From b792476d36d510fa2824a4cc29a66d2d3e29cf4e Mon Sep 17 00:00:00 2001 From: Ben Visness Date: Wed, 28 Jun 2023 20:43:52 -0500 Subject: [PATCH] We can render text! --- cstdlib/include/bits/float.h | 16 ++ cstdlib/include/float.h | 52 ++++++ cstdlib/include/math.h | 61 +++++++ cstdlib/include/stdio.h | 13 ++ cstdlib/include/stdlib.h | 13 ++ cstdlib/src/acos.c | 101 +++++++++++ cstdlib/src/ceil.c | 31 ++++ cstdlib/src/floor.c | 31 ++++ cstdlib/src/fmod.c | 68 ++++++++ cstdlib/src/libm.h | 73 ++++++++ cstdlib/src/sqrt.c | 158 ++++++++++++++++++ cstdlib/src/sqrt_data.c | 19 +++ cstdlib/src/sqrt_data.h | 13 ++ samples/pong/data/Literata-SemiBoldItalic.ttf | Bin 0 -> 317648 bytes samples/pong/src/main.c | 33 ++++ 15 files changed, 682 insertions(+) create mode 100644 cstdlib/include/bits/float.h create mode 100644 cstdlib/include/float.h create mode 100644 cstdlib/src/acos.c create mode 100644 cstdlib/src/ceil.c create mode 100644 cstdlib/src/floor.c create mode 100644 cstdlib/src/fmod.c create mode 100644 cstdlib/src/sqrt.c create mode 100644 cstdlib/src/sqrt_data.c create mode 100644 cstdlib/src/sqrt_data.h create mode 100644 samples/pong/data/Literata-SemiBoldItalic.ttf diff --git a/cstdlib/include/bits/float.h b/cstdlib/include/bits/float.h new file mode 100644 index 0000000..c4a655e --- /dev/null +++ b/cstdlib/include/bits/float.h @@ -0,0 +1,16 @@ +#define FLT_EVAL_METHOD 0 + +#define LDBL_TRUE_MIN 4.94065645841246544177e-324L +#define LDBL_MIN 2.22507385850720138309e-308L +#define LDBL_MAX 1.79769313486231570815e+308L +#define LDBL_EPSILON 2.22044604925031308085e-16L + +#define LDBL_MANT_DIG 53 +#define LDBL_MIN_EXP (-1021) +#define LDBL_MAX_EXP 1024 + +#define LDBL_DIG 15 +#define LDBL_MIN_10_EXP (-307) +#define LDBL_MAX_10_EXP 308 + +#define DECIMAL_DIG 17 diff --git a/cstdlib/include/float.h b/cstdlib/include/float.h new file mode 100644 index 0000000..713aadb --- /dev/null +++ b/cstdlib/include/float.h @@ -0,0 +1,52 @@ +#ifndef _FLOAT_H +#define _FLOAT_H + +#ifdef __cplusplus +extern "C" { +#endif + +int __flt_rounds(void); +#define FLT_ROUNDS (__flt_rounds()) + +#define FLT_RADIX 2 + +#define FLT_TRUE_MIN 1.40129846432481707092e-45F +#define FLT_MIN 1.17549435082228750797e-38F +#define FLT_MAX 3.40282346638528859812e+38F +#define FLT_EPSILON 1.1920928955078125e-07F + +#define FLT_MANT_DIG 24 +#define FLT_MIN_EXP (-125) +#define FLT_MAX_EXP 128 +#define FLT_HAS_SUBNORM 1 + +#define FLT_DIG 6 +#define FLT_DECIMAL_DIG 9 +#define FLT_MIN_10_EXP (-37) +#define FLT_MAX_10_EXP 38 + +#define DBL_TRUE_MIN 4.94065645841246544177e-324 +#define DBL_MIN 2.22507385850720138309e-308 +#define DBL_MAX 1.79769313486231570815e+308 +#define DBL_EPSILON 2.22044604925031308085e-16 + +#define DBL_MANT_DIG 53 +#define DBL_MIN_EXP (-1021) +#define DBL_MAX_EXP 1024 +#define DBL_HAS_SUBNORM 