commit 1697016838bf4acd4423f9d4b50733de889f7d93 Author: Thibaud Date: Wed Sep 16 17:43:19 2026 +0200 Initial commit diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..19e1bce --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +*.wasm diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..fbbeb7b --- /dev/null +++ b/Makefile @@ -0,0 +1,29 @@ +CFLAGS := \ + --target=wasm32 \ + -O2 \ + -flto \ + -ffreestanding \ + -fno-builtin \ + -nostdlib + +EXPORTS := \ + init \ + get_buffer_ptr \ + get_buffer_len \ + render_frame + +comma := , + +LDFLAGS := -Wl,--no-entry -Wl,--lto-O2 +# comment the line below to fail on undefined symbols at link-time instead of runtime +#LDFLAGS += -Wl,--allow-undefined +LDFLAGS += $(addprefix -Wl$(comma)--export=,$(EXPORTS)) + +FDLIBM_SRC := \ + fdlibm/k_cos.c fdlibm/s_cos.c \ + fdlibm/k_sin.c fdlibm/s_sin.c \ + fdlibm/k_rem_pio2.c fdlibm/e_rem_pio2.c \ + fdlibm/s_scalbn.c + +main.wasm: main.c math.c $(FDLIBM_SRC) + clang $(CFLAGS) $(LDFLAGS) -o $@ $^ diff --git a/README.md b/README.md new file mode 100644 index 0000000..a353a90 --- /dev/null +++ b/README.md @@ -0,0 +1,5 @@ +# wasm-test + +Minimal WebAssembly canvas demo written in C. + +Build with `make`, then serve this directory over HTTP and open `index.html`. \ No newline at end of file diff --git a/fdlibm/e_rem_pio2.c b/fdlibm/e_rem_pio2.c new file mode 100644 index 0000000..7242bb2 --- /dev/null +++ b/fdlibm/e_rem_pio2.c @@ -0,0 +1,175 @@ + +/* @(#)e_rem_pio2.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, 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_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include "fdlibm.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +#ifdef __STDC__ +static const int two_over_pi[] = { +#else +static int 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, +}; + +#ifdef __STDC__ +static const int npio2_hw[] = { +#else +static int 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, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * 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 */ + +#ifdef __STDC__ + int __ieee754_rem_pio2(double x, double *y) +#else + int __ieee754_rem_pio2(x,y) + double x,y[]; +#endif +{ + double z,w,t,r,fn; + double tx[3]; + int e0,i,j,nx,n,ix,hx; + + hx = __HI(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 = (int) (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 { + j = ix>>20; + y[0] = r-w; + i = j-(((__HI(y[0]))>>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; + i = j-(((__HI(y[0]))>>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; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + __LO(z) = __LO(x); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + __HI(z) = ix - (e0<<20); + for(i=0;i<2;i++) { + tx[i] = (double)((int)(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/fdlibm/fdlibm.h b/fdlibm/fdlibm.h new file mode 100644 index 0000000..084e91e --- /dev/null +++ b/fdlibm/fdlibm.h @@ -0,0 +1,216 @@ +#pragma once +/* @(#)fdlibm.h 1.5 04/04/22 */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Sometimes it's necessary to define __LITTLE_ENDIAN explicitly + but these catch some common cases. */ + +#if defined(__wasm__) || defined(i386) || defined(i486) || \ + defined(intel) || defined(x86) || defined(i86pc) || \ + defined(__alpha) || defined(__osf__) +#define __LITTLE_ENDIAN +#endif + +#ifdef __LITTLE_ENDIAN +#define __HI(x) *(1+(int*)&x) +#define __LO(x) *(int*)&x +#define __HIp(x) *(1+(int*)x) +#define __LOp(x) *(int*)x +#else +#define __HI(x) *(int*)&x +#define __LO(x) *(1+(int*)&x) +#define __HIp(x) *(int*)x +#define __LOp(x) *(1+(int*)x) +#endif + +#ifdef __STDC__ +#define __P(p) p +#else +#define __P(p) () +#endif + +/* + * ANSI/POSIX + */ + +extern int signgam; + +#define MAXFLOAT ((float)3.40282346638528860e+38) + +enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix}; + +#define _LIB_VERSION_TYPE enum fdversion +#define _LIB_VERSION _fdlib_version + +/* if global variable _LIB_VERSION is not desirable, one may + * change the following to be a constant by: + * #define _LIB_VERSION_TYPE const enum version + * In that case, after one initializes the value _LIB_VERSION (see + * s_lib_version.c) during compile time, it cannot be modified + * in the middle of a program + */ +extern _LIB_VERSION_TYPE _LIB_VERSION; + +#define _IEEE_ fdlibm_ieee +#define _SVID_ fdlibm_svid +#define _XOPEN_ fdlibm_xopen +#define _POSIX_ fdlibm_posix + +struct exception { + int type; + char *name; + double arg1; + double arg2; + double retval; +}; + +#define HUGE MAXFLOAT + +/* + * 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 + +#define DOMAIN 1 +#define SING 2 +#define OVERFLOW 3 +#define UNDERFLOW 4 +#define TLOSS 5 +#define PLOSS 6 + +/* + * ANSI/POSIX + */ +extern double acos __P((double)); +extern double asin __P((double)); +extern double atan __P((double)); +extern double atan2 __P((double, double)); +extern double cos __P((double)); +extern double sin __P((double)); +extern double tan __P((double)); + +extern double cosh __P((double)); +extern double sinh __P((double)); +extern double tanh __P((double)); + +extern double exp __P((double)); +extern double frexp __P((double, int *)); +extern double ldexp __P((double, int)); +extern double log __P((double)); +extern double log10 __P((double)); +extern double modf __P((double, double *)); + +extern double pow __P((double, double)); +extern double sqrt __P((double)); + +extern double ceil __P((double)); +extern double fabs __P((double)); +extern double floor __P((double)); +extern double fmod __P((double, double)); + +extern double erf __P((double)); +extern double erfc __P((double)); +extern double gamma __P((double)); +extern double hypot __P((double, double)); +extern int isnan __P((double)); +extern int finite __P((double)); +extern double j0 __P((double)); +extern double j1 __P((double)); +extern double jn __P((int, double)); +extern double lgamma __P((double)); +extern double y0 __P((double)); +extern double y1 __P((double)); +extern double yn __P((int, double)); + +extern double acosh __P((double)); +extern double asinh __P((double)); +extern double atanh __P((double)); +extern double cbrt __P((double)); +extern double logb __P((double)); +extern double nextafter __P((double, double)); +extern double remainder __P((double, double)); +#ifdef _SCALB_INT +extern double scalb __P((double, int)); +#else +extern double scalb __P((double, double)); +#endif + +extern int matherr __P((struct exception *)); + +/* + * IEEE Test Vector + */ +extern double significand __P((double)); + +/* + * Functions callable from C, intended to support IEEE arithmetic. + */ +extern double copysign __P((double, double)); +extern int ilogb __P((double)); +extern double rint __P((double)); +extern double scalbn __P((double, int)); + +/* + * BSD math library entry points + */ +extern double expm1 __P((double)); +extern double log1p __P((double)); + +/* + * Reentrant version of gamma & lgamma; passes signgam back by reference + * as the second argument; user must allocate space for signgam. + */ +#ifdef _REENTRANT +extern double gamma_r __P((double, int *)); +extern double lgamma_r __P((double, int *)); +#endif /* _REENTRANT */ + +/* 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_lgamma __P((double)); +extern double __ieee754_gamma __P((double)); +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 int __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 int*)); diff --git a/fdlibm/k_cos.c b/fdlibm/k_cos.c new file mode 100644 index 0000000..7fb855d --- /dev/null +++ b/fdlibm/k_cos.c @@ -0,0 +1,92 @@ + +/* @(#)k_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy when x > 0.3, let qx = |x|/4 with + * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. + * Then + * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). + * Note that 1-qx and (x*x/2-qx) is EXACT here, and the + * magnitude of the latter is at least a quarter of x*x/2, + * thus, reducing the rounding error in the subtraction. + */ + +#include "fdlibm.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 */ + +#ifdef __STDC__ + double __kernel_cos(double x, double y) +#else + double __kernel_cos(x, y) + double x,y; +#endif +{ + double a,hz,z,r,qx; + int ix; + ix = __HI(x)&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 { + __HI(qx) = ix-0x00200000; /* x/4 */ + __LO(qx) = 0; + } + hz = 0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/fdlibm/k_rem_pio2.c b/fdlibm/k_rem_pio2.c new file mode 100644 index 0000000..ec473ac --- /dev/null +++ b/fdlibm/k_rem_pio2.c @@ -0,0 +1,316 @@ + +/* @(#)k_rem_pio2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precison, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "fdlibm.h" + +#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 */ +}; + +#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 */ + +#ifdef __STDC__ + int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) +#else + int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + double x[], y[]; int e0,nx,prec; int ipio2[]; +#endif +{ + int 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*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + 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]; + + /* 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 = (double)((int)(twon24* z)); + iq[i] = (int)(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 = (int) 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;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 */ + + 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)((int)(twon24*z)); + iq[jz] = (int)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int) fw; + } else iq[jz] = (int) 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; + } + + /* 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/fdlibm/k_sin.c b/fdlibm/k_sin.c new file mode 100644 index 0000000..dfcad76 --- /dev/null +++ b/fdlibm/k_sin.c @@ -0,0 +1,74 @@ + +/* @(#)k_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __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. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "fdlibm.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 */ + +#ifdef __STDC__ + double __kernel_sin(double x, double y, int iy) +#else + double __kernel_sin(x, y, iy) + double x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + double z,r,v; + int ix; + ix = __HI(x)&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/fdlibm/readme b/fdlibm/readme new file mode 100644 index 0000000..590b894 --- /dev/null +++ b/fdlibm/readme @@ -0,0 +1,12 @@ +clang --target=wasm32 -O2 -ffreestanding -fno-builtin -nostdlib -Wl,--no-entry -Wl,--export=sin -Wl,--export=cos -o fdlibm.wasm \ + s_sin.c s_cos.c k_sin.c k_cos.c e_rem_pio2.c k_rem_pio2.c s_scalbn.c + +define __LITTLE_ENDIAN for wasm +must provide implementation for the functions below + +# wasm-ld-21: error: /tmp/e_rem_pio2-14e979.o: undefined symbol: fabs +# wasm-ld-21: error: /tmp/k_rem_pio2-6d7f33.o: undefined symbol: floor +# wasm-ld-21: error: /tmp/s_scalbn-8b4ff9.o: undefined symbol: copysign +# wasm-ld-21: error: /tmp/s_scalbn-8b4ff9.o: undefined symbol: copysign +# wasm-ld-21: error: /tmp/s_scalbn-8b4ff9.o: undefined symbol: copysign +# clang: error: linker command failed with exit code 1 (use -v to see invocation) diff --git a/fdlibm/s_cos.c b/fdlibm/s_cos.c new file mode 100644 index 0000000..3bab516 --- /dev/null +++ b/fdlibm/s_cos.c @@ -0,0 +1,78 @@ + +/* @(#)s_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double cos(double x) +#else + double cos(x) + double x; +#endif +{ + double y[2],z=0.0; + int n, ix; + + /* High word of x. */ + ix = __HI(x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_cos(x,z); + + /* cos(Inf or NaN) is NaN */ + 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); + } + } +} diff --git a/fdlibm/s_scalbn.c b/fdlibm/s_scalbn.c new file mode 100644 index 0000000..b457500 --- /dev/null +++ b/fdlibm/s_scalbn.c @@ -0,0 +1,72 @@ + +/* @(#)s_scalbn.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif + two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ + twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ + huge = 1.0e+300, tiny = 1.0e-300; + +#ifdef __STDC__ +double scalbn(double x, int n) +#else +double scalbn(x, n) +double x; +int n; +#endif +{ + int k, hx, lx; + hx = __HI(x); + lx = __LO(x); + k = (hx & 0x7ff00000) >> 20; /* extract exponent */ + if (k == 0) { /* 0 or subnormal x */ + if ((lx | (hx & 0x7fffffff)) == 0) + return x; /* +-0 */ + x *= two54; + hx = __HI(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 * copysign(huge, x); /* overflow */ + if (k > 0) /* normal result */ + { + __HI(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*/ + else + return tiny * copysign(tiny, x); /*underflow*/ + } + k += 54; /* subnormal result */ + __HI(x) = (hx & 0x800fffff) | (k << 20); + return x * twom54; +} diff --git a/fdlibm/s_sin.c b/fdlibm/s_sin.c new file mode 100644 index 0000000..43394e5 --- /dev/null +++ b/fdlibm/s_sin.c @@ -0,0 +1,78 @@ + +/* @(#)s_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double sin(double x) +#else + double sin(x) + double x; +#endif +{ + double y[2],z=0.0; + int n, ix; + + /* High word of x. */ + ix = __HI(x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); + + /* sin(Inf or NaN) is NaN */ + 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]); + } + } +} diff --git a/index.html b/index.html new file mode 100644 index 0000000..8259be4 --- /dev/null +++ b/index.html @@ -0,0 +1,39 @@ + + + + + + Test + + + +
