diff options
98 files changed, 784 insertions, 784 deletions
diff --git a/libm/Makefile b/libm/Makefile index 7a0edbea5..e8aaddc12 100644 --- a/libm/Makefile +++ b/libm/Makefile @@ -6,14 +6,14 @@ # math library for Apple's MacOS X/Darwin math library, which was # itself swiped from FreeBSD. The original copyright information # is as follows: -# +# # 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. -# +# # It has been ported to work with uClibc and generally behave # by Erik Andersen <andersen@codepoet.org> # @@ -36,7 +36,7 @@ include $(TOPDIR)Rules.mak CFLAGS+=$(SSP_ALL_CFLAGS) -DIRS = +DIRS = ifeq ($(strip $(HAS_FPU)),y) ifeq ($(TARGET_ARCH),$(wildcard $(TARGET_ARCH))) DIRS = $(TARGET_ARCH) @@ -71,7 +71,7 @@ else CSRC = w_acos.c w_asin.c s_atan.c w_atan2.c s_ceil.c s_cos.c \ w_cosh.c w_exp.c s_fabs.c s_floor.c w_fmod.c s_frexp.c \ s_ldexp.c w_log.c w_log10.c s_modf.c w_pow.c s_sin.c \ - w_sinh.c w_sqrt.c s_tan.c s_tanh.c + w_sinh.c w_sqrt.c s_tan.c s_tanh.c CSRC+= s_expm1.c s_scalbn.c s_copysign.c e_acos.c e_asin.c e_atan2.c \ k_cos.c e_cosh.c e_exp.c e_fmod.c e_log.c e_log10.c e_pow.c \ k_sin.c e_sinh.c e_sqrt.c k_tan.c e_rem_pio2.c k_rem_pio2.c \ diff --git a/libm/README b/libm/README index c275d1b9a..2c69a54af 100644 --- a/libm/README +++ b/libm/README @@ -7,10 +7,10 @@ is as follows: Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this - software is freely granted, provided that this notice + software is freely granted, provided that this notice is preserved. -It has been ported to work with uClibc and generally behave +It has been ported to work with uClibc and generally behave by Erik Andersen <andersen@codepoet.org> 22 May, 2001 diff --git a/libm/e_acos.c b/libm/e_acos.c index 78bdae9f8..9f6305e1e 100644 --- a/libm/e_acos.c +++ b/libm/e_acos.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -15,14 +15,14 @@ static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $"; #endif /* __ieee754_acos(x) - * Method : + * Method : * acos(x) = pi/2 - asin(x) * acos(-x) = pi/2 + asin(x) * For |x|<=0.5 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) * For x>0.5 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) - * = 2asin(sqrt((1-x)/2)) + * = 2asin(sqrt((1-x)/2)) * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) * = 2f + (2c + 2s*z*R(z)) * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term @@ -42,9 +42,9 @@ static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ diff --git a/libm/e_acosh.c b/libm/e_acosh.c index 8383519df..3b3c6251e 100644 --- a/libm/e_acosh.c +++ b/libm/e_acosh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -16,7 +16,7 @@ static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $"; /* __ieee754_acosh(x) * Method : - * Based on + * Based on * acosh(x) = log [ x + sqrt(x*x-1) ] * we have * acosh(x) := log(x)+ln2, if x is large; else @@ -32,9 +32,9 @@ static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif one = 1.0, ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ @@ -45,7 +45,7 @@ ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ double __ieee754_acosh(x) double x; #endif -{ +{ double t; int32_t hx; u_int32_t lx; @@ -55,7 +55,7 @@ ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ } else if(hx >=0x41b00000) { /* x > 2**28 */ if(hx >=0x7ff00000) { /* x is inf of NaN */ return x+x; - } else + } else return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ } else if(((hx-0x3ff00000)|lx)==0) { return 0.0; /* acosh(1) = 0 */ diff --git a/libm/e_asin.c b/libm/e_asin.c index 210fdbf3b..d7a785350 100644 --- a/libm/e_asin.c +++ b/libm/e_asin.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -15,12 +15,12 @@ static char rcsid[] = "$NetBSD: e_asin.c,v 1.9 1995/05/12 04:57:22 jtc Exp $"; #endif /* __ieee754_asin(x) - * Method : + * Method : * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... * we approximate asin(x) on [0,0.5] by * asin(x) = x + x*x^2*R(x^2) * where - * R(x^2) is a rational approximation of (asin(x)-x)/x^3 + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 * and its remez error is bounded by * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) * @@ -49,9 +49,9 @@ static char rcsid[] = "$NetBSD: e_asin.c,v 1.9 1995/05/12 04:57:22 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ huge = 1.000e+300, @@ -86,12 +86,12 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ GET_LOW_WORD(lx,x); if(((ix-0x3ff00000)|lx)==0) /* asin(1)=+-pi/2 with inexact */ - return x*pio2_hi+x*pio2_lo; - return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ } else if (ix<0x3fe00000) { /* |x|<0.5 */ if(ix<0x3e400000) { /* if |x| < 2**-27 */ if(huge+x>one) return x;/* return x with inexact if x!=0*/ - } else { + } else { t = x*x; p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); @@ -116,6 +116,6 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ p = 2.0*s*r-(pio2_lo-2.0*c); q = pio4_hi-2.0*w; t = pio4_hi-(p-q); - } - if(hx>0) return t; else return -t; + } + if(hx>0) return t; else return -t; } diff --git a/libm/e_atan2.c b/libm/e_atan2.c index 2b5edeacf..8bfc79232 100644 --- a/libm/e_atan2.c +++ b/libm/e_atan2.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -17,7 +17,7 @@ static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $"; /* __ieee754_atan2(y,x) * Method : * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). - * 2. Reduce x to positive by (if x and y are unexceptional): + * 2. Reduce x to positive by (if x and y are unexceptional): * ARG (x+iy) = arctan(y/x) ... if x > 0, * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, * @@ -35,9 +35,9 @@ static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $"; * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; * * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough * to produce the hexadecimal values shown. */ @@ -45,9 +45,9 @@ static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif tiny = 1.0e-300, zero = 0.0, @@ -62,7 +62,7 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ double __ieee754_atan2(y,x) double y,x; #endif -{ +{ double z; int32_t k,m,hx,hy,ix,iy; u_int32_t lx,ly; @@ -80,7 +80,7 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ /* when y = 0 */ if((iy|ly)==0) { switch(m) { - case 0: + case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi+tiny;/* atan(+0,-anything) = pi */ case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ @@ -88,7 +88,7 @@ pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ } /* when x = 0 */ if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - + /* when x is INF */ if(ix==0x7ff00000) { if(iy==0x7ff00000) { diff --git a/libm/e_atanh.c b/libm/e_atanh.c index 559e8f158..d199a05cc 100644 --- a/libm/e_atanh.c +++ b/libm/e_atanh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -21,7 +21,7 @@ static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $"; * 1 2x x * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) * 2 1 - x 1 - x - * + * * For x<0.5 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) * @@ -61,14 +61,14 @@ static double zero = 0.0; ix = hx&0x7fffffff; if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ return (x-x)/(x-x); - if(ix==0x3ff00000) + if(ix==0x3ff00000) return x/zero; if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ SET_HIGH_WORD(x,ix); if(ix<0x3fe00000) { /* x < 0.5 */ t = x+x; t = 0.5*log1p(t+t*x/(one-x)); - } else + } else t = 0.5*log1p((x+x)/(one-x)); if(hx>=0) return t; else return -t; } diff --git a/libm/e_cosh.c b/libm/e_cosh.c index 5d73fb5c4..88499684a 100644 --- a/libm/e_cosh.c +++ b/libm/e_cosh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -15,18 +15,18 @@ static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; #endif /* __ieee754_cosh(x) - * Method : + * Method : * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 - * 1. Replace x by |x| (cosh(x) = cosh(-x)). - * 2. - * [ exp(x) - 1 ]^2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- * 2*exp(x) * * exp(x) + 1/exp(x) * ln2/2 <= x <= 22 : cosh(x) := ------------------- * 2 - * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : cosh(x) := huge*huge (overflow) * @@ -50,7 +50,7 @@ static double one = 1.0, half=0.5, huge = 1.0e300; double __ieee754_cosh(x) double x; #endif -{ +{ double t,w; int32_t ix; u_int32_t lx; @@ -60,7 +60,7 @@ static double one = 1.0, half=0.5, huge = 1.0e300; ix &= 0x7fffffff; /* x is INF or NaN */ - if(ix>=0x7ff00000) return x*x; + if(ix>=0x7ff00000) return x*x; /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ if(ix<0x3fd62e43) { @@ -81,7 +81,7 @@ static double one = 1.0, half=0.5, huge = 1.0e300; /* |x| in [log(maxdouble), overflowthresold] */ GET_LOW_WORD(lx,x); - if (ix<0x408633CE || + if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { w = __ieee754_exp(half*fabs(x)); t = half*w; diff --git a/libm/e_exp.c b/libm/e_exp.c index f92910e85..f4d832bbb 100644 --- a/libm/e_exp.c +++ b/libm/e_exp.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -22,36 +22,36 @@ static char rcsid[] = "$NetBSD: e_exp.c,v 1.8 1995/05/10 20:45:03 jtc Exp $"; * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. * Given x, find r and integer k such that * - * x = k*ln2 + r, |r| <= 0.5*ln2. + * x = k*ln2 + r, |r| <= 0.5*ln2. * - * Here r will be represented as r = hi-lo for better + * Here r will be represented as r = hi-lo for better * accuracy. * * 2. Approximation of exp(r) by a special rational function on * the interval [0,0.34658]: * Write * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... - * We use a special Reme algorithm on [0,0.34658] to generate - * a polynomial of degree 5 to approximate R. The maximum error + * We use a special Reme algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error * of this polynomial approximation is bounded by 2**-59. In * other words, * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 * (where z=r*r, and the values of P1 to P5 are listed below) * and * | 5 | -59 - * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 * | | * The computation of exp(r) thus becomes * 2*r * exp(r) = 1 + ------- * R - r - * r*R1(r) + * r*R1(r) * = 1 + r + ----------- (for better accuracy) * 2 - R1(r) * where * 2 4 10 * R1(r) = r - (P1*r + P2*r + ... + P5*r ). - * + * * 3. Scale back to obtain exp(x): * From step 1, we have * exp(x) = 2^k * exp(r) @@ -66,13 +66,13 @@ static char rcsid[] = "$NetBSD: e_exp.c,v 1.8 1995/05/10 20:45:03 jtc Exp $"; * 1 ulp (unit in the last place). * * Misc. info. - * For IEEE double + * For IEEE double * if x > 7.09782712893383973096e+02 then exp(x) overflow * if x < -7.45133219101941108420e+02 then exp(x) underflow * * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the + * 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. */ @@ -128,7 +128,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ if(hx>=0x7ff00000) { u_int32_t lx; GET_LOW_WORD(lx,x); - if(((hx&0xfffff)|lx)!=0) + if(((hx&0xfffff)|lx)!=0) return x+x; /* NaN */ else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ } @@ -137,7 +137,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ } /* argument reduction */ - if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; } else { @@ -147,7 +147,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ lo = t*ln2LO[0]; } x = hi - lo; - } + } else if(hx < 0x3e300000) { /* when |x|<2**-28 */ if(huge+x>one) return one+x;/* trigger inexact */ } @@ -156,7 +156,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ /* x is now in primary range */ t = x*x; c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); - if(k==0) return one-((x*c)/(c-2.0)-x); + if(k==0) return one-((x*c)/(c-2.0)-x); else y = one-((lo-(x*c)/(2.0-c))-hi); if(k >= -1021) { u_int32_t hy; diff --git a/libm/e_fmod.c b/libm/e_fmod.c index 2ce613574..565c3772b 100644 --- a/libm/e_fmod.c +++ b/libm/e_fmod.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. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: e_fmod.c,v 1.8 1995/05/10 20:45:07 jtc Exp $"; #endif -/* +/* * __ieee754_fmod(x,y) * Return x mod y in exact arithmetic * Method: shift and subtract @@ -51,7 +51,7 @@ static double one = 1.0, Zero[] = {0.0, -0.0,}; return (x*y)/(x*y); if(hx<=hy) { if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ - if(lx==ly) + if(lx==ly) return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ } @@ -74,7 +74,7 @@ static double one = 1.0, Zero[] = {0.0, -0.0,}; } else iy = (hy>>20)-1023; /* set up {hx,lx}, {hy,ly} and align y to x */ - if(ix >= -1022) + if(ix >= -1022) hx = 0x00100000|(0x000fffff&hx); else { /* subnormal x, shift x to normal */ n = -1022-ix; @@ -86,7 +86,7 @@ static double one = 1.0, Zero[] = {0.0, -0.0,}; lx = 0; } } - if(iy >= -1022) + if(iy >= -1022) hy = 0x00100000|(0x000fffff&hy); else { /* subnormal y, shift y to normal */ n = -1022-iy; @@ -115,7 +115,7 @@ static double one = 1.0, Zero[] = {0.0, -0.0,}; /* convert back to floating value and restore the sign */ if((hx|lx)==0) /* return sign(x)*0 */ - return Zero[(u_int32_t)sx>>31]; + return Zero[(u_int32_t)sx>>31]; while(hx<0x00100000) { /* normalize x */ hx = hx+hx+(lx>>31); lx = lx+lx; iy -= 1; diff --git a/libm/e_gamma.c b/libm/e_gamma.c index c4ea7a903..a82261370 100644 --- a/libm/e_gamma.c +++ b/libm/e_gamma.c @@ -6,7 +6,7 @@ * * 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. * ==================================================== * diff --git a/libm/e_gamma_r.c b/libm/e_gamma_r.c index 909c4203d..039eba49b 100644 --- a/libm/e_gamma_r.c +++ b/libm/e_gamma_r.c @@ -6,15 +6,15 @@ * * 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. * ==================================================== * */ /* __ieee754_gamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). * * Method: See __ieee754_lgamma_r */ diff --git a/libm/e_hypot.c b/libm/e_hypot.c index 24c8ae452..2052e215b 100644 --- a/libm/e_hypot.c +++ b/libm/e_hypot.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. * ==================================================== */ @@ -16,12 +16,12 @@ static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $"; /* __ieee754_hypot(x,y) * - * Method : - * If (assume round-to-nearest) z=x*x+y*y - * has error less than sqrt(2)/2 ulp, than + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than * sqrt(z) has error less than 1 ulp (exercise). * - * So, compute sqrt(x*x+y*y) with some care as + * So, compute sqrt(x*x+y*y) with some care as * follows to get the error below 1 ulp: * * Assume x>y>0; @@ -31,10 +31,10 @@ static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $"; * where x1 = x with lower 32 bits cleared, x2 = x-x1; else * 2. if x <= 2y use * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) - * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, * y1= y with lower 32 bits chopped, y2 = y-y1. - * - * NOTE: scaling may be necessary if some argument is too + * + * NOTE: scaling may be necessary if some argument is too * large or too tiny * * Special cases: @@ -42,8 +42,8 @@ static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $"; * hypot(x,y) is NAN if x or y is NAN. * * Accuracy: - * hypot(x,y) returns sqrt(x^2+y^2) with error less - * than 1 ulps (units in the last place) + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) */ #include "math.h" @@ -84,7 +84,7 @@ static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $"; SET_HIGH_WORD(b,hb); } if(hb < 0x20b00000) { /* b < 2**-500 */ - if(hb <= 0x000fffff) { /* subnormal b or 0 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ u_int32_t low; GET_LOW_WORD(low,b); if((hb|low)==0) return a; diff --git a/libm/e_j0.c b/libm/e_j0.c index 46fa16656..b347481ec 100644 --- a/libm/e_j0.c +++ b/libm/e_j0.