From 6cf065753c84790e50926eaace8d62e42184d407 Mon Sep 17 00:00:00 2001 From: Sam Lantinga Date: Sat, 4 Nov 2017 15:53:19 -0700 Subject: [PATCH] Updated math code from the uClibc 0.9.33 release --- src/libm/e_atan2.c | 26 +- src/libm/e_log.c | 170 +++++------- src/libm/e_pow.c | 596 ++++++++++++++++++++-------------------- src/libm/e_rem_pio2.c | 277 ++++++++----------- src/libm/e_sqrt.c | 209 +++++++------- src/libm/k_cos.c | 76 ++--- src/libm/k_rem_pio2.c | 344 +++++++++-------------- src/libm/k_sin.c | 60 ++-- src/libm/k_tan.c | 2 +- src/libm/math_libm.h | 1 + src/libm/math_private.h | 3 + src/libm/s_atan.c | 1 - src/libm/s_copysign.c | 25 +- src/libm/s_cos.c | 52 ++-- src/libm/s_fabs.c | 26 +- src/libm/s_floor.c | 113 +++----- src/libm/s_scalbn.c | 110 ++++---- src/libm/s_sin.c | 52 ++-- 18 files changed, 945 insertions(+), 1198 deletions(-) diff --git a/src/libm/e_atan2.c b/src/libm/e_atan2.c index f7b91a3e1..7c089f09b 100644 --- a/src/libm/e_atan2.c +++ b/src/libm/e_atan2.c @@ -57,8 +57,8 @@ double attribute_hidden __ieee754_atan2(double y, double x) ix = hx&0x7fffffff; EXTRACT_WORDS(hy,ly,y); iy = hy&0x7fffffff; - if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)|| - ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */ + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ return x+y; if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ @@ -81,8 +81,8 @@ double attribute_hidden __ieee754_atan2(double y, double x) switch(m) { case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ - case 2: return 3.0*pi_o_4+tiny;/* atan(+INF,-INF) */ - case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ } } else { switch(m) { @@ -114,3 +114,21 @@ double attribute_hidden __ieee754_atan2(double y, double x) return (z-pi_lo)-pi;/* atan(-,-) */ } } + +/* + * wrapper atan2(y,x) + */ +#ifndef _IEEE_LIBM +double atan2(double y, double x) +{ + double z = __ieee754_atan2(y, x); + if (_LIB_VERSION == _IEEE_ || isnan(x) || isnan(y)) + return z; + if (x == 0.0 && y == 0.0) + return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */ + return z; +} +#else +strong_alias(__ieee754_atan2, atan2) +#endif +libm_hidden_def(atan2) diff --git a/src/libm/e_log.c b/src/libm/e_log.c index da64138cd..66b6b36c1 100644 --- a/src/libm/e_log.c +++ b/src/libm/e_log.c @@ -1,4 +1,3 @@ -/* @(#)e_log.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; -#endif - /* __ieee754_log(x) * Return the logrithm of x * @@ -69,99 +63,85 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -#ifdef __STDC__ static const double -#else -static double -#endif - ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ - ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ - two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ - Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ - Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ - Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ - Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ - Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ - Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ - Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ -#ifdef __STDC__ -static const double zero = 0.0; -#else -static double zero = 0.0; -#endif +static const double zero = 0.0; -#ifdef __STDC__ -double attribute_hidden -__ieee754_log(double x) -#else -double attribute_hidden -__ieee754_log(x) - double x; -#endif +double attribute_hidden __ieee754_log(double x) { - double hfsq, f, s, z, R, w, t1, t2, dk; - int32_t k, hx, i, j; - u_int32_t lx; + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; - EXTRACT_WORDS(hx, lx, x); + EXTRACT_WORDS(hx,lx,x); - k = 0; - if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx & 0x7fffffff) | lx) == 0) - return -two54 / zero; /* log(+-0)=-inf */ - if (hx < 0) - return (x - x) / zero; /* log(-#) = NaN */ - k -= 54; - x *= two54; /* subnormal number, scale up x */ - GET_HIGH_WORD(hx, x); - } - if (hx >= 0x7ff00000) - return x + x; - k += (hx >> 20) - 1023; - hx &= 0x000fffff; - i = (hx + 0x95f64) & 0x100000; - SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */ - k += (i >> 20); - f = x - 1.0; - if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */ - if (f == zero) { - if (k == 0) - return zero; - else { - dk = (double) k; - return dk * ln2_hi + dk * ln2_lo; - } - } - R = f * f * (0.5 - 0.33333333333333333 * f); - if (k == 0) - return f - R; - else { - dk = (double) k; - return dk * ln2_hi - ((R - dk * ln2_lo) - 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))); - i |= j; - R = t2 + t1; - if (i > 0) { - hfsq = 0.5 * f * f; - if (k == 0) - return f - (hfsq - s * (hfsq + R)); - else - return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - - f); - } else { - if (k == 0) - return f - s * (f - R); - else - return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f); - } + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) {if(k==0) return zero; else {dk=(double)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-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))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } } + +/* + * wrapper log(x) + */ +#ifndef _IEEE_LIBM +double log(double x) +{ + double z = __ieee754_log(x); + if (_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) + return z; + if (x == 0.0) + return __kernel_standard(x, x, 16); /* log(0) */ + return __kernel_standard(x, x, 17); /* log(x<0) */ +} +#else +strong_alias(__ieee754_log, log) +#endif +libm_hidden_def(log) diff --git a/src/libm/e_pow.c b/src/libm/e_pow.c index 686da2e55..a1cb26f40 100644 --- a/src/libm/e_pow.c +++ b/src/libm/e_pow.c @@ -1,4 +1,3 @@ -/* @(#)e_pow.