn;
110	float tx[3];
111	int32_t e0,i,j,nx,n,ix,hx;
112
113	GET_FLOAT_WORD(hx,x);
114	ix = hx&0x7fffffff;
115	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
116	    {y[0] = x; y[1] = 0; return 0;}
117	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
118	    t  = fabsf(x);
119	    n  = (int32_t) (t*invpio2+half);
120	    fn = (float)n;
121	    r  = t-fn*pio2_1;
122	    w  = fn*pio2_1t;	/* 1st round good to 40 bit */
123	    if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
124		y[0] = r-w;	/* quick check no cancellation */
125	    } else {
126	        u_int32_t high;
127	        j  = ix>>23;
128	        y[0] = r-w;
129		GET_FLOAT_WORD(high,y[0]);
130	        i = j-((high>>23)&0xff);
131	        if(i>8) {  /* 2nd iteration needed, good to 57 */
132		    t  = r;
133		    w  = fn*pio2_2;
134		    r  = t-w;
135		    w  = fn*pio2_2t-((t-r)-w);
136		    y[0] = r-w;
137		    GET_FLOAT_WORD(high,y[0]);
138		    i = j-((high>>23)&0xff);
139		    if(i>25)  {	/* 3rd iteration need, 74 bits acc */
140		    	t  = r;	/* will cover all possible cases */
141		    	w  = fn*pio2_3;
142		    	r  = t-w;
143		    	w  = fn*pio2_3t-((t-r)-w);
144		    	y[0] = r-w;
145		    }
146		}
147	    }
148	    y[1] = (r-y[0])-w;
149	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
150	    else	 return n;
151	}
152    /*
153     * all other (large) arguments
154     */
155	if(ix>=0x7f800000) {		/* x is inf or NaN */
156	    y[0]=y[1]=x-x; return 0;
157	}
158    /* set z = scalbn(|x|,ilogb(x)-7) */
159	e0 	= (ix>>23)-134;		/* e0 = ilogb(z)-7; */
160	SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
161	for(i=0;i<2;i++) {
162		tx[i] = (float)((int32_t)(z));
163		z     = (z-tx[i])*two8;
164	}
165	tx[2] = z;
166	nx = 3;
167	while(tx[nx-1]==zero) nx--;	/* skip zero term */
168	n  =  __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
169	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
170	return n;
171}
172