1 + +#define DBL_DIG 15 +#define DBL_DECIMAL_DIG 17 +#define DBL_MIN_10_EXP (-307) +#define DBL_MAX_10_EXP 308 + +#define LDBL_HAS_SUBNORM 1 +#define LDBL_DECIMAL_DIG DECIMAL_DIG + +#include + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/cstdlib/include/math.h b/cstdlib/include/math.h index 77b813d..92a168e 100644 --- a/cstdlib/include/math.h +++ b/cstdlib/include/math.h @@ -1,3 +1,10 @@ +#ifndef _MATH_H +#define _MATH_H + +#ifdef __cplusplus +extern "C" { +#endif + // NOTE(orca): not doing anything fancy for float_t and double_t typedef float float_t; typedef double double_t; @@ -5,6 +12,60 @@ typedef double double_t; #define NAN __builtin_nanf("") #define INFINITY __builtin_inff() +#define FP_NAN 0 +#define FP_INFINITE 1 +#define FP_ZERO 2 +#define FP_SUBNORMAL 3 +#define FP_NORMAL 4 + +int __fpclassify(double); +int __fpclassifyf(float); +int __fpclassifyl(long double); + +static __inline unsigned __FLOAT_BITS(float __f) +{ + union {float __f; unsigned __i;} __u; + __u.__f = __f; + return __u.__i; +} +static __inline unsigned long long __DOUBLE_BITS(double __f) +{ + union {double __f; unsigned long long __i;} __u; + __u.__f = __f; + return __u.__i; +} + +#define fpclassify(x) ( \ + sizeof(x) == sizeof(float) ? __fpclassifyf(x) : \ + sizeof(x) == sizeof(double) ? __fpclassify(x) : \ + __fpclassifyl(x) ) + +#define isinf(x) ( \ + sizeof(x) == sizeof(float) ? (__FLOAT_BITS(x) & 0x7fffffff) == 0x7f800000 : \ + sizeof(x) == sizeof(double) ? (__DOUBLE_BITS(x) & -1ULL>>1) == 0x7ffULL<<52 : \ + __fpclassifyl(x) == FP_INFINITE) + +#define isnan(x) ( \ + sizeof(x) == sizeof(float) ? (__FLOAT_BITS(x) & 0x7fffffff) > 0x7f800000 : \ + sizeof(x) == sizeof(double) ? (__DOUBLE_BITS(x) & -1ULL>>1) > 0x7ffULL<<52 : \ + __fpclassifyl(x) == FP_NAN) + +double acos(double); + +double ceil(double); + double fabs(double); +double floor(double); + +double fmod(double, double); + double pow(double, double); + +double sqrt(double); + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/cstdlib/include/stdio.h b/cstdlib/include/stdio.h index 0ef60b4..53a3f35 100644 --- a/cstdlib/include/stdio.h +++ b/cstdlib/include/stdio.h @@ -1,3 +1,10 @@ +#ifndef _STDIO_H +#define _STDIO_H + +#ifdef __cplusplus +extern "C" { +#endif + struct _IO_FILE { char __x; }; typedef struct _IO_FILE FILE; @@ -10,3 +17,9 @@ extern FILE *const stderr; #define stderr (stderr) int fprintf(FILE *__restrict, const char *__restrict, ...); + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/cstdlib/include/stdlib.h b/cstdlib/include/stdlib.h index 64d1b15..92f9469 100644 --- a/cstdlib/include/stdlib.h +++ b/cstdlib/include/stdlib.h @@ -1,3 +1,16 @@ +#ifndef _STDLIB_H +#define _STDLIB_H + +#ifdef __cplusplus +extern "C" { +#endif + _Noreturn void abort (void); int abs (int); + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/cstdlib/src/acos.c