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,10 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; -#endif - /* __ieee754_pow(x,y) return x**y * * n @@ -26,25 +21,26 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; * 3. Return x**y = 2**n*exp(y'*log2) * * Special cases: - * 1. (anything) ** 0 is 1 - * 2. (anything) ** 1 is itself - * 3. (anything) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. +-1 ** +-INF is NAN - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF - * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) - * 15. +INF ** (+anything except 0,NAN) is +INF - * 16. +INF ** (-anything except 0,NAN) is +0 - * 17. -INF ** (anything) = -0 ** (-anything) - * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * 1. +-1 ** anything is 1.0 + * 2. +-1 ** +-INF is 1.0 + * 3. (anything) ** 0 is 1 + * 4. (anything) ** 1 is itself + * 5. (anything) ** NAN is NAN + * 6. NAN ** (anything except 0) is NAN + * 7. +-(|x| > 1) ** +INF is +INF + * 8. +-(|x| > 1) ** -INF is +0 + * 9. +-(|x| < 1) ** +INF is +0 + * 10 +-(|x| < 1) ** -INF is +INF + * 11. +0 ** (+anything except 0, NAN) is +0 + * 12. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 13. +0 ** (-anything except 0, NAN) is +INF + * 14. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 15. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 16. +INF ** (+anything except 0,NAN) is +INF + * 17. +INF ** (-anything except 0,NAN) is +0 + * 18. -INF ** (anything) = -0 ** (-anything) + * 19. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 20. (-anything except 0 and inf) ** (non-integer) is NAN * * Accuracy: * pow(x,y) returns x**y nearly rounded. In particular @@ -62,281 +58,281 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; #include "math_libm.h" #include "math_private.h" -libm_hidden_proto(scalbn) - libm_hidden_proto(fabs) -#ifdef __STDC__ - static const double +static const double +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +zero = 0.0, +one = 1.0, +two = 2.0, +two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ +huge = 1.0e300, +tiny = 1.0e-300, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ +L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ +L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ +L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ +L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ +L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ +lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ +lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ +ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ +cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ +cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ +cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ +ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ +ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ +ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ + +double attribute_hidden __ieee754_pow(double x, double y) +{ + double z,ax,z_h,z_l,p_h,p_l; + double y1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + /* x==1: 1**y = 1 (even if y is NaN) */ + if (hx==0x3ff00000 && lx==0) { + return x; + } + ix = hx&0x7fffffff; + + EXTRACT_WORDS(hy,ly,y); + iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + 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; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if((j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if (((ix-0x3ff00000)|lx)==0) + return one; /* +-1**+-inf is 1 (yes, weird rule) */ + if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ + return (hy>=0) ? y : zero; + /* (|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); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } 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); + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + } + /* 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 + 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)); + u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + SET_LOW_WORD(t1,0); + t2 = v-(t1-u); + } else { + double s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = 3.0+s2+r; + SET_LOW_WORD(t_h,0); + t_l = r-((t_h-3.0)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + SET_LOW_WORD(p_h,0); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (double)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + SET_LOW_WORD(t1,0); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) + s = -one;/* (-ve)**(odd int) */ + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = y; + SET_LOW_WORD(y1,0); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + EXTRACT_WORDS(j,i,z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*huge*huge; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*tiny*tiny; /* underflow */ + else { + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = zero; + SET_HIGH_WORD(t,n&~(0x000fffff>>k)); + 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; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; +} + +/* + * wrapper pow(x,y) return x**y + */ +#ifndef _IEEE_LIBM +double pow(double x, double y) +{ + double z = __ieee754_pow(x, y); + if (_LIB_VERSION == _IEEE_|| isnan(y)) + return z; + if (isnan(x)) { + if (y == 0.0) + return __kernel_standard(x, y, 42); /* pow(NaN,0.0) */ + return z; + } + if (x == 0.0) { + if (y == 0.0) + return __kernel_standard(x, y, 20); /* pow(0.0,0.0) */ + if (isfinite(y) && y < 0.0) + return __kernel_standard(x,y,23); /* pow(0.0,negative) */ + return z; + } + if (!isfinite(z)) { + if (isfinite(x) && isfinite(y)) { + if (isnan(z)) + return __kernel_standard(x, y, 24); /* pow neg**non-int */ + return __kernel_standard(x, y, 21); /* pow overflow */ + } + } + if (z == 0.0 && isfinite(x) && isfinite(y)) + return __kernel_standard(x, y, 22); /* pow underflow */ + return z; +} #else - static double +strong_alias(__ieee754_pow, pow) #endif - bp[] = { 1.0, 1.5, }, dp_h[] = { - 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ - - dp_l[] = { - 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ - - zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ - huge_val = 1.0e300, tiny = 1.0e-300, - /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ - L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ - L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ - L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ - L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ - L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ - L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ - P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ - P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ - P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ - P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ - P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ - lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ - lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ - lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ - ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ - cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ - cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ - cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */ - ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ - ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */ - ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */ - -#ifdef __STDC__ - double attribute_hidden __ieee754_pow(double x, double y) -#else - double attribute_hidden __ieee754_pow(x, y) - double x, y; -#endif - { - double z, ax, z_h, z_l, p_h, p_l; - double y1, t1, t2, r, s, t, u, v, w; - int32_t i, j, k, yisint, n; - int32_t hx, hy, ix, iy; - u_int32_t lx, ly; - - EXTRACT_WORDS(hx, lx, x); - EXTRACT_WORDS(hy, ly, y); - ix = hx & 0x7fffffff; - iy = hy & 0x7fffffff; - - /* y==zero: x**0 = 1 */ - 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; - - /* determine if y is an odd int when x < 0 - * yisint = 0 ... y is not an integer - * yisint = 1 ... y is an odd int - * yisint = 2 ... y is an even int - */ - yisint = 0; - if (hx < 0) { - if (iy >= 0x43400000) - yisint = 2; /* even integer y */ - else if (iy >= 0x3ff00000) { - k = (iy >> 20) - 0x3ff; /* exponent */ - if (k > 20) { - j = ly >> (52 - k); - if ((j << (52 - k)) == ly) - yisint = 2 - (j & 1); - } else if (ly == 0) { - j = iy >> (20 - k); - if ((j << (20 - k)) == iy) - yisint = 2 - (j & 1); - } - } - } - - /* special value of y */ - if (ly == 0) { - if (iy == 0x7ff00000) { /* y is +-inf */ - if (((ix - 0x3ff00000) | lx) == 0) - return y - y; /* inf**+-1 is NaN */ - else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ - 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); - } - } - - ax = fabs(x); - /* special value of x */ - if (lx == 0) { - if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { - z = ax; /* x is +-0,+-inf,+-1 */ - if (hy < 0) - z = one / z; /* z = (1/|x|) */ - if (hx < 0) { - if (((ix - 0x3ff00000) | yisint) == 0) { - z = (z - z) / (z - z); /* (-1)**non-int is NaN */ - } 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); - - /* |y| is huge */ - if (iy > 0x41e00000) { /* if |y| > 2**31 */ - if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */ - if (ix <= 0x3fefffff) - return (hy < 0) ? huge_val * huge_val : tiny * tiny; - if (ix >= 0x3ff00000) - return (hy > 0) ? huge_val * huge_val : tiny * tiny; - } - /* over/underflow if x is not close to one */ - if (ix < 0x3fefffff) - return (hy < 0) ? huge_val * huge_val : tiny * tiny; - if (ix > 0x3ff00000) - return (hy > 0) ? huge_val * huge_val : tiny * tiny; - /* 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)); - u = ivln2_h * t; /* ivln2_h has 21 sig. bits */ - v = t * ivln2_l - w * ivln2; - t1 = u + v; - SET_LOW_WORD(t1, 0); - t2 = v - (t1 - u); - } else { - double s2, s_h, s_l, t_h, t_l; - n = 0; - /* take care subnormal number */ - if (ix < 0x00100000) { - ax *= two53; - n -= 53; - GET_HIGH_WORD(ix, ax); - } - n += ((ix) >> 20) - 0x3ff; - j = ix & 0x000fffff; - /* determine interval */ - ix = j | 0x3ff00000; /* normalize ix */ - if (j <= 0x3988E) - k = 0; /* |x|> 1) | 0x20000000) + 0x00080000 + (k << 18)); - t_l = ax - (t_h - bp[k]); - s_l = v * ((u - s_h * t_h) - s_h * t_l); - /* compute log(ax) */ - s2 = s * s; - r = s2 * s2 * (L1 + - s2 * (L2 + - s2 * (L3 + - s2 * (L4 + s2 * (L5 + s2 * L6))))); - r += s_l * (s_h + s); - s2 = s_h * s_h; - t_h = 3.0 + s2 + r; - SET_LOW_WORD(t_h, 0); - t_l = r - ((t_h - 3.0) - s2); - /* u+v = s*(1+...) */ - u = s_h * t_h; - v = s_l * t_h + t_l * s; - /* 2/(3log2)*(s+...) */ - p_h = u + v; - SET_LOW_WORD(p_h, 0); - p_l = v - (p_h - u); - z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ - z_l = cp_l * p_h + p_l * cp + dp_l[k]; - /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ - t = (double) n; - t1 = (((z_h + z_l) + dp_h[k]) + t); - SET_LOW_WORD(t1, 0); - t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); - } - - s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ - if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) - s = -one; /* (-ve)**(odd int) */ - - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ - y1 = y; - SET_LOW_WORD(y1, 0); - p_l = (y - y1) * t1 + y * t2; - p_h = y1 * t1; - z = p_l + p_h; - EXTRACT_WORDS(j, i, z); - if (j >= 0x40900000) { /* z >= 1024 */ - if (((j - 0x40900000) | i) != 0) /* if z > 1024 */ - return s * huge_val * huge_val; /* overflow */ - else { - if (p_l + ovt > z - p_h) - return s * huge_val * huge_val; /* overflow */ - } - } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */ - if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */ - return s * tiny * tiny; /* underflow */ - else { - if (p_l <= z - p_h) - return s * tiny * tiny; /* underflow */ - } - } - /* - * compute 2**(p_h+p_l) - */ - i = j & 0x7fffffff; - k = (i >> 20) - 0x3ff; - n = 0; - if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ - n = j + (0x00100000 >> (k + 1)); - k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */ - t = zero; - SET_HIGH_WORD(t, n & ~(0x000fffff >> k)); - 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; - v = (p_l - (t - p_h)) * lg2 + t * lg2_l; - z = u + v; - w = v - (z - u); - t = z * z; - t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); - r = (z * t1) / (t1 - two) - (w + z * w); - z = one - (r - z); - GET_HIGH_WORD(j, z); - j += (n << 20); - if ((j >> 20) <= 0) - z = scalbn(z, n); /* subnormal output */ - else - SET_HIGH_WORD(z, j); - return s * z; - } +libm_hidden_def(pow) diff --git a/src/libm/e_rem_pio2.c b/src/libm/e_rem_pio2.c index dfa5d941c..df7c2b823 100644 --- a/src/libm/e_rem_pio2.c +++ b/src/libm/e_rem_pio2.c @@ -1,4 +1,3 @@ -/* @(#)e_rem_pio2.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const 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] @@ -24,42 +18,30 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -#include "SDL_assert.h" - -libm_hidden_proto(fabs) - /* * 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, - }; +static const int32_t two_over_pi[] = { +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__ static const int32_t npio2_hw[] = { -#else -static int32_t npio2_hw[] = { -#endif - 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, - 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, - 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, - 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, - 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, - 0x404858EB, 0x404921FB, +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, }; /* @@ -72,137 +54,108 @@ static int32_t npio2_hw[] = { * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) */ -#ifdef __STDC__ static const double -#else -static double -#endif - zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ - two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ - invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ - pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ - pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ - pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ - pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ - pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ -#ifdef __STDC__ -int32_t attribute_hidden -__ieee754_rem_pio2(double x, double *y) -#else -int32_t attribute_hidden -__ieee754_rem_pio2(x, y) - double x, y[]; -#endif +int32_t attribute_hidden __ieee754_rem_pio2(double x, double *y) { - double z = 0.0, w, t, r, fn; - double tx[3]; - int32_t e0, i, j, nx, n, ix, hx; - u_int32_t low; + double z=0.0,w,t,r,fn; + double tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; - GET_HIGH_WORD(hx, x); /* high word of x */ - ix = hx & 0x7fffffff; - 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) { - z = x - pio2_1; - if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */ - y[0] = z - pio2_1t; - y[1] = (z - y[0]) - pio2_1t; - } else { /* near pi/2, use 33+33+53 bit pi */ - z -= pio2_2; - y[0] = z - pio2_2t; - y[1] = (z - y[0]) - pio2_2t; - } - return 1; - } else { /* negative x */ - z = x + pio2_1; - if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */ - y[0] = z + pio2_1t; - y[1] = (z - y[0]) + pio2_1t; - } else { /* near pi/2, use 33+33+53 bit pi */ - z += pio2_2; - y[0] = z + pio2_2t; - y[1] = (z - y[0]) + pio2_2t; - } - return -1; - } - } - if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ - t = fabs(x); - n = (int32_t) (t * invpio2 + half); - 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]) { - y[0] = r - w; /* quick check no cancellation */ - } else { - u_int32_t high; - j = ix >> 20; - 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; - r = t - 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; - r = t - w; - w = fn * pio2_3t - ((t - r) - w); - y[0] = r - w; - } - } - } - y[1] = (r - y[0]) - w; - if (hx < 0) { - y[0] = -y[0]; - y[1] = -y[1]; - return -n; - } else - return n; - } + GET_HIGH_WORD(hx,x); /* high word of x */ + ix = hx&0x7fffffff; + 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) { + z = x - pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ + t = fabs(x); + n = (int32_t) (t*invpio2+half); + 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]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>20; + 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; + r = t-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; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + 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 */ - y[0] = y[1] = x - x; - return 0; - } + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } /* set z = scalbn(|x|,ilogb(x)-23) */ - GET_LOW_WORD(low, x); - SET_LOW_WORD(z, low); - e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ - SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20))); - for (i = 0; i < 2; i++) { - tx[i] = (double) ((int32_t) (z)); - z = (z - tx[i]) * two24; - } - tx[2] = z; - nx = 3; - - /* If this assertion ever fires, here's the static analysis that warned about it: - http://buildbot.libsdl.org/sdl-static-analysis/sdl-macosx-static-analysis/sdl-macosx-static-analysis-1101/report-8c6ccb.html#EndPath */ - SDL_assert((tx[0] != zero) || (tx[1] != zero) || (tx[2] != zero)); - - while (nx && tx[nx - 1] == zero) - nx--; /* skip zero term */ - n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi); - if (hx < 0) { - y[0] = -y[0]; - y[1] = -y[1]; - return -n; - } - return n; + GET_LOW_WORD(low,x); + SET_LOW_WORD(z,low); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; } diff --git a/src/libm/e_sqrt.c b/src/libm/e_sqrt.c index b8b8bec6f..39c83e1f3 100644 --- a/src/libm/e_sqrt.c +++ b/src/libm/e_sqrt.c @@ -1,4 +1,3 @@ -/* @(#)e_sqrt.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; -#endif - /* __ieee754_sqrt(x) * Return correctly rounded sqrt. * ------------------------------------------ @@ -88,124 +82,123 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -#ifdef __STDC__ static const double one = 1.0, tiny = 1.0e-300; -#else -static double one = 1.0, tiny = 1.0e-300; -#endif -#ifdef __STDC__ -double attribute_hidden -__ieee754_sqrt(double x) -#else -double attribute_hidden -__ieee754_sqrt(x) - double x; -#endif +double attribute_hidden __ieee754_sqrt(double x) { - double z; - int32_t sign = (int) 0x80000000; - int32_t ix0, s0, q, m, t, i; - u_int32_t r, t1, s1, ix1, q1; + double z; + 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); + EXTRACT_WORDS(ix0,ix1,x); /* take care of Inf and NaN */ - if ((ix0 & 0x7ff00000) == 0x7ff00000) { - return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf - sqrt(-inf)=sNaN */ - } + 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 */ - else if (ix0 < 0) - return (x - x) / (x - x); /* sqrt(-ve) = sNaN */ - } + if(ix0<=0) { + if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix0<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } /* normalize x */ - m = (ix0 >> 20); - if (m == 0) { /* subnormal x */ - while (ix0 == 0) { - m -= 21; - ix0 |= (ix1 >> 11); - ix1 <<= 21; - } - for (i = 0; (ix0 & 0x00100000) == 0; i++) - ix0 <<= 1; - m -= i - 1; - ix0 |= (ix1 >> (32 - i)); - ix1 <<= i; - } - m -= 1023; /* unbias exponent */ - ix0 = (ix0 & 0x000fffff) | 0x00100000; - if (m & 1) { /* odd m, double x to make it even */ - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - } - m >>= 1; /* m = [m/2] */ + m = (ix0>>20); + if(m==0) { /* subnormal x */ + while(ix0==0) { + m -= 21; + ix0 |= (ix1>>11); ix1 <<= 21; + } + for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; + m -= i-1; + ix0 |= (ix1>>(32-i)); + ix1 <<= i; + } + m -= 1023; /* unbias exponent */ + ix0 = (ix0&0x000fffff)|0x00100000; + if(m&1){ /* odd m, double x to make it even */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + } + m >>= 1; /* m = [m/2] */ /* generate sqrt(x) bit by bit */ - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ - r = 0x00200000; /* r = moving bit from right to left */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ + 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; - } - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - r >>= 1; - } + while(r!=0) { + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } - r = sign; - while (r != 0) { - t1 = s1 + r; - t = s0; - if ((t < ix0) || ((t == ix0) && (t1 <= ix1))) { - s1 = t1 + r; - if (((t1 & sign) == sign) && (s1 & sign) == 0) - s0 += 1; - ix0 -= t; - if (ix1 < t1) - ix0 -= 1; - ix1 -= t1; - q1 += r; - } - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - r >>= 1; - } + r = sign; + while(r!=0) { + t1 = s1+r; + t = s0; + if((t>31); + ix1 += ix1; + r>>=1; + } /* use floating add to find out rounding direction */ - if ((ix0 | ix1) != 0) { - z = one - tiny; /* trigger inexact flag */ - if (z >= one) { - z = one + tiny; - if (q1 == (u_int32_t) 0xffffffff) { - q1 = 0; - q += 1; - } else if (z > one) { - if (q1 == (u_int32_t) 0xfffffffe) - q += 1; - q1 += 2; - } else - q1 += (q1 & 1); - } - } - ix0 = (q >> 1) + 0x3fe00000; - ix1 = q1 >> 1; - if ((q & 1) == 1) - ix1 |= sign; - ix0 += (m << 20); - INSERT_WORDS(z, ix0, ix1); - return z; + if((ix0|ix1)!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} + else if (z>one) { + if (q1==(u_int32_t)0xfffffffe) q+=1; + q1+=2; + } else + q1 += (q1&1); + } + } + ix0 = (q>>1)+0x3fe00000; + ix1 = q1>>1; + if ((q&1)==1) ix1 |= sign; + ix0 += (m <<20); + INSERT_WORDS(z,ix0,ix1); + return z; } +/* + * wrapper sqrt(x) + */ +#ifndef _IEEE_LIBM +double sqrt(double x) +{ + double z = __ieee754_sqrt(x); + if (_LIB_VERSION == _IEEE_ || isnan(x)) + return z; + if (x < 0.0) + return __kernel_standard(x, x, 26); /* sqrt(negative) */ + return z; +} +#else +strong_alias(__ieee754_sqrt, sqrt) +#endif +libm_hidden_def(sqrt) + + /* Other methods (use floating-point arithmetic) ------------- diff --git a/src/libm/k_cos.c b/src/libm/k_cos.c index 64c50e3fb..e1326fa64 100644 --- a/src/libm/k_cos.c +++ b/src/libm/k_cos.c @@ -1,4 +1,3 @@ -/* @(#)k_cos.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; -#endif - /* * __kernel_cos( x, y ) * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 @@ -53,48 +47,36 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -#ifdef __STDC__ static const double -#else -static double -#endif - one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ - C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ - C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ - C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ - C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ - C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ - C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ -#ifdef __STDC__ -double attribute_hidden -__kernel_cos(double x, double y) -#else -double attribute_hidden -__kernel_cos(x, y) - double x, y; -#endif +double attribute_hidden __kernel_cos(double x, double y) { - double a, hz, z, r, qx; - int32_t ix; - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; /* ix = |x|'s high word */ - if (ix < 0x3e400000) { /* if x < 2**27 */ - if (((int) x) == 0) - return one; /* generate inexact */ - } - z = x * x; - r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6))))); - if (ix < 0x3FD33333) /* if |x| < 0.3 */ - return one - (0.5 * z - (z * r - x * y)); - else { - if (ix > 0x3fe90000) { /* x > 0.78125 */ - qx = 0.28125; - } else { - INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */ - } - hz = 0.5 * z - qx; - a = one - qx; - return a - (hz - (z * r - x * y)); - } + double a,hz,z,r,qx; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x3e400000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return one - (0.5*z - (z*r - x*y)); + else { + if(ix > 0x3fe90000) { /* x > 0.78125 */ + qx = 0.28125; + } else { + INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ + } + hz = 0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } } diff --git a/src/libm/k_rem_pio2.c b/src/libm/k_rem_pio2.c index 50e1d52fb..9956d95b7 100644 --- a/src/libm/k_rem_pio2.c +++ b/src/libm/k_rem_pio2.c @@ -1,4 +1,3 @@ -/* @(#)k_rem_pio2.