diff options
Diffstat (limited to 'src/math/e_rem_pio2f.c')
| -rw-r--r-- | src/math/e_rem_pio2f.c | 175 |
1 files changed, 175 insertions, 0 deletions
diff --git a/src/math/e_rem_pio2f.c b/src/math/e_rem_pio2f.c new file mode 100644 index 00000000..4992ea0c --- /dev/null +++ b/src/math/e_rem_pio2f.c @@ -0,0 +1,175 @@ +/* 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. + * ==================================================== + */ + +/* __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&&(ix&0xffffff00)!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + uint32_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; +} |