From: Keith Packard Date: Fri, 25 Oct 2013 11:00:49 +0000 (-0700) Subject: altos: Add floating point math functions from newlib X-Git-Tag: 1.2.9.4~40 X-Git-Url: https://git.gag.com/?p=fw%2Faltos;a=commitdiff_plain;h=b83876718b1a535ee04ca0351ad57814454ec646 altos: Add floating point math functions from newlib These are all BSD licensed, so we can simply include them directly Signed-off-by: Keith Packard --- diff --git a/src/math/ef_acos.c b/src/math/ef_acos.c new file mode 100644 index 00000000..f73f97de --- /dev/null +++ b/src/math/ef_acos.c @@ -0,0 +1,84 @@ +/* ef_acos.c -- float version of e_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +#ifdef __STDC__ + float __ieee754_acosf(float x) +#else + float __ieee754_acosf(x) + float x; +#endif +{ + float z,p,q,r,w,s,c,df; + __int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } else if(ix>0x3f800000) { /* |x| >= 1 */ + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*(float)0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = __ieee754_sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + __int32_t idf; + z = (one-x)*(float)0.5; + s = __ieee754_sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return (float)2.0*(df+w); + } +} diff --git a/src/math/ef_rem_pio2.c b/src/math/ef_rem_pio2.c new file mode 100644 index 00000000..f1191d09 --- /dev/null +++ b/src/math/ef_rem_pio2.c @@ -0,0 +1,193 @@ +/* ef_rem_pio2.c -- float version of e_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2f() + */ + +#include "fdlibm.h" + +/* + * 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 +0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, +0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, +0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, +0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, +0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, +0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, +0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, +0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, +0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, +0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, +0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, +0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, +0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, +0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, +0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, +0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, +0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, +0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, +0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, +0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, +0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, +0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, +}; + +/* This array is like the one in e_rem_pio2.c, but the numbers are + single precision and the last 8 bits are forced to 0. */ +#ifdef __STDC__ +static const __int32_t npio2_hw[] = { +#else +static __int32_t npio2_hw[] = { +#endif +0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, +0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, +0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, +0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, +0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, +0x4242c700, 0x42490f00 +}; + +/* + * invpio2: 24 bits of 2/pi + * pio2_1: first 17 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 17 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 17 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +#ifdef __STDC__ +static const float +#else +static float +#endif +zero = 0.0000000000e+00, /* 0x00000000 */ +half = 5.0000000000e-01, /* 0x3f000000 */ +two8 = 2.5600000000e+02, /* 0x43800000 */ +invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ +pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ +pio2_1t = 1.0804334124e-05, /* 0x37354443 */ +pio2_2 = 1.0804273188e-05, /* 0x37354400 */ +pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ +pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ +pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ + +#ifdef __STDC__ + __int32_t __ieee754_rem_pio2f(float x, float *y) +#else + __int32_t __ieee754_rem_pio2f(x,y) + float x,y[]; +#endif +{ + float z,w,t,r,fn; + float tx[3]; + __int32_t i,j,n,ix,hx; + int e0,nx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 24+24+24 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&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ + t = fabsf(x); + n = (__int32_t) (t*invpio2+half); + fn = (float)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 40 bit */ + if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + __uint32_t high; + j = ix>>23; + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>8) { /* 2nd iteration needed, good to 57 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>25) { /* 3rd iteration need, 74 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(!FLT_UWORD_IS_FINITE(ix)) { + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-7) */ + e0 = (int)((ix>>23)-134); /* e0 = ilogb(z)-7; */ + SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23)); + for(i=0;i<2;i++) { + tx[i] = (float)((__int32_t)(z)); + z = (z-tx[i])*two8; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2f(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/math/ef_sqrt.c b/src/math/ef_sqrt.c new file mode 100644 index 00000000..80e7f360 --- /dev/null +++ b/src/math/ef_sqrt.c @@ -0,0 +1,89 @@ +/* ef_sqrtf.c -- float version of e_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float one = 1.0, tiny=1.0e-30; +#else +static float one = 1.0, tiny=1.0e-30; +#endif + +#ifdef __STDC__ + float __ieee754_sqrtf(float x) +#else + float __ieee754_sqrtf(x) + float x; +#endif +{ + float z; + __uint32_t r,hx; + __int32_t ix,s,q,m,t,i; + + GET_FLOAT_WORD(ix,x); + hx = ix&0x7fffffff; + + /* take care of Inf and NaN */ + if(!FLT_UWORD_IS_FINITE(hx)) + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + /* take care of zero and -ves */ + if(FLT_UWORD_IS_ZERO(hx)) return x;/* sqrt(+-0) = +-0 */ + if(ix<0) return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + + /* normalize x */ + m = (ix>>23); + if(FLT_UWORD_IS_SUBNORMAL(hx)) { /* subnormal x */ + for(i=0;(ix&0x00800000L)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffffL)|0x00800000L; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000L; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000L; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} diff --git a/src/math/fdlibm.h b/src/math/fdlibm.h new file mode 100644 index 00000000..821619ad --- /dev/null +++ b/src/math/fdlibm.h @@ -0,0 +1,413 @@ + +/* @(#)fdlibm.h 5.1 93/09/24 */ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +/* AltOS local */ +#include +#include +#define __int32_t int32_t +#define __uint32_t uint32_t + +#define __ieee754_acosf acosf +#define __ieee754_sqrtf sqrtf + +/* REDHAT LOCAL: Include files. */ +#include +/* #include */ +#include + +/* REDHAT LOCAL: Default to XOPEN_MODE. */ +#define _XOPEN_MODE + +/* Most routines need to check whether a float is finite, infinite, or not a + number, and many need to know whether the result of an operation will + overflow. These conditions depend on whether the largest exponent is + used for NaNs & infinities, or whether it's used for finite numbers. The + macros below wrap up that kind of information: + + FLT_UWORD_IS_FINITE(X) + True if a positive float with bitmask X is finite. + + FLT_UWORD_IS_NAN(X) + True if a positive float with bitmask X is not a number. + + FLT_UWORD_IS_INFINITE(X) + True if a positive float with bitmask X is +infinity. + + FLT_UWORD_MAX + The bitmask of FLT_MAX. + + FLT_UWORD_HALF_MAX + The bitmask of FLT_MAX/2. + + FLT_UWORD_EXP_MAX + The bitmask of the largest finite exponent (129 if the largest + exponent is used for finite numbers, 128 otherwise). + + FLT_UWORD_LOG_MAX + The bitmask of log(FLT_MAX), rounded down. This value is the largest + input that can be passed to exp() without producing overflow. + + FLT_UWORD_LOG_2MAX + The bitmask of log(2*FLT_MAX), rounded down. This value is the + largest input than can be passed to cosh() without producing + overflow. + + FLT_LARGEST_EXP + The largest biased exponent that can be used for finite numbers + (255 if the largest exponent is used for finite numbers, 254 + otherwise) */ + +#ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL +#define FLT_UWORD_IS_FINITE(x) 1 +#define FLT_UWORD_IS_NAN(x) 0 +#define FLT_UWORD_IS_INFINITE(x) 0 +#define FLT_UWORD_MAX 0x7fffffff +#define FLT_UWORD_EXP_MAX 0x43010000 +#define FLT_UWORD_LOG_MAX 0x42b2d4fc +#define FLT_UWORD_LOG_2MAX 0x42b437e0 +#define HUGE ((float)0X1.FFFFFEP128) +#else +#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L) +#define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L) +#define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L) +#define FLT_UWORD_MAX 0x7f7fffffL +#define FLT_UWORD_EXP_MAX 0x43000000 +#define FLT_UWORD_LOG_MAX 0x42b17217 +#define FLT_UWORD_LOG_2MAX 0x42b2d4fc +#define HUGE ((float)3.40282346638528860e+38) +#endif +#define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1L<<23)) +#define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23) + +/* Many routines check for zero and subnormal numbers. Such things depend + on whether the target supports denormals or not: + + FLT_UWORD_IS_ZERO(X) + True if a positive float with bitmask X is +0. Without denormals, + any float with a zero exponent is a +0 representation. With + denormals, the only +0 representation is a 0 bitmask. + + FLT_UWORD_IS_SUBNORMAL(X) + True if a non-zero positive float with bitmask X is subnormal. + (Routines should check for zeros first.) + + FLT_UWORD_MIN + The bitmask of the smallest float above +0. Call this number + REAL_FLT_MIN... + + FLT_UWORD_EXP_MIN + The bitmask of the float representation of REAL_FLT_MIN's exponent. + + FLT_UWORD_LOG_MIN + The bitmask of |log(REAL_FLT_MIN)|, rounding down. + + FLT_SMALLEST_EXP + REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported, + -22 if they are). +*/ + +#ifdef _FLT_NO_DENORMALS +#define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L) +#define FLT_UWORD_IS_SUBNORMAL(x) 0 +#define FLT_UWORD_MIN 0x00800000 +#define FLT_UWORD_EXP_MIN 0x42fc0000 +#define FLT_UWORD_LOG_MIN 0x42aeac50 +#define FLT_SMALLEST_EXP 1 +#else +#define