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $"; -#endif - /* * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) * double x[],y[]; int e0,nx,prec; int ipio2[]; @@ -134,235 +128,171 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -#include "SDL_assert.h" +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ -libm_hidden_proto(scalbn) - libm_hidden_proto(floor) -#ifdef __STDC__ - static const int init_jk[] = { 2, 3, 4, 6 }; /* initial value for jk */ -#else - static int init_jk[] = { 2, 3, 4, 6 }; -#endif - -#ifdef __STDC__ static const double PIo2[] = { -#else -static double PIo2[] = { -#endif - 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ - 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ - 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ - 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ - 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ - 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ - 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ - 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ }; -#ifdef __STDC__ static const double -#else -static double -#endif - zero = 0.0, one = 1.0, two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ - twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ -#ifdef __STDC__ -int attribute_hidden -__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, - const int32_t * ipio2) -#else -int attribute_hidden -__kernel_rem_pio2(x, y, e0, nx, prec, ipio2) - double x[], y[]; - int e0, nx, prec; - int32_t ipio2[]; -#endif +int attribute_hidden __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2) { - int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih; - double z, fw, f[20], fq[20], q[20]; + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; - /* initialize jk */ - SDL_assert((prec >= 0) && (prec < SDL_arraysize(init_jk))); - jk = init_jk[prec]; - SDL_assert((jk >= 2) && (jk <= 6)); - jp = jk; + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; /* determine jx,jv,q0, note that 3>q0 */ - SDL_assert(nx > 0); - jx = nx - 1; - jv = (e0 - 3) / 24; - if (jv < 0) - jv = 0; - q0 = e0 - 24 * (jv + 1); + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ - j = jv - jx; - m = jx + jk; - for (i = 0; i <= m; i++, j++) - f[i] = (j < 0) ? zero : (double) ipio2[j]; + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; /* compute q[0],q[1],...q[jk] */ - for (i = 0; i <= jk; i++) { - for (j = 0, fw = 0.0; j <= jx; j++) { - const int32_t idx = jx + i - j; - SDL_assert(idx >= 0); - SDL_assert(idx < 20); - SDL_assert(idx <= m); - fw += x[j] * f[idx]; - } - q[i] = fw; - } + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } - jz = jk; - recompute: + jz = jk; +recompute: /* distill q[] into iq[] reversingly */ - for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) { - fw = (double) ((int32_t) (twon24 * z)); - iq[i] = (int32_t) (z - two24 * fw); - z = q[j - 1] + fw; - } + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); + z = q[j-1]+fw; + } /* compute n */ - z = scalbn(z, q0); /* actual value of z */ - z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */ - n = (int32_t) z; - z -= (double) n; - ih = 0; - if (q0 > 0) { /* need iq[jz-1] to determine n */ - 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; + z = scalbn(z,q0); /* actual value of z */ + z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + 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; - if (ih > 0) { /* q > 0.5 */ - n += 1; - carry = 0; - for (i = 0; i < jz; i++) { /* compute 1-q */ - j = iq[i]; - if (carry == 0) { - if (j != 0) { - carry = 1; - iq[i] = 0x1000000 - j; - } - } else - iq[i] = 0xffffff - j; - } - if (q0 > 0) { /* rare case: chance is 1 in 12 */ - switch (q0) { - case 1: - iq[jz - 1] &= 0x7fffff; - break; - case 2: - iq[jz - 1] &= 0x3fffff; - break; - } - } - if (ih == 2) { - z = one - z; - if (carry != 0) - z -= scalbn(one, q0); - } - } + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbn(one,q0); + } + } /* check if recomputation is needed */ - if (z == zero) { - j = 0; - for (i = jz - 1; i >= jk; i--) - j |= iq[i]; - if (j == 0) { /* need recomputation */ - for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ - for (i = jz + 1; i <= jz + k; i++) { /* add q[jz+1] to q[jz+k] */ - f[jx + i] = (double) ipio2[jv + i]; - for (j = 0, fw = 0.0; j <= jx; j++) - fw += x[j] * f[jx + i - j]; - q[i] = fw; - } - jz += k; - goto recompute; - } - } + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } /* chop off zero terms */ - if (z == 0.0) { - jz -= 1; - q0 -= 24; - while (iq[jz] == 0) { - jz--; - q0 -= 24; - } - } else { /* break z into 24-bit if necessary */ - z = scalbn(z, -q0); - if (z >= two24) { - fw = (double) ((int32_t) (twon24 * z)); - iq[jz] = (int32_t) (z - two24 * fw); - jz += 1; - q0 += 24; - iq[jz] = (int32_t) fw; - } else - iq[jz] = (int32_t) z; - } + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int32_t)(twon24*z)); + iq[jz] = (int32_t)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } /* convert integer "bit" chunk to floating-point value */ - fw = scalbn(one, q0); - for (i = jz; i >= 0; i--) { - q[i] = fw * (double) iq[i]; - fw *= twon24; - } + fw = scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } /* compute PIo2[0,...,jp]*q[jz,...,0] */ - for (i = jz; i >= 0; i--) { - for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++) - fw += PIo2[k] * q[i + k]; - fq[jz - i] = fw; - } + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } /* compress fq[] into y[] */ - switch (prec) { - case 0: - fw = 0.0; - for (i = jz; i >= 0; i--) - fw += fq[i]; - 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; - fw = fq[0] - fw; - for (i = 1; i <= jz; i++) - fw += fq[i]; - y[1] = (ih == 0) ? fw : -fw; - break; - case 3: /* painful */ - for (i = jz; i > 0; 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]; - fq[i] += fq[i - 1] - fw; - fq[i - 1] = fw; - } - 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 { - y[0] = -fq[0]; - y[1] = -fq[1]; - y[2] = -fw; - } - } - return n & 7; + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + 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; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;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]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + 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 { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; } diff --git a/src/libm/k_sin.c b/src/libm/k_sin.c index 60881575a..3520d6b4c 100644 --- a/src/libm/k_sin.c +++ b/src/libm/k_sin.c @@ -1,4 +1,3 @@ -/* @(#)k_sin.