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -33,20 +33,20 @@ static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; * (To avoid cancellation, use * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * to compute the worse one.) - * + * * 3 Special cases * j0(nan)= nan * j0(0) = 1 * j0(inf) = 0 - * + * * Method -- y0(x): * 1. For x<2. - * Since + * Since * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. * We use the following function to approximate y0, * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 - * where + * where * U(z) = u00 + u01*z + ... + u06*z^6 * V(z) = 1 + v01*z + ... + v04*z^4 * with absolute approximation error bounded by 2**-72. @@ -69,9 +69,9 @@ static double pzero(), qzero(); #endif #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif huge = 1e300, one = 1.0, @@ -94,9 +94,9 @@ static double zero = 0.0; #endif #ifdef __STDC__ - double __ieee754_j0(double x) + double __ieee754_j0(double x) #else - double __ieee754_j0(x) + double __ieee754_j0(x) double x; #endif { @@ -163,9 +163,9 @@ v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ #ifdef __STDC__ - double __ieee754_y0(double x) + double __ieee754_y0(double x) #else - double __ieee754_y0(x) + double __ieee754_y0(x) double x; #endif { @@ -175,7 +175,7 @@ v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ EXTRACT_WORDS(hx,lx,x); ix = 0x7fffffff&hx; /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); + if(ix>=0x7ff00000) return one/(x+x*x); if((ix|lx)==0) return -one/zero; if(hx<0) return zero/zero; if(ix >= 0x40000000) { /* |x| >= 2.0 */ @@ -349,7 +349,7 @@ static double pS2[5] = { s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); return one+ r/s; } - + /* For x >= 8, the asymptotic expansions of qzero is * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. diff --git a/libm/e_j1.c b/libm/e_j1.c index 5eb81ee73..e57049e84 100644 --- a/libm/e_j1.c +++ b/libm/e_j1.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. * ==================================================== */ @@ -34,16 +34,16 @@ static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $"; * (To avoid cancellation, use * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) * to compute the worse one.) - * + * * 3 Special cases * j1(nan)= nan * j1(0) = 0 * j1(inf) = 0 - * + * * Method -- y1(x): - * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN * 2. For x<2. - * Since + * Since * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. * We use the following function to approximate y1, @@ -69,9 +69,9 @@ static double pone(), qone(); #endif #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif huge = 1e300, one = 1.0, @@ -95,9 +95,9 @@ static double zero = 0.0; #endif #ifdef __STDC__ - double __ieee754_j1(double x) + double __ieee754_j1(double x) #else - double __ieee754_j1(x) + double __ieee754_j1(x) double x; #endif { @@ -164,9 +164,9 @@ static double V0[5] = { }; #ifdef __STDC__ - double __ieee754_y1(double x) + double __ieee754_y1(double x) #else - double __ieee754_y1(x) + double __ieee754_y1(x) double x; #endif { @@ -176,7 +176,7 @@ static double V0[5] = { EXTRACT_WORDS(hx,lx,x); ix = 0x7fffffff&hx; /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); + if(ix>=0x7ff00000) return one/(x+x*x); if((ix|lx)==0) return -one/zero; if(hx<0) return zero/zero; if(ix >= 0x40000000) { /* |x| >= 2.0 */ @@ -206,10 +206,10 @@ static double V0[5] = { z = invsqrtpi*(u*ss+v*cc)/sqrt(x); } return z; - } + } if(ix<=0x3c900000) { /* x < 2**-54 */ return(-tpi/x); - } + } z = x*x; u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); @@ -347,7 +347,7 @@ static double ps2[5] = { s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); return one+ r/s; } - + /* For x >= 8, the asymptotic expansions of qone is * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. diff --git a/libm/e_jn.c b/libm/e_jn.c index 870824cf8..857c4a3f5 100644 --- a/libm/e_jn.c +++ b/libm/e_jn.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. * ==================================================== */ @@ -18,7 +18,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $"; * __ieee754_jn(n, x), __ieee754_yn(n, x) * floating point Bessel's function of the 1st and 2nd kind * of order n - * + * * Special cases: * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. @@ -37,7 +37,7 @@ static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $"; * yn(n,x) is similar in all respects, except * that forward recursion is used for all * values of n>1. - * + * */ #include "math.h" @@ -76,7 +76,7 @@ static double zero = 0.00000000000000000000e+00; ix = 0x7fffffff&hx; /* if J(n,NaN) is NaN */ if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; - if(n<0){ + if(n<0){ n = -n; x = -x; hx ^= 0x80000000; @@ -87,13 +87,13 @@ static double zero = 0.00000000000000000000e+00; x = fabs(x); if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ b = zero; - else if((double)n<=x) { + else if((double)n<=x) { /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) + /* (x >> n**2) * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Let s=sin(x), c=cos(x), + * Let s=sin(x), c=cos(x), * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then * * n sin(xn)*sqt2 cos(xn)*sqt2 @@ -110,7 +110,7 @@ static double zero = 0.00000000000000000000e+00; case 3: temp = cos(x)-sin(x); break; } b = invsqrtpi*temp/sqrt(x); - } else { + } else { a = __ieee754_j0(x); b = __ieee754_j1(x); for(i=1;i<n;i++){ @@ -121,7 +121,7 @@ static double zero = 0.00000000000000000000e+00; } } else { if(ix<0x3e100000) { /* 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 */ @@ -136,14 +136,14 @@ static double zero = 0.00000000000000000000e+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 @@ -159,9 +159,9 @@ static double zero = 0.00000000000000000000e+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 */ double t,v; @@ -183,7 +183,7 @@ static double zero = 0.00000000000000000000e+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; @@ -219,9 +219,9 @@ static double zero = 0.00000000000000000000e+00; } #ifdef __STDC__ - double __ieee754_yn(int n, double x) + double __ieee754_yn(int n, double x) #else - double __ieee754_yn(n,x) + double __ieee754_yn(n,x) int n; double x; #endif { @@ -244,10 +244,10 @@ static double zero = 0.00000000000000000000e+00; if(n==1) return(sign*__ieee754_y1(x)); if(ix==0x7ff00000) return zero; if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) + /* (x >> n**2) * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Let s=sin(x), c=cos(x), + * Let s=sin(x), c=cos(x), * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then * * n sin(xn)*sqt2 cos(xn)*sqt2 @@ -270,7 +270,7 @@ static double zero = 0.00000000000000000000e+00; b = __ieee754_y1(x); /* quit if b is -inf */ GET_HIGH_WORD(high,b); - for(i=1;i<n&&high!=0xfff00000;i++){ + for(i=1;i<n&&high!=0xfff00000;i++){ temp = b; b = ((double)(i+i)/x)*b - a; GET_HIGH_WORD(high,b); diff --git a/libm/e_lgamma.c b/libm/e_lgamma.c index 2789f3b18..f5f24ce64 100644 --- a/libm/e_lgamma.c +++ b/libm/e_lgamma.c @@ -6,7 +6,7 @@ * * 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. * ==================================================== * diff --git a/libm/e_lgamma_r.c b/libm/e_lgamma_r.c index 2b92ea2a2..09bae2af3 100644 --- a/libm/e_lgamma_r.c +++ b/libm/e_lgamma_r.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. * ==================================================== */ @@ -15,12 +15,12 @@ static char rcsid[] = "$NetBSD: e_lgamma_r.c,v 1.7 1995/05/10 20:45:42 jtc Exp $ #endif /* __ieee754_lgamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). * * Method: * 1. Argument Reduction for 0 < x <= 8 - * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may * reduce x to a number in [1.5,2.5] by * lgamma(1+s) = log(s) + lgamma(s) * for example, @@ -58,36 +58,36 @@ static char rcsid[] = "$NetBSD: e_lgamma_r.c,v 1.7 1995/05/10 20:45:42 jtc Exp $ * by * 3 5 11 * w = w0 + w1*z + w2*z + w3*z + ... + w6*z - * where + * where * |w - f(z)| < 2**-58.74 - * + * * 4. For negative x, since (G is gamma function) * -x*G(-x)*G(x) = pi/sin(pi*x), * we have * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 - * Hence, for x<0, signgam = sign(sin(pi*x)) and + * Hence, for x<0, signgam = sign(sin(pi*x)) and * lgamma(x) = log(|Gamma(x)|) * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); - * Note: one should avoid compute pi*(-x) directly in the + * Note: one should avoid compute pi*(-x) directly in the * computation of sin(pi*(-x)). - * + * * 5. Special Cases * lgamma(2+s) ~ s*(1-Euler) for tiny s * lgamma(1)=lgamma(2)=0 * lgamma(x) ~ -log(x) for tiny x * lgamma(0) = lgamma(inf) = inf * lgamma(-integer) = +-inf - * + * */ #include "math.h" #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ @@ -204,9 +204,9 @@ __inline__ } switch (n) { case 0: y = __kernel_sin(pi*y,zero,0); break; - case 1: + case 1: case 2: y = __kernel_cos(pi*(0.5-y),zero); break; - case 3: + case 3: case 4: y = __kernel_sin(pi*(one-y),zero,0); break; case 5: case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; @@ -279,7 +279,7 @@ __inline__ p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); p = z*p1-(tt-w*(p2+y*p3)); r += (tf + p); break; - case 2: + case 2: p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); r += (-0.5*y + p1/p2); @@ -308,7 +308,7 @@ __inline__ y = z*z; w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); r = (x-half)*(t-one)+w; - } else + } else /* 2**58 <= x <= inf */ r = x*(__ieee754_log(x)-one); if(hx<0) r = nadj - r; diff --git a/libm/e_log.c b/libm/e_log.c index 9325903e0..0464014cb 100644 --- a/libm/e_log.c +++ b/libm/e_log.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. * ==================================================== */ @@ -17,17 +17,17 @@ static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; /* __ieee754_log(x) * Return the logrithm of x * - * Method : - * 1. Argument Reduction: find k and f such that - * x = 2^k * (1+f), + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), * where sqrt(2)/2 < 1+f < sqrt(2) . * * 2. Approximation of log(1+f). * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) * = 2s + 2/3 s**3 + 2/5 s**5 + ....., * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error * of this polynomial approximation is bounded by 2**-58.45. In * other words, * 2 4 6 8 10 12 14 @@ -35,22 +35,22 @@ static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; * (the values of Lg1 to Lg7 are listed in the program) * and * | 2 14 | -58.45 - * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 * | | * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. * In order to guarantee error in log below 1ulp, we compute log * by * log(1+f) = f - s*(f - R) (if f is not too large) * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) - * - * 3. Finally, log(x) = k*ln2 + log(1+f). + * + * 3. Finally, log(x) = k*ln2 + log(1+f). * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: + * Here ln2 is split into two floating point number: * ln2_hi + ln2_lo, * where n*ln2_hi is always exact for |n| < 2000. * * Special cases: - * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(x) is NaN with signal if x < 0 (including -INF) ; * log(+INF) is +INF; log(0) is -INF with signal; * log(NaN) is that NaN with no signal. * @@ -59,9 +59,9 @@ static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; * 1 ulp (unit in the last place). * * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough * to produce the hexadecimal values shown. */ @@ -105,12 +105,12 @@ static double zero = 0.0; k=0; if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx)==0) + if (((hx&0x7fffffff)|lx)==0) return -two54/zero; /* log(+-0)=-inf */ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ k -= 54; x *= two54; /* subnormal number, scale up x */ GET_HIGH_WORD(hx,x); - } + } if (hx >= 0x7ff00000) return x+x; k += (hx>>20)-1023; hx &= 0x000fffff; @@ -126,14 +126,14 @@ static double zero = 0.0; if(k==0) return f-R; else {dk=(double)k; return dk*ln2_hi-((R-dk*ln2_lo)-f);} } - s = f/(2.0+f); + s = f/(2.0+f); dk = (double)k; z = s*s; i = hx-0x6147a; w = z*z; j = 0x6b851-hx; - t1= w*(Lg2+w*(Lg4+w*Lg6)); - t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); i |= j; R = t2+t1; if(i>0) { diff --git a/libm/e_log10.c b/libm/e_log10.c index 5d004ac4e..2716a72c1 100644 --- a/libm/e_log10.c +++ b/libm/e_log10.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -16,26 +16,26 @@ static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $"; /* __ieee754_log10(x) * Return the base 10 logarithm of x - * + * * Method : * Let log10_2hi = leading 40 bits of log10(2) and * log10_2lo = log10(2) - log10_2hi, * ivln10 = 1/log(10) rounded. * Then - * n = ilogb(x), + * n = ilogb(x), * if(n<0) n = n+1; * x = scalbn(x,-n); * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) * * Note 1: - * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding * mode must set to Round-to-Nearest. * Note 2: * [1/log(10)] rounded to 53 bits has error .198 ulps; * log10 is monotonic at all binary break points. * * Special cases: - * log10(x) is NaN with signal if x < 0; + * log10(x) is NaN with signal if x < 0; * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; * log10(NaN) is that NaN with no signal; * log10(10**N) = N for N=0,1,...,22. diff --git a/libm/e_pow.c b/libm/e_pow.c index 4f6a44f20..b970775cd 100644 --- a/libm/e_pow.c +++ b/libm/e_pow.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -21,7 +21,7 @@ static char rcsid[] = "$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 @@ -130,7 +130,7 @@ 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 */ @@ -141,11 +141,11 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ j = iy>>(20-k); if((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/libm/e_rem_pio2.c b/libm/e_rem_pio2.c index e98c699cd..3dd7f7b49 100644 --- a/libm/e_rem_pio2.c +++ b/libm/e_rem_pio2.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. * ==================================================== */ @@ -15,8 +15,8 @@ static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $ #endif /* __ieee754_rem_pio2(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_pio2() */ @@ -24,24 +24,24 @@ static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 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[] = { #else static int32_t two_over_pi[] = { #endif -0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, -0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, -0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, -0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, -0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, -0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, -0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, -0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, -0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, -0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, -0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, }; #ifdef __STDC__ @@ -68,9 +68,9 @@ static int32_t npio2_hw[] = { */ #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ @@ -100,7 +100,7 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ {y[0] = x; y[1] = 0; return 0;} if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ - if(hx>0) { + if(hx>0) { z = x - pio2_1; if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ y[0] = z - pio2_1t; @@ -130,27 +130,27 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ fn = (double)n; r = t-fn*pio2_1; w = fn*pio2_1t; /* 1st round good to 85 bit */ - if(n<32&&ix!=npio2_hw[n-1]) { + if(n<32&&ix!