[git] CMU Common Lisp branch master updated. snapshot-2014-06-40-ge0b1f9f
Raymond Toy
rtoy at common-lisp.net
Sat Aug 2 02:31:53 UTC 2014
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commit e0b1f9f8b2142397cbf4ea76dd3ba862862baa49
Author: Raymond Toy <toy.raymond at gmail.com>
Date: Fri Aug 1 19:31:39 2014 -0700
Compile s_log1p and s_expm1.
diff --git a/src/lisp/Config.x86_darwin b/src/lisp/Config.x86_darwin
index 3dcdc61..70c2df4 100644
--- a/src/lisp/Config.x86_darwin
+++ b/src/lisp/Config.x86_darwin
@@ -18,7 +18,7 @@ OS_LIBS =
EXEC_FINAL_OBJ = exec-final.o
-OS_SRC += k_sin.c k_cos.c k_tan.c s_sin.c s_cos.c s_tan.c sincos.c
+OS_SRC += k_sin.c k_cos.c k_tan.c s_sin.c s_cos.c s_tan.c sincos.c s_log1p.c s_expm1.c
k_sin.o : k_sin.c
$(CC) -c $(CFLAGS) $(CPPFLAGS) $(CC_REM_PIO2) $<
@@ -37,3 +37,7 @@ s_tan.o : s_tan.c
sincos.o : sincos.c
$(CC) -c $(CFLAGS) $(CPPFLAGS) $(CC_REM_PIO2) $<
+s_log1p.o : s_log1p.c
+ $(CC) -c $(CFLAGS) $(CPPFLAGS) $(CC_REM_PIO2) $<
+s_exmp1.o : s_expm1.c
+ $(CC) -c $(CFLAGS) $(CPPFLAGS) $(CC_REM_PIO2) $<
commit e19642f9bb877846f2fa05701bebcef1073821f3
Author: Raymond Toy <toy.raymond at gmail.com>
Date: Fri Aug 1 19:30:45 2014 -0700
Modify to use unions and change name to include fdlibm prefix.
diff --git a/src/lisp/s_expm1.c b/src/lisp/s_expm1.c
index e4dd820..d6a1827 100644
--- a/src/lisp/s_expm1.c
+++ b/src/lisp/s_expm1.c
@@ -127,17 +127,20 @@ Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
#ifdef __STDC__
- double expm1(double x)
+ double fdlibm_expm1(double x)
#else
- double expm1(x)
+ double fdlibm_expm1(x)
double x;
#endif
{
double y,hi,lo,c,t,e,hxs,hfx,r1;
int k,xsb;
unsigned hx;
+ union { int i[2]; double d; } ux;
+ union { int i[2]; double d; } utmp;
- hx = __HI(x); /* high word of x */
+ ux.d = x;
+ hx = ux.i[HIWORD]; /* high word of x */
xsb = hx&0x80000000; /* sign bit of x */
if(xsb==0) y=x; else y= -x; /* y = |x| */
hx &= 0x7fffffff; /* high word of |x| */
@@ -146,7 +149,7 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
- if(((hx&0xfffff)|__LO(x))!=0)
+ if(((hx&0xfffff)|ux.i[LOWORD])!=0)
return x+x; /* NaN */
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
}
@@ -196,19 +199,29 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
else return one+2.0*(x-e);
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
y = one-(e-x);
- __HI(y) += (k<<20); /* add k to y's exponent */
+ utmp.d = y;
+ utmp.i[HIWORD] += (k<<20); /* add k to y's exponent */
+ y = utmp.d;
return y-one;
}
t = one;
if(k<20) {
- __HI(t) = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */
+ utmp.d = t;
+ utmp.i[HIWORD] = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */
+ t = utmp.d;
y = t-(e-x);
- __HI(y) += (k<<20); /* add k to y's exponent */
+ utmp.d = y;
+ utmp.i[HIWORD] += (k<<20); /* add k to y's exponent */
+ y = utmp.d;
} else {
- __HI(t) = ((0x3ff-k)<<20); /* 2^-k */
+ utmp.d = t;
+ utmp.i[HIWORD] = ((0x3ff-k)<<20); /* 2^-k */
+ t = utmp.d;
y = x-(e+t);
y += one;
- __HI(y) += (k<<20); /* add k to y's exponent */
+ utmp.d = y;
+ utmp.i[HIWORD] += (k<<20); /* add k to y's exponent */
+ y = utmp.d;
}
}
return y;
diff --git a/src/lisp/s_log1p.c b/src/lisp/s_log1p.c
index 3d1059a..eaec38a 100644
--- a/src/lisp/s_log1p.c
+++ b/src/lisp/s_log1p.c
@@ -97,16 +97,18 @@ Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static double zero = 0.0;
#ifdef __STDC__
- double log1p(double x)
+ double fdlibm_log1p(double x)
#else
- double log1p(x)
+ double fdlibm_log1p(x)
double x;
#endif
{
double hfsq,f,c,s,z,R,u;
int k,hx,hu,ax;
+ union { int i[2]; double d; } ux;
- hx = __HI(x); /* high word of x */
+ ux.d = x;
+ hx = ux.i[HIWORD]; /* high word of x */
ax = hx&0x7fffffff;
k = 1;
@@ -128,23 +130,29 @@ static double zero = 0.0;
if (hx >= 0x7ff00000) return x+x;
if(k!=0) {
if(hx<0x43400000) {
- u = 1.0+x;
- hu = __HI(u); /* high word of u */
+ u = 1.0+x;
+ ux.d = u;
+ hu = ux.i[HIWORD]; /* high word of u */
k = (hu>>20)-1023;
c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
c /= u;
} else {
u = x;
- hu = __HI(u); /* high word of u */
+ ux.d = u;
+ hu = ux.i[HIWORD]; /* high word of u */
k = (hu>>20)-1023;
c = 0;
}
hu &= 0x000fffff;
if(hu<0x6a09e) {
- __HI(u) = hu|0x3ff00000; /* normalize u */
+ ux.d = u;
+ ux.i[HIWORD] = hu|0x3ff00000; /* normalize u */
+ u = ux.d;
} else {
- k += 1;
- __HI(u) = hu|0x3fe00000; /* normalize u/2 */
+ k += 1;
+ ux.d = u;
+ ux.i[HIWORD] = hu|0x3fe00000; /* normalize u/2 */
+ u = ux.d;
hu = (0x00100000-hu)>>2;
}
f = u-1.0;
commit ae8eb31e7757d351eca8fd5b9693637843cda611
Author: Raymond Toy <toy.raymond at gmail.com>
Date: Fri Aug 1 19:21:05 2014 -0700
Import expm1 from fdlibm, as is.