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; -#endif - /* __kernel_sin( x, y, iy) * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 * Input x is assumed to be bounded by ~pi/4 in magnitude. @@ -46,42 +40,26 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -#ifdef __STDC__ static const double -#else -static double -#endif - half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ - S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ - S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ - S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ - S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ - S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ - S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ -#ifdef __STDC__ -double attribute_hidden -__kernel_sin(double x, double y, int iy) -#else -double attribute_hidden -__kernel_sin(x, y, iy) - double x, y; - int iy; /* iy=0 if y is zero */ -#endif +double attribute_hidden __kernel_sin(double x, double y, int iy) { - double z, r, v; - int32_t ix; - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; /* high word of x */ - if (ix < 0x3e400000) { /* |x| < 2**-27 */ - if ((int) x == 0) - return x; - } /* generate inexact */ - z = x * x; - v = z * x; - r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6))); - if (iy == 0) - return x + v * (S1 + z * r); - else - return x - ((z * (half * y - v * r) - y) - v * S1); + double z,r,v; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); } diff --git a/src/libm/k_tan.c b/src/libm/k_tan.c index 27e6639b0..47b4e3dcd 100644 --- a/src/libm/k_tan.c +++ b/src/libm/k_tan.c @@ -66,7 +66,7 @@ T[] = { 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ }; -double __kernel_tan(double x, double y, int iy) +double attribute_hidden __kernel_tan(double x, double y, int iy) { double z,r,v,w,s; int32_t ix,hx; diff --git a/src/libm/math_libm.h b/src/libm/math_libm.h index a30fa3fa8..304939544 100644 --- a/src/libm/math_libm.h +++ b/src/libm/math_libm.h @@ -28,6 +28,7 @@ double SDL_uclibc_copysign(double x, double y); double SDL_uclibc_cos(double x); double SDL_uclibc_fabs(double x); double SDL_uclibc_floor(double x); +double SDL_uclibc_fmod(double x, double y); double SDL_uclibc_log(double x); double SDL_uclibc_pow(double x, double y); double SDL_uclibc_scalbn(double x, int n); diff --git a/src/libm/math_private.h b/src/libm/math_private.h index 74c8b3d45..d3701944b 100644 --- a/src/libm/math_private.h +++ b/src/libm/math_private.h @@ -21,9 +21,11 @@ #include "SDL_endian.h" /* #include */ +#define _IEEE_LIBM #define attribute_hidden #define libm_hidden_proto(x) #define libm_hidden_def(x) +#define strong_alias(x, y) #ifndef __HAIKU__ /* already defined in a system header. */ typedef unsigned int u_int32_t; @@ -35,6 +37,7 @@ typedef unsigned int u_int32_t; #define cos SDL_uclibc_cos #define fabs SDL_uclibc_fabs #define floor SDL_uclibc_floor +#define __ieee754_fmod SDL_uclibc_fmod #define __ieee754_log SDL_uclibc_log #define __ieee754_pow SDL_uclibc_pow #define scalbn SDL_uclibc_scalbn diff --git a/src/libm/s_atan.c b/src/libm/s_atan.c index 970ea4dbf..f664f0eb3 100644 --- a/src/libm/s_atan.c +++ b/src/libm/s_atan.c @@ -112,4 +112,3 @@ double atan(double x) } } libm_hidden_def(atan) - diff --git a/src/libm/s_copysign.c b/src/libm/s_copysign.c index afd43e9a7..a2f275bf7 100644 --- a/src/libm/s_copysign.c +++ b/src/libm/s_copysign.c @@ -1,4 +1,3 @@ -/* @(#)s_copysign.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_copysign.c,v 1.8 1995/05/10 20:46:57 jtc Exp $"; -#endif - /* * copysign(double x, double y) * copysign(x,y) returns a value with the magnitude of x and @@ -24,19 +18,12 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -libm_hidden_proto(copysign) -#ifdef __STDC__ - double copysign(double x, double y) -#else - double copysign(x, y) - double x, y; -#endif +double copysign(double x, double y) { - u_int32_t hx, hy; - GET_HIGH_WORD(hx, x); - GET_HIGH_WORD(hy, y); - SET_HIGH_WORD(x, (hx & 0x7fffffff) | (hy & 0x80000000)); - return x; + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; } - libm_hidden_def(copysign) diff --git a/src/libm/s_cos.c b/src/libm/s_cos.c index 66b156c9f..554026053 100644 --- a/src/libm/s_cos.c +++ b/src/libm/s_cos.c @@ -1,4 +1,3 @@ -/* @(#)s_cos.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $"; -#endif - /* cos(x) * Return cosine function of x. * @@ -49,43 +43,31 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -libm_hidden_proto(cos) -#ifdef __STDC__ - double cos(double x) -#else - double cos(x) - double x; -#endif +double cos(double x) { - double y[2], z = 0.0; - int32_t n, ix; + double y[2],z=0.0; + int32_t n, ix; /* High word of x. */ - GET_HIGH_WORD(ix, x); + GET_HIGH_WORD(ix,x); /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if (ix <= 0x3fe921fb) - return __kernel_cos(x, z); + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_cos(x,z); /* cos(Inf or NaN) is NaN */ - else if (ix >= 0x7ff00000) - return x - x; + else if (ix>=0x7ff00000) return x-x; /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x, y); - switch (n & 3) { - case 0: - return __kernel_cos(y[0], y[1]); - case 1: - return -__kernel_sin(y[0], y[1], 1); - case 2: - return -__kernel_cos(y[0], y[1]); - default: - return __kernel_sin(y[0], y[1], 1); - } - } + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } } - libm_hidden_def(cos) diff --git a/src/libm/s_fabs.c b/src/libm/s_fabs.c index 5cf0c3977..9ee943c40 100644 --- a/src/libm/s_fabs.c +++ b/src/libm/s_fabs.c @@ -1,4 +1,3 @@ -/* @(#)s_fabs.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,30 +9,21 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_fabs.c,v 1.7 1995/05/10 20:47:13 jtc Exp $"; -#endif - /* * fabs(x) returns the absolute value of x. */ +/*#include */ +/* Prevent math.h from defining a colliding inline */ +#undef __USE_EXTERN_INLINES #include "math_libm.h" #include "math_private.h" -libm_hidden_proto(fabs) -#ifdef __STDC__ - double fabs(double x) -#else - double fabs(x) - double x; -#endif +double fabs(double x) { - u_int32_t high; - GET_HIGH_WORD(high, x); - SET_HIGH_WORD(x, high & 0x7fffffff); - return x; + u_int32_t high; + GET_HIGH_WORD(high,x); + SET_HIGH_WORD(x,high&0x7fffffff); + return x; } - libm_hidden_def(fabs) diff --git a/src/libm/s_floor.c b/src/libm/s_floor.c index b553d3038..f0be5cbf1 100644 --- a/src/libm/s_floor.c +++ b/src/libm/s_floor.c @@ -1,4 +1,3 @@ -/* @(#)s_floor.