b/cstdlib/src/acos.c new file mode 100644 index 0000000..ea9c87b --- /dev/null +++ b/cstdlib/src/acos.c @@ -0,0 +1,101 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */ +/* + * ==================================================== + * 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. + * ==================================================== + */ +/* acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ + +#include "libm.h" + +static const double +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +static double R(double z) +{ + double_t p, q; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + return p/q; +} + +double acos(double x) +{ + double z,w,s,c,df; + uint32_t hx,ix; + + GET_HIGH_WORD(hx, x); + ix = hx & 0x7fffffff; + /* |x| >= 1 or nan */ + if (ix >= 0x3ff00000) { + uint32_t lx; + + GET_LOW_WORD(lx,x); + if ((ix-0x3ff00000 | lx) == 0) { + /* acos(1)=0, acos(-1)=pi */ + if (hx >> 31) + return 2*pio2_hi + 0x1p-120f; + return 0; + } + return 0/(x-x); + } + /* |x| < 0.5 */ + if (ix < 0x3fe00000) { + if (ix <= 0x3c600000) /* |x| < 2**-57 */ + return pio2_hi + 0x1p-120f; + return pio2_hi - (x - (pio2_lo-x*R(x*x))); + } + /* x < -0.5 */ + if (hx >> 31) { + z = (1.0+x)*0.5; + s = sqrt(z); + w = R(z)*s-pio2_lo; + return 2*(pio2_hi - (s+w)); + } + /* x > 0.5 */ + z = (1.0-x)*0.5; + s = sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); + w = R(z)*s+c; + return 2*(df+w); +} diff --git a/cstdlib/src/ceil.c b/cstdlib/src/ceil.c new file mode 100644 index 0000000..b13e6f2 --- /dev/null +++ b/cstdlib/src/ceil.c @@ -0,0 +1,31 @@ +#include "libm.h" + +#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 +#define EPS DBL_EPSILON +#elif FLT_EVAL_METHOD==2 +#define EPS LDBL_EPSILON +#endif +static const double_t toint = 1/EPS; + +double ceil(double x) +{ + union {double f; uint64_t i;} u = {x}; + int e = u.i >> 52 & 0x7ff; + double_t y; + + if (e >= 0x3ff+52 || x == 0) + return x; + /* y = int(x) - x, where int(x) is an integer neighbor of x */ + if (u.i >> 63) + y = x - toint + toint - x; + else + y = x + toint - toint - x; + /* special case because of non-nearest rounding modes */ + if (e <= 0x3ff-1) { + FORCE_EVAL(y); + return u.i >> 63 ? -0.0 : 1; + } + if (y < 0) + return x + y + 1; + return x + y; +} diff --git a/cstdlib/src/floor.c b/cstdlib/src/floor.c new file mode 100644 index 0000000..14a31cd --- /dev/null +++ b/cstdlib/src/floor.c @@ -0,0 +1,31 @@ +#include "libm.h" + +#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 +#define EPS DBL_EPSILON +#elif FLT_EVAL_METHOD==2 +#define EPS LDBL_EPSILON +#endif +static const double_t toint = 1/EPS; + +double floor(double x) +{ + union {double f; uint64_t i;} u = {x}; + int e = u.i >> 52 & 0x7ff; + double_t y; + + if (e >= 0x3ff+52 || x == 0) + return x; + /* y = int(x) - x, where int(x) is an integer neighbor of x */ + if (u.i >> 63) + y = x - toint + toint - x; + else + y = x + toint - toint - x; + /* special case because of non-nearest rounding modes */ + if (e <= 0x3ff-1) { + FORCE_EVAL(y); + return u.i >> 63 ? -1 : 0; + } + if (y > 0) + return x + y - 1; + return x + y; +} diff --git a/cstdlib/src/fmod.c b/cstdlib/src/fmod.c new file mode 100644 index 0000000..6849722 --- /dev/null +++ b/cstdlib/src/fmod.c @@ -0,0 +1,68 @@ +#include +#include + +double fmod(double x, double y) +{ + union {double f; uint64_t i;} ux = {x}, uy = {y}; + int ex = ux.i>>52 & 0x7ff; + int ey = uy.i>>52 & 0x7ff; + int sx = ux.i>>63; + uint64_t i; + + /* in the followings uxi should be ux.i, but then gcc wrongly adds */ + /* float load/store to inner loops ruining performance and code size */ + uint64_t uxi = ux.i; + + if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff) + return (x*y)/(x*y); + if (uxi<<1 <= uy.i<<1) { + if (uxi<<1 == uy.i<<1) + return 0*x; + return x; + } + + /* normalize x and y */ + if (!ex) { + for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1); + uxi <<= -ex + 1; + } else { + uxi &= -1ULL >> 12; + uxi |= 1ULL << 52; + } + if (!ey) { + for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1); + uy.i <<= -ey + 1; + } else { + uy.i &= -1ULL >> 12; + uy.i |= 1ULL << 52; + } + + /* x mod y */ + for (; ex > ey; ex--) { + i = uxi - uy.i; + if (i >> 63 == 0) { + if (i == 0) + return 0*x; + uxi = i; + } + uxi <<= 1; + } + i = uxi - uy.i; + if (i >> 63 == 0) { + if (i == 0) + return 0*x; + uxi = i; + } + for (; uxi>>52 == 0; uxi <<= 1, ex--); + + /* scale result */ + if (ex > 0) { + uxi -= 1ULL << 52; + uxi |= (uint64_t)ex << 52; + } else { + uxi >>= -ex + 1; + } + uxi |= (uint64_t)sx << 63; + ux.i = uxi; + return ux.f; +} diff --git a/cstdlib/src/libm.h b/cstdlib/src/libm.h index 9109265..f54ca1b 100644 --- a/cstdlib/src/libm.h +++ b/cstdlib/src/libm.h @@ -1,4 +1,6 @@ #include +#include +#include #define WANT_ROUNDING 1 @@ -30,11 +32,82 @@ static inline double eval_as_double(double x) return y; } +/* fp_force_eval ensures that the input value is computed when that's + otherwise unused. To prevent the constant folding of the input + expression, an additional fp_barrier may be needed or a compilation + mode that does so (e.g. -frounding-math in gcc). Then it can be + used to evaluate an expression for its fenv side-effects only. */ + +#ifndef fp_force_evalf +#define fp_force_evalf fp_force_evalf +static inline void fp_force_evalf(float x) +{ + volatile float y; + y = x; +} +#endif + +#ifndef fp_force_eval +#define fp_force_eval fp_force_eval +static inline void fp_force_eval(double x) +{ + volatile double y; + y = x; +} +#endif + +#ifndef fp_force_evall +#define fp_force_evall fp_force_evall +static inline void fp_force_evall(long