diff --git a/src/lisp/s_expm1.c b/src/lisp/s_expm1.c
new file mode 100644
index 0000000..e4dd820
--- /dev/null
+++ b/src/lisp/s_expm1.c
@@ -0,0 +1,215 @@
+
+/* @(#)s_expm1.c 1.5 04/04/22 */
+/*
+ * ====================================================
+ * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/* expm1(x)
+ * Returns exp(x)-1, the exponential of x minus 1.
+ *
+ * Method
+ * 1. Argument reduction:
+ * Given x, find r and integer k such that
+ *
+ * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
+ *
+ * Here a correction term c will be computed to compensate
+ * the error in r when rounded to a floating-point number.
+ *
+ * 2. Approximating expm1(r) by a special rational function on
+ * the interval [0,0.34658]:
+ * Since
+ * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
+ * we define R1(r*r) by
+ * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
+ * That is,
+ * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
+ * = 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 Remes algorithm on [0,0.347] to generate
+ * 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)
+ * 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:
+ * 2 3
+ * r r [ 3 - (R1 + R1*r/2) ]
+ * expm1(r) = r + --- + --- * [--------------------]
+ * 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 )
+ * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
+ * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
+ * ( )
+ *
+ * = r - E
+ * 3. Scale back to obtain expm1(x):
+ * From step 1, we have
+ * expm1(x) = either 2^k*[expm1(r)+1] - 1
+ * = or 2^k*[expm1(r) + (1-2^-k)]
+ * 4. Implementation notes:
+ * (A). To save one multiplication, we scale the coefficient Qi
+ * to Qi*2^i, and replace z by (x^2)/2.
+ * (B). To achieve maximum accuracy, we compute expm1(x) by
+ * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
+ * (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);
+ * (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))
+ *
+ * Special cases:
+ * expm1(INF) is INF, expm1(NaN) is NaN;
+ * expm1(-INF) is -1, and
+ * for finite argument, only expm1(0)=0 is exact.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ * For IEEE double
+ * if x > 7.09782712893383973096e+02 then expm1(x) overflow
+ *
+ * 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
+ * to produce the hexadecimal values shown.
+ */
+
+#include "fdlibm.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one = 1.0,
+huge = 1.0e+300,
+tiny = 1.0e-300,
+o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
+ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
+ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
+invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
+ /* scaled coefficients related to expm1 */
+Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
+Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
+Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
+Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
+Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
+
+#ifdef __STDC__
+ double expm1(double x)
+#else
+ double expm1(x)
+ double x;
+#endif
+{
+ double y,hi,lo,c,t,e,hxs,hfx,r1;
+ int k,xsb;
+ unsigned hx;
+
+ hx = __HI(x); /* high word of x */
+ xsb = hx&0x80000000; /* sign bit of x */
+ if(xsb==0) y=x; else y= -x; /* y = |x| */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* 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&0xfffff)|__LO(x))!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ }
+ if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
+ if(x+tiny<0.0) /* raise inexact */
+ return tiny-one; /* return -1 */
+ }
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ if(xsb==0)
+ {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
+ else
+ {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
+ } else {
+ k = invln2*x+((xsb==0)?0.5:-0.5);
+ t = k;
+ hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
+ lo = t*ln2_lo;
+ }
+ x = hi - lo;
+ c = (hi-x)-lo;
+ }
+ 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));
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ hfx = 0.5*x;
+ hxs = x*hfx;
+ r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
+ t = 3.0-r1*hfx;
+ e = hxs*((r1-t)/(6.0 - x*t));
+ if(k==0) return x - (x*e-hxs); /* c is 0 */
+ else {
+ e = (x*(e-c)-c);
+ 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 (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
+ y = one-(e-x);
+ __HI(y) += (k<<20); /* add k to y's exponent */
+ return y-one;
+ }
+ t = one;
+ if(k<20) {
+ __HI(t) = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */
+ y = t-(e-x);
+ __HI(y) += (k<<20); /* add k to y's exponent */
+ } else {
+ __HI(t) = ((0x3ff-k)<<20); /* 2^-k */
+ y = x-(e+t);
+ y += one;
+ __HI(y) += (k<<20); /* add k to y's exponent */
+ }
+ }
+ return y;
+}
-----------------------------------------------------------------------
Summary of changes:
src/lisp/Config.x86_darwin | 6 +-
src/lisp/s_expm1.c | 228 ++++++++++++++++++++++++++++++++++++++++++++
src/lisp/s_log1p.c | 26 +++--
3 files changed, 250 insertions(+), 10 deletions(-)
create mode 100644 src/lisp/s_expm1.c
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