FLT_UWORD_IS_ZERO(x) ((x)==0) +#define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L) +#define FLT_UWORD_MIN 0x00000001 +#define FLT_UWORD_EXP_MIN 0x43160000 +#define FLT_UWORD_LOG_MIN 0x42cff1b5 +#define FLT_SMALLEST_EXP -22 +#endif + +#ifdef __STDC__ +#undef __P +#define __P(p) p +#else +#define __P(p) () +#endif + +/* + * set X_TLOSS = pi*2**52, which is possibly defined in + * (one may replace the following line by "#include ") + */ + +#define X_TLOSS 1.41484755040568800000e+16 + +/* Functions that are not documented, and are not in . */ + +#ifdef _SCALB_INT +extern double scalb __P((double, int)); +#else +extern double scalb __P((double, double)); +#endif +extern double significand __P((double)); + +/* 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_exp __P((double)); +extern double __ieee754_cosh __P((double)); +extern double __ieee754_fmod __P((double,double)); +extern double __ieee754_pow __P((double,double)); +extern double __ieee754_lgamma_r __P((double,int *)); +extern double __ieee754_gamma_r __P((double,int *)); +extern double __ieee754_log10 __P((double)); +extern double __ieee754_sinh __P((double)); +extern double __ieee754_hypot __P((double,double)); +extern double __ieee754_j0 __P((double)); +extern double __ieee754_j1 __P((double)); +extern double __ieee754_y0 __P((double)); +extern double __ieee754_y1 __P((double)); +extern double __ieee754_jn __P((int,double)); +extern double __ieee754_yn __P((int,double)); +extern double __ieee754_remainder __P((double,double)); +extern __int32_t __ieee754_rem_pio2 __P((double,double*)); +#ifdef _SCALB_INT +extern double __ieee754_scalb __P((double,int)); +#else +extern double __ieee754_scalb __P((double,double)); +#endif + +/* fdlibm kernel function */ +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)); +extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const __int32_t*)); + +/* Undocumented float functions. */ +#ifdef _SCALB_INT +extern float scalbf __P((float, int)); +#else +extern float scalbf __P((float, float)); +#endif +extern float significandf __P((float)); + +/* 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_expf __P((float)); +extern float __ieee754_coshf __P((float)); +extern float __ieee754_fmodf __P((float,float)); +extern float __ieee754_powf __P((float,float)); +extern float __ieee754_lgammaf_r __P((float,int *)); +extern float __ieee754_gammaf_r __P((float,int *)); +extern float __ieee754_log10f __P((float)); +extern float __ieee754_sinhf __P((float)); +extern float __ieee754_hypotf __P((float,float)); +extern float __ieee754_j0f __P((float)); +extern float __ieee754_j1f __P((float)); +extern float __ieee754_y0f __P((float)); +extern float __ieee754_y1f __P((float)); +extern float __ieee754_jnf __P((int,float)); +extern float __ieee754_ynf __P((int,float)); +extern float __ieee754_remainderf __P((float,float)); +extern __int32_t __ieee754_rem_pio2f __P((float,float*)); +#ifdef _SCALB_INT +extern float __ieee754_scalbf __P((float,int)); +#else +extern float __ieee754_scalbf __P((float,float)); +#endif + +/* float versions of fdlibm kernel functions */ +extern float __kernel_sinf __P((float,float,int)); +extern float __kernel_cosf __P((float,float)); +extern float __kernel_tanf __P((float,float,int)); +extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __int32_t*)); + +/* The original code used statements like + n0 = ((*(int*)&one)>>29)^1; * index of high word * + ix0 = *(n0+(int*)&x); * high word of x * + ix1 = *((1-n0)+(int*)&x); * low word of x * + to dig two 32 bit words out of the 64 bit IEEE floating point + value. That is non-ANSI, and, moreover, the gcc instruction + scheduler gets it wrong. We instead use the following macros. + Unlike the original code, we determine the endianness at compile + time, not at run time; I don't see much benefit to selecting + endianness at run time. */ + +#ifndef __IEEE_BIG_ENDIAN +#ifndef __IEEE_LITTLE_ENDIAN + #error Must define endianness +#endif +#endif + +/* A union which permits us to convert between a double and two 32 bit + ints. */ + +#ifdef __IEEE_BIG_ENDIAN + +typedef union +{ + double value; + struct + { + __uint32_t msw; + __uint32_t lsw; + } parts; +} ieee_double_shape_type; + +#endif + +#ifdef __IEEE_LITTLE_ENDIAN + +typedef union +{ + double value; + struct + { + __uint32_t lsw; + __uint32_t msw; + } parts; +} ieee_double_shape_type; + +#endif + +/* Get two 32 bit ints from a double. */ + +#define EXTRACT_WORDS(ix0,ix1,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (0) + +/* Get the more significant 32 bit int from a double. */ + +#define GET_HIGH_WORD(i,d) \ +do { \ + ieee_double_shape_type gh_u; \ + gh_u.value = (d); \ + (i) = gh_u.parts.msw; \ +} while (0) + +/* Get the less significant 32 bit int from a double. */ + +#define GET_LOW_WORD(i,d) \ +do { \ + ieee_double_shape_type gl_u; \ + gl_u.value = (d); \ + (i) = gl_u.parts.lsw; \ +} while (0) + +/* Set a double from two 32 bit ints. */ + +#define INSERT_WORDS(d,ix0,ix1) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (0) + +/* Set the more significant 32 bits of a double from an int. */ + +#define SET_HIGH_WORD(d,v) \ +do { \ + ieee_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (0) + +/* Set the less significant 32 bits