diff options
Diffstat (limited to 'libc/sysdeps/ieee754/dbl-64/s_expm1.c')
| -rw-r--r-- | libc/sysdeps/ieee754/dbl-64/s_expm1.c | 78 |
1 files changed, 33 insertions, 45 deletions
diff --git a/libc/sysdeps/ieee754/dbl-64/s_expm1.c b/libc/sysdeps/ieee754/dbl-64/s_expm1.c index 324354336..589128c08 100644 --- a/libc/sysdeps/ieee754/dbl-64/s_expm1.c +++ b/libc/sysdeps/ieee754/dbl-64/s_expm1.c @@ -13,10 +13,6 @@ for performance improvement on pipelined processors. */ -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; -#endif - /* expm1(x) * Returns exp(x)-1, the exponential of x minus 1. * @@ -40,38 +36,38 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... * We use a special Reme algorithm on [0,0.347] to generate - * a polynomial of degree 5 in r*r to approximate R1. The + * a polynomial of degree 5 in r*r to approximate R1. The * maximum error of this polynomial approximation is bounded * by 2**-61. In other words, * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 - * where Q1 = -1.6666666666666567384E-2, - * Q2 = 3.9682539681370365873E-4, - * Q3 = -9.9206344733435987357E-6, - * Q4 = 2.5051361420808517002E-7, - * Q5 = -6.2843505682382617102E-9; - * (where z=r*r, and the values of Q1 to Q5 are listed below) + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * (where z=r*r, and the values of Q1 to Q5 are listed below) * with error bounded by * | 5 | -61 * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 * | | * * expm1(r) = exp(r)-1 is then computed by the following - * specific way which minimize the accumulation rounding error: + * specific way which minimize the accumulation rounding error: * 2 3 * r r [ 3 - (R1 + R1*r/2) ] * expm1(r) = r + --- + --- * [--------------------] - * 2 2 [ 6 - r*(3 - R1*r/2) ] + * 2 2 [ 6 - r*(3 - R1*r/2) ] * * To compensate the error in the argument reduction, we use * expm1(r+c) = expm1(r) + c + expm1(r)*c * ~ expm1(r) + c + r*c * Thus c+r*c will be added in as the correction terms for * expm1(r+c). Now rearrange the term to avoid optimization - * screw up: - * ( 2 2 ) - * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) - * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) * ( ) * * = r - E @@ -87,7 +83,7 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; * (ii) if k=0, return r-E * (iii) if k=-1, return 0.5*(r-E)-0.5 * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) - * else return 1.0+2.0*(r-E); + * else return 1.0+2.0*(r-E); * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else * (vii) return 2^k(1-((E+2^-k)-r)) @@ -116,11 +112,7 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; #include "math.h" #include "math_private.h" #define one Q[0] -#ifdef __STDC__ static const double -#else -static double -#endif huge = 1.0e+300, tiny = 1.0e-300, o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ @@ -134,12 +126,8 @@ Q[] = {1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */ 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ -2.01099218183624371326e-07}; /* BE8AFDB7 6E09C32D */ -#ifdef __STDC__ - double __expm1(double x) -#else - double __expm1(x) - double x; -#endif +double +__expm1(double x) { double y,hi,lo,c,t,e,hxs,hfx,r1,h2,h4,R1,R2,R3; int32_t k,xsb; @@ -153,20 +141,20 @@ Q[] = {1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */ /* filter out huge and non-finite argument */ if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ if(hx >= 0x40862E42) { /* if |x|>=709.78... */ - if(hx>=0x7ff00000) { + if(hx>=0x7ff00000) { u_int32_t low; GET_LOW_WORD(low,x); if(((hx&0xfffff)|low)!=0) - return x+x; /* NaN */ + return x+x; /* NaN */ else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ - } - if(x > o_threshold) { + } + if(x > o_threshold) { __set_errno (ERANGE); return huge*huge; /* overflow */ } } if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ - if(x+tiny<0.0) /* raise inexact */ + math_force_eval(x+tiny); /* raise inexact */ return tiny-one; /* return -1 */ } } @@ -187,7 +175,7 @@ Q[] = {1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */ x = hi - lo; c = (hi-x)-lo; } - else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ + else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ t = huge+x; /* return x with inexact flags when x!=0 */ return x - (t-(huge+x)); } @@ -212,28 +200,28 @@ Q[] = {1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */ e -= hxs; if(k== -1) return 0.5*(x-e)-0.5; if(k==1) { - if(x < -0.25) return -2.0*(e-(x+0.5)); - else return one+2.0*(x-e); + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); } if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ - u_int32_t high; - y = one-(e-x); + u_int32_t high; + y = one-(e-x); GET_HIGH_WORD(high,y); SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ - return y-one; + return y-one; } t = one; if(k<20) { - u_int32_t high; - SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ - y = t-(e-x); + u_int32_t high; + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); GET_HIGH_WORD(high,y); SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ } else { - u_int32_t high; + u_int32_t high; SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ - y = x-(e+t); - y += one; + y = x-(e+t); + y += one; GET_HIGH_WORD(high,y); SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ } |