diff options
Diffstat (limited to 'sysdeps/libm-ieee754')
| -rw-r--r-- | sysdeps/libm-ieee754/s_cexpf.c | 37 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_cexpl.c | 45 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_log2.c | 129 | ||||
| -rw-r--r-- | sysdeps/libm-ieee754/s_log2f.c | 90 |
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) |