of a double from an int. */ + +#define SET_LOW_WORD(d,v) \ +do { \ + ieee_double_shape_type sl_u; \ + sl_u.value = (d); \ + sl_u.parts.lsw = (v); \ + (d) = sl_u.value; \ +} while (0) + +/* A union which permits us to convert between a float and a 32 bit + int. */ + +typedef union +{ + float value; + __uint32_t word; +} ieee_float_shape_type; + +/* Get a 32 bit int from a float. */ + +#define GET_FLOAT_WORD(i,d) \ +do { \ + ieee_float_shape_type gf_u; \ + gf_u.value = (d); \ + (i) = gf_u.word; \ +} while (0) + +/* Set a float from a 32 bit int. */ + +#define SET_FLOAT_WORD(d,i) \ +do { \ + ieee_float_shape_type sf_u; \ + sf_u.word = (i); \ + (d) = sf_u.value; \ +} while (0) + +/* Macros to avoid undefined behaviour that can arise if the amount + of a shift is exactly equal to the size of the shifted operand. */ + +#define SAFE_LEFT_SHIFT(op,amt) \ + (((amt) < 8 * sizeof(op)) ? ((op) << (amt)) : 0) + +#define SAFE_RIGHT_SHIFT(op,amt) \ + (((amt) < 8 * sizeof(op)) ? ((op) >> (amt)) : 0) + +#ifdef _COMPLEX_H + +/* + * Quoting from ISO/IEC 9899:TC2: + * + * 6.2.5.13 Types + * Each complex type has the same representation and alignment requirements as + * an array type containing exactly two elements of the corresponding real type; + * the first element is equal to the real part, and the second element to the + * imaginary part, of the complex number. + */ +typedef union { + float complex z; + float parts[2]; +} float_complex; + +typedef union { + double complex z; + double parts[2]; +} double_complex; + +typedef union { + long double complex z; + long double parts[2]; +} long_double_complex; + +#define REAL_PART(z) ((z).parts[0]) +#define IMAG_PART(z) ((z).parts[1]) + +#endif /* _COMPLEX_H */ + diff --git a/src/math/ieeefp.h b/src/math/ieeefp.h new file mode 100644 index 00000000..0b06fb78 --- /dev/null +++ b/src/math/ieeefp.h @@ -0,0 +1,256 @@ +#ifndef _IEEE_FP_H_ +#define _IEEE_FP_H_ + +#include "_ansi.h" + +#include + +_BEGIN_STD_C + +/* FIXME FIXME FIXME: + Neither of __ieee_{float,double}_shape_tape seem to be used anywhere + except in libm/test. If that is the case, please delete these from here. + If that is not the case, please insert documentation here describing why + they're needed. */ + +#ifdef __IEEE_BIG_ENDIAN + +typedef union +{ + double value; + struct + { + unsigned int sign : 1; + unsigned int exponent: 11; + unsigned int fraction0:4; + unsigned int fraction1:16; + unsigned int fraction2:16; + unsigned int fraction3:16; + + } number; + struct + { + unsigned int sign : 1; + unsigned int exponent: 11; + unsigned int quiet:1; + unsigned int function0:3; + unsigned int function1:16; + unsigned int function2:16; + unsigned int function3:16; + } nan; + struct + { + unsigned long msw; + unsigned long lsw; + } parts; + long aslong[2]; +} __ieee_double_shape_type; + +#endif + +#ifdef __IEEE_LITTLE_ENDIAN + +typedef union +{ + double value; + struct + { +#ifdef __SMALL_BITFIELDS + unsigned int fraction3:16; + unsigned int fraction2:16; + unsigned int fraction1:16; + unsigned int fraction0: 4; +#else + unsigned int fraction1:32; + unsigned int fraction0:20; +#endif + unsigned int exponent :11; + unsigned int sign : 1; + } number; + struct + { +#ifdef __SMALL_BITFIELDS + unsigned int function3:16; + unsigned int function2:16; + unsigned int function1:16; + unsigned int function0:3; +#else + unsigned int function1:32; + unsigned int function0:19; +#endif + unsigned int quiet:1; + unsigned int exponent: 11; + unsigned int sign : 1; + } nan; + struct + { + unsigned long lsw; + unsigned long msw; + } parts; + + long aslong[2]; + +} __ieee_double_shape_type; + +#endif + +#ifdef __IEEE_BIG_ENDIAN + +typedef union +{ + float value; + struct + { + unsigned int sign : 1; + unsigned int exponent: 8; + unsigned int fraction0: 7; + unsigned int fraction1: 16; + } number; + struct + { + unsigned int sign:1; + unsigned int exponent:8; + unsigned int quiet:1; + unsigned int function0:6; + unsigned int function1:16; + } nan; + long p1; + +} __ieee_float_shape_type; + +#endif + +#ifdef __IEEE_LITTLE_ENDIAN + +typedef union +{ + float value; + struct + { + unsigned int fraction0: 7; + unsigned int fraction1: 16; + unsigned int exponent: 8; + unsigned int sign : 1; + } number; + struct + { + unsigned int function1:16; + unsigned int function0:6; + unsigned int quiet:1; + unsigned int exponent:8; + unsigned int sign:1; + } nan; + long p1; + +} __ieee_float_shape_type; + +#endif + + + + + +/* FLOATING ROUNDING */ + +typedef int fp_rnd; +#define FP_RN 0 /* Round to nearest */ +#define FP_RM 1 /* Round down */ +#define FP_RP 2 /* Round up */ +#define FP_RZ 3 /* Round to zero (trunate) */ + +fp_rnd _EXFUN(fpgetround,(void)); +fp_rnd _EXFUN(fpsetround, (fp_rnd)); + +/* EXCEPTIONS */ + +typedef int fp_except; +#define FP_X_INV 0x10 /* Invalid operation */ +#define FP_X_DX 0x80 /* Divide by zero */ +#define FP_X_OFL 0x04 /* Overflow exception */ +#define FP_X_UFL 0x02 /* Underflow exception */ +#define FP_X_IMP 0x01 /* imprecise exception */ + +fp_except _EXFUN(fpgetmask,(void)); +fp_except _EXFUN(fpsetmask,(fp_except)); +fp_except _EXFUN(fpgetsticky,(void)); +fp_except _EXFUN(fpsetsticky, (fp_except)); + +/* INTEGER ROUNDING */ + +typedef int fp_rdi; +#define