=npio2_hw[n-1]) { y[0] = r-w; /* quick check no cancellation */ } else { u_int32_t high; j = ix>>20; - y[0] = r-w; + y[0] = r-w; GET_HIGH_WORD(high,y[0]); i = j-((high>>20)&0x7ff); if(i>16) { /* 2nd iteration needed, good to 118 */ 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_HIGH_WORD(high,y[0]); i = j-((high>>20)&0x7ff); if(i>49) { /* 3rd iteration need, 151 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; } } @@ -159,7 +159,7 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} else return n; } - /* + /* * all other (large) arguments */ if(ix>=0x7ff00000) { /* x is inf or NaN */ diff --git a/libm/e_remainder.c b/libm/e_remainder.c index 641808118..52e8a28d3 100644 --- a/libm/e_remainder.c +++ b/libm/e_remainder.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. * ==================================================== */ @@ -15,11 +15,11 @@ static char rcsid[] = "$NetBSD: e_remainder.c,v 1.8 1995/05/10 20:46:05 jtc Exp #endif /* __ieee754_remainder(x,p) - * Return : - * returns x REM p = x - [x/p]*p as if in infinite - * precise arithmetic, where [x/p] is the (infinite bit) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) * integer nearest x/p (in half way case choose the even one). - * Method : + * Method : * Based on fmod() return x-[x/p]chopped*p exactlp. */ diff --git a/libm/e_scalb.c b/libm/e_scalb.c index 7f66ec773..9a366f330 100644 --- a/libm/e_scalb.c +++ b/libm/e_scalb.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -16,7 +16,7 @@ static char rcsid[] = "$NetBSD: e_scalb.c,v 1.6 1995/05/10 20:46:09 jtc Exp $"; /* * __ieee754_scalb(x, fn) is provide for - * passing various standard test suite. One + * passing various standard test suite. One * should use scalbn() instead. */ diff --git a/libm/e_sinh.c b/libm/e_sinh.c index e1e614c9e..c63ff8ade 100644 --- a/libm/e_sinh.c +++ b/libm/e_sinh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -15,15 +15,15 @@ static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $"; #endif /* __ieee754_sinh(x) - * Method : + * Method : * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 - * 1. Replace x by |x| (sinh(-x) = -sinh(x)). - * 2. + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. * E + E/(E+1) * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) * 2 * - * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : sinh(x) := x*shuge (overflow) * @@ -47,7 +47,7 @@ static double one = 1.0, shuge = 1.0e307; double __ieee754_sinh(x) double x; #endif -{ +{ double t,w,h; int32_t ix,jx; u_int32_t lx; @@ -57,7 +57,7 @@ static double one = 1.0, shuge = 1.0e307; ix = jx&0x7fffffff; /* x is INF or NaN */ - if(ix>=0x7ff00000) return x+x; + if(ix>=0x7ff00000) return x+x; h = 0.5; if (jx<0) h = -h; diff --git a/libm/e_sqrt.c b/libm/e_sqrt.c index 15fba001d..fae52c842 100644 --- a/libm/e_sqrt.c +++ b/libm/e_sqrt.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -19,10 +19,10 @@ static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; * ------------------------------------------ * | Use the hardware sqrt if you have one | * ------------------------------------------ - * Method: - * Bit by bit method using integer arithmetic. (Slow, but portable) + * Method: + * Bit by bit method using integer arithmetic. (Slow, but portable) * 1. Normalization - * Scale x to y in [1,4) with even powers of 2: + * Scale x to y in [1,4) with even powers of 2: * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then * sqrt(x) = 2^k * sqrt(y) * 2. Bit by bit computation @@ -31,9 +31,9 @@ static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; * i+1 2 * s = 2*q , and y = 2 * ( y - q ). (1) * i i i i - * - * To compute q from q , one checks whether - * i+1 i + * + * To compute q from q , one checks whether + * i+1 i * * -(i+1) 2 * (q + 2 ) <= y. (2) @@ -43,12 +43,12 @@ static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; * i+1 i i+1 i * * With some algebric manipulation, it is not difficult to see - * that (2) is equivalent to + * that (2) is equivalent to * -(i+1) * s + 2 <= y (3) * i i * - * The advantage of (3) is that s and y can be computed by + * The advantage of (3) is that s and y can be computed by * i i * the following recurrence formula: * if (3) is false @@ -60,10 +60,10 @@ static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; * -i -(i+1) * s = s + 2 , y = y - s - 2 (5) * i+1 i i+1 i i - * - * One may easily use induction to prove (4) and (5). + * + * One may easily use induction to prove (4) and (5). * Note. Since the left hand side of (3) contain only i+2 bits, - * it does not necessary to do a full (53-bit) comparison + * it does not necessary to do a full (53-bit) comparison * in (3). * 3. Final rounding * After generating the 53 bits result, we compute one more bit. @@ -73,7 +73,7 @@ static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; * The rounding mode can be detected by checking whether * huge + tiny is equal to huge, and whether huge - tiny is * equal to huge for some floating point number "huge" and "tiny". - * + * * Special cases: * sqrt(+-0) = +-0 ... exact * sqrt(inf) = inf @@ -101,17 +101,17 @@ static double one = 1.0, tiny=1.0e-300; #endif { double z; - int32_t sign = (int)0x80000000; + int32_t sign = (int)0x80000000; int32_t ix0,s0,q,m,t,i; u_int32_t r,t1,s1,ix1,q1; EXTRACT_WORDS(ix0,ix1,x); /* take care of Inf and NaN */ - if((ix0&0x7ff00000)==0x7ff00000) { + if((ix0&0x7ff00000)==0x7ff00000) { return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf sqrt(-inf)=sNaN */ - } + } /* take care of zero */ if(ix0<=0) { if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ @@ -145,12 +145,12 @@ static double one = 1.0, tiny=1.0e-300; r = 0x00200000; /* r = moving bit from right to left */ while(r!=0) { - t = s0+r; - if(t<=ix0) { - s0 = t+r; - ix0 -= t; - q += r; - } + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } ix0 += ix0 + ((ix1&sign)>>31); ix1 += ix1; r>>=1; @@ -158,9 +158,9 @@ static double one = 1.0, tiny=1.0e-300; r = sign; while(r!=0) { - t1 = s1+r; + t1 = s1+r; t = s0; - if((t<ix0)||((t==ix0)&&(t1<=ix1))) { + if((t<ix0)||((t==ix0)&&(t1<=ix1))) { s1 = t1+r; if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1; ix0 -= t; @@ -181,7 +181,7 @@ static double one = 1.0, tiny=1.0e-300; if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} else if (z>one) { if (q1==(u_int32_t)0xfffffffe) q+=1; - q1+=2; + q1+=2; } else q1 += (q1&1); } @@ -197,18 +197,18 @@ static double one = 1.0, tiny=1.0e-300; /* Other methods (use floating-point arithmetic) ------------- -(This is a copy of a drafted paper by Prof W. Kahan +(This is a copy of a drafted paper by Prof W. Kahan and K.C. Ng, written in May, 1986) - Two algorithms are given here to implement sqrt(x) + Two algorithms are given here to implement sqrt(x) (IEEE double precision arithmetic) in software. Both supply sqrt(x) correctly rounded. The first algorithm (in Section A) uses newton iterations and involves four divisions. The second one uses reciproot iterations to avoid division, but requires more multiplications. Both algorithms need the ability - to chop results of arithmetic operations instead of round them, + to chop results of arithmetic operations instead of round them, and the INEXACT flag to indicate when an arithmetic operation - is executed exactly with no roundoff error, all part of the + is executed exactly with no roundoff error, all part of the standard (IEEE 754-1985). The ability to perform shift, add, subtract and logical AND operations upon 32-bit words is needed too, though not part of the standard. @@ -218,7 +218,7 @@ A. sqrt(x) by Newton Iteration (1) Initial approximation Let x0 and x1 be the leading and the trailing 32-bit words of - a floating point number x (in IEEE double format) respectively + a floating point number x (in IEEE double format) respectively 1 11 52 ...widths ------------------------------------------------------ @@ -226,7 +226,7 @@ A. sqrt(x) by Newton Iteration ------------------------------------------------------ msb lsb msb lsb ...order - + ------------------------ ------------------------ x0: |s| e | f1 | x1: | f2 | ------------------------ ------------------------ @@ -251,7 +251,7 @@ A. sqrt(x) by Newton Iteration (2) Iterative refinement - Apply Heron's rule three times to y, we have y approximates + Apply Heron's rule three times to y, we have y approximates sqrt(x) to within 1 ulp (Unit in the Last Place): y := (y+x/y)/2 ... almost 17 sig. bits @@ -276,12 +276,12 @@ A. sqrt(x) by Newton Iteration it requires more multiplications and additions. Also x must be scaled in advance to avoid spurious overflow in evaluating the expression 3y*y+x. Hence it is not recommended uless division - is slow. If division is very slow, then one should use the + is slow. If division is very slow, then one should use the reciproot algorithm given in section B. (3) Final adjustment - By twiddling y's last bit it is possible to force y to be + By twiddling y's last bit it is possible to force y to be correctly rounded according to the prevailing rounding mode as follows. Let r and i be copies of the rounding mode and inexact flag before entering the square root program. Also we @@ -312,7 +312,7 @@ A. sqrt(x) by Newton Iteration I := i; ... restore inexact flag R := r; ... restore rounded mode return sqrt(x):=y. - + (4) Special cases Square root of +inf, +-0, or NaN is itself; @@ -331,7 +331,7 @@ B. sqrt(x) by Reciproot Iteration k := 0x5fe80000 - (x0>>1); y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits - Here k is a 32-bit integer and T2[] is an integer array + Here k is a 32-bit integer and T2[] is an integer array containing correction terms. Now magically the floating value of y (y's leading 32-bit word is y0, the value of its trailing word y1 is set to zero) approximates 1/sqrt(x) @@ -352,9 +352,9 @@ B. sqrt(x) by Reciproot Iteration Apply Reciproot iteration three times to y and multiply the result by x to get an approximation z that matches sqrt(x) - to about 1 ulp. To be exact, we will have + to about 1 ulp. To be exact, we will have -1ulp < sqrt(x)-z<1.0625ulp. - + ... set rounding mode to Round-to-nearest y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) @@ -363,14 +363,14 @@ B. sqrt(x) by Reciproot Iteration z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that - (a) the term z*y in the final iteration is always less than 1; + (a) the term z*y in the final iteration is always less than 1; (b) the error in the final result is biased upward so that -1 ulp < sqrt(x) - z < 1.0625 ulp instead of |sqrt(x)-z|<1.03125ulp. (3) Final adjustment - By twiddling y's last bit it is possible to force y to be + By twiddling y's last bit it is possible to force y to be correctly rounded according to the prevailing rounding mode as follows. Let r and i be copies of the rounding mode and inexact flag before entering the square root program. Also we @@ -410,27 +410,27 @@ B. sqrt(x) by Reciproot Iteration I := 1; ... Raise Inexact flag: z is not exact else { j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 - k := z1 >> 26; ... get z's 25-th and 26-th + k := z1 >> 26; ... get z's 25-th and 26-th fraction bits I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); } R:= r ... restore rounded mode return sqrt(x):=z. - If multiplication is cheaper then the foregoing red tape, the + If multiplication is cheaper then the foregoing red tape, the Inexact flag can be evaluated by I := i; I := (z*z!=x) or I. - Note that z*z can overwrite I; this value must be sensed if it is + Note that z*z can overwrite I; this value must be sensed if it is True. Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be zero. -------------------- - z1: | f2 | + z1: | f2 | -------------------- bit 31 bit 0 @@ -447,7 +447,7 @@ B. sqrt(x) by Reciproot Iteration 11 01 even ------------------------------------------------- - (4) Special cases (see (4) of Section A). - + (4) Special cases (see (4) of Section A). + */ - + diff --git a/libm/fp_private.h b/libm/fp_private.h index c16836a12..505400e33 100644 --- a/libm/fp_private.h +++ b/libm/fp_private.h @@ -56,13 +56,13 @@ //#define Infinity(x) ( x.hex.exponent & ExpMask ) == ExpMask #define dInfinity(x) ( x.hex.high & dExpMask ) == dExpMask -#define sInfinity(x) ( ( x.hexsgl << 1 ) & sExpMask ) == sExpMask +#define sInfinity(x) ( ( x.hexsgl << 1 ) & sExpMask ) == sExpMask //#define Exponent(x) x.hex.exponent & ExpMask #define dExponent(x) x.hex.high & dExpMask #define sExponent(x) ( ( x.hexsgl << 1 ) & sExpMask ) -#define sZero(x) ( x.hexsgl & sSgnMask ) == 0 +#define sZero(x) ( x.hexsgl & sSgnMask ) == 0 //#define Sign(x) ( x.hex.exponent & SgnMask ) == SgnMask /******************************************************************************* diff --git a/libm/fpmacros.c b/libm/fpmacros.c index 0fa4f9e7e..78cc46e9a 100644 --- a/libm/fpmacros.c +++ b/libm/fpmacros.c @@ -1,6 +1,6 @@ /*********************************************************************** ** File: fpmacros.c -** +** ** Contains: C source code for implementations of floating-point ** functions which involve float format numbers, as ** defined in header <fp.h>. In particular, this file @@ -8,16 +8,16 @@ ** __fpclassify(d,f), __isnormal(d,f), __isfinite(d,f), ** __isnan(d,f), and __signbit(d,f). This file targets ** PowerPC platforms. -** +** ** Written by: Robert A. Murley, Ali Sazegari -** +** ** Copyright: c 2001 by Apple Computer, Inc., all rights reserved -** +** ** Change History (most recent first): ** -** 07 Jul 01 ram First created from fpfloatfunc.c, fp.c, +** 07 Jul 01 ram First created from fpfloatfunc.c, fp.c, ** classify.c and sign.c in MathLib v3 Mac OS9. -** +** ***********************************************************************/ #include <features.h> @@ -33,48 +33,48 @@ /*********************************************************************** int __fpclassifyf(float x) returns the classification code of the argument x, as defined in <fp.h>. - + Exceptions: INVALID signaled if x is a signaling NaN; in this case, the FP_QNAN code is returned. - + Calls: none ***********************************************************************/ int __fpclassifyf ( float x ) { unsigned int iexp; - + union { u_int32_t lval; float fval; } z; - + z.fval = x; - iexp = z.lval & FEXP_MASK; /* isolate float exponent */ - + iexp = z.lval & FEXP_MASK; /* isolate float exponent */ + if (iexp == FEXP_MASK) { /* NaN or INF case */ if ((z.lval & 0x007fffff) == 0) return FP_INFINITE; return FP_NAN; } - + if (iexp != 0) /* normal float */ return FP_NORMAL; - + if (x == 0.0) return FP_ZERO; /* zero */ else return FP_SUBNORMAL; /* must be subnormal */ } - + /*********************************************************************** - Function __fpclassify, - Implementation of classify of a double number for the PowerPC. - + Function __fpclassify, + Implementation of classify of a double number for the PowerPC. + Exceptions: INVALID signaled if x is a signaling NaN; in this case, the FP_QNAN code is returned. - + Calls: none ***********************************************************************/ @@ -86,16 +86,16 @@ int __fpclassify ( double arg ) dHexParts hex; double dbl; } x; - + x.dbl = arg; - + exponent = x.hex.high & dExpMask; if ( exponent == dExpMask ) { if ( ( ( x.hex.high & dHighMan ) | x.hex.low ) == 0 ) return FP_INFINITE; else - return FP_NAN; + return FP_NAN; } else if ( exponent != 0) return FP_NORMAL; @@ -111,10 +111,10 @@ int __fpclassify ( double arg ) /*********************************************************************** int __isnormalf(float x) returns nonzero if and only if x is a normalized float number and zero otherwise. - + Exceptions: INVALID is raised if x is a