double x) +{ + volatile long double y; + y = x; +} +#endif + +#define FORCE_EVAL(x) do { \ + if (sizeof(x) == sizeof(float)) { \ + fp_force_evalf(x); \ + } else if (sizeof(x) == sizeof(double)) { \ + fp_force_eval(x); \ + } else { \ + fp_force_evall(x); \ + } \ +} while(0) + #define asuint(f) ((union{float _f; uint32_t _i;}){f})._i #define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f #define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i #define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f +#define EXTRACT_WORDS(hi,lo,d) \ +do { \ + uint64_t __u = asuint64(d); \ + (hi) = __u >> 32; \ + (lo) = (uint32_t)__u; \ +} while (0) + +#define GET_HIGH_WORD(hi,d) \ +do { \ + (hi) = asuint64(d) >> 32; \ +} while (0) + +#define GET_LOW_WORD(lo,d) \ +do { \ + (lo) = (uint32_t)asuint64(d); \ +} while (0) + +#define INSERT_WORDS(d,hi,lo) \ +do { \ + (d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \ +} while (0) + +#define SET_HIGH_WORD(d,hi) \ + INSERT_WORDS(d, hi, (uint32_t)asuint64(d)) + +#define SET_LOW_WORD(d,lo) \ + INSERT_WORDS(d, asuint64(d)>>32, lo) + double __math_xflow(uint32_t, double); double __math_uflow(uint32_t); double __math_oflow(uint32_t); diff --git a/cstdlib/src/sqrt.c b/cstdlib/src/sqrt.c new file mode 100644 index 0000000..5ba2655 --- /dev/null +++ b/cstdlib/src/sqrt.c @@ -0,0 +1,158 @@ +#include +#include +#include "libm.h" +#include "sqrt_data.h" + +#define FENV_SUPPORT 1 + +/* returns a*b*2^-32 - e, with error 0 <= e < 1. */ +static inline uint32_t mul32(uint32_t a, uint32_t b) +{ + return (uint64_t)a*b >> 32; +} + +/* returns a*b*2^-64 - e, with error 0 <= e < 3. */ +static inline uint64_t mul64(uint64_t a, uint64_t b) +{ + uint64_t ahi = a>>32; + uint64_t alo = a&0xffffffff; + uint64_t bhi = b>>32; + uint64_t blo = b&0xffffffff; + return ahi*bhi + (ahi*blo >> 32) + (alo*bhi >> 32); +} + +double sqrt(double x) +{ + uint64_t ix, top, m; + + /* special case handling. */ + ix = asuint64(x); + top = ix >> 52; + if (predict_false(top - 0x001 >= 0x7ff - 0x001)) { + /* x < 0x1p-1022 or inf or nan. */ + if (ix * 2 == 0) + return x; + if (ix == 0x7ff0000000000000) + return x; + if (ix > 0x7ff0000000000000) + return __math_invalid(x); + /* x is subnormal, normalize it. */ + ix = asuint64(x * 0x1p52); + top = ix >> 52; + top -= 52; + } + + /* argument reduction: + x = 4^e m; with integer e, and m in [1, 4) + m: fixed point representation [2.62] + 2^e is the exponent part of the result. */ + int even = top & 1; + m = (ix << 11) | 0x8000000000000000; + if (even) m >>= 1; + top = (top + 0x3ff) >> 1; + + /* approximate r ~ 1/sqrt(m) and s ~ sqrt(m) when m in [1,4) + + initial estimate: + 7bit table lookup (1bit exponent and 6bit significand). + + iterative approximation: + using 2 goldschmidt iterations with 32bit int arithmetics + and