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_floor.c,v 1.8 1995/05/10 20:47:20 jtc Exp $"; -#endif - /* * floor(x) * Return x rounded toward -inf to integral value @@ -24,73 +18,54 @@ static const char rcsid[] = * Inexact flag raised if x not equal to floor(x). */ +/*#include */ +/* Prevent math.h from defining a colliding inline */ +#undef __USE_EXTERN_INLINES #include "math_libm.h" #include "math_private.h" -#ifdef __STDC__ -static const double huge_val = 1.0e300; -#else -static double huge_val = 1.0e300; -#endif +static const double huge = 1.0e300; -libm_hidden_proto(floor) -#ifdef __STDC__ - double floor(double x) -#else - double floor(x) - double x; -#endif +double floor(double x) { - int32_t i0, i1, j0; - u_int32_t i, j; - EXTRACT_WORDS(i0, i1, x); - j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; - if (j0 < 20) { - if (j0 < 0) { /* raise inexact if x != 0 */ - if (huge_val + x > 0.0) { /* return 0*sign(x) if |x|<1 */ - if (i0 >= 0) { - i0 = i1 = 0; - } else if (((i0 & 0x7fffffff) | i1) != 0) { - i0 = 0xbff00000; - i1 = 0; - } - } - } else { - i = (0x000fffff) >> j0; - if (((i0 & i) | i1) == 0) - return x; /* x is integral */ - if (huge_val + x > 0.0) { /* raise inexact flag */ - if (i0 < 0) - i0 += (0x00100000) >> j0; - i0 &= (~i); - i1 = 0; - } - } - } else if (j0 > 51) { - if (j0 == 0x400) - return x + x; /* inf or NaN */ - else - return x; /* x is integral */ - } else { - i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); - if ((i1 & i) == 0) - return x; /* x is integral */ - if (huge_val + x > 0.0) { /* raise inexact flag */ - if (i0 < 0) { - if (j0 == 20) - i0 += 1; - else { - j = i1 + (1 << (52 - j0)); - if (j < (u_int32_t) i1) - i0 += 1; /* got a carry */ - i1 = j; - } - } - i1 &= (~i); - } - } - INSERT_WORDS(x, i0, i1); - return x; + int32_t i0,i1,j0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + 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;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(j0-20); + 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; + else { + j = i1+(1<<(52-j0)); + if(j -libm_hidden_proto(copysign) -#ifdef __STDC__ - static const double -#else - static double -#endif - two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ - twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ - huge_val = 1.0e+300, tiny = 1.0e-300; +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; -libm_hidden_proto(scalbn) -#ifdef __STDC__ - double scalbn(double x, int n) -#else - double scalbn(x, n) - double x; - int n; -#endif +double scalbln(double x, long n) { - int32_t k, hx, lx; - EXTRACT_WORDS(hx, lx, x); - k = (hx & 0x7ff00000) >> 20; /* extract exponent */ - if (k == 0) { /* 0 or subnormal x */ - if ((lx | (hx & 0x7fffffff)) == 0) - return x; /* +-0 */ - x *= two54; - GET_HIGH_WORD(hx, x); - k = ((hx & 0x7ff00000) >> 20) - 54; - if (n < -50000) - return tiny * x; /* underflow */ - } - if (k == 0x7ff) - return x + x; /* NaN or Inf */ - k = k + n; - if (k > 0x7fe) - return huge_val * copysign(huge_val, x); /* overflow */ - if (k > 0) { /* normal result */ - SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); - return x; - } - if (k <= -54) { - if (n > 50000) /* in case integer overflow in n+k */ - return huge_val * copysign(huge_val, x); /* overflow */ - else - return tiny * copysign(tiny, x); /* underflow */ - } - k += 54; /* subnormal result */ - SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); - return x * twom54; -} + int32_t k, hx, lx; + EXTRACT_WORDS(hx, lx, x); + k = (hx & 0x7ff00000) >> 20; /* extract exponent */ + if (k == 0) { /* 0 or subnormal x */ + if ((lx | (hx & 0x7fffffff)) == 0) + return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD(hx, x); + k = ((hx & 0x7ff00000) >> 20) - 54; + } + if (k == 0x7ff) + return x + x; /* NaN or Inf */ + k = k + n; + if (k > 0x7fe) + return huge * copysign(huge, x); /* overflow */ + if (n < -50000) + return tiny * copysign(tiny, x); /* underflow */ + if (k > 0) { /* normal result */ + SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); + return x; + } + if (k <= -54) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge * copysign(huge, x); /* overflow */ + return tiny * copysign(tiny, x); /* underflow */ + } + k += 54; /* subnormal result */ + SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); + return x * twom54; +} +libm_hidden_def(scalbln) + +#if LONG_MAX == INT_MAX +/* strong_alias(scalbln, scalbn) - "error: conflicting types for 'scalbn'" + * because it tries to declare "typeof(scalbln) scalbn;" + * which tries to give "long" parameter to scalbn. + * Doing it by hand: + */ +__typeof(scalbn) scalbn __attribute__((alias("scalbln"))); +#else +double scalbn(double x, int n) +{ + return scalbln(x, n); +} +#endif libm_hidden_def(scalbn) diff --git a/src/libm/s_sin.c b/src/libm/s_sin.c index 771176619..b3cd7a0e3 100644 --- a/src/libm/s_sin.c +++ b/src/libm/s_sin.c @@ -1,4 +1,3 @@ -/* @(#)s_sin.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -10,11 +9,6 @@ * ==================================================== */ -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $"; -#endif - /* sin(x) * Return sine function of x. * @@ -49,43 +43,31 @@ static const char rcsid[] = #include "math_libm.h" #include "math_private.h" -libm_hidden_proto(sin) -#ifdef __STDC__ - double sin(double x) -#else - double sin(x) - double x; -#endif +double sin(double x) { - double y[2], z = 0.0; - int32_t n, ix; + double y[2],z=0.0; + int32_t n, ix; /* High word of x. */ - GET_HIGH_WORD(ix, x); + GET_HIGH_WORD(ix,x); /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if (ix <= 0x3fe921fb) - return __kernel_sin(x, z, 0); + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); /* sin(Inf or NaN) is NaN */ - else if (ix >= 0x7ff00000) - return x - x; + else if (ix>=0x7ff00000) return x-x; /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x, y); - switch (n & 3) { - case 0: - return __kernel_sin(y[0], y[1], 1); - case 1: - return __kernel_cos(y[0], y[1]); - case 2: - return -__kernel_sin(y[0], y[1], 1); - default: - return -__kernel_cos(y[0], y[1]); - } - } + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } } - libm_hidden_def(sin)