signaling NaN; in this case, zero is returned. - + Calls: none ***********************************************************************/ @@ -125,44 +125,44 @@ int __isnormalf ( float x ) u_int32_t lval; float fval; } z; - + z.fval = x; iexp = z.lval & FEXP_MASK; /* isolate float exponent */ return ((iexp != FEXP_MASK) && (iexp != 0)); } - + int __isnormal ( double x ) { - return ( __fpclassify ( x ) == FP_NORMAL ); + return ( __fpclassify ( x ) == FP_NORMAL ); } /*********************************************************************** int __isfinitef(float x) returns nonzero if and only if x is a finite (normal, subnormal, or zero) float number and zero otherwise. - + Exceptions: INVALID is raised if x is a signaling NaN; in this case, zero is returned. - + Calls: none ***********************************************************************/ int __finitef ( float x ) -{ +{ union { u_int32_t lval; float fval; } z; - + z.fval = x; return ((z.lval & FEXP_MASK) != FEXP_MASK); } weak_alias (__finitef, finitef) - + int __finite ( double x ) { - return ( __fpclassify ( x ) >= FP_ZERO ); + return ( __fpclassify ( x ) >= FP_ZERO ); } weak_alias (__finite, finite) @@ -170,28 +170,28 @@ weak_alias (__finite, finite) /*********************************************************************** int __signbitf(float x) returns nonzero if and only if the sign bit of x is set and zero otherwise. - + Exceptions: INVALID is raised if x is a signaling NaN. - + Calls: none ***********************************************************************/ int __signbitf ( float x ) -{ +{ union { u_int32_t lval; float fval; } z; - + z.fval = x; return ((z.lval & SIGN_MASK) != 0); } /*********************************************************************** - Function sign of a double. - Implementation of sign bit for the PowerPC. - + Function sign of a double. + Implementation of sign bit for the PowerPC. + Calls: none ***********************************************************************/ @@ -252,20 +252,20 @@ weak_alias (__isinfl, isinfl); /*********************************************************************** int __isnanf(float x) returns nonzero if and only if x is a NaN and zero otherwise. - + Exceptions: INVALID is raised if x is a signaling NaN; in this case, nonzero is returned. - + Calls: none ***********************************************************************/ int __isnanf ( float x ) -{ +{ union { u_int32_t lval; float fval; } z; - + z.fval = x; return (((z.lval&FEXP_MASK) == FEXP_MASK) && ((z.lval&FFRAC_MASK) != 0)); } @@ -274,7 +274,7 @@ weak_alias (__isnanf, isnanf); int __isnan ( double x ) { int class = __fpclassify(x); - return ( class == FP_NAN ); + return ( class == FP_NAN ); } weak_alias (__isnan, isnan); @@ -282,7 +282,7 @@ weak_alias (__isnan, isnan); int __isnanl ( long double x ) { int class = __fpclassify(x); - return ( class == FP_NAN ); + return ( class == FP_NAN ); } weak_alias (__isnanl, isnanl); #endif diff --git a/libm/k_cos.c b/libm/k_cos.c index d8740b350..03c208aac 100644 --- a/libm/k_cos.c +++ b/libm/k_cos.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. * ==================================================== */ @@ -18,7 +18,7 @@ static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; * __kernel_cos( x, y ) * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. + * Input y is the tail of x. * * Algorithm * 1. Since cos(-x) = cos(x), we need only to consider positive x. @@ -28,15 +28,15 @@ static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; * 4 14 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x * where the remez error is - * + * * | 2 4 6 8 10 12 14 | -58 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 - * | | - * - * 4 6 8 10 12 14 + * | | + * + * 4 6 8 10 12 14 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then * cos(x) = 1 - x*x/2 + r - * since cos(x+y) ~ cos(x) - sin(x)*y + * since cos(x+y) ~ cos(x) - sin(x)*y * ~ cos(x) - x*y, * a correction term is necessary in cos(x) and hence * cos(x+y) = 1 - (x*x/2 - (r - x*y)) @@ -53,9 +53,9 @@ static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ @@ -81,7 +81,7 @@ C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ } z = x*x; r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); - if(ix < 0x3FD33333) /* if |x| < 0.3 */ + if(ix < 0x3FD33333) /* if |x| < 0.3 */ return one - (0.5*z - (z*r - x*y)); else { if(ix > 0x3fe90000) { /* x > 0.78125 */ diff --git a/libm/k_rem_pio2.c b/libm/k_rem_pio2.c index 7ff69a4c7..9113d8762 100644 --- a/libm/k_rem_pio2.c +++ b/libm/k_rem_pio2.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -17,12 +17,12 @@ static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $ /* * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) * double x[],y[]; int e0,nx,prec; int ipio2[]; - * - * __kernel_rem_pio2 return the last three digits of N with + * + * __kernel_rem_pio2 return the last three digits of N with * y = x - N*pi/2 * so that |y| < pi/2. * - * The method is to compute the integer (mod 8) and fraction parts of + * The method is to compute the integer (mod 8) and fraction parts of * (2/pi)*x without doing the full multiplication. In general we * skip the part of the product that are known to be a huge integer ( * more accurately, = 0 mod 8 ). Thus the number of operations are @@ -31,10 +31,10 @@ static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $ * (2/pi) is represented by an array of 24-bit integers in ipio2[]. * * Input parameters: - * x[] The input value (must be positive) is broken into nx + * x[] The input value (must be positive) is broken into nx * pieces of 24-bit integers in double precision format. - * x[i] will be the i-th 24 bit of x. The scaled exponent - * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 * match x's up to 24 bits. * * Example of breaking a double positive z into x[0]+x[1]+x[2]: @@ -71,8 +71,8 @@ static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $ * 3 113 bits (quad) * * ipio2[] - * integer array, contains the (24*i)-th to (24*i+23)-th - * bit of 2/pi after binary point. The corresponding + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding * floating value is * * ipio2[i] * 2^(-24(i+1)). @@ -87,8 +87,8 @@ static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $ * in the computation. The recommended value is 2,3,4, * 6 for single, double, extended,and quad. * - * jz local integer variable indicating the number of - * terms of ipio2[] used. + * jz local integer variable indicating the number of + * terms of ipio2[] used. * * jx nx - 1 * @@ -108,9 +108,9 @@ static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $ * exponent for q[i] would be q0-24*i. * * PIo2[] double precision array, obtained by cutting pi/2 - * into 24 bits chunks. + * into 24 bits chunks. * - * f[] ipio2[] in floating point + * f[] ipio2[] in floating point * * iq[] integer array by breaking up q[] in 24-bits chunk. * @@ -124,9 +124,9 @@ static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $ /* * 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. */ @@ -136,7 +136,7 @@ static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $ #ifdef __STDC__ static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ #else -static int init_jk[] = {2,3,4,6}; +static int init_jk[] = {2,3,4,6}; #endif #ifdef __STDC__ @@ -155,9 +155,9 @@ static double PIo2[] = { }; #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif zero = 0.0, one = 1.0, @@ -165,9 +165,9 @@ two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ #ifdef __STDC__ - int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2) + int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2) #else - int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) double x[], y[]; int e0,nx,prec; int32_t ipio2[]; #endif { @@ -211,7 +211,7 @@ recompute: i = (iq[jz-1]>>(24-q0)); n += i; iq[jz-1] -= i<<(24-q0); ih = iq[jz-1]>>(23-q0); - } + } else if(q0==0) ih = iq[jz-1]>>23; else if(z>=0.5) ih=2; @@ -262,7 +262,7 @@ recompute: while(iq[jz]==0) { jz--; q0-=24;} } else { /* break z into 24-bit if necessary */ z = scalbn(z,-q0); - if(z>=two24) { + if(z>=two24) { fw = (double)((int32_t)(twon24*z)); iq[jz] = (int32_t)(z-two24*fw); jz += 1; q0 += 24; @@ -287,29 +287,29 @@ recompute: case 0: fw = 0.0; for (i=jz;i>=0;i--) fw += fq[i]; - y[0] = (ih==0)? fw: -fw; + y[0] = (ih==0)? fw: -fw; break; case 1: case 2: fw = 0.0; - for (i=jz;i>=0;i--) fw += fq[i]; - y[0] = (ih==0)? fw: -fw; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; fw = fq[0]-fw; for (i=1;i<=jz;i++) fw += fq[i]; - y[1] = (ih==0)? fw: -fw; + y[1] = (ih==0)? fw: -fw; break; case 3: /* painful */ for (i=jz;i>0;i--) { - fw = fq[i-1]+fq[i]; + fw = fq[i-1]+fq[i]; fq[i] += fq[i-1]-fw; fq[i-1] = fw; } for (i=jz;i>1;i--) { - fw = fq[i-1]+fq[i]; + fw = fq[i-1]+fq[i]; fq[i] += fq[i-1]-fw; fq[i-1] = fw; } - for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; if(ih==0) { y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; } else { diff --git a/libm/k_sin.c b/libm/k_sin.c index 86b95529b..5bfc1d680 100644 --- a/libm/k_sin.c +++ b/libm/k_sin.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. * ==================================================== */ @@ -18,24 +18,24 @@ static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 * Input x is assumed to be bounded by ~pi/4 in magnitude. * Input y is the tail of x. - * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). * * Algorithm - * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. * 3. sin(x) is approximated by a polynomial of degree 13 on * [0,pi/4] * 3 13 * sin(x) ~ x + S1*x + ... + S6*x * where - * + * * |sin(x) 2 4 6 8 10 12 | -58 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 - * | x | - * + * | x | + * * 4. sin(x+y) = sin(x) + sin'(x')*y * ~ sin(x) + (1-x*x/2)*y - * For better accuracy, let + * For better accuracy, let * 3 2 2 2 2 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) * then 3 2 @@ -46,9 +46,9 @@ static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ diff --git a/libm/k_standard.c b/libm/k_standard.c index 3f6fad841..c56d5e490 100644 --- a/libm/k_standard.c +++ b/libm/k_standard.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. * ==================================================== */ @@ -33,7 +33,7 @@ static const double zero = 0.0; /* used as const */ static double zero = 0.0; /* used as const */ #endif -/* +/* * Standard conformance (non-IEEE) on exception cases. * Mapping: * 1 -- acos(|x|>1) @@ -58,7 +58,7 @@ static double zero = 0.0; /* used as const */ * 20-- pow(0.0,0.0) * 21-- pow(x,y) overflow * 22-- pow(x,y) underflow - * 23-- pow(0,negative) + * 23-- pow(0,negative) * 24-- pow(neg,non-integral) * 25-- sinh(finite) overflow * 26-- sqrt(negative) @@ -82,14 +82,14 @@ static double zero = 0.0; /* used as const */ #ifdef __STDC__ - double __kernel_standard(double x, double y, int type) + double __kernel_standard(double x, double y, int type) #else - double __kernel_standard(x,y,type) + double __kernel_standard(x,y,type) double x,y; int type; #endif { struct exception exc; -#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ +#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ #define HUGE_VAL inf double inf = 0.0; @@ -469,7 +469,7 @@ static double zero = 0.0; /* used as const */ /* 0**neg */ exc.type = DOMAIN; exc.name = type < 100 ? "pow" : "powf"; - if (_LIB_VERSION == _SVID_) + if (_LIB_VERSION == _SVID_) exc.retval = zero; else exc.retval = -HUGE_VAL; @@ -487,11 +487,11 @@ static double zero = 0.0; /* used as const */ /* neg**non-integral */ exc.type = DOMAIN; exc.name = type < 100 ? "pow" : "powf"; - if (_LIB_VERSION == _SVID_) + if (_LIB_VERSION == _SVID_) exc.retval = zero; - else + else exc.retval = zero/zero; /* X/Open allow NaN */ - if (_LIB_VERSION == _POSIX_) + if (_LIB_VERSION == _POSIX_) errno = EDOM; else if (!matherr(&exc)) { if (_LIB_VERSION == _SVID_) { @@ -649,7 +649,7 @@ static double zero = 0.0; /* used as const */ (void) WRITE2(": TLOSS error\n", 14); } errno = ERANGE; - } + } break; case 35: case 135: @@ -665,7 +665,7 @@ static double zero = 0.0; /* used as const */ (void) WRITE2(": TLOSS error\n", 14); } errno = ERANGE; - } + } break; case 36: case 136: @@ -681,7 +681,7 @@ static double zero = 0.0; /* used as const */ (void) WRITE2(": TLOSS error\n", 14); } errno = ERANGE; - } + } break; case 37: case 137: @@ -697,7 +697,7 @@ static double zero = 0.0; /* used as const */ (void) WRITE2(": TLOSS error\n", 14); } errno = ERANGE; - } + } break; case 38: case 138: @@ -713,7 +713,7 @@ static double zero = 0.0; /* used as const */ (void) WRITE2(": TLOSS error\n", 14); } errno = ERANGE; - } + } break; case 39: case 139: @@ -729,7 +729,7 @@ static double zero = 0.0; /* used as const */ (void) WRITE2(": TLOSS error\n", 14); } errno = ERANGE; - } + } break; case 40: case 140: @@ -778,5 +778,5 @@ static double zero = 0.0; /* used as const */ } break; } - return exc.retval; + return exc.retval; } diff --git a/libm/k_tan.c b/libm/k_tan.c index aa9c67c9d..8f7822a3d 100644 --- a/libm/k_tan.c +++ b/libm/k_tan.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. * ==================================================== */ @@ -18,25 +18,25 @@ static char rcsid[] = "$NetBSD: k_tan.c,v 1.8 1995/05/10 20:46:37 jtc Exp $"; * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 * Input x is assumed to be bounded by ~pi/4 in magnitude. * Input y is the tail of x. - * Input k indicates whether tan (if k=1) or + * Input k indicates whether tan (if k=1) or * -1/tan (if k= -1) is returned. * * Algorithm - * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. * 3. tan(x) is approximated by a odd polynomial of degree 27 on * [0,0.67434] * 3 27 * tan(x) ~ x + T1*x + ... + T13*x * where - * + * * |tan(x) 2 4 26 | -59.2 * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 - * | x | - * + * | x | + * * Note: tan(x+y) = tan(x) + tan'(x)*y * ~ tan(x) + (1+x*x)*y - * Therefore, for better accuracy in computing tan(x+y), let + * Therefore, for better accuracy in computing tan(x+y), let * 3 2 2 2 2 * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) * then @@ -51,9 +51,9 @@ static char rcsid[] = "$NetBSD: k_tan.c,v 1.8 1995/05/10 20:46:37 jtc Exp $"; #include "math.h" #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ @@ -116,7 +116,7 @@ T[] = { return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); } if(iy==1) return w; - else { /* if allow error up to 2 ulp, + else { /* if allow error up to 2 ulp, simply return -1.0/(x+r) here */ /* compute -1.0/(x+r) accurately */ double a,t; diff --git a/libm/math_private.h b/libm/math_private.h index cc876607f..900e2a0db 100644 --- a/libm/math_private.h +++ b/libm/math_private.h @@ -4,7 +4,7 @@ * * 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. * ==================================================== */ @@ -42,10 +42,10 @@ #if (__BYTE_ORDER == __BIG_ENDIAN) || defined(__arm__) && !defined(__VFP_FP__) -typedef union +typedef union { double value; - struct + struct { u_int32_t msw; u_int32_t lsw; @@ -56,10 +56,10 @@ typedef union #if (__BYTE_ORDER == __LITTLE_ENDIAN) && (!defined(__arm__) || defined(__VFP_FP__)) -typedef union +typedef union { double value; - struct + struct { u_int32_t lsw; u_int32_t msw; @@ -154,13 +154,13 @@ do { \ } while (0) /* ieee style elementary functions */ -extern double __ieee754_sqrt __P((double)); -extern double __ieee754_acos __P((double)); -extern double __ieee754_acosh __P((double)); -extern double __ieee754_log __P((double)); -extern double __ieee754_atanh __P((double)); -extern double __ieee754_asin __P((double)); -extern double __ieee754_atan2 __P((double,double)); +extern double __ieee754_sqrt __P((double)); +extern double __ieee754_acos __P((double)); +extern double __ieee754_acosh __P((double)); +extern double __ieee754_log __P((double)); +extern double __ieee754_atanh __P((double)); +extern double __ieee754_asin __P((double)); +extern double __ieee754_atan2 __P((double,double)); extern double __ieee754_exp __P((double)); extern double __ieee754_cosh __P((double)); extern double __ieee754_fmod __P((double,double)); @@ -187,7 +187,7 @@ extern double __ieee754_scalb __P((double,double)); #endif /* fdlibm kernel function */ -extern double __kernel_standard __P((double,double,int)); +extern double __kernel_standard __P((double,double,int)); extern double __kernel_sin __P((double,double,int)); extern double __kernel_cos __P((double,double)); extern double __kernel_tan __P((double,double,int)); @@ -195,13 +195,13 @@ extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*)); /* ieee style elementary float functions */ -extern float __ieee754_sqrtf __P((float)); -extern float __ieee754_acosf __P((float)); -extern float __ieee754_acoshf __P((float)); -extern float __ieee754_logf __P((float)); -extern float __ieee754_atanhf __P((float)); -extern float __ieee754_asinf __P((float)); -extern float __ieee754_atan2f __P((float,float)); +extern float __ieee754_sqrtf __P((float)); +extern float __ieee754_acosf __P((float)); +extern float __ieee754_acoshf __P((float)); +extern float __ieee754_logf __P((float)); +extern float __ieee754_atanhf __P((float)); +extern float __ieee754_asinf __P((float)); +extern float __ieee754_atan2f __P((float,float)); extern float __ieee754_expf __P((float)); extern float __ieee754_coshf __P((float)); extern float __ieee754_fmodf __P((float,float)); diff --git a/libm/powerpc/Makefile b/libm/powerpc/Makefile index 84e0b94c9..9e4a309da 100644 --- a/libm/powerpc/Makefile +++ b/libm/powerpc/Makefile @@ -6,14 +6,14 @@ # math library for Apple's MacOS X/Darwin math library, which was # itself swiped from FreeBSD. The original copyright information # is as follows: -# +# # 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. -# +# # It has been ported to work with uClibc and generally behave # by Erik Andersen <andersen@codepoet.org> # @@ -66,6 +66,6 @@ $(OBJ): Makefile tags: ctags -R -clean: +clean: $(RM) *.