212 lines
6.4 KiB
C
212 lines
6.4 KiB
C
/*
|
|
* This file is part of the MicroPython project, http://micropython.org/
|
|
*
|
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
|
*
|
|
* Appropriate copyright headers are reproduced below.
|
|
*/
|
|
|
|
/* ef_rem_pio2.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 "fdlibm.h"
|
|
|
|
/*
|
|
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
|
*/
|
|
#ifdef __STDC__
|
|
static const __uint8_t two_over_pi[] = {
|
|
#else
|
|
static __uint8_t two_over_pi[] = {
|
|
#endif
|
|
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. */
|
|
#ifdef __STDC__
|
|
static const __int32_t npio2_hw[] = {
|
|
#else
|
|
static __int32_t npio2_hw[] = {
|
|
#endif
|
|
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)
|
|
*/
|
|
|
|
#ifdef __STDC__
|
|
static const float
|
|
#else
|
|
static float
|
|
#endif
|
|
zero = 0.0000000000e+00f, /* 0x00000000 */
|
|
half = 5.0000000000e-01f, /* 0x3f000000 */
|
|
two8 = 2.5600000000e+02f, /* 0x43800000 */
|
|
invpio2 = 6.3661980629e-01f, /* 0x3f22f984 */
|
|
pio2_1 = 1.5707855225e+00f, /* 0x3fc90f80 */
|
|
pio2_1t = 1.0804334124e-05f, /* 0x37354443 */
|
|
pio2_2 = 1.0804273188e-05f, /* 0x37354400 */
|
|
pio2_2t = 6.0770999344e-11f, /* 0x2e85a308 */
|
|
pio2_3 = 6.0770943833e-11f, /* 0x2e85a300 */
|
|
pio2_3t = 6.1232342629e-17f; /* 0x248d3132 */
|
|
|
|
#ifdef __STDC__
|
|
__int32_t __ieee754_rem_pio2f(float x, float *y)
|
|
#else
|
|
__int32_t __ieee754_rem_pio2f(x,y)
|
|
float x,y[];
|
|
#endif
|
|
{
|
|
float z,w,t,r,fn;
|
|
float tx[3];
|
|
__int32_t i,j,n,ix,hx;
|
|
int e0,nx;
|
|
|
|
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 CIRCUITPY_FULL_BUILD
|
|
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 {
|
|
__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;
|
|
}
|
|
#else
|
|
// Suppress "defined but not used" diagnostics
|
|
(void) j; (void) fn; (void) r; (void) t; (void) w; (void) pio2_3t;
|
|
(void) pio2_3; (void) invpio2; (void)half; (void)npio2_hw;
|
|
#endif
|
|
/*
|
|
* all other (large) arguments
|
|
*/
|
|
if(!FLT_UWORD_IS_FINITE(ix)) {
|
|
y[0]=y[1]=x-x; return 0;
|
|
}
|
|
/* set z = scalbn(|x|,ilogb(x)-7) */
|
|
e0 = (int)((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;
|
|
#pragma GCC diagnostic push
|
|
#pragma GCC diagnostic ignored "-Wfloat-equal"
|
|
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
|
#pragma GCC diagnostic pop
|
|
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;
|
|
}
|