+ +
+ + + diff --git a/main.c b/main.c new file mode 100644 index 0000000..6df0527 --- /dev/null +++ b/main.c @@ -0,0 +1,68 @@ +#include "math.h" + +#define HEIGHT 600 +#define WIDTH 800 +#define SQ_SIZE 100 + +typedef struct { double x, y; } Vec2d; +typedef struct { unsigned char r, g, b, a; } Color; + +Color gradient[SQ_SIZE*SQ_SIZE] = {0}; +Color buffer[WIDTH*HEIGHT] = {0}; +Vec2d pos = {0}; +double time = 0; + +Color* get_buffer_ptr() { + return buffer; +} + +int get_buffer_len() { + return WIDTH*HEIGHT; +} + +void compute_gradient(Color* output_buffer, int width, int height) { + for (int y = 0; y < height; y++) { + for (int x = 0; x < width; x++) { + output_buffer[y*width+x] = (Color){ + .r = (x * 255) / (width - 1), + .g = (y * 255) / (height - 1), + .b = 0, + .a = 255 + }; + } + } +} + +void init() { + compute_gradient(gradient, SQ_SIZE, SQ_SIZE); +} + +void render_frame(double dt) { + time += dt; + double x = 0.5 + __builtin_cos(2.0 * PI / 10.0 * time) * 0.5; + double y = 0.5 + __builtin_sin(2.0 * PI / 10.0 * time) * 0.5; + pos.x = x * (WIDTH - SQ_SIZE); + pos.y = y * (HEIGHT - SQ_SIZE); + + // Clear the framebuffer before drawing the next frame. + __builtin_memset(buffer, 0, sizeof(buffer)); + + // Clamp coordinates before indexing the framebuffer to avoid a bad + // coordinate from turning into an out-of-bounds write. + int pos_x = (int)pos.x; + int pos_y = (int)pos.y; + if (pos_x < 0) pos_x = 0; + if (pos_y < 0) pos_y = 0; + if (pos_x > WIDTH - SQ_SIZE) pos_x = WIDTH - SQ_SIZE; + if (pos_y > HEIGHT - SQ_SIZE) pos_y = HEIGHT - SQ_SIZE; + + for (int y = pos_y; y < pos_y + SQ_SIZE; ++y) { + for (int x = pos_x; x < pos_x + SQ_SIZE; ++x) { + // Sample point from gradient + int local_x = x - pos_x; + int local_y = y - pos_y; + Color c = gradient[local_y * SQ_SIZE + local_x]; + buffer[y * WIDTH + x] = c; + } + } +} diff --git a/main.js b/main.js new file mode 100644 index 0000000..b3e086b --- /dev/null +++ b/main.js @@ -0,0 +1,58 @@ +// Fill the environment with js functions we want to expose to the wasm module. +// since we compile with -Wl,--allow-undefined, the linked does not complain +// about undefined symbols. So we use make_environment to resolve from env below +// and fail at runtime if a symbol is not found. +function make_environment(...envs) { + return new Proxy(envs, { + get(_target, prop, _receiver) { + for (let env of envs) { + if (env.hasOwnProperty(prop)) { + return env[prop]; + } + } + return (...args) => { + throw "NOT IMPLEMENTED: " + prop + " " + args + ""; + } + } + }); +} + +async function init() { + const WIDTH = 800; + const HEIGHT = 600; + const { instance } = await WebAssembly.instantiateStreaming(fetch("./main.wasm"), { + env: make_environment({}) + }); + const canvas = document.getElementById("canvas"); + const ctx = canvas.getContext("2d"); + canvas.width = WIDTH; + canvas.height = HEIGHT; + + // Fill the gradient before the first frame is displayed. + instance.exports.init(); + + const ptr = instance.exports.get_buffer_ptr(); + const len = instance.exports.get_buffer_len(); + const image = new ImageData( + new Uint8ClampedArray( + instance.exports.memory.buffer, + ptr, + len * 4, + ), + WIDTH, + ); + + let previousTimestamp; + const render = (timestamp) => { + const dt = previousTimestamp === undefined + ? 0 + : Math.min((timestamp - previousTimestamp) / 1000, 0.05); + previousTimestamp = timestamp; + instance.exports.render_frame(dt); + ctx.putImageData(image, 0, 0); + window.requestAnimationFrame(render); + }; + + window.requestAnimationFrame(render); +} +init(); diff --git a/math.c b/math.c new file mode 100644 index 0000000..d76499a --- /dev/null +++ b/math.c @@ -0,0 +1,6 @@ +#include "math.h" + +// Definition of math functions needed for fdlibm +inline double fabs(double x) { return __builtin_fabs(x); } +inline double floor(double x) { return __builtin_floor(x); } +inline double copysign(double x, double y) { return __builtin_copysign(x, y); } diff --git a/math.h b/math.h new file mode 100644 index 0000000..49f8507 --- /dev/null +++ b/math.h @@ -0,0 +1,10 @@ +#pragma once + +#define PI 3.14159265358979323846 + +double fabs(double x); +double floor(double x); +double copysign(double x, double y); +// Provided by fdlibm +double cos(double x); +double sin(double x);