[oa] *~ core diff --git a/libm/powerpc/s_ceil.c b/libm/powerpc/s_ceil.c index 790dd7ba0..fd073de7b 100644 --- a/libm/powerpc/s_ceil.c +++ b/libm/powerpc/s_ceil.c @@ -52,24 +52,24 @@ double ceil ( double x ) register double y; register unsigned long int xhi; register int target; - + xInHex.dbl = x; xhi = xInHex.words.hi & 0x7fffffffUL; // xhi is the high half of |x| target = ( xInHex.words.hi < signMask ); - - if ( xhi < 0x43300000ul ) + + if ( xhi < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^52? * *******************************************************************************/ { - if ( xhi < 0x3ff00000ul ) + if ( xhi < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ { if ( ( xhi | xInHex.words.lo ) == 0ul ) // zero x is exact case return ( x ); - else + else { // inexact case asm ("mffs %0" : "=f" (OldEnvironment.dbl)); OldEnvironment.words.lo |= 0x02000000ul; @@ -83,7 +83,7 @@ double ceil ( double x ) /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ - if ( target ) + if ( target ) { y = ( x + twoTo52 ) - twoTo52; // round at binary pt. if ( y < x ) @@ -91,8 +91,8 @@ double ceil ( double x ) else return ( y ); } - - else + + else { y = ( x - twoTo52 ) + twoTo52; // round at binary pt. if ( y < x ) diff --git a/libm/powerpc/s_copysign.c b/libm/powerpc/s_copysign.c index 18e91998a..d3fb5f40b 100644 --- a/libm/powerpc/s_copysign.c +++ b/libm/powerpc/s_copysign.c @@ -45,12 +45,12 @@ double copysign ( double arg2, double arg1 ) /******************************************************************************* * No need to flush NaNs out. * *******************************************************************************/ - + x.dbl = arg1; y.dbl = arg2; - + y.hex.high = y.hex.high & 0x7FFFFFFF; y.hex.high = ( y.hex.high | ( x.hex.high & dSgnMask ) ); - + return y.dbl; } diff --git a/libm/powerpc/s_floor.c b/libm/powerpc/s_floor.c index f7b4534bb..94677b4d2 100644 --- a/libm/powerpc/s_floor.c +++ b/libm/powerpc/s_floor.c @@ -52,24 +52,24 @@ double floor ( double x ) register double y; register unsigned long int xhi; register long int target; - + xInHex.dbl = x; xhi = xInHex.words.hi & 0x7fffffffUL; // xhi is the high half of |x| target = ( xInHex.words.hi < signMask ); - - if ( xhi < 0x43300000ul ) + + if ( xhi < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^52? * *******************************************************************************/ { - if ( xhi < 0x3ff00000ul ) + if ( xhi < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ { if ( ( xhi | xInHex.words.lo ) == 0ul ) // zero x is exact case return ( x ); - else + else { // inexact case asm ("mffs %0" : "=f" (OldEnvironment.dbl)); OldEnvironment.words.lo |= 0x02000000ul; @@ -83,7 +83,7 @@ double floor ( double x ) /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ - if ( target ) + if ( target ) { y = ( x + twoTo52 ) - twoTo52; // round at binary pt. if ( y > x ) @@ -91,8 +91,8 @@ double floor ( double x ) else return ( y ); } - - else + + else { y = ( x - twoTo52 ) + twoTo52; // round at binary pt. if ( y > x ) diff --git a/libm/powerpc/s_frexp.c b/libm/powerpc/s_frexp.c index 0ca7c1514..9909f2ce7 100644 --- a/libm/powerpc/s_frexp.c +++ b/libm/powerpc/s_frexp.c @@ -31,12 +31,12 @@ typedef union unsigned long int hi; unsigned long int lo; #else - unsigned long int lo; - unsigned long int hi; + unsigned long int lo; + unsigned long int hi; #endif } words; double dbl; - } DblInHex; + } DblInHex; double frexp ( double value, int *eptr ) { @@ -49,7 +49,7 @@ double frexp ( double value, int *eptr ) *eptr = 0; if ( valueHead >= 0x7ff00000 || ( valueHead | argument.words.lo ) == 0 ) return value; // 0, inf, or NaN - + if ( valueHead < 0x00100000 ) { // denorm argument.dbl = two54 * value; diff --git a/libm/powerpc/s_ldexp.c b/libm/powerpc/s_ldexp.c index 0e9a66611..ce9ec8b1b 100644 --- a/libm/powerpc/s_ldexp.c +++ b/libm/powerpc/s_ldexp.c @@ -29,18 +29,18 @@ typedef union unsigned long int hi; unsigned long int lo; #else - unsigned long int lo; - unsigned long int hi; + unsigned long int lo; + unsigned long int hi; #endif } words; double dbl; - } DblInHex; + } DblInHex; -double ldexp ( double value, int exp ) +double ldexp ( double value, int exp ) { - if ( exp > SHRT_MAX ) + if ( exp > SHRT_MAX ) exp = SHRT_MAX; - else if ( exp < -SHRT_MAX ) + else if ( exp < -SHRT_MAX ) exp = -SHRT_MAX; return scalb ( value, exp ); } diff --git a/libm/powerpc/s_logb.c b/libm/powerpc/s_logb.c index 3a410ba5c..23c7270f9 100644 --- a/libm/powerpc/s_logb.c +++ b/libm/powerpc/s_logb.c @@ -32,8 +32,8 @@ * Standard 754. * *******************************************************************************/ -typedef union - { +typedef union + { struct { #if defined(__BIG_ENDIAN__) unsigned long int hi; @@ -62,38 +62,38 @@ double logb ( double x ) { DblInHex xInHex; long int shiftedExp; - + xInHex.dbl = x; shiftedExp = ( xInHex.words.hi & 0x7ff00000UL ) >> 20; - - if ( shiftedExp == 2047 ) + + if ( shiftedExp == 2047 ) { // NaN or INF if ( ( ( xInHex.words.hi & signMask ) == 0 ) || ( x != x ) ) return x; // NaN or +INF return x else return -x; // -INF returns +INF } - + if ( shiftedExp != 0 ) // normal number shiftedExp -= 1023; // unbias exponent - - else if ( x == 0.0 ) + + else if ( x == 0.0 ) { // zero xInHex.words.hi = 0x0UL; // return -infinity return ( minusInf.dbl ); } - - else + + else { // subnormal number xInHex.dbl *= twoTo52; // scale up shiftedExp = ( xInHex.words.hi & 0x7ff00000UL ) >> 20; shiftedExp -= 1075; // unbias exponent } - + if ( shiftedExp == 0 ) // zero result return ( 0.0 ); - - else + + else { // nonzero result xInHex.dbl = klTod; xInHex.words.lo += shiftedExp; diff --git a/libm/powerpc/s_modf.c b/libm/powerpc/s_modf.c index 66c0655f5..403c54b79 100644 --- a/libm/powerpc/s_modf.c +++ b/libm/powerpc/s_modf.c @@ -1,18 +1,18 @@ /******************************************************************************* ** File: rndint.c -** +** ** Contains: C source code for implementations of floating-point ** functions which round to integral value or format, as ** defined in header <fp.h>. In particular, this file ** contains implementations of functions rint, nearbyint, ** rinttol, round, roundtol, trunc, modf and modfl. This file ** targets PowerPC or Power platforms. -** +** ** Written by: A. Sazegari, Apple AltiVec Group ** Created originally by Jon Okada, Apple Numerics Group -** +** ** Copyright: © 1992-2001 by Apple Computer, Inc., all rights reserved -** +** ** Change History (most recent first): ** ** 13 Jul 01 ram replaced --setflm calls with inline assembly @@ -21,7 +21,7 @@ ** 1. removed double_t, put in double for now. ** 2. removed iclass from nearbyint. ** 3. removed wrong comments intrunc. -** 4. +** 4. ** 13 May 97 ali made performance improvements in rint, rinttol, roundtol ** and trunc by folding some of the taligent ideas into this ** implementation. nearbyint is faster than the one in taligent, @@ -33,7 +33,7 @@ ** 18 Feb 93 ali Changed the return value of fenv functions ** feclearexcept and feraiseexcept to their new ** NCEG X3J11.1/93-001 definitions. -** 16 Dec 92 JPO Removed __itrunc implementation to a +** 16 Dec 92 JPO Removed __itrunc implementation to a ** separate file. ** 15 Dec 92 JPO Added __itrunc implementation and modified ** rinttol to include conversion from double @@ -41,7 +41,7 @@ ** call __itrunc. ** 10 Dec 92 JPO Added modf (double) implementation. ** 04 Dec 92 JPO First created. -** +** *******************************************************************************/ #include <limits.h> @@ -81,14 +81,14 @@ static const DblInHex TOWARDZERO = {{ 0x00000000, 0x00000001 }}; * This function calls fabs and copysign. * * * *******************************************************************************/ - + double nearbyint ( double x ) { double y; double OldEnvironment; - + y = twoTo52; - + asm ("mffs %0" : "=f" (OldEnvironment)); /* get the environement */ if ( fabs ( x ) >= y ) /* huge case is exact */ @@ -99,9 +99,9 @@ double nearbyint ( double x ) y = copysign ( y, x ); // restore old flags asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment )); - return ( y ); + return ( y ); } - + /******************************************************************************* * * * The function rinttol converts its double argument to integral value * @@ -120,38 +120,38 @@ long int rinttol ( double x ) DblInHex argument, OldEnvironment; unsigned long int xHead; register long int target; - + argument.dbl = x; target = ( argument.words.hi < signMask ); // flag positive sign xHead = argument.words.hi & 0x7ffffffful; // high 32 bits of x - - if ( target ) + + if ( target ) /******************************************************************************* * Sign of x is positive. * *******************************************************************************/ { - if ( xHead < 0x41dffffful ) + if ( xHead < 0x41dffffful ) { // x is safely in long range y = ( x + twoTo52 ) - twoTo52; // round at binary point argument.dbl = y + doubleToLong; // force result into argument.words.lo return ( ( long ) argument.words.lo ); } - + asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment - - if ( xHead > 0x41dffffful ) + + if ( xHead > 0x41dffffful ) { // x is safely out of long range OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MAX ); } - + /******************************************************************************* * x > 0.0 and may or may not be out of range of long. * *******************************************************************************/ y = ( x + twoTo52 ) - twoTo52; // do rounding - if ( y > ( double ) LONG_MAX ) + if ( y > ( double ) LONG_MAX ) { // out of range of long OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); @@ -160,32 +160,32 @@ long int rinttol ( double x ) argument.dbl = y + doubleToLong; // in range return ( ( long ) argument.words.lo ); // return result & flags } - + /******************************************************************************* * Sign of x is negative. * *******************************************************************************/ - if ( xHead < 0x41e00000ul ) + if ( xHead < 0x41e00000ul ) { // x is safely in long range y = ( x - twoTo52 ) + twoTo52; argument.dbl = y + doubleToLong; return ( ( long ) argument.words.lo ); } - + asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment - - if ( xHead > 0x41e00000ul ) + + if ( xHead > 0x41e00000ul ) { // x is safely out of long range OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( LONG_MIN ); } - + /******************************************************************************* * x < 0.0 and may or may not be out of range of long. * *******************************************************************************/ y = ( x - twoTo52 ) + twoTo52; // do rounding - if ( y < ( double ) LONG_MIN ) + if ( y < ( double ) LONG_MIN ) { // out of range of long OldEnvironment.words.lo |= SET_INVALID; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); @@ -204,30 +204,30 @@ long int rinttol ( double x ) * return value is not equal to the operand. * * * *******************************************************************************/ - + double round ( double x ) - { + { DblInHex argument, OldEnvironment; register double y, z; register unsigned long int xHead; register long int target; - + argument.dbl = x; xHead = argument.words.hi & 0x7fffffffUL; // xHead <- high half of |x| target = ( argument.words.hi < signMask ); // flag positive sign - - if ( xHead < 0x43300000ul ) + + if ( xHead < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^52? * *******************************************************************************/ { - if ( xHead < 0x3ff00000ul ) + if ( xHead < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ { asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // get environment - if ( xHead < 0x3fe00000ul ) + if ( xHead < 0x3fe00000ul ) /******************************************************************************* * Is |x| < 0.5? * *******************************************************************************/ @@ -235,7 +235,7 @@ double round ( double x ) if ( ( xHead | argument.words.lo ) != 0ul ) OldEnvironment.words.lo |= 0x02000000ul; asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); - if ( target ) + if ( target ) return ( 0.0 ); else return ( -0.0 ); @@ -253,7 +253,7 @@ double round ( double x ) /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ - if ( target ) + if ( target ) { // positive x y = ( x + twoTo52 ) - twoTo52; // round at binary point if ( y == x ) // exact case @@ -265,11 +265,11 @@ double round ( double x ) else return ( y ); } - + /******************************************************************************* * Is x < 0? * *******************************************************************************/ - else + else { y = ( x - twoTo52 ) + twoTo52; // round at binary point if ( y == x ) @@ -302,19 +302,19 @@ double round ( double x ) *******************************************************************************/ long int roundtol ( double x ) - { + { register double y, z; DblInHex argument, OldEnvironment; register unsigned long int xhi; register long int target; const DblInHex kTZ = {{ 0x0, 0x1 }}; const DblInHex kUP = {{ 0x0, 0x2 }}; - + argument.dbl = x; xhi = argument.words.hi & 0x7ffffffful; // high 32 bits of x target = ( argument.words.hi < signMask ); // flag positive sign - - if ( xhi > 0x41e00000ul ) + + if ( xhi > 0x41e00000ul ) /******************************************************************************* * Is x is out of long range or NaN? * *******************************************************************************/ @@ -327,19 +327,19 @@ long int roundtol ( double x ) else return ( LONG_MIN ); } - - if ( target ) + + if ( target ) /******************************************************************************* * Is sign of x is "+"? * *******************************************************************************/ { - if ( x < 2147483647.5 ) + if ( x < 2147483647.5 ) /******************************************************************************* * x is in the range of a long. * *******************************************************************************/ { y = ( x + doubleToLong ) - doubleToLong; // round at binary point - if ( y != x ) + if ( y != x ) { // inexact case asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kTZ.dbl )); // truncate rounding @@ -348,7 +348,7 @@ long int roundtol ( double x ) asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( ( long ) argument.words.lo ); } - + argument.dbl = y + doubleToLong; // force result into argument.words.lo return ( ( long ) argument.words.lo ); // return long result } @@ -363,13 +363,13 @@ long int roundtol ( double x ) /******************************************************************************* * x < 0.0 and may or may not be out of the range of a long. * *******************************************************************************/ - if ( x > -2147483648.5 ) + if ( x > -2147483648.5 ) /******************************************************************************* * x is in the range of a long. * *******************************************************************************/ { y = ( x + doubleToLong ) - doubleToLong; // round at binary point - if ( y != x ) + if ( y != x ) { // inexact case asm ("mffs %0" : "=f" (OldEnvironment.dbl)); // save environment asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( kUP.dbl )); // round up @@ -378,7 +378,7 @@ long int roundtol ( double x ) asm ("mtfsf 255,%0" : /*NULLOUT*/ : /*IN*/ "f" ( OldEnvironment.dbl )); return ( ( long ) argument.words.lo ); } - + argument.dbl = y + doubleToLong; return ( ( long ) argument.words.lo ); // return long result } @@ -398,29 +398,29 @@ long int roundtol ( double x ) * inexact if an ordered return value is not equal to the operand. * * * *******************************************************************************/ - + double trunc ( double x ) - { + { DblInHex argument,OldEnvironment; register double y; register unsigned long int xhi; register long int target; - + argument.dbl = x; xhi = argument.words.hi & 0x7fffffffUL; // xhi <- high half of |x| target = ( argument.words.hi < signMask ); // flag positive sign - - if ( xhi < 0x43300000ul ) + + if ( xhi < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^53? * *******************************************************************************/ { - if ( xhi < 0x3ff00000ul ) + if ( xhi < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ { - if ( ( xhi | argument.words.lo ) != 0ul ) + if ( ( xhi | argument.words.lo ) != 0ul ) { // raise deserved INEXACT asm ("mffs %0" : "=f" (OldEnvironment.dbl)); OldEnvironment.words.lo |= 0x02000000ul; @@ -434,7 +434,7 @@ double trunc ( double x ) /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ - if ( target ) + if ( target ) { y = ( x + twoTo52 ) - twoTo52; // round at binary point if ( y > x ) @@ -442,8 +442,8 @@ double trunc ( double x ) else return ( y ); } - - else + + else { y = ( x - twoTo52 ) + twoTo52; // round at binary point. if ( y < x ) @@ -470,7 +470,7 @@ double trunc ( double x ) *******************************************************************************/ /******************************************************************************* -* modf is the double implementation. * +* modf is the double implementation. * *******************************************************************************/ double modf ( double x, double *iptr ) @@ -478,19 +478,19 @@ double modf ( double x, double *iptr ) register double OldEnvironment, xtrunc; register unsigned long int xHead, signBit; DblInHex argument; - + argument.dbl = x; xHead = argument.words.hi & 0x7ffffffful; // |x| high bit pattern signBit = ( argument.words.hi & 0x80000000ul ); // isolate sign bit if (xHead == 0x7ff81fe0) signBit = signBit | 0; - - if ( xHead < 0x43300000ul ) + + if ( xHead < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^53? * *******************************************************************************/ { - if ( xHead < 0x3ff00000ul ) + if ( xHead < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ @@ -515,18 +515,18 @@ double modf ( double x, double *iptr ) *iptr = xtrunc; // store integral part if ( x != xtrunc ) // nonzero fraction return ( x - xtrunc ); - else + else { // zero with x's sign argument.words.hi = signBit; argument.words.lo = 0ul; return ( argument.dbl ); } } - + *iptr = x; // x is integral or NaN if ( x != x ) // NaN is returned return x; - else + else { // zero with x's sign argument.words.hi = signBit; argument.words.lo = 0ul; diff --git a/libm/powerpc/s_rint.c b/libm/powerpc/s_rint.c index 47a79ae5e..72c4834d0 100644 --- a/libm/powerpc/s_rint.c +++ b/libm/powerpc/s_rint.c @@ -1,18 +1,18 @@ /******************************************************************************* ** File: rndint.c -** +** ** Contains: C source code for implementations of floating-point ** functions which round to integral value or format, as ** defined in header <fp.h>. In particular, this file ** contains implementations of functions rint, nearbyint, ** rinttol, round, roundtol, trunc, modf and modfl. This file ** targets PowerPC or Power platforms. -** +** ** Written by: A. Sazegari, Apple AltiVec Group ** Created originally by Jon Okada, Apple Numerics Group -** +** ** Copyright: © 1992-2001 by Apple Computer, Inc., all rights reserved -** +** ** Change History (most recent first): ** ** 13 Jul 01 ram replaced --setflm calls with inline assembly @@ -21,7 +21,7 @@ ** 1. removed double_t, put in double for now. ** 2. removed iclass from nearbyint. ** 3. removed wrong comments intrunc. -** 4. +** 4. ** 13 May 97 ali made performance improvements in rint, rinttol, roundtol ** and trunc by folding some of the taligent ideas into this ** implementation. nearbyint is faster than the one in taligent, @@ -33,7 +33,7 @@ ** 18 Feb 93 ali Changed the return value of fenv functions ** feclearexcept and feraiseexcept to their new ** NCEG X3J11.1/93-001 definitions. -** 16 Dec 92 JPO Removed __itrunc implementation to a +** 16 Dec 92 JPO Removed __itrunc implementation to a ** separate file. ** 15 Dec 92 JPO Added __itrunc implementation and modified ** rinttol to include conversion from double @@ -41,7 +41,7 @@ ** call __itrunc. ** 10 Dec 92 JPO Added modf (double) implementation. ** 04 Dec 92 JPO First created. -** +** *******************************************************************************/ #include <limits.h> @@ -73,7 +73,7 @@ static const DblInHex TOWARDZERO = {{ 0x00000000, 0x00000001 }}; * * * The function rint rounds its double argument to integral value * * according to the current rounding direction and returns the result in * -* double format. This function signals inexact if an ordered return * +* double format. This function signals inexact if an ordered return * * value is not equal to the operand. * * * ******************************************************************************** @@ -89,16 +89,16 @@ static const DblInHex TOWARDZERO = {{ 0x00000000, 0x00000001 }}; *double rint ( double x ) * { * double y; -* +* * y = twoTo52.fval; -* -* if ( fabs ( x ) >= y ) // huge case is exact +* +* if ( fabs ( x ) >= y ) // huge case is exact * return x; -* if ( x < 0 ) y = -y; // negative case -* y = ( x + y ) - y; // force rounding -* if ( y == 0.0 ) // zero results mirror sign of x +* if ( x < 0 ) y = -y; // negative case +* y = ( x + y ) - y; // force rounding +* if ( y == 0.0 ) // zero results mirror sign of x * y = copysign ( y, x ); -* return ( y ); +* return ( y ); * } ******************************************************************************** * Now a bit twidling version that is about %30 faster. * @@ -110,17 +110,17 @@ double rint ( double x ) register double y; unsigned long int xHead; register long int target; - + argument.dbl = x; xHead = argument.words.hi & 0x7fffffffUL; // xHead <- high half of |x| target = ( argument.words.hi < signMask ); // flags positive sign - - if ( xHead < 0x43300000ul ) + + if ( xHead < 0x43300000ul ) /******************************************************************************* * Is |x| < 2.0^52? * *******************************************************************************/ { - if ( xHead < 0x3ff00000ul ) + if ( xHead < 0x3ff00000ul ) /******************************************************************************* * Is |x| < 1.0? * *******************************************************************************/ @@ -129,7 +129,7 @@ double rint ( double x ) y = ( x + twoTo52 ) - twoTo52; // round at binary point else y = ( x - twoTo52 ) + twoTo52; // round at binary point - if ( y == 0.0 ) + if ( y == 0.0 ) { // fix sign of zero result if ( target ) return ( 0.0 ); @@ -138,7 +138,7 @@ double rint ( double x ) } return y; } - + /******************************************************************************* * Is 1.0 < |x| < 2.0^52? * *******************************************************************************/ @@ -148,7 +148,7 @@ double rint ( double x ) else return ( ( x - twoTo52 ) + twoTo52 ); } - + /******************************************************************************* * |x| >= 2.0^52 or x is a NaN. * *******************************************************************************/ diff --git a/libm/powerpc/w_scalb.c b/libm/powerpc/w_scalb.c index 98a2b7d3f..c93c74b68 100644 --- a/libm/powerpc/w_scalb.c +++ b/libm/powerpc/w_scalb.c @@ -1,26 +1,26 @@ /*********************************************************************** ** File: scalb.c -** +** ** Contains: C source code for implementations of floating-point ** scalb functions defined in header <fp.h>. In ** particular, this file contains implementations of ** functions scalb and scalbl for double and long double ** formats on PowerPC platforms. -** +** ** Written by: Jon Okada, SANEitation Engineer, ext. 4-4838 -** +** ** Copyright: © 1992 by Apple Computer, Inc., all rights reserved -** +** ** Change History ( most recent first ): ** ** 28 May 97 ali made an speed improvement for large n, ** removed scalbl. ** 12 Dec 92 JPO First created. -** +** ***********************************************************************/ -typedef union - { +typedef union + { struct { #if defined(__BIG_ENDIAN__) unsigned long int hi; @@ -41,35 +41,35 @@ static const double twoToM1022 = 2.225073858507201383e-308; // 0x1p-1022 double scalb( double x, long int n ) returns its argument x scaled by the factor 2^m. NaNs, signed zeros, and infinities are propagated by this function regardless of the value of n. - + Exceptions: OVERFLOW/INEXACT or UNDERFLOW inexact may occur; INVALID for signaling NaN inputs ( quiet NaN returned ). - + Calls: none. ***********************************************************************/ double scalb ( double x, int n ) { DblInHex xInHex; - + xInHex.words.lo = 0UL; // init. low half of xInHex - - if ( n > 1023 ) + + if ( n > 1023 ) { // large positive scaling if ( n > 2097 ) // huge scaling return ( ( x * twoTo1023 ) * twoTo1023 ) * twoTo1023; - while ( n > 1023 ) + while ( n > 1023 ) { // scale reduction loop x *= twoTo1023; // scale x by 2^1023 n -= 1023; // reduce n by 1023 } } - - else if ( n < -1022 ) + + else if ( n < -1022 ) { // large negative scaling if ( n < -2098 ) // huge negative scaling return ( ( x * twoToM1022 ) * twoToM1022 ) * twoToM1022; - while ( n < -1022 ) + while ( n < -1022 ) { // scale reduction loop x *= twoToM1022; // scale x by 2^( -1022 ) n += 1022; // incr n by 1022 diff --git a/libm/s_asinh.c b/libm/s_asinh.c index 6cad188ca..e9e3b9302 100644 --- a/libm/s_asinh.c +++ b/libm/s_asinh.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. * ==================================================== */ @@ -16,26 +16,26 @@ static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; /* asinh(x) * Method : - * Based on + * Based on * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] * we have * asinh(x) := x if 1+x*x=1, * := sign(x)*(log(x)+ln2)) for large |x|, else * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else - * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) */ #include "math.h" #include "math_private.h" #ifdef __STDC__ -static const double +static const double #else -static double +static double #endif one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ -huge= 1.00000000000000000000e+300; +huge= 1.00000000000000000000e+300; #ifdef __STDC__ double asinh(double x) @@ -43,7 +43,7 @@ huge= 1.00000000000000000000e+300; double asinh(x) double x; #endif -{ +{ double t,w; int32_t hx,ix; GET_HIGH_WORD(hx,x); @@ -51,7 +51,7 @@ huge= 1.00000000000000000000e+300; if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ if(ix< 0x3e300000) { /* |x|<2**-28 */ if(huge+x>one) return x; /* return x inexact except 0 */ - } + } if(ix>0x41b00000) { /* |x| > 2**28 */ w = __ieee754_log(fabs(x))+ln2; } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ diff --git a/libm/s_atan.c b/libm/s_atan.c index af4d4927a..53e48e45f 100644 --- a/libm/s_atan.c +++ b/libm/s_atan.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -28,9 +28,9 @@ static char rcsid[] = "$NetBSD: s_atan.c,v 1.8 1995/05/10 20:46:45 jtc Exp $"; * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) * * 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. */ @@ -78,9 +78,9 @@ static double aT[] = { }; #ifdef __STDC__ - static const double + static const double #else - static double + static double #endif one = 1.0, huge = 1.0e300; @@ -114,9 +114,9 @@ huge = 1.0e300; x = fabs(x); if (ix < 0x3ff30000) { /* |x| < 1.1875 */ if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ - id = 0; x = (2.0*x-one)/(2.0+x); + id = 0; x = (2.0*x-one)/(2.0+x); } else { /* 11/16<=|x|< 19/16 */ - id = 1; x = (x-one)/(x+one); + id = 1; x = (x-one)/(x+one); } } else { if (ix < 0x40038000) { /* |x| < 2.4375 */ diff --git a/libm/s_cbrt.c b/libm/s_cbrt.c index ef8e2e209..cf75dcfc6 100644 --- a/libm/s_cbrt.c +++ b/libm/s_cbrt.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. * ==================================================== */ @@ -40,9 +40,9 @@ F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ #ifdef __STDC__ - double cbrt(double x) + double cbrt(double x) #else - double cbrt(x) + double cbrt(x) double x; #endif { @@ -56,7 +56,7 @@ G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ hx ^=sign; if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ GET_LOW_WORD(low,x); - if((hx|low)==0) + if((hx|low)==0) return(x); /* cbrt(0) is itself */ SET_HIGH_WORD(x,hx); /* x <- |x| */ @@ -72,9 +72,9 @@ G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ /* new cbrt to 23 bits, may be implemented in single precision */ r=t*t/x; s=C+r*t; - t*=G+F/(s+E+D/s); + t*=G+F/(s+E+D/s); - /* chopped to 20 bits and make it larger than cbrt(x) */ + /* chopped to 20 bits and make it larger than cbrt(x) */ GET_HIGH_WORD(high,t); INSERT_WORDS(t,high+0x00000001,0); diff --git a/libm/s_ceil.c b/libm/s_ceil.c index 8616d0f54..c888e5190 100644 --- a/libm/s_ceil.c +++ b/libm/s_ceil.