diff options
Diffstat (limited to 'sysdeps/libm-ieee754')
| -rw-r--r-- | sysdeps/libm-ieee754/e_jnf.c | 31 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/e_pow.c | 46 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/e_powf.c | 26 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/e_rem_pio2f.c | 50 |
4 files changed, 77 insertions, 76 deletions
diff --git a/sysdeps/libm-ieee754/e_jnf.c b/sysdeps/libm-ieee754/e_jnf.c index b9951f6b43..9e5279c30a 100644 --- a/sysdeps/libm-ieee754/e_jnf.c +++ b/sysdeps/libm-ieee754/e_jnf.c @@ -8,7 +8,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -53,7 +53,7 @@ static float zero = 0.0000000000e+00; ix = 0x7fffffff&hx; /* if J(n,NaN) is NaN */ if(ix>0x7f800000) return x+x; - if(n<0){ + if(n<0){ n = -n; x = -x; hx ^= 0x80000000; @@ -64,7 +64,7 @@ static float zero = 0.0000000000e+00; x = fabsf(x); if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */ b = zero; - else if((float)n<=x) { + else if((float)n<=x) { /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ a = __ieee754_j0f(x); b = __ieee754_j1f(x); @@ -75,7 +75,7 @@ static float zero = 0.0000000000e+00; } } else { if(ix<0x30800000) { /* x < 2**-29 */ - /* x is tiny, return the first Taylor expansion of J(n,x) + /* x is tiny, return the first Taylor expansion of J(n,x) * J(n,x) = 1/n!*(x/2)^n - ... */ if(n>33) /* underflow */ @@ -90,14 +90,14 @@ static float zero = 0.0000000000e+00; } } else { /* use backward recurrence */ - /* x x^2 x^2 + /* x x^2 x^2 * J(n,x)/J(n-1,x) = ---- ------ ------ ..... * 2n - 2(n+1) - 2(n+2) * - * 1 1 1 + * 1 1 1 * (for large x) = ---- ------ ------ ..... * 2n 2(n+1) 2(n+2) - * -- - ------ - ------ - + * -- - ------ - ------ - * x x x * * Let w = 2n/x and h=2/x, then the above quotient @@ -113,9 +113,9 @@ static float zero = 0.0000000000e+00; * To determine how many terms needed, let * Q(0) = w, Q(1) = w(w+h) - 1, * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), - * When Q(k) > 1e4 good for single - * When Q(k) > 1e9 good for double - * When Q(k) > 1e17 good for quadruple + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple */ /* determine k */ float t,v; @@ -137,7 +137,7 @@ static float zero = 0.0000000000e+00; * single 8.8722839355e+01 * double 7.09782712893383973096e+02 * long double 1.1356523406294143949491931077970765006170e+04 - * then recurrent value may overflow and the result is + * then recurrent value may overflow and the result is * likely underflow to zero */ tmp = n; @@ -173,13 +173,14 @@ static float zero = 0.0000000000e+00; } #ifdef __STDC__ - float __ieee754_ynf(int n, float x) + float __ieee754_ynf(int n, float x) #else - float __ieee754_ynf(n,x) + float __ieee754_ynf(n,x) int n; float x; #endif { - int32_t i,hx,ix,ib; + int32_t i,hx,ix; + u_int32_t ib; int32_t sign; float a, b, temp; @@ -202,7 +203,7 @@ static float zero = 0.0000000000e+00; b = __ieee754_y1f(x); /* quit if b is -inf */ GET_FLOAT_WORD(ib,b); - for(i=1;i<n&&ib!=0xff800000;i++){ + for(i=1;i<n&&ib!=0xff800000;i++){ temp = b; b = ((float)(i+i)/x)*b - a; GET_FLOAT_WORD(ib,b); diff --git a/sysdeps/libm-ieee754/e_pow.c b/sysdeps/libm-ieee754/e_pow.c index 0d42381946..4b9ba3d5eb 100644 --- a/sysdeps/libm-ieee754/e_pow.c +++ b/sysdeps/libm-ieee754/e_pow.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -21,7 +21,7 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; * 1. Compute and return log2(x) in two pieces: * log2(x) = w1 + w2, * where w1 has 53-24 = 29 bit trailing zeros. - * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * 2. Perform y*log2(x) = n+y' by simulating muti-precision * arithmetic, where |y'|<=0.5. * 3. Return x**y = 2**n*exp(y'*log2) * @@ -49,13 +49,13 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; * Accuracy: * pow(x,y) returns x**y nearly rounded. In particular * pow(integer,integer) - * always returns the correct integer provided it is + * always returns the correct integer provided it is * representable. * * Constants : - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough * to produce the hexadecimal values shown. */ @@ -63,9 +63,9 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif bp[] = {1.0, 1.5,}, dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ @@ -117,12 +117,12 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ ix = hx&0x7fffffff; iy = hy&0x7fffffff; /* y==zero: x**0 = 1 */ - if((iy|ly)==0) return one; + if((iy|ly)==0) return one; /* +-NaN return x+y */ if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || - iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) - return x+y; + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return x+y; /* determine if y is an odd int when x < 0 * yisint = 0 ... y is not an integer @@ -130,22 +130,22 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ * yisint = 2 ... y is an even int */ yisint = 0; - if(hx<0) { + if(hx<0) { if(iy>=0x43400000) yisint = 2; /* even integer y */ else if(iy>=0x3ff00000) { k = (iy>>20)-0x3ff; /* exponent */ if(k>20) { j = ly>>(52-k); - if((j<<(52-k))==ly) yisint = 2-(j&1); + if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1); } else if(ly==0) { j = iy>>(20-k); - if((j<<(20-k))==iy) yisint = 2-(j&1); + if((int32_t)(j<<(20-k))==iy) yisint = 2-(j&1); } - } - } + } + } /* special value of y */ - if(ly==0) { + if(ly==0) { if (iy==0x7ff00000) { /* y is +-inf */ if(((ix-0x3ff00000)|lx)==0) return y - y; /* inf**+-1 is NaN */ @@ -153,14 +153,14 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ return (hy>=0)? y: zero; else /* (|x|<1)**-,+inf = inf,0 */ return (hy<0)?-y: zero; - } + } if(iy==0x3ff00000) { /* y is +-1 */ if(hy<0) return one/x; else return x; } if(hy==0x40000000) return x*x; /* y is 2 */ if(hy==0x3fe00000) { /* y is 0.5 */ if(hx>=0) /* x >= +0 */ - return __ieee754_sqrt(x); + return __ieee754_sqrt(x); } } @@ -173,13 +173,13 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ if(hx<0) { if(((ix-0x3ff00000)|yisint)==0) { z = (z-z)/(z-z); /* (-1)**non-int is NaN */ - } else if(yisint==1) + } else if(yisint==1) z = -z; /* (x<0)**odd = -(|x|**odd) */ } return z; } } - + /* (x<0)**(non-int) is NaN */ if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); @@ -192,7 +192,7 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ /* over/underflow if x is not close to one */ if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; - /* now |1-x| is tiny <= 2**-20, suffice to compute + /* now |1-x| is tiny <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 */ t = x-1; /* t has 20 trailing zeros */ w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); @@ -289,7 +289,7 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ n = ((n&0x000fffff)|0x00100000)>>(20-k); if(j<0) n = -n; p_h -= t; - } + } t = p_l+p_h; SET_LOW_WORD(t,0); u = t*lg2_h; diff --git a/sysdeps/libm-ieee754/e_powf.c b/sysdeps/libm-ieee754/e_powf.c index 37e32ab3ca..1358555128 100644 --- a/sysdeps/libm-ieee754/e_powf.c +++ b/sysdeps/libm-ieee754/e_powf.c @@ -8,7 +8,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -74,12 +74,12 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ ix = hx&0x7fffffff; iy = hy&0x7fffffff; /* y==zero: x**0 = 1 */ - if(iy==0) return one; + if(iy==0) return one; /* +-NaN return x+y */ if(ix > 0x7f800000 || iy > 0x7f800000) - return x+y; + return x+y; /* determine if y is an odd int when x < 0 * yisint = 0 ... y is not an integer @@ -87,14 +87,14 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ * yisint = 2 ... y is an even int */ yisint = 0; - if(hx<0) { + if(hx<0) { if(iy>=0x4b800000) yisint = 2; /* even integer y */ else if(iy>=0x3f800000) { k = (iy>>23)-0x7f; /* exponent */ j = iy>>(23-k); if((j<<(23-k))==iy) yisint = 2-(j&1); - } - } + } + } /* special value of y */ if (iy==0x7f800000) { /* y is +-inf */ @@ -104,14 +104,14 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ return (hy>=0)? y: zero; else /* (|x|<1)**-,+inf = inf,0 */ return (hy<0)?