summaryrefslogtreecommitdiff
path: root/sysdeps/libm-ieee754
diff options
context:
space:
mode:
Diffstat (limited to 'sysdeps/libm-ieee754')
-rw-r--r--sysdeps/libm-ieee754/s_cexpf.c37
-rw-r--r--sysdeps/libm-ieee754/s_cexpl.c45
-rw-r--r--sysdeps/libm-ieee754/s_log2.c129
-rw-r--r--sysdeps/libm-ieee754/s_log2f.c90
4 files changed, 275 insertions, 26 deletions
diff --git a/sysdeps/libm-ieee754/s_cexpf.c b/sysdeps/libm-ieee754/s_cexpf.c
index 14cfb19766..261b18cb3a 100644
--- a/sysdeps/libm-ieee754/s_cexpf.c
+++ b/sysdeps/libm-ieee754/s_cexpf.c
@@ -31,13 +31,18 @@ __cexpf (__complex__ float x)
{
if (isfinite (__imag__ x))
{
- retval = __expf (__real__ x) * (__cosf (__imag__ x)
- + 1i * __sinf (__imag__ x));
+ float exp_val = __expf (__real__ x);
+
+ __real__ retval = exp_val * __cosf (__imag__ x);
+ __imag__ retval = exp_val * __sinf (__imag__ x);
}
else
- /* If the imaginary part is +-inf or NaN and the real part is
- not +-inf the result is NaN + iNan. */
- retval = __nanf ("") + 1.0i * __nanf ("");
+ {
+ /* If the imaginary part is +-inf or NaN and the real part
+ is not +-inf the result is NaN + iNaN. */
+ __real__ retval = __nanf ("");
+ __imag__ retval = __nanf ("");
+ }
}
else if (__isinff (__real__ x))
{
@@ -46,17 +51,27 @@ __cexpf (__complex__ float x)
if (signbit (__real__ x) == 0 && __imag__ x == 0.0)
retval = HUGE_VALF;
else
- retval = ((signbit (__real__ x) ? 0.0 : HUGE_VALF)
- * (__cosf (__imag__ x) + 1i * __sinf (__imag__ x)));
+ {
+ float value = signbit (__real__ x) ? 0.0 : HUGE_VALF;
+
+ __real__ retval = value * __cosf (__imag__ x);
+ __imag__ retval = value * __sinf (__imag__ x);
+ }
+ }
+ else if (signbit (__real__ x) == 0)
+ {
+ __real__ retval = HUGE_VALF;
+ __imag__ retval = __nanf ("");
}
- else if (signbit (__real__ x))
- retval = HUGE_VALF + 1.0i * __nanf ("");
else
retval = 0.0;
}
else
- /* If the real part is NaN the result is NaN + iNan. */
- retval = __nanf ("") + 1.0i * __nanf ("");
+ {
+ /* If the real part is NaN the result is NaN + iNan. */
+ __real__ retval = __nanf ("");
+ __imag__ retval = __nanf ("");
+ }
return retval;
}
diff --git a/sysdeps/libm-ieee754/s_cexpl.c b/sysdeps/libm-ieee754/s_cexpl.c
index 6b3d409158..779286f6b3 100644
--- a/sysdeps/libm-ieee754/s_cexpl.c
+++ b/sysdeps/libm-ieee754/s_cexpl.c
@@ -1,4 +1,4 @@
-/* Return value of complex exponential function for long double complex value.
+/* Return value of complex exponential function for float complex value.
Copyright (C) 1997 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
@@ -31,33 +31,48 @@ __cexpl (__complex__ long double x)
{
if (isfinite (__imag__ x))
{
- retval = __expl (__real__ x) * (__cosl (__imag__ x)
- + 1i * __sinl (__imag__ x));
+ long double exp_val = __expl (__real__ x);
+
+ __real__ retval = exp_val * __cosl (__imag__ x);
+ __imag__ retval = exp_val * __sinl (__imag__ x);
}
else
- /* If the imaginary part is +-inf or NaN and the real part is
- not +-inf the result is NaN + iNan. */
- retval = __nanl ("") + 1.0i * __nanl ("");
+ {
+ /* If the imaginary part is +-inf or NaN and the real part
+ is not +-inf the result is NaN + iNaN. */
+ __real__ retval = __nanl ("");
+ __imag__ retval = __nanl ("");
+ }
}
else if (__isinfl (__real__ x))
{
- if (isfinite (__imag x))
+ if (isfinite (__imag__ x))
{
if (signbit (__real__ x) == 0 && __imag__ x == 0.0)
- retval = HUGE_VALL;
+ retval = HUGE_VAL;
else
- retval = ((signbit (__real__ x) ? 0.0 : HUGE_VALL)
- * (__cosl (__imag__ x) + 1i * __sinl (__imag__ x)));
+ {
+ long double value = signbit (__real__ x) ? 0.0 : HUGE_VALL;
+
+ __real__ retval = value * __cosl (__imag__ x);
+ __imag__ retval = value * __sinl (__imag__ x);
+ }
+ }
+ else if (signbit (__real__ x) == 0)
+ {
+ __real__ retval = HUGE_VALL;
+ __imag__ retval = __nanl ("");
}
- else if (signbit (__real__ x))
- retval = HUGE_VALL + 1.0i * __nanl ("");
else
retval = 0.0;
}
else
- /* If the real part is NaN the result is NaN + iNan. */
- retval = __nanl ("") + 1.0i * __nanl ("");
+ {
+ /* If the real part is NaN the result is NaN + iNaN. */
+ __real__ retval = __nanl ("");
+ __imag__ retval = __nanl ("");
+ }
return retval;
}
-weak_alias (__cexpl, cexpl)
+weak_alias (__cexp, cexp)
diff --git a/sysdeps/libm-ieee754/s_log2.c b/sysdeps/libm-ieee754/s_log2.c
new file mode 100644
index 0000000000..03a7deaa67
--- /dev/null
+++ b/sysdeps/libm-ieee754/s_log2.c
@@ -0,0 +1,129 @@
+/* Adapted for log2 by Ulrich Drepper <drepper@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.