a final iteration with 64bit int arithmetics. + + details: + + the relative error (e = r0 sqrt(m)-1) of a linear estimate + (r0 = a m + b) is |e| < 0.085955 ~ 0x1.6p-4 at best, + a table lookup is faster and needs one less iteration + 6 bit lookup table (128b) gives |e| < 0x1.f9p-8 + 7 bit lookup table (256b) gives |e| < 0x1.fdp-9 + for single and double prec 6bit is enough but for quad + prec 7bit is needed (or modified iterations). to avoid + one more iteration >=13bit table would be needed (16k). + + a newton-raphson iteration for r is + w = r*r + u = 3 - m*w + r = r*u/2 + can use a goldschmidt iteration for s at the end or + s = m*r + + first goldschmidt iteration is + s = m*r + u = 3 - s*r + r = r*u/2 + s = s*u/2 + next goldschmidt iteration is + u = 3 - s*r + r = r*u/2 + s = s*u/2 + and at the end r is not computed only s. + + they use the same amount of operations and converge at the + same quadratic rate, i.e. if + r1 sqrt(m) - 1 = e, then + r2 sqrt(m) - 1 = -3/2 e^2 - 1/2 e^3 + the advantage of goldschmidt is that the mul for s and r + are independent (computed in parallel), however it is not + "self synchronizing": it only uses the input m in the + first iteration so rounding errors accumulate. at the end + or when switching to larger precision arithmetics rounding + errors dominate so the first iteration should be used. + + the fixed point representations are + m: 2.30 r: 0.32, s: 2.30, d: 2.30, u: 2.30, three: 2.30 + and after switching to 64 bit + m: 2.62 r: 0.64, s: 2.62, d: 2.62, u: 2.62, three: 2.62 */ + + static const uint64_t three = 0xc0000000; + uint64_t r, s, d, u, i; + + i = (ix >> 46) % 128; + r = (uint32_t)__rsqrt_tab[i] << 16; + /* |r sqrt(m) - 1| < 0x1.fdp-9 */ + s = mul32(m>>32, r); + /* |s/sqrt(m) - 1| < 0x1.fdp-9 */ + d = mul32(s, r); + u = three - d; + r = mul32(r, u) << 1; + /* |r sqrt(m) - 1| < 0x1.7bp-16 */ + s = mul32(s, u) << 1; + /* |s/sqrt(m) - 1| < 0x1.7bp-16 */ + d = mul32(s, r); + u = three - d; + r = mul32(r, u) << 1; + /* |r sqrt(m) - 1| < 0x1.3704p-29 (measured worst-case) */ + r = r << 32; + s = mul64(m, r); + d = mul64(s, r); + u = (three<<32) - d; + s = mul64(s, u); /* repr: 3.61 */ + /* -0x1p-57 < s - sqrt(m) < 0x1.8001p-61 */ + s = (s - 2) >> 9; /* repr: 12.52 */ + /* -0x1.09p-52 < s - sqrt(m) < -0x1.fffcp-63 */ + + /* s < sqrt(m) < s + 0x1.09p-52, + compute nearest rounded result: + the nearest result to 52 bits is either s or s+0x1p-52, + we can decide by comparing (2^52 s + 0.5)^2 to 2^104 m. */ + uint64_t d0, d1, d2; + double y, t; + d0 = (m << 42) - s*s; + d1 = s - d0; + d2 = d1 + s + 1; + s += d1 >> 63; + s &= 0x000fffffffffffff; + s |= top << 52; + y = asdouble(s); + if (FENV_SUPPORT) { + /* handle rounding modes and inexact exception: + only (s+1)^2 == 2^42 m case is exact otherwise + add a tiny value to cause the fenv effects. */ + uint64_t tiny = predict_false(d2==0) ? 