FP_RDI_TOZ 0 /* Round to Zero */ +#define FP_RDI_RD 1 /* Follow float mode */ + +fp_rdi _EXFUN(fpgetroundtoi,(void)); +fp_rdi _EXFUN(fpsetroundtoi,(fp_rdi)); + +#undef isnan +#undef isinf + +int _EXFUN(isnan, (double)); +int _EXFUN(isinf, (double)); +int _EXFUN(finite, (double)); + + + +int _EXFUN(isnanf, (float)); +int _EXFUN(isinff, (float)); +int _EXFUN(finitef, (float)); + +#define __IEEE_DBL_EXPBIAS 1023 +#define __IEEE_FLT_EXPBIAS 127 + +#define __IEEE_DBL_EXPLEN 11 +#define __IEEE_FLT_EXPLEN 8 + + +#define __IEEE_DBL_FRACLEN (64 - (__IEEE_DBL_EXPLEN + 1)) +#define __IEEE_FLT_FRACLEN (32 - (__IEEE_FLT_EXPLEN + 1)) + +#define __IEEE_DBL_MAXPOWTWO ((double)(1L << 32 - 2) * (1L << (32-11) - 32 + 1)) +#define __IEEE_FLT_MAXPOWTWO ((float)(1L << (32-8) - 1)) + +#define __IEEE_DBL_NAN_EXP 0x7ff +#define __IEEE_FLT_NAN_EXP 0xff + +#ifndef __ieeefp_isnanf +#define __ieeefp_isnanf(x) (((*(long *)&(x) & 0x7f800000L)==0x7f800000L) && \ + ((*(long *)&(x) & 0x007fffffL)!=0000000000L)) +#endif +#define isnanf(x) __ieeefp_isnanf(x) + +#ifndef __ieeefp_isinff +#define __ieeefp_isinff(x) (((*(long *)&(x) & 0x7f800000L)==0x7f800000L) && \ + ((*(long *)&(x) & 0x007fffffL)==0000000000L)) +#endif +#define isinff(x) __ieeefp_isinff(x) + +#ifndef __ieeefp_finitef +#define __ieeefp_finitef(x) (((*(long *)&(x) & 0x7f800000L)!=0x7f800000L)) +#endif +#define finitef(x) __ieeefp_finitef(x) + +#ifdef _DOUBLE_IS_32BITS +#undef __IEEE_DBL_EXPBIAS +#define __IEEE_DBL_EXPBIAS __IEEE_FLT_EXPBIAS + +#undef __IEEE_DBL_EXPLEN +#define __IEEE_DBL_EXPLEN __IEEE_FLT_EXPLEN + +#undef __IEEE_DBL_FRACLEN +#define __IEEE_DBL_FRACLEN __IEEE_FLT_FRACLEN + +#undef __IEEE_DBL_MAXPOWTWO +#define __IEEE_DBL_MAXPOWTWO __IEEE_FLT_MAXPOWTWO + +#undef __IEEE_DBL_NAN_EXP +#define __IEEE_DBL_NAN_EXP __IEEE_FLT_NAN_EXP + +#undef __ieee_double_shape_type +#define __ieee_double_shape_type __ieee_float_shape_type + +#endif /* _DOUBLE_IS_32BITS */ + +_END_STD_C + +#endif /* _IEEE_FP_H_ */ diff --git a/src/math/kf_cos.c b/src/math/kf_cos.c new file mode 100644 index 00000000..4f71af23 --- /dev/null +++ b/src/math/kf_cos.c @@ -0,0 +1,59 @@ +/* kf_cos.c -- float version of k_cos.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0000000000e+00, /* 0x3f800000 */ +C1 = 4.1666667908e-02, /* 0x3d2aaaab */ +C2 = -1.3888889225e-03, /* 0xbab60b61 */ +C3 = 2.4801587642e-05, /* 0x37d00d01 */ +C4 = -2.7557314297e-07, /* 0xb493f27c */ +C5 = 2.0875723372e-09, /* 0x310f74f6 */ +C6 = -1.1359647598e-11; /* 0xad47d74e */ + +#ifdef __STDC__ + float __kernel_cosf(float x, float y) +#else + float __kernel_cosf(x, y) + float x,y; +#endif +{ + float a,hz,z,r,qx; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x32000000) { /* 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 < 0x3e99999a) /* if |x| < 0.3 */ + return one - ((float)0.5*z - (z*r - x*y)); + else { + if(ix > 0x3f480000) { /* x > 0.78125 */ + qx = (float)0.28125; + } else { + SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */ + } + hz = (float)0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/src/math/kf_rem_pio2.c b/src/math/kf_rem_pio2.c new file mode 100644 index 00000000..261c4812 --- /dev/null +++ b/src/math/kf_rem_pio2.c @@ -0,0 +1,208 @@ +/* kf_rem_pio2.c -- float version of k_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "fdlibm.h" + +/* In the float version, the input parameter x contains 8 bit + integers, not 24 bit integers. 113 bit precision is not supported. */ + +#ifdef __STDC__ +static const int init_jk[] = {4,7,9}; /* initial value for jk */ +#else +static int init_jk[] = {4,7,9}; +#endif + +#ifdef __STDC__ +static const float PIo2[] = { +#else +static float PIo2[] = { +#endif + 1.5703125000e+00, /* 0x3fc90000 */ + 4.5776367188e-04, /* 0x39f00000 */ + 2.5987625122e-05, /* 0x37da0000 */ + 7.5437128544e-08, /* 0x33a20000 */ + 6.0026650317e-11, /* 0x2e840000 */ + 7.3896444519e-13, /* 0x2b500000 */ + 5.3845816694e-15, /* 0x27c20000 */ + 5.6378512969e-18, /* 0x22d00000 */ + 8.3009228831e-20, /* 0x1fc40000 */ + 3.2756352257e-22, /* 0x1bc60000 */ + 6.3331015649e-25, /* 0x17440000 */ +}; + +#ifdef __STDC__ +static const float +#else +static float +#endif +zero = 0.0, +one = 1.0, +two8 = 2.5600000000e+02, /* 0x43800000 */ +twon8 = 3.9062500000e-03; /* 0x3b800000 */ + +#ifdef __STDC__ + int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2) +#else + int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) + float x[], y[]; int e0,nx,prec; __int32_t ipio2[]; +#endif +{ + __int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + float z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/8; if(jv<0) jv=0; + q0 = e0-8*(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 : (float) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + 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: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (float)((__int32_t)(twon8* z)); + iq[i] = (__int32_t)(z-two8*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbnf(z,(int)q0); /* actual value of z */ + z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ + n = (__int32_t) z; + z -= (float)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(8-q0)); n += i; + iq[jz-1] -= i<<(8-q0); + ih = iq[jz-1]>>(7-q0); + } + else