+ * ====================================================
+ */
+
+/* __log2(x)
+ * Return the logarithm to base 2 of x
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * 2. Approximation of log(1+f).
+ * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ * = 2s + s*R
+ * We use a special Reme algorithm on [0,0.1716] to generate
+ * a polynomial of degree 14 to approximate R The maximum error
+ * of this polynomial approximation is bounded by 2**-58.45. In
+ * other words,
+ * 2 4 6 8 10 12 14
+ * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
+ * (the values of Lg1 to Lg7 are listed in the program)
+ * and
+ * | 2 14 | -58.45
+ * | Lg1*s +...+Lg7*s - R(z) | <= 2
+ * | |
+ * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ * In order to guarantee error in log below 1ulp, we compute log
+ * by
+ * log(1+f) = f - s*(f - R) (if f is not too large)
+ * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
+ *
+ * 3. Finally, log(x) = k + log(1+f).
+ * = k+(f-(hfsq-(s*(hfsq+R))))
+ *
+ * Special cases:
+ * log2(x) is NaN with signal if x < 0 (including -INF) ;
+ * log2(+INF) is +INF; log(0) is -INF with signal;
+ * log2(NaN) is that NaN with no signal.
+ *
+ * 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 "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
+Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ double __log2(double x)
+#else
+ double __log2(x)
+ double x;
+#endif
+{
+ double hfsq,f,s,z,R,w,t1,t2,dk;
+ int32_t k,hx,i,j;
+ u_int32_t lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+
+ k=0;
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx&0x7fffffff)|lx)==0)
+ return -two54/zero; /* log(+-0)=-inf */
+ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
+ k -= 54; x *= two54; /* subnormal number, scale up x */
+ GET_HIGH_WORD(hx,x);
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ k += (hx>>20)-1023;
+ hx &= 0x000fffff;
+ i = (hx+0x95f64)&0x100000;
+ SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
+ k += (i>>20);
+ dk = (double) k;
+ f = x-1.0;
+ if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
+ if(f==zero) return dk;
+ R = f*f*(0.5-0.33333333333333333*f);
+ return dk-(R-f);
+ }
+ s = f/(2.0+f);
+ z = s*s;
+ i = hx-0x6147a;
+ w = z*z;
+ j = 0x6b851-hx;
+ t1= w*(Lg2+w*(Lg4+w*Lg6));
+ t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+ i |= j;
+ R = t2+t1;
+ if(i>0) {
+ hfsq=0.5*f*f;
+ return dk-((hfsq-(s*(hfsq+R)))-f);
+ } else {
+ return dk-((s*(f-R))-f);
+ }
+}
diff --git a/sysdeps/libm-ieee754/s_log2f.c b/sysdeps/libm-ieee754/s_log2f.c
new file mode 100644
index 0000000000..c204e2266a
--- /dev/null
+++ b/sysdeps/libm-ieee754/s_log2f.c
@@ -0,0 +1,90 @@
+/* e_logf.c -- float version of e_log.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * adapted for log2 by Ulrich Drepper <drepper@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.
+ * ====================================================
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+two25 = 3.355443200e+07, /* 0x4c000000 */
+Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
+Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
+Lg3 = 2.8571429849e-01, /* 3E924925 */
+Lg4 = 2.2222198546e-01, /* 3E638E29 */
+Lg5 = 1.8183572590e-01, /* 3E3A3325 */
+Lg6 = 1.5313838422e-01, /* 3E1CD04F */
+Lg7 = 1.4798198640e-01; /* 3E178897 */
+
+#ifdef __STDC__
+static const float zero = 0.0;
+#else
+static float zero = 0.0;
+#endif
+
+#ifdef __STDC__
+ float __log2f(float x)
+#else
+ float __log2f(x)
+ float x;
+#endif
+{
+ float hfsq,f,s,z,R,w,t1,t2,dk;
+ int32_t k,ix,i,j;
+
+ GET_FLOAT_WORD(ix,x);
+
+ k=0;
+ if (ix < 0x00800000) { /* x < 2**-126 */
+ if ((ix&0x7fffffff)==0)
+ return -two25/zero; /* log(+-0)=-inf */
+ if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
+ k -= 25; x *= two25; /* subnormal number, scale up x */
+ GET_FLOAT_WORD(ix,x);
+ }
+ if (ix >= 0x7f800000) return x+x;
+ k += (ix>>23)-127;
+ ix &= 0x007fffff;
+ i = (ix+(0x95f64<<3))&0x800000;
+ SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
+ k += (i>>23);
+ dk = (float)k;
+ f = x-(float)1.0;
+ if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
+ if(f==zero) return dk;
+ R = f*f*((float)0.5-(float)0.33333333333333333*f);
+ return dk-(R-f);}
+ }
+ s = f/((float)2.0+f);
+ z = s*s;
+ i = ix-(0x6147a<<3);
+ w = z*z;
+ j = (0x6b851<<3)-ix;
+ t1= w*(Lg2+w*(Lg4+w*Lg6));
+ t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+ i |= j;
+ R = t2+t1;
+ if(i>0) {
+ hfsq=(float)0.5*f*f;
+ return dk-((hfsq-(s*(hfsq+R)))-f);
+ } else {
+ return dk-((s*(f-R))-f);
+ }
+}
+weak_alias (__log2f, log2f)
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-17 07:18:56 +0000