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. * ==================================================== */ @@ -46,7 +46,7 @@ static double huge = 1.0e300; if(j0<20) { if(j0<0) { /* raise inexact if x != 0 */ if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ - if(i0<0) {i0=0x80000000;i1=0;} + if(i0<0) {i0=0x80000000;i1=0;} else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} } } else { @@ -65,7 +65,7 @@ static double huge = 1.0e300; if((i1&i)==0) return x; /* x is integral */ if(huge+x>0.0) { /* raise inexact flag */ if(i0>0) { - if(j0==20) i0+=1; + if(j0==20) i0+=1; else { j = i1 + (1<<(52-j0)); if(j<i1) i0+=1; /* got a carry */ diff --git a/libm/s_ceilf.c b/libm/s_ceilf.c index 29ccadb04..d43bede8c 100644 --- a/libm/s_ceilf.c +++ b/libm/s_ceilf.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. * ==================================================== */ @@ -41,7 +41,7 @@ static float huge = 1.0e30; if(j0<23) { if(j0<0) { /* raise inexact if x != 0 */ if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ - if(i0<0) {i0=0x80000000;} + if(i0<0) {i0=0x80000000;} else if(i0!=0) { i0=0x3f800000;} } } else { diff --git a/libm/s_copysign.c b/libm/s_copysign.c index 63261fc96..e276f733d 100644 --- a/libm/s_copysign.c +++ b/libm/s_copysign.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. * ==================================================== */ diff --git a/libm/s_cos.c b/libm/s_cos.c index dc0c38334..d458b746e 100644 --- a/libm/s_cos.c +++ b/libm/s_cos.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. * ==================================================== */ @@ -23,8 +23,8 @@ static char rcsid[] = "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $"; * __ieee754_rem_pio2 ... argument reduction routine * * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 * in [-pi/4 , +pi/4], and let n = k mod 4. * We have * @@ -42,7 +42,7 @@ static char rcsid[] = "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $"; * trig(NaN) is that NaN; * * Accuracy: - * TRIG(x) returns trig(x) nearly rounded + * TRIG(x) returns trig(x) nearly rounded */ #include "math.h" diff --git a/libm/s_erf.c b/libm/s_erf.c index e0bf2a115..44568abb2 100644 --- a/libm/s_erf.c +++ b/libm/s_erf.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -19,11 +19,11 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * x * 2 |\ * erf(x) = --------- | exp(-t*t)dt - * sqrt(pi) \| + * sqrt(pi) \| * 0 * * erfc(x) = 1-erf(x) - * Note that + * Note that * erf(-x) = -erf(x) * erfc(-x) = 2 - erfc(x) * @@ -36,7 +36,7 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * Q is an odd poly of degree 10. * -57.90 * | R - (erf(x)-x)/x | <= 2 - * + * * * Remark. The formula is derived by noting * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) @@ -59,14 +59,14 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * That is, we use rational approximation to approximate * erf(1+s) - (c = (single)0.84506291151) * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] - * where + * where * P1(s) = degree 6 poly in s * Q1(s) = degree 6 poly in s * - * 3. For x in [1.25,1/0.35(~2.857143)], + * 3. For x in [1.25,1/0.35(~2.857143)], * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) * erf(x) = 1 - erfc(x) - * where + * where * R1(z) = degree 7 poly in z, (z=1/x^2) * S1(z) = degree 8 poly in z * @@ -84,7 +84,7 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * To compute exp(-x*x-0.5625+R/S), let s be a single * precision number and s := x; then * -x*x = -s*s + (s-x)*(s+x) - * exp(-x*x-0.5626+R/S) = + * exp(-x*x-0.5626+R/S) = * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); * Note2: * Here 4 and 5 make use of the asymptotic series @@ -104,7 +104,7 @@ static char rcsid[] = "$NetBSD: s_erf.c,v 1.8 1995/05/10 20:47:05 jtc Exp $"; * * 7. Special case: * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, - * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, * erfc/erf(NaN) is NaN */ @@ -139,7 +139,7 @@ qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ /* - * Coefficients for approximation to erf in [0.84375,1.25] + * Coefficients for approximation to erf in [0.84375,1.25] */ pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ @@ -192,9 +192,9 @@ sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ #ifdef __STDC__ - double erf(double x) + double erf(double x) #else - double erf(x) + double erf(x) double x; #endif { @@ -209,7 +209,7 @@ sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ if(ix < 0x3feb0000) { /* |x|<0.84375 */ if(ix < 0x3e300000) { /* |x|<2**-28 */ - if (ix < 0x00800000) + if (ix < 0x00800000) return 0.125*(8.0*x+efx8*x); /*avoid underflow */ return x + efx*x; } @@ -241,16 +241,16 @@ sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( sb5+s*(sb6+s*sb7)))))); } - z = x; + z = x; SET_LOW_WORD(z,0); r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); if(hx>=0) return one-r/x; else return r/x-one; } #ifdef __STDC__ - double erfc(double x) + double erfc(double x) #else - double erfc(x) + double erfc(x) double x; #endif { @@ -283,7 +283,7 @@ sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); if(hx>=0) { - z = one-erx; return z - P/Q; + z = one-erx; return z - P/Q; } else { z = erx+P/Q; return one+z; } diff --git a/libm/s_expm1.c b/libm/s_expm1.c index 5e7e9d84f..aee70835b 100644 --- a/libm/s_expm1.c +++ b/libm/s_expm1.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. * ==================================================== */ @@ -21,9 +21,9 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; * 1. Argument reduction: * Given x, find r and integer k such that * - * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 * - * Here a correction term c will be computed to compensate + * Here a correction term c will be computed to compensate * the error in r when rounded to a floating-point number. * * 2. Approximating expm1(r) by a special rational function on @@ -36,9 +36,9 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... - * We use a special Reme algorithm on [0,0.347] to generate - * a polynomial of degree 5 in r*r to approximate R1. The - * maximum error of this polynomial approximation is bounded + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded * by 2**-61. In other words, * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 * where Q1 = -1.6666666666666567384E-2, @@ -49,28 +49,28 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; * (where z=r*r, and the values of Q1 to Q5 are listed below) * with error bounded by * | 5 | -61 - * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 * | | - * - * expm1(r) = exp(r)-1 is then computed by the following - * specific way which minimize the accumulation rounding error: + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: * 2 3 * r r [ 3 - (R1 + R1*r/2) ] * expm1(r) = r + --- + --- * [--------------------] * 2 2 [ 6 - r*(3 - R1*r/2) ] - * + * * To compensate the error in the argument reduction, we use - * expm1(r+c) = expm1(r) + c + expm1(r)*c - * ~ expm1(r) + c + r*c + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c * Thus c+r*c will be added in as the correction terms for - * expm1(r+c). Now rearrange the term to avoid optimization + * expm1(r+c). Now rearrange the term to avoid optimization * screw up: * ( 2 2 ) * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) * ( ) - * + * * = r - E * 3. Scale back to obtain expm1(x): * From step 1, we have @@ -87,7 +87,7 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; * else return 1.0+2.0*(r-E); * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else - * (vii) return 2^k(1-((E+2^-k)-r)) + * (vii) return 2^k(1-((E+2^-k)-r)) * * Special cases: * expm1(INF) is INF, expm1(NaN) is NaN; @@ -99,12 +99,12 @@ static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $"; * 1 ulp (unit in the last place). * * Misc. info. - * For IEEE double + * 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 + * 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. */ @@ -153,7 +153,7 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ if(hx>=0x7ff00000) { u_int32_t low; GET_LOW_WORD(low,x); - if(((hx&0xfffff)|low)!=0) + if(((hx&0xfffff)|low)!=0) return x+x; /* NaN */ else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ } @@ -166,7 +166,7 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ } /* argument reduction */ - if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + 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;} @@ -180,10 +180,10 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ } 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)); + return x - (t-(huge+x)); } else k = 0; @@ -198,7 +198,7 @@ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ e = (x*(e-c)-c); e -= hxs; if(k== -1) return 0.5*(x-e)-0.5; - if(k==1) { + if(k==1) { if(x < -0.25) return -2.0*(e-(x+0.5)); else return one+2.0*(x-e); } diff --git a/libm/s_fabs.c b/libm/s_fabs.c index 351aea143..b9aacc282 100644 --- a/libm/s_fabs.c +++ b/libm/s_fabs.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. * ==================================================== */ diff --git a/libm/s_finite.c b/libm/s_finite.c index 91711db55..428570c14 100644 --- a/libm/s_finite.c +++ b/libm/s_finite.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. * ==================================================== */ diff --git a/libm/s_floor.c b/libm/s_floor.c index 5a36b2d6f..d7e5307e0 100644 --- a/libm/s_floor.c +++ b/libm/s_floor.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. * ==================================================== */ @@ -46,7 +46,7 @@ static double huge = 1.0e300; if(j0<20) { if(j0<0) { /* raise inexact if x != 0 */ if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ - if(i0>=0) {i0=i1=0;} + if(i0>=0) {i0=i1=0;} else if(((i0&0x7fffffff)|i1)!=0) { i0=0xbff00000;i1=0;} } @@ -66,7 +66,7 @@ static double huge = 1.0e300; if((i1&i)==0) return x; /* x is integral */ if(huge+x>0.0) { /* raise inexact flag */ if(i0<0) { - if(j0==20) i0+=1; + if(j0==20) i0+=1; else { j = i1+(1<<(52-j0)); if(j<i1) i0 +=1 ; /* got a carry */ diff --git a/libm/s_floorf.c b/libm/s_floorf.c index e8822b088..1cdc792c6 100644 --- a/libm/s_floorf.c +++ b/libm/s_floorf.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. * ==================================================== */ @@ -49,7 +49,7 @@ static float huge = 1.0e30; if(j0<23) { if(j0<0) { /* raise inexact if x != 0 */ if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ - if(i0>=0) {i0=0;} + if(i0>=0) {i0=0;} else if((i0&0x7fffffff)!=0) { i0=0xbf800000;} } diff --git a/libm/s_frexp.c b/libm/s_frexp.c index bfc9dba03..3feeffcfb 100644 --- a/libm/s_frexp.c +++ b/libm/s_frexp.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. * ==================================================== */ @@ -15,13 +15,13 @@ static char rcsid[] = "$NetBSD: s_frexp.c,v 1.9 1995/05/10 20:47:24 jtc Exp $"; #endif /* - * for non-zero x + * for non-zero x * x = frexp(arg,&exp); * return a double fp quantity x such that 0.5 <= |x| <1.0 * and the corresponding binary exponent "exp". That is * arg = x*2^exp. - * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg - * with *exp=0. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. */ #include "math.h" diff --git a/libm/s_ilogb.c b/libm/s_ilogb.c index ee81570aa..3a6e964e8 100644 --- a/libm/s_ilogb.c +++ b/libm/s_ilogb.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -36,7 +36,7 @@ static char rcsid[] = "$NetBSD: s_ilogb.c,v 1.9 1995/05/10 20:47:28 jtc Exp $"; hx &= 0x7fffffff; if(hx<0x00100000) { GET_LOW_WORD(lx,x); - if((hx|lx)==0) + if((hx|lx)==0) return 0x80000001; /* ilogb(0) = 0x80000001 */ else /* subnormal x */ if(hx==0) { diff --git a/libm/s_ldexp.c b/libm/s_ldexp.c index 085823aea..bd3c90bac 100644 --- a/libm/s_ldexp.c +++ b/libm/s_ldexp.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ diff --git a/libm/s_lib_version.c b/libm/s_lib_version.c index c4cfae37a..fde8e3bf6 100644 --- a/libm/s_lib_version.c +++ b/libm/s_lib_version.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ diff --git a/libm/s_log1p.c b/libm/s_log1p.c index 6c8739471..d6f5523e8 100644 --- a/libm/s_log1p.c +++ b/libm/s_log1p.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -16,9 +16,9 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; /* double log1p(double x) * - * Method : - * 1. Argument Reduction: find k and f such that - * 1+x = 2^k * (1+f), + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), * where sqrt(2)/2 < 1+f < sqrt(2) . * * Note. If k=0, then f=x is exact. However, if k!=0, then f @@ -32,8 +32,8 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) * = 2s + 2/3 s**3 + 2/5 s**5 + ....., * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error * of this polynomial approximation is bounded by 2**-58.45. In * other words, * 2 4 6 8 10 12 14 @@ -41,21 +41,21 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; * (the values of Lp1 to Lp7 are listed in the program) * and * | 2 14 | -58.45 - * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 * | | * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. * In order to guarantee error in log below 1ulp, we compute log * by * log1p(f) = f - (hfsq - s*(hfsq+R)). - * - * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: + * Here ln2 is split into two floating point number: * ln2_hi + ln2_lo, * where n*ln2_hi is always exact for |n| < 2000. * * Special cases: - * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(x) is NaN with signal if x < -1 (including -INF) ; * log1p(+INF) is +INF; log1p(-1) is -INF with signal; * log1p(NaN) is that NaN with no signal. * @@ -64,14 +64,14 @@ static char rcsid[] = "$NetBSD: s_log1p.c,v 1.8 1995/05/10 20:47:46 jtc Exp $"; * 1 ulp (unit in the last place). * * 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. * * Note: Assuming log() return accurate answer, the following * algorithm can be used to compute log1p(x) to within a few ULP: - * + * * u = 1+x; * if(u==1.0) return x ; else * return log(u)*(x/(u-1.0)); @@ -132,11 +132,11 @@ static double zero = 0.0; } if(hx>0||hx<=((int32_t)0xbfd2bec3)) { k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */ - } + } if (hx >= 0x7ff00000) return x+x; if(k!=0) { if(hx<0x43400000) { - u = 1.0+x; + u = 1.0+x; GET_HIGH_WORD(hu,u); k = (hu>>20)-1023; c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ @@ -151,7 +151,7 @@ static double zero = 0.0; if(hu<0x6a09e) { SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ } else { - k += 1; + k += 1; SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ hu = (0x00100000-hu)>>2; } @@ -159,14 +159,14 @@ static double zero = 0.0; } hfsq=0.5*f*f; if(hu==0) { /* |f| < 2**-20 */ - if(f==zero) {if(k==0) return zero; + if(f==zero) {if(k==0) return zero; else {c += k*ln2_lo; return k*ln2_hi+c;} } R = hfsq*(1.0-0.66666666666666666*f); if(k==0) return f-R; else return k*ln2_hi-((R-(k*ln2_lo+c))-f); } - s = f/(2.0+f); + s = f/(2.0+f); z = s*s; R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); if(k==0) return f-(hfsq-s*(hfsq+R)); else diff --git a/libm/s_logb.c b/libm/s_logb.c index 02bb99f3c..85b539886 100644 --- a/libm/s_logb.c +++ b/libm/s_logb.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. * ==================================================== */ @@ -36,7 +36,7 @@ static char rcsid[] = "$NetBSD: s_logb.c,v 1.8 1995/05/10 20:47:50 jtc Exp $"; if((ix|lx)==0) return -1.0/fabs(x); if(ix>=0x7ff00000) return x*x; if((ix>>=20)==0) /* IEEE 754 logb */ - return -1022.0; + return -1022.0; else - return (double) (ix-1023); + return (double) (ix-1023); } diff --git a/libm/s_matherr.c b/libm/s_matherr.c index 11a58af2b..b76c51407 100644 --- a/libm/s_matherr.c +++ b/libm/s_matherr.