if(q0==0) ih = iq[jz-1]>>8; + else if(z>=(float)0.5) ih=2; + + 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] &= 0x7f; break; + case 2: + iq[jz-1] &= 0x3f; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbnf(one,(int)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 */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (float) 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==(float)0.0) { + jz -= 1; q0 -= 8; + while(iq[jz]==0) { jz--; q0-=8;} + } else { /* break z into 8-bit if necessary */ + z = scalbnf(z,-(int)q0); + if(z>=two8) { + fw = (float)((__int32_t)(twon8*z)); + iq[jz] = (__int32_t)(z-two8*fw); + jz += 1; q0 += 8; + iq[jz] = (__int32_t) fw; + } else iq[jz] = (__int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbnf(one,(int)q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(float)iq[i]; fw*=twon8; + } + + /* 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; + } + + /* 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; +} diff --git a/src/math/kf_sin.c b/src/math/kf_sin.c new file mode 100644 index 00000000..e81fa0bd --- /dev/null +++ b/src/math/kf_sin.c @@ -0,0 +1,49 @@ +/* kf_sin.c -- float version of k_sin.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float +#else +static float +#endif +half = 5.0000000000e-01,/* 0x3f000000 */ +S1 = -1.6666667163e-01, /* 0xbe2aaaab */ +S2 = 8.3333337680e-03, /* 0x3c088889 */ +S3 = -1.9841270114e-04, /* 0xb9500d01 */ +S4 = 2.7557314297e-06, /* 0x3638ef1b */ +S5 = -2.5050759689e-08, /* 0xb2d72f34 */ +S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ + +#ifdef __STDC__ + float __kernel_sinf(float x, float y, int iy) +#else + float __kernel_sinf(x, y, iy) + float x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + float z,r,v; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x32000000) /* |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/math/machine/ieeefp.h b/src/math/machine/ieeefp.h new file mode 100644 index 00000000..fffa3804 --- /dev/null +++ b/src/math/machine/ieeefp.h @@ -0,0 +1,382 @@ +#ifndef __IEEE_BIG_ENDIAN +#ifndef __IEEE_LITTLE_ENDIAN + +/* This file can define macros to choose variations of the IEEE float + format: + + _FLT_LARGEST_EXPONENT_IS_NORMAL + + Defined if the float format uses the largest exponent for finite + numbers rather than NaN and infinity representations. Such a + format cannot represent NaNs or infinities at all, but it's FLT_MAX + is twice the IEEE value. + + _FLT_NO_DENORMALS + + Defined if the float format does not support IEEE denormals. Every + float with a zero exponent is taken to be a zero representation. + + ??? At the moment, there are no equivalent macros above for doubles and + the macros are not fully supported by --enable-newlib-hw-fp. + + __IEEE_BIG_ENDIAN + + Defined if the float format is big endian. This is mutually exclusive + with __IEEE_LITTLE_ENDIAN. + + __IEEE_LITTLE_ENDIAN + + Defined if the float format is little endian. This is mutually exclusive + with __IEEE_BIG_ENDIAN. + + Note that one of __IEEE_BIG_ENDIAN or __IEEE_LITTLE_ENDIAN must be specified for a + platform or error will occur. + + __IEEE_BYTES_LITTLE_ENDIAN + + This flag is used in conjunction with __IEEE_BIG_ENDIAN to describe a situation + whereby multiple words of an IEEE floating point are in big endian order, but the + words themselves are little endian with respect to the bytes. + + _DOUBLE_IS_32BITS + + This is used on platforms that support double by using the 32-bit IEEE + float type. + + _FLOAT_ARG + + This represents what type a float arg is passed as. It is used when the type is + not promoted to double. + +*/ + +#if (defined(__arm__) || defined(__thumb__)) && !defined(__MAVERICK__) +/* ARM traditionally used big-endian words; and within those words the + byte ordering was big or little endian depending upon the target. + Modern floating-point formats are naturally ordered; in this case + __VFP_FP__ will be defined, even if soft-float. */ +#ifdef __VFP_FP__ +# ifdef __ARMEL__ +# define __IEEE_LITTLE_ENDIAN +# else +# define __IEEE_BIG_ENDIAN +# endif +#else +# define __IEEE_BIG_ENDIAN +# ifdef __ARMEL__ +# define __IEEE_BYTES_LITTLE_ENDIAN +# endif +#endif +#endif + +#ifdef __hppa__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __SPU__ +#define __IEEE_BIG_ENDIAN + +#define isfinite(__y) \ + (__extension__ ({int __cy; \ + (sizeof (__y) == sizeof (float)) ? (1) : \ + (__cy = fpclassify(__y)) != FP_INFINITE && __cy != FP_NAN;})) + +#define isinf(__x) ((sizeof (__x) == sizeof (float)) ? (0) : __isinfd(__x)) +#define isnan(__x) ((sizeof (__x) == sizeof (float)) ? (0) : __isnand(__x)) + +/* + * Macros for use in ieeefp.h. We can't just define the real ones here + * (like those above) as we have name space issues when this is *not* + * included via generic the ieeefp.h. + */ +#define __ieeefp_isnanf(x) 0 +#define __ieeefp_isinff(x) 0 +#define __ieeefp_finitef(x) 1 +#endif + +#ifdef __sparc__ +#ifdef __LITTLE_ENDIAN_DATA__ +#define __IEEE_LITTLE_ENDIAN +#else +#define __IEEE_BIG_ENDIAN +#endif +#endif + +#if defined(__m68k__) || defined(__mc68000__) +#define __IEEE_BIG_ENDIAN +#endif + +#if defined(__mc68hc11__) || defined(__mc68hc12__) || defined(__mc68hc1x__) +#define __IEEE_BIG_ENDIAN +#ifdef __HAVE_SHORT_DOUBLE__ +# define _DOUBLE_IS_32BITS +#endif +#endif + +#if defined (__H8300__) || defined (__H8300H__) || defined (__H8300S__) || defined (__H8500__) || defined (__H8300SX__) +#define __IEEE_BIG_ENDIAN +#define _FLOAT_ARG float +#define _DOUBLE_IS_32BITS +#endif + +#if defined (__xc16x__) || defined (__xc16xL__) || defined (__xc16xS__) +#define __IEEE_LITTLE_ENDIAN +#define _FLOAT_ARG float +#define _DOUBLE_IS_32BITS +#endif + + +#ifdef __sh__ +#ifdef __LITTLE_ENDIAN__ +#define __IEEE_LITTLE_ENDIAN +#else +#define __IEEE_BIG_ENDIAN +#endif +#if defined(__SH2E__) || defined(__SH3E__) || defined(__SH4_SINGLE_ONLY__) || defined(__SH2A_SINGLE_ONLY__) +#define _DOUBLE_IS_32BITS +#endif +#endif + +#ifdef _AM29K +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef _WIN32 +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __i386__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __i960__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __lm32__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __M32R__ +#define __IEEE_BIG_ENDIAN +#endif + +#if defined(_C4x) || defined(_C3x) +#define __IEEE_BIG_ENDIAN +#define _DOUBLE_IS_32BITS +#endif + +#ifdef __TMS320C6X__ +#ifdef _BIG_ENDIAN +#define __IEEE_BIG_ENDIAN +#else +#define __IEEE_LITTLE_ENDIAN +#endif +#endif + +#ifdef __TIC80__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __MIPSEL__ +#define __IEEE_LITTLE_ENDIAN +#endif +#ifdef __MIPSEB__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __MMIX__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __D30V__ +#define __IEEE_BIG_ENDIAN +#endif + +/* necv70 was __IEEE_LITTLE_ENDIAN. */ + +#ifdef __W65__ +#define __IEEE_LITTLE_ENDIAN +#define _DOUBLE_IS_32BITS +#endif + +#if defined(__Z8001__) || defined(__Z8002__) +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __m88k__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __mn10300__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __mn10200__ +#define __IEEE_LITTLE_ENDIAN +#define _DOUBLE_IS_32BITS +#endif + +#ifdef __v800 +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __v850 +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __D10V__ +#define __IEEE_BIG_ENDIAN +#if __DOUBLE__ == 32 +#define _DOUBLE_IS_32BITS +#endif +#endif + +#ifdef __PPC__ +#if (defined(_BIG_ENDIAN) && _BIG_ENDIAN) || (defined(_AIX) && _AIX) +#define __IEEE_BIG_ENDIAN +#else +#if (defined(_LITTLE_ENDIAN) && _LITTLE_ENDIAN) || (defined(__sun__) && __sun__) || (defined(_WIN32) && _WIN32) +#define __IEEE_LITTLE_ENDIAN +#endif +#endif +#endif + +#ifdef __xstormy16__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __arc__ +#ifdef __big_endian__ +#define __IEEE_BIG_ENDIAN +#else +#define __IEEE_LITTLE_ENDIAN +#endif +#endif + +#ifdef __CRX__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __fr30__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __mcore__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __mt__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __frv__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __moxie__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __ia64__ +#ifdef __BIG_ENDIAN__ +#define __IEEE_BIG_ENDIAN +#else +#define __IEEE_LITTLE_ENDIAN +#endif +#endif + +#ifdef __AVR__ +#define __IEEE_LITTLE_ENDIAN +#define _DOUBLE_IS_32BITS +#endif + +#if defined(__or32__) || defined(__or1k__) || defined(__or16__) +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __IP2K__ +#define __IEEE_BIG_ENDIAN +#define __SMALL_BITFIELDS +#define _DOUBLE_IS_32BITS +#endif + +#ifdef __iq2000__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __MAVERICK__ +#ifdef __ARMEL__ +# define __IEEE_LITTLE_ENDIAN +#else /* must be __ARMEB__ */ +# define __IEEE_BIG_ENDIAN +#endif /* __ARMEL__ */ +#endif /* __MAVERICK__ */ + +#ifdef __m32c__ +#define __IEEE_LITTLE_ENDIAN +#define __SMALL_BITFIELDS +#endif + +#ifdef __CRIS__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __BFIN__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __x86_64__ +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifdef __mep__ +#ifdef __LITTLE_ENDIAN__ +#define __IEEE_LITTLE_ENDIAN +#else +#define __IEEE_BIG_ENDIAN +#endif +#endif + +#ifdef __MICROBLAZE__ +#define __IEEE_BIG_ENDIAN +#endif + +#ifdef __RL78__ +#define __IEEE_LITTLE_ENDIAN +#define __SMALL_BITFIELDS /* 16 Bit INT */ +#define _DOUBLE_IS_32BITS +#endif + +#ifdef __RX__ + +#ifdef __RX_BIG_ENDIAN__ +#define __IEEE_BIG_ENDIAN +#else +#define __IEEE_LITTLE_ENDIAN +#endif + +#ifndef __RX_64BIT_DOUBLES__ +#define _DOUBLE_IS_32BITS +#endif + +#ifdef __RX_16BIT_INTS__ +#define __SMALL_BITFIELDS +#endif + +#endif + +#if (defined(__CR16__) || defined(__CR16C__) ||defined(__CR16CP__)) +#define __IEEE_LITTLE_ENDIAN +#define __SMALL_BITFIELDS /* 16 Bit INT */ +#endif + +#ifndef __IEEE_BIG_ENDIAN +#ifndef __IEEE_LITTLE_ENDIAN +#error Endianess not declared!! +#endif /* not __IEEE_LITTLE_ENDIAN */ +#endif /* not __IEEE_BIG_ENDIAN */ + +#endif /* not __IEEE_LITTLE_ENDIAN */ +#endif /* not __IEEE_BIG_ENDIAN */ + diff --git a/src/math/math.h b/src/math/math.h new file mode 100644 index 00000000..c62f583d --- /dev/null +++ b/src/math/math.h @@ -0,0 +1,35 @@ +/* + * Copyright © 2013 Keith Packard + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation; version 2 of the License. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License along + * with this program; if not, write to the Free Software Foundation, Inc., + * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA. + */ + +#ifndef _MATH_H_ +#define _MATH_H_ + +float acosf(float x); + +float cosf(float x); + +float sqrtf(float x); + +float fabsf(float x); + +float floorf(float x); + +float scalbnf(float x, int n); + +float copysignf(float x, float y); + +#endif diff --git a/src/math/sf_copysign.c b/src/math/sf_copysign.c new file mode 100644 index 00000000..f547c82e --- /dev/null +++ b/src/math/sf_copysign.c @@ -0,0 +1,50 @@ +/* sf_copysign.c -- float version of s_copysign.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * copysignf(float x, float y) + * copysignf(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + float copysignf(float x, float y) +#else + float copysignf(x,y) + float x,y; +#endif +{ + __uint32_t ix,iy; + GET_FLOAT_WORD(ix,x); + GET_FLOAT_WORD(iy,y); + SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000)); + return x; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double copysign(double x, double y) +#else + double copysign(x,y) + double x,y; +#endif +{ + return (double) copysignf((float) x, (float) y); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/src/math/sf_cos.c b/src/math/sf_cos.c new file mode 100644 index 00000000..4c0a9a53 --- /dev/null +++ b/src/math/sf_cos.c @@ -0,0 +1,68 @@ +/* sf_cos.c -- float version of s_cos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float one=1.0; +#else +static float one=1.0; +#endif + +#ifdef __STDC__ + float cosf(float x) +#else + float cosf(x) + float x; +#endif +{ + float y[2],z=0.0; + __int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_cosf(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (!FLT_UWORD_IS_FINITE(ix)) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_cosf(y[0],y[1]); + case 1: return -__kernel_sinf(y[0],y[1],1); + case 2: return -__kernel_cosf(y[0],y[1]); + default: + return __kernel_sinf(y[0],y[1],1); + } + } +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double cos(double x) +#else + double cos(x) + double x; +#endif +{ + return (double) cosf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/src/math/sf_fabs.c b/src/math/sf_fabs.c new file mode 100644 index 00000000..2aaed326 --- /dev/null +++ b/src/math/sf_fabs.c @@ -0,0 +1,47 @@ +/* sf_fabs.c -- float version of s_fabs.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + float fabsf(float x) +#else + float fabsf(x) + float x; +#endif +{ + __uint32_t ix; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x7fffffff); + return x; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double fabs(double x) +#else + double fabs(x) + double x; +#endif +{ + return (double) fabsf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/src/math/sf_floor.c b/src/math/sf_floor.c new file mode 100644 index 00000000..9264d81e --- /dev/null +++ b/src/math/sf_floor.c @@ -0,0 +1,80 @@ +/* sf_floor.c -- float version of s_floor.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorf(x). + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float huge = 1.0e30; +#else +static float huge = 1.0e30; +#endif + +#ifdef __STDC__ + float floorf(float x) +#else + float floorf(x) + float x; +#endif +{ + __int32_t i0,j0; + __uint32_t i,ix; + GET_FLOAT_WORD(i0,x); + ix = (i0&0x7fffffff); + j0 = (ix>>23)-0x7f; + 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;} + else if(!FLT_UWORD_IS_ZERO(ix)) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(!FLT_UWORD_IS_FINITE(ix)) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double floor(double x) +#else + double floor(x) + double x; +#endif +{ + return (double) floorf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/src/math/sf_scalbn.c b/src/math/sf_scalbn.c new file mode 100644 index 00000000..70006001 --- /dev/null +++ b/src/math/sf_scalbn.c @@ -0,0 +1,86 @@ +/* sf_scalbn.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "fdlibm.h" +#include +#include + +#if INT_MAX > 50000 +#define OVERFLOW_INT 50000 +#else +#define OVERFLOW_INT 30000 +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +#ifdef __STDC__ + float scalbnf (float x, int n) +#else + float scalbnf (x,n) + float x; int n; +#endif +{ + __int32_t k,ix; + __uint32_t hx; + + GET_FLOAT_WORD(ix,x); + hx = ix&0x7fffffff; + k = hx>>23; /* extract exponent */ + if (FLT_UWORD_IS_ZERO(hx)) + return x; + if (!FLT_UWORD_IS_FINITE(hx)) + return x+x; /* NaN or Inf */ + if (FLT_UWORD_IS_SUBNORMAL(hx)) { + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + if (n< -50000) return tiny*x; /*underflow*/ + } + k = k+n; + if (k > FLT_LARGEST_EXP) return huge*copysignf(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k < FLT_SMALLEST_EXP) { + if (n > OVERFLOW_INT) /* in case integer overflow in n+k */ + return huge*copysignf(huge,x); /*overflow*/ + else return tiny*copysignf(tiny,x); /*underflow*/ + } + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double scalbn(double x, int n) +#else + double scalbn(x,n) + double x; + int n; +#endif +{ + return (double) scalbnf((float) x, n); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */