| /* e_rem_pio2f.c -- float version of e_rem_pio2.c |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| */ |
| |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $"; |
| #endif |
| |
| /* __ieee754_rem_pio2f(x,y) |
| * |
| * return the remainder of x rem pi/2 in y[0]+y[1] |
| * use __kernel_rem_pio2f() |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| /* |
| * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
| */ |
| static const int32_t two_over_pi[] = { |
| 0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, |
| 0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, |
| 0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, |
| 0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, |
| 0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, |
| 0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, |
| 0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, |
| 0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, |
| 0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, |
| 0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, |
| 0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, |
| 0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, |
| 0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, |
| 0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, |
| 0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, |
| 0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, |
| 0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, |
| 0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, |
| 0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, |
| 0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, |
| 0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, |
| 0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, |
| }; |
| |
| /* This array is like the one in e_rem_pio2.c, but the numbers are |
| single precision and the last 8 bits are forced to 0. */ |
| static const int32_t npio2_hw[] = { |
| 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, |
| 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, |
| 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, |
| 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, |
| 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, |
| 0x4242c700, 0x42490f00 |
| }; |
| |
| /* |
| * invpio2: 24 bits of 2/pi |
| * pio2_1: first 17 bit of pi/2 |
| * pio2_1t: pi/2 - pio2_1 |
| * pio2_2: second 17 bit of pi/2 |
| * pio2_2t: pi/2 - (pio2_1+pio2_2) |
| * pio2_3: third 17 bit of pi/2 |
| * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
| */ |
| |
| static const float |
| zero = 0.0000000000e+00, /* 0x00000000 */ |
| half = 5.0000000000e-01, /* 0x3f000000 */ |
| two8 = 2.5600000000e+02, /* 0x43800000 */ |
| invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ |
| pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ |
| pio2_1t = 1.0804334124e-05, /* 0x37354443 */ |
| pio2_2 = 1.0804273188e-05, /* 0x37354400 */ |
| pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ |
| pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ |
| pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ |
| |
| int32_t __ieee754_rem_pio2f(float x, float *y) |
| { |
| float z,w,t,r,fn; |
| float tx[3]; |
| int32_t e0,i,j,nx,n,ix,hx; |
| |
| GET_FLOAT_WORD(hx,x); |
| ix = hx&0x7fffffff; |
| if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ |
| {y[0] = x; y[1] = 0; return 0;} |
| if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ |
| if(hx>0) { |
| z = x - pio2_1; |
| if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ |
| y[0] = z - pio2_1t; |
| y[1] = (z-y[0])-pio2_1t; |
| } else { /* near pi/2, use 24+24+24 bit pi */ |
| z -= pio2_2; |
| y[0] = z - pio2_2t; |
| y[1] = (z-y[0])-pio2_2t; |
| } |
| return 1; |
| } else { /* negative x */ |
| z = x + pio2_1; |
| if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ |
| y[0] = z + pio2_1t; |
| y[1] = (z-y[0])+pio2_1t; |
| } else { /* near pi/2, use 24+24+24 bit pi */ |
| z += pio2_2; |
| y[0] = z + pio2_2t; |
| y[1] = (z-y[0])+pio2_2t; |
| } |
| return -1; |
| } |
| } |
| if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ |
| t = fabsf(x); |
| n = (int32_t) (t*invpio2+half); |
| fn = (float)n; |
| r = t-fn*pio2_1; |
| w = fn*pio2_1t; /* 1st round good to 40 bit */ |
| if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) { |
| y[0] = r-w; /* quick check no cancellation */ |
| } else { |
| u_int32_t high; |
| j = ix>>23; |
| y[0] = r-w; |
| GET_FLOAT_WORD(high,y[0]); |
| i = j-((high>>23)&0xff); |
| if(i>8) { /* 2nd iteration needed, good to 57 */ |
| t = r; |
| w = fn*pio2_2; |
| r = t-w; |
| w = fn*pio2_2t-((t-r)-w); |
| y[0] = r-w; |
| GET_FLOAT_WORD(high,y[0]); |
| i = j-((high>>23)&0xff); |
| if(i>25) { /* 3rd iteration need, 74 bits acc */ |
| t = r; /* will cover all possible cases */ |
| w = fn*pio2_3; |
| r = t-w; |
| w = fn*pio2_3t-((t-r)-w); |
| y[0] = r-w; |
| } |
| } |
| } |
| y[1] = (r-y[0])-w; |
| if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| else return n; |
| } |
| /* |
| * all other (large) arguments |
| */ |
| if(ix>=0x7f800000) { /* x is inf or NaN */ |
| y[0]=y[1]=x-x; return 0; |
| } |
| /* set z = scalbn(|x|,ilogb(x)-7) */ |
| e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ |
| SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); |
| for(i=0;i<2;i++) { |
| tx[i] = (float)((int32_t)(z)); |
| z = (z-tx[i])*two8; |
| } |
| tx[2] = z; |
| nx = 3; |
| while(tx[nx-1]==zero) nx--; /* skip zero term */ |
| n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); |
| if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| return n; |
| } |