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ diff --git a/libm/s_modf.c b/libm/s_modf.c index 9d71c01d1..d5737c44a 100644 --- a/libm/s_modf.c +++ b/libm/s_modf.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -15,7 +15,7 @@ static char rcsid[] = "$NetBSD: s_modf.c,v 1.8 1995/05/10 20:47:55 jtc Exp $"; #endif /* - * modf(double x, double *iptr) + * modf(double x, double *iptr) * return fraction part of x, and return x's integral part in *iptr. * Method: * Bit twiddling. diff --git a/libm/s_nextafter.c b/libm/s_nextafter.c index 2a9c6f490..a1369ced0 100644 --- a/libm/s_nextafter.c +++ b/libm/s_nextafter.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -39,15 +39,15 @@ static char rcsid[] = "$NetBSD: s_nextafter.c,v 1.8 1995/05/10 20:47:58 jtc Exp ix = hx&0x7fffffff; /* |x| */ iy = hy&0x7fffffff; /* |y| */ - if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ - ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ - return x+y; + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ + return x+y; if(x==y) return x; /* x=y, return x */ if((ix|lx)==0) { /* x == 0 */ INSERT_WORDS(x,hy&0x80000000,1); /* return +-minsubnormal */ y = x*x; if(y==x) return y; else return x; /* raise underflow flag */ - } + } if(hx>=0) { /* x > 0 */ if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ if(lx==0) hx -= 1; diff --git a/libm/s_rint.c b/libm/s_rint.c index 880885759..7cff5e498 100644 --- a/libm/s_rint.c +++ b/libm/s_rint.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. * ==================================================== */ @@ -30,7 +30,7 @@ static char rcsid[] = "$NetBSD: s_rint.c,v 1.8 1995/05/10 20:48:04 jtc Exp $"; #ifdef __STDC__ static const double #else -static double +static double #endif TWO52[2]={ 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ @@ -51,7 +51,7 @@ TWO52[2]={ sx = (i0>>31)&1; j0 = ((i0>>20)&0x7ff)-0x3ff; if(j0<20) { - if(j0<0) { + if(j0<0) { if(((i0&0x7fffffff)|i1)==0) return x; i1 |= (i0&0x0fffff); i0 &= 0xfffe0000; diff --git a/libm/s_scalbn.c b/libm/s_scalbn.c index b10bd7028..9bb054ac4 100644 --- a/libm/s_scalbn.c +++ b/libm/s_scalbn.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,10 +14,10 @@ static char rcsid[] = "$NetBSD: s_scalbn.c,v 1.8 1995/05/10 20:48:08 jtc Exp $"; #endif -/* +/* * scalbn (double x, int n) - * scalbn(x,n) returns x* 2**n computed by exponent - * manipulation rather than by actually performing an + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an * exponentiation or a multiplication. */ @@ -46,13 +46,13 @@ tiny = 1.0e-300; k = (hx&0x7ff00000)>>20; /* extract exponent */ if (k==0) { /* 0 or subnormal x */ if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ - x *= two54; + x *= two54; GET_HIGH_WORD(hx,x); - k = ((hx&0x7ff00000)>>20) - 54; + k = ((hx&0x7ff00000)>>20) - 54; if (n< -50000) return tiny*x; /*underflow*/ } if (k==0x7ff) return x+x; /* NaN or Inf */ - k = k+n; + k = k+n; if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */ if (k > 0) /* normal result */ {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;} diff --git a/libm/s_significand.c b/libm/s_significand.c index d56e68d19..9aa5476b9 100644 --- a/libm/s_significand.c +++ b/libm/s_significand.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ diff --git a/libm/s_sin.c b/libm/s_sin.c index e732eae44..bcdb7e4e4 100644 --- a/libm/s_sin.c +++ b/libm/s_sin.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -23,8 +23,8 @@ static char rcsid[] = "$NetBSD: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $"; * __ieee754_rem_pio2 ... argument reduction routine * * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 * in [-pi/4 , +pi/4], and let n = k mod 4. * We have * @@ -42,7 +42,7 @@ static char rcsid[] = "$NetBSD: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $"; * trig(NaN) is that NaN; * * Accuracy: - * TRIG(x) returns trig(x) nearly rounded + * TRIG(x) returns trig(x) nearly rounded */ #include "math.h" diff --git a/libm/s_tan.c b/libm/s_tan.c index 7c72bf234..eca0f6cd5 100644 --- a/libm/s_tan.c +++ b/libm/s_tan.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -22,8 +22,8 @@ static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $"; * __ieee754_rem_pio2 ... argument reduction routine * * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 * in [-pi/4 , +pi/4], and let n = k mod 4. * We have * @@ -41,7 +41,7 @@ static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $"; * trig(NaN) is that NaN; * * Accuracy: - * TRIG(x) returns trig(x) nearly rounded + * TRIG(x) returns trig(x) nearly rounded */ #include "math.h" diff --git a/libm/s_tanh.c b/libm/s_tanh.c index 60e2acfe1..6276e8971 100644 --- a/libm/s_tanh.c +++ b/libm/s_tanh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -62,7 +62,7 @@ static double one=1.0, two=2.0, tiny = 1.0e-300; ix = jx&0x7fffffff; /* x is INF or NaN */ - if(ix>=0x7ff00000) { + if(ix>=0x7ff00000) { if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ else return one/x-one; /* tanh(NaN) = NaN */ } diff --git a/libm/w_acos.c b/libm/w_acos.c index c3fe8c191..69d6732d2 100644 --- a/libm/w_acos.c +++ b/libm/w_acos.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ diff --git a/libm/w_acosh.c b/libm/w_acosh.c index f05887972..e332e3b2f 100644 --- a/libm/w_acosh.c +++ b/libm/w_acosh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_acosh.c,v 1.6 1995/05/10 20:48:31 jtc Exp $"; #endif -/* +/* * wrapper acosh(x) */ diff --git a/libm/w_asin.c b/libm/w_asin.c index 04e9f78e0..1c663333c 100644 --- a/libm/w_asin.c +++ b/libm/w_asin.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_asin.c,v 1.6 1995/05/10 20:48:35 jtc Exp $"; #endif -/* +/* * wrapper asin(x) */ diff --git a/libm/w_atan2.c b/libm/w_atan2.c index 0b67e0b02..cd6b57b54 100644 --- a/libm/w_atan2.c +++ b/libm/w_atan2.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_atan2.c,v 1.6 1995/05/10 20:48:39 jtc Exp $"; #endif -/* +/* * wrapper atan2(y,x) */ #include "math.h" diff --git a/libm/w_atanh.c b/libm/w_atanh.c index e0716c2b3..afb44e382 100644 --- a/libm/w_atanh.c +++ b/libm/w_atanh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_atanh.c,v 1.6 1995/05/10 20:48:43 jtc Exp $"; #endif -/* +/* * wrapper atanh(x) */ @@ -39,7 +39,7 @@ static char rcsid[] = "$NetBSD: w_atanh.c,v 1.6 1995/05/10 20:48:43 jtc Exp $"; if(y>=1.0) { if(y>1.0) return __kernel_standard(x,x,30); /* atanh(|x|>1) */ - else + else return __kernel_standard(x,x,31); /* atanh(|x|==1) */ } else return z; diff --git a/libm/w_cabs.c b/libm/w_cabs.c index e5092a401..69188a0dd 100644 --- a/libm/w_cabs.c +++ b/libm/w_cabs.c @@ -1,6 +1,6 @@ /* * cabs() wrapper for hypot(). - * + * * Written by J.T. Conklin, <jtc@wimsey.com> * Placed into the Public Domain, 1994. */ diff --git a/libm/w_cosh.c b/libm/w_cosh.c index 67d15a25a..2228032a1 100644 --- a/libm/w_cosh.c +++ b/libm/w_cosh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_cosh.c,v 1.6 1995/05/10 20:48:47 jtc Exp $"; #endif -/* +/* * wrapper cosh(x) */ @@ -34,7 +34,7 @@ static char rcsid[] = "$NetBSD: w_cosh.c,v 1.6 1995/05/10 20:48:47 jtc Exp $"; double z; z = __ieee754_cosh(x); if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; - if(fabs(x)>7.10475860073943863426e+02) { + if(fabs(x)>7.10475860073943863426e+02) { return __kernel_standard(x,x,5); /* cosh overflow */ } else return z; diff --git a/libm/w_drem.c b/libm/w_drem.c index 7f5049340..0f6840934 100644 --- a/libm/w_drem.c +++ b/libm/w_drem.c @@ -1,6 +1,6 @@ /* * drem() wrapper for remainder(). - * + * * Written by J.T. Conklin, <jtc@wimsey.com> * Placed into the Public Domain, 1994. */ diff --git a/libm/w_exp.c b/libm/w_exp.c index 81a6bf702..9226b03a9 100644 --- a/libm/w_exp.c +++ b/libm/w_exp.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_exp.c,v 1.6 1995/05/10 20:48:51 jtc Exp $"; #endif -/* +/* * wrapper exp(x) */ @@ -47,7 +47,7 @@ u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */ return __kernel_standard(x,x,6); /* exp overflow */ else if(x<u_threshold) return __kernel_standard(x,x,7); /* exp underflow */ - } + } return z; #endif } diff --git a/libm/w_fmod.c b/libm/w_fmod.c index 67bea8c58..6956861f4 100644 --- a/libm/w_fmod.c +++ b/libm/w_fmod.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_fmod.c,v 1.6 1995/05/10 20:48:55 jtc Exp $"; #endif -/* +/* * wrapper fmod(x,y) */ diff --git a/libm/w_gamma.c b/libm/w_gamma.c index 59fe8f640..f5b00d024 100644 --- a/libm/w_gamma.c +++ b/libm/w_gamma.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -46,4 +46,4 @@ extern int signgam; } else return y; #endif -} +} diff --git a/libm/w_gamma_r.c b/libm/w_gamma_r.c index b0ed3c1b4..8dc6cefbb 100644 --- a/libm/w_gamma_r.c +++ b/libm/w_gamma_r.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_gamma_r.c,v 1.7 1995/11/20 22:06:45 jtc Exp $"; #endif -/* +/* * wrapper double gamma_r(double x, int *signgamp) */ @@ -43,4 +43,4 @@ static char rcsid[] = "$NetBSD: w_gamma_r.c,v 1.7 1995/11/20 22:06:45 jtc Exp $" } else return y; #endif -} +} diff --git a/libm/w_hypot.c b/libm/w_hypot.c index 8ff7efaba..0504b3c30 100644 --- a/libm/w_hypot.c +++ b/libm/w_hypot.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ diff --git a/libm/w_j0.c b/libm/w_j0.c index 6899e02f7..61f4f20fc 100644 --- a/libm/w_j0.c +++ b/libm/w_j0.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ diff --git a/libm/w_j1.c b/libm/w_j1.c index 4b90a4cb3..389dc156c 100644 --- a/libm/w_j1.c +++ b/libm/w_j1.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,8 +14,8 @@ static char rcsid[] = "$NetBSD: w_j1.c,v 1.6 1995/05/10 20:49:15 jtc Exp $"; #endif -/* - * wrapper of j1,y1 +/* + * wrapper of j1,y1 */ #include "math.h" diff --git a/libm/w_jn.c b/libm/w_jn.c index 20ba79beb..173f6aa9e 100644 --- a/libm/w_jn.c +++ b/libm/w_jn.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -18,7 +18,7 @@ static char rcsid[] = "$NetBSD: w_jn.c,v 1.6 1995/05/10 20:49:19 jtc Exp $"; * wrapper jn(int n, double x), yn(int n, double x) * floating point Bessel's function of the 1st and 2nd kind * of order n - * + * * Special cases: * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. @@ -37,7 +37,7 @@ static char rcsid[] = "$NetBSD: w_jn.c,v 1.6 1995/05/10 20:49:19 jtc Exp $"; * yn(n,x) is similar in all respects, except * that forward recursion is used for all * values of n>1. - * + * */ #include "math.h" diff --git a/libm/w_lgamma.c b/libm/w_lgamma.c index 3a8d6de48..9d122a94f 100644 --- a/libm/w_lgamma.c +++ b/libm/w_lgamma.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -46,4 +46,4 @@ extern int signgam; } else return y; #endif -} +} diff --git a/libm/w_lgamma_r.c b/libm/w_lgamma_r.c index b73a6425b..6ca56d6da 100644 --- a/libm/w_lgamma_r.c +++ b/libm/w_lgamma_r.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_lgamma_r.c,v 1.6 1995/05/10 20:49:27 jtc Exp $"; #endif -/* +/* * wrapper double lgamma_r(double x, int *signgamp) */ @@ -43,4 +43,4 @@ static char rcsid[] = "$NetBSD: w_lgamma_r.c,v 1.6 1995/05/10 20:49:27 jtc Exp $ } else return y; #endif -} +} diff --git a/libm/w_log.c b/libm/w_log.c index 507c18c69..d7ac66c67 100644 --- a/libm/w_log.c +++ b/libm/w_log.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. * ==================================================== */ @@ -37,7 +37,7 @@ static char rcsid[] = "$NetBSD: w_log.c,v 1.6 1995/05/10 20:49:33 jtc Exp $"; if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z; if(x==0.0) return __kernel_standard(x,x,16); /* log(0) */ - else + else return __kernel_standard(x,x,17); /* log(x<0) */ #endif } diff --git a/libm/w_log10.c b/libm/w_log10.c index 9986ad7b9..6e4345750 100644 --- a/libm/w_log10.c +++ b/libm/w_log10.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_log10.c,v 1.6 1995/05/10 20:49:35 jtc Exp $"; #endif -/* +/* * wrapper log10(X) */ @@ -38,7 +38,7 @@ static char rcsid[] = "$NetBSD: w_log10.c,v 1.6 1995/05/10 20:49:35 jtc Exp $"; if(x<=0.0) { if(x==0.0) return __kernel_standard(x,x,18); /* log10(0) */ - else + else return __kernel_standard(x,x,19); /* log10(x<0) */ } else return z; diff --git a/libm/w_pow.c b/libm/w_pow.c index 6d87ee558..571897cca 100644 --- a/libm/w_pow.c +++ b/libm/w_pow.c @@ -7,12 +7,12 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ -/* +/* * wrapper pow(x,y) return x**y */ @@ -34,12 +34,12 @@ z=__ieee754_pow(x,y); if(_LIB_VERSION == _IEEE_|| isnan(y)) return z; if(isnan(x)) { - if(y==0.0) + if(y==0.0) return __kernel_standard(x,y,42); /* pow(NaN,0.0) */ - else + else return z; } - if(x==0.0){ + if(x==0.0){ if(y==0.0) return __kernel_standard(x,y,20); /* pow(0.0,0.0) */ if(finite(y)&&y<0.0) @@ -50,10 +50,10 @@ if(finite(x)&&finite(y)) { if(isnan(z)) return __kernel_standard(x,y,24); /* pow neg**non-int */ - else + else return __kernel_standard(x,y,21); /* pow overflow */ } - } + } if(z==0.0&&finite(x)&&finite(y)) return __kernel_standard(x,y,22); /* pow underflow */ return z; diff --git a/libm/w_remainder.c b/libm/w_remainder.c index 33b80d8a6..0fbe9b0e4 100644 --- a/libm/w_remainder.c +++ b/libm/w_remainder.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_remainder.c,v 1.6 1995/05/10 20:49:44 jtc Exp $"; #endif -/* +/* * wrapper remainder(x,p) */ @@ -34,7 +34,7 @@ static char rcsid[] = "$NetBSD: w_remainder.c,v 1.6 1995/05/10 20:49:44 jtc Exp double z; z = __ieee754_remainder(x,y); if(_LIB_VERSION == _IEEE_ || isnan(y)) return z; - if(y==0.0) + if(y==0.0) return __kernel_standard(x,y,28); /* remainder(x,0) */ else return z; diff --git a/libm/w_scalb.c b/libm/w_scalb.c index 50026bed9..673006120 100644 --- a/libm/w_scalb.c +++ b/libm/w_scalb.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. * ==================================================== */ @@ -16,7 +16,7 @@ static char rcsid[] = "$NetBSD: w_scalb.c,v 1.6 1995/05/10 20:49:48 jtc Exp $"; /* * wrapper scalb(double x, double fn) is provide for - * passing various standard test suite. One + * passing various standard test suite. One * should use scalbn() instead. */ @@ -51,10 +51,10 @@ static char rcsid[] = "$NetBSD: w_scalb.c,v 1.6 1995/05/10 20:49:48 jtc Exp $"; } if(z==0.0&&z!=x) { return __kernel_standard(x,(double)fn,33); /* scalb underflow */ - } + } #ifndef _SCALB_INT if(!finite(fn)) errno = ERANGE; #endif return z; -#endif +#endif } diff --git a/libm/w_sinh.c b/libm/w_sinh.c index 7abd682eb..f9a6c60a9 100644 --- a/libm/w_sinh.c +++ b/libm/w_sinh.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_sinh.c,v 1.6 1995/05/10 20:49:51 jtc Exp $"; #endif -/* +/* * wrapper sinh(x) */ @@ -31,7 +31,7 @@ static char rcsid[] = "$NetBSD: w_sinh.c,v 1.6 1995/05/10 20:49:51 jtc Exp $"; #ifdef _IEEE_LIBM return __ieee754_sinh(x); #else - double z; + double z; z = __ieee754_sinh(x); if(_LIB_VERSION == _IEEE_) return z; if(!finite(z)&&finite(x)) { diff --git a/libm/w_sqrt.c b/libm/w_sqrt.c index d77e5a109..e9c6cb693 100644 --- a/libm/w_sqrt.c +++ b/libm/w_sqrt.c @@ -5,7 +5,7 @@ * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice + * software is freely granted, provided that this notice * is preserved. * ==================================================== */ @@ -14,7 +14,7 @@ static char rcsid[] = "$NetBSD: w_sqrt.c,v 1.6 1995/05/10 20:49:55 jtc Exp $"; #endif -/* +/* * wrapper sqrt(x) */ diff --git a/libm/w_sqrtf.c b/libm/w_sqrtf.c index 771d5b198..971acf466 100644 --- a/libm/w_sqrtf.c +++ b/libm/w_sqrtf.c @@ -18,7 +18,7 @@ * Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ -/* +/* * wrapper for sqrt(x) */ |