-y: zero; - } + } if(iy==0x3f800000) { /* y is +-1 */ if(hy<0) return one/x; else return x; } if(hy==0x40000000) return x*x; /* y is 2 */ if(hy==0x3f000000) { /* y is 0.5 */ if(hx>=0) /* x >= +0 */ - return __ieee754_sqrtf(x); + return __ieee754_sqrtf(x); } ax = fabsf(x); @@ -122,12 +122,12 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ if(hx<0) { if(((ix-0x3f800000)|yisint)==0) { z = (z-z)/(z-z); /* (-1)**non-int is NaN */ - } else if(yisint==1) + } else if(yisint==1) z = -z; /* (x<0)**odd = -(|x|**odd) */ } return z; } - + /* (x<0)**(non-int) is NaN */ if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); @@ -136,7 +136,7 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ /* over/underflow if x is not close to one */ if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; - /* now |1-x| is tiny <= 2**-20, suffice to compute + /* now |1-x| is tiny <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 */ t = x-1; /* t has 20 trailing zeros */ w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); @@ -217,7 +217,7 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ } else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ return s*tiny*tiny; /* underflow */ - else if (j==0xc3160000){ /* z == -150 */ + else if ((u_int32_t) j==0xc3160000){ /* z == -150 */ if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ } /* @@ -233,7 +233,7 @@ ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ n = ((n&0x007fffff)|0x00800000)>>(23-k); if(j<0) n = -n; p_h -= t; - } + } t = p_l+p_h; GET_FLOAT_WORD(is,t); SET_FLOAT_WORD(t,is&0xfffff000); diff --git a/sysdeps/libm-ieee754/e_rem_pio2f.c b/sysdeps/libm-ieee754/e_rem_pio2f.c index e5d50a11b4..4b8c4466bd 100644 --- a/sysdeps/libm-ieee754/e_rem_pio2f.c +++ b/sysdeps/libm-ieee754/e_rem_pio2f.c @@ -8,7 +8,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -18,8 +18,8 @@ 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] + * + * return the remainder of x rem pi/2 in y[0]+y[1] * use __kernel_rem_pio2f() */ @@ -27,7 +27,7 @@ static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp #include "math_private.h" /* - * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi */ #ifdef __STDC__ static const int32_t two_over_pi[] = { @@ -35,27 +35,27 @@ static const int32_t two_over_pi[] = { static int32_t two_over_pi[] = { #endif 0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, -0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, +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, +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, +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, +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, +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, +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, +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, +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, +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, +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, +0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, }; /* This array is like the one in e_rem_pio2.c, but the numbers are @@ -84,9 +84,9 @@ static int32_t npio2_hw[] = { */ #ifdef __STDC__ -static const float +static const float #else -static float +static float #endif zero = 0.0000000000e+00, /* 0x00000000 */ half = 5.0000000000e-01, /* 0x3f000000 */ @@ -115,7 +115,7 @@ pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ 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) { + if(hx>0) { z = x - pio2_1; if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ y[0] = z - pio2_1t; @@ -145,27 +145,27 @@ pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ 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]) { + 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; + 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; + w = fn*pio2_2; r = t-w; - w = fn*pio2_2t-((t-r)-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; + w = fn*pio2_3; r = t-w; - w = fn*pio2_3t-((t-r)-w); + w = fn*pio2_3t-((t-r)-w); y[0] = r-w; } } @@ -174,7 +174,7 @@ pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ 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 */ |