0 : 0x0010000000000000; + tiny |= (d1^d2) & 0x8000000000000000; + t = asdouble(tiny); + y = eval_as_double(y + t); + } + return y; +} diff --git a/cstdlib/src/sqrt_data.c b/cstdlib/src/sqrt_data.c new file mode 100644 index 0000000..61bc22f --- /dev/null +++ b/cstdlib/src/sqrt_data.c @@ -0,0 +1,19 @@ +#include "sqrt_data.h" +const uint16_t __rsqrt_tab[128] = { +0xb451,0xb2f0,0xb196,0xb044,0xaef9,0xadb6,0xac79,0xab43, +0xaa14,0xa8eb,0xa7c8,0xa6aa,0xa592,0xa480,0xa373,0xa26b, +0xa168,0xa06a,0x9f70,0x9e7b,0x9d8a,0x9c9d,0x9bb5,0x9ad1, +0x99f0,0x9913,0x983a,0x9765,0x9693,0x95c4,0x94f8,0x9430, +0x936b,0x92a9,0x91ea,0x912e,0x9075,0x8fbe,0x8f0a,0x8e59, +0x8daa,0x8cfe,0x8c54,0x8bac,0x8b07,0x8a64,0x89c4,0x8925, +0x8889,0x87ee,0x8756,0x86c0,0x862b,0x8599,0x8508,0x8479, +0x83ec,0x8361,0x82d8,0x8250,0x81c9,0x8145,0x80c2,0x8040, +0xff02,0xfd0e,0xfb25,0xf947,0xf773,0xf5aa,0xf3ea,0xf234, +0xf087,0xeee3,0xed47,0xebb3,0xea27,0xe8a3,0xe727,0xe5b2, +0xe443,0xe2dc,0xe17a,0xe020,0xdecb,0xdd7d,0xdc34,0xdaf1, +0xd9b3,0xd87b,0xd748,0xd61a,0xd4f1,0xd3cd,0xd2ad,0xd192, +0xd07b,0xcf69,0xce5b,0xcd51,0xcc4a,0xcb48,0xca4a,0xc94f, +0xc858,0xc764,0xc674,0xc587,0xc49d,0xc3b7,0xc2d4,0xc1f4, +0xc116,0xc03c,0xbf65,0xbe90,0xbdbe,0xbcef,0xbc23,0xbb59, +0xba91,0xb9cc,0xb90a,0xb84a,0xb78c,0xb6d0,0xb617,0xb560, +}; diff --git a/cstdlib/src/sqrt_data.h b/cstdlib/src/sqrt_data.h new file mode 100644 index 0000000..619193c --- /dev/null +++ b/cstdlib/src/sqrt_data.h @@ -0,0 +1,13 @@ +#ifndef _SQRT_DATA_H +#define _SQRT_DATA_H + +#include +#include + +/* if x in [1,2): i = (int)(64*x); + if x in [2,4): i = (int)(32*x-64); + __rsqrt_tab[i]*2^-16 is estimating 1/sqrt(x) with small relative error: + |__rsqrt_tab[i]*0x1p-16*sqrt(x) - 1| < -0x1.fdp-9 < 2^-8 */ +extern const uint16_t __rsqrt_tab[128]; + +#endif diff --git a/samples/pong/data/Literata-SemiBoldItalic.ttf b/samples/pong/data/Literata-SemiBoldItalic.ttf new file mode 100644 index 0000000000000000000000000000000000000000..d49c4416e1bfb825cb6c7aaa73a1c574cd7801fd GIT binary patch literal 317648 zcmcef34D~r`S_oCug!g55J)!JT#$osh9f{o!hIO-M6QH03Me8fC@Lx{A}T5>T53_z z(n{@usHmu@w4&0A6%`dLt)SRarHYCblK*$!-HizzJwBh`A3xvB?94OI+%wP2`|c`A zL=yR9N$Jq)!9!+!(D00y{fk75w}#f7HU578;v6w6EK&7ihK`?Dd1vyLBVuiwAkty` zS>wBOEBnK5!bH>#wA9a9*sy5doNtpwI_?ySs+o215^tAZ$KNZ`2N^jqchS6sGrM@M z66qWz5)(DA;lf3P$B|zSZrHp9%jW*P_MMMKCax0W?u#4eG|cYs+kehQe>w5J8VLwH z8U1@cFX3}e z=l13Cr8p}FsF+ACszOMHp_Ch2@`Oz@BMiI(B-)#8zx#3p5lOv5L#F(!(>QeqjG z7`4QRvD&C@J}o1)D^Y5?bW`10>pCPxbB%aug}}cF^qpKK-fxXS8LYci53i_S=vdWc z&~xGyQyr6T#$E~gQ66m-*V_M6X?`Tm+$LcfW3?0**GSoqa!Ly9vys7tte{(99SnY+ zi~B>&3WjSp#1F}}4m(rMFWrsdq<@I={RC#b6hLm!)&2r?6=Bf@%ukUd< z7gN&JtvMtU-r+F-4x zjtx@y{|hrm3N^;r5^f0Yk1&-hyM)Sb<58Kb4>-!hN3 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