Float division functions

bake.cmd

@@ -13,7 +13,7 @@ if "%~1" neq "_start_" (
 )
 shift /1
 
-set CIABATTA_OPTIONS=-Iinc -Wall -g -gcodeview -nodefaultlibs -D_CRT_SECURE_NO_WARNINGS
+set CIABATTA_OPTIONS=-Iinc -Wall -g -gcodeview -nodefaultlibs -D_CRT_SECURE_NO_WARNINGS -mfma
 set PLATFORM=win
 
 if "%1"=="test" (

code/math/_util.h

@@ -0,0 +1,10 @@
+
+#define asuint64(x) ((union {double f; uint64_t i;}){x}).i
+#define asdouble(x) ((union {double f; uint64_t i;}){x}).f
+
+#include <_compiler.h>
+#if defined(_compiler_clang) || defined(_compiler_gnu)
+    #define just_do_it(t) __attribute__((unused)) volatile t
+#else
+    #define just_do_it(t) volatile t
+#endif

code/math/basic.c

@@ -0,0 +1,112 @@
+
+#include <math.h>
+#include <stdint.h>
+
+#if !defined(__FMA__)
+    #error "Get a better CPU (the kind that supports FMA) or enable -mfma"
+#endif
+
+#include <immintrin.h>
+
+double fabs(double x) {
+    union {double f; uint64_t i;} u = {x};
+    u.i &= -1ULL/2;
+    return u.f;
+}
+
+float fabsf(float x) {
+    union {float f; uint32_t i;} u = {x};
+    u.i &= 0x7fffffff;
+    return u.f;
+}
+
+long double fabsl(long double x) {
+    return fabs(x);
+}
+
+double fdim(double x, double y) {
+    if (isnan(x)) return x;
+    if (isnan(y)) return y;
+    return x > y ? x - y : 0;
+}
+
+float fdimf(float x, float y) {
+    if (isnan(x)) return x;
+    if (isnan(y)) return y;
+    return x > y ? x - y : 0;
+}
+
+long double fdiml(long double x, long double y) {
+    return fdim(x, y);
+}
+
+double fmax(double x, double y) {
+    if (isnan(x)) return y;
+    if (isnan(y)) return x;
+    /* handle signed zeros, see C99 Annex F.9.9.2 */
+    if (signbit(x) != signbit(y))
+        return signbit(x) ? y : x;
+    return x < y ? y : x;
+}
+
+float fmaxf(float x, float y) {
+    if (isnan(x)) return y;
+    if (isnan(y)) return x;
+    /* handle signed zeroes, see C99 Annex F.9.9.2 */
+    if (signbit(x) != signbit(y))
+        return signbit(x) ? y : x;
+    return x < y ? y : x;
+}
+
+long double fmaxl(long double x, long double y) {
+    return fmax(x, y);
+}
+
+double fmin(double x, double y) {
+    if (isnan(x)) return y;
+    if (isnan(y)) return x;
+    /* handle signed zeros, see C99 Annex F.9.9.2 */
+    if (signbit(x) != signbit(y))
+        return signbit(x) ? x : y;
+    return x < y ? x : y;
+}
+
+float fminf(float x, float y) {
+    if (isnan(x)) return y;
+    if (isnan(y)) return x;
+    /* handle signed zeros, see C99 Annex F.9.9.2 */
+    if (signbit(x) != signbit(y))
+        return signbit(x) ? x : y;
+    return x < y ? x : y;
+}
+
+long double fminl(long double x, long double y) {
+    return fmin(x, y);
+}
+
+double fma(double x, double y, double z) {
+    __m128d xd = _mm_set_sd(x);
+    __m128d yd = _mm_set_sd(y);
+    __m128d zd = _mm_set_sd(z);
+    __m128d rd = _mm_fmadd_sd(xd, yd, zd);
+    double res = _mm_cvtsd_f64(rd);
+    return res;
+}
+
+float fmaf(float x, float y, float z) {
+    __m128 xd = _mm_set_ss(x);
+    __m128 yd = _mm_set_ss(y);
+    __m128 zd = _mm_set_ss(z);
+    __m128 rd = _mm_fmadd_sd(xd, yd, zd);
+    float res = _mm_cvtsd_f64(rd);
+    return res;
+}
+
+long double fmal(long double x, long double y, long double z) {
+    return fma(x, y, z);
+}
+
+float remainderf(float x, float y) {
+    int q;
+    return remquof(x, y, &q);
+}

code/math/division.c

@@ -0,0 +1,250 @@
+
+#include <math.h>
+#include <stdint.h>
+
+double remquo(double x, double y, int *quo) {
+    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;
+    int sy = uy.i>>63;
+    uint32_t q;
+    uint64_t i;
+    uint64_t uxi = ux.i;
+
+    *quo = 0;
+    if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
+        return (x*y)/(x*y);
+    if (ux.i<<1 == 0)
+        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;
+    }
+
+    q = 0;
+    if (ex < ey) {
+        if (ex+1 == ey)
+            goto end;
+        return x;
+    }
+
+    /* x mod y */
+    for (; ex > ey; ex--) {
+        i = uxi - uy.i;
+        if (i >> 63 == 0) {
+            uxi = i;
+            q++;
+        }
+        uxi <<= 1;
+        q <<= 1;
+    }
+    i = uxi - uy.i;
+    if (i >> 63 == 0) {
+        uxi = i;
+        q++;
+    }
+    if (uxi == 0)
+        ex = -60;
+    else
+        for (; uxi>>52 == 0; uxi <<= 1, ex--);
+end:
+    /* scale result and decide between |x| and |x|-|y| */
+    if (ex > 0) {
+        uxi -= 1ULL << 52;
+        uxi |= (uint64_t)ex << 52;
+    } else {
+        uxi >>= -ex + 1;
+    }
+    ux.i = uxi;
+    x = ux.f;
+    if (sy)
+        y = -y;
+    if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) {
+        x -= y;
+        q++;
+    }
+    q &= 0x7fffffff;
+    *quo = sx^sy ? -(int)q : (int)q;
+    return sx ? -x : x;
+}
+
+float remquof(float x, float y, int *quo) {
+    union {float f; uint32_t i;} ux = {x}, uy = {y};
+    int ex = ux.i>>23 & 0xff;
+    int ey = uy.i>>23 & 0xff;
+    int sx = ux.i>>31;
+    int sy = uy.i>>31;
+    uint32_t q;
+    uint32_t i;
+    uint32_t uxi = ux.i;
+
+    *quo = 0;
+    if (uy.i<<1 == 0 || isnan(y) || ex == 0xff)
+        return (x*y)/(x*y);
+    if (ux.i<<1 == 0)
+        return x;
+
+    /* normalize x and y */
+    if (!ex) {
+        for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1);
+        uxi <<= -ex + 1;
+    } else {
+        uxi &= -1U >> 9;
+        uxi |= 1U << 23;
+    }
+    if (!ey) {
+        for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1);
+        uy.i <<= -ey + 1;
+    } else {
+        uy.i &= -1U >> 9;
+        uy.i |= 1U << 23;
+    }
+
+    q = 0;
+    if (ex < ey) {
+        if (ex+1 == ey)
+            goto end;
+        return x;
+    }
+
+    /* x mod y */
+    for (; ex > ey; ex--) {
+        i = uxi - uy.i;
+        if (i >> 31 == 0) {
+            uxi = i;
+            q++;
+        }
+        uxi <<= 1;
+        q <<= 1;
+    }
+    i = uxi - uy.i;
+    if (i >> 31 == 0) {
+        uxi = i;
+        q++;
+    }
+    if (uxi == 0)
+        ex = -30;
+    else
+        for (; uxi>>23 == 0; uxi <<= 1, ex--);
+end:
+    /* scale result and decide between |x| and |x|-|y| */
+    if (ex > 0) {
+        uxi -= 1U << 23;
+        uxi |= (uint32_t)ex << 23;
+    } else {
+        uxi >>= -ex + 1;
+    }
+    ux.i = uxi;
+    x = ux.f;
+    if (sy)
+        y = -y;
+    if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) {
+        x -= y;
+        q++;
+    }
+    q &= 0x7fffffff;
+    *quo = sx^sy ? -(int)q : (int)q;
+    return sx ? -x : x;
+}
+
+long double remquol(long double x, long double y, int *quo) {
+    return remquo(x, y, quo);
+}
+
+double remainder(double x, double y) {
+    int q;
+    return remquo(x, y, &q);
+}
+
+float remainderf(float x, float y) {
+    int q;
+    return remquof(x, y, &q);
+}
+
+long double remainderl(long double x, long double y) {
+    return remainder(x, y);
+}
+
+double modf(double x, double *iptr) {
+    union {double f; uint64_t i;} u = {x};
+    uint64_t mask;
+    int e = (int)(u.i>>52 & 0x7ff) - 0x3ff;
+
+    /* no fractional part */
+    if (e >= 52) {
+        *iptr = x;
+        if (e == 0x400 && u.i<<12 != 0) /* nan */
+            return x;
+        u.i &= 1ULL<<63;
+        return u.f;
+    }
+
+    /* no integral part*/
+    if (e < 0) {
+        u.i &= 1ULL<<63;
+        *iptr = u.f;
+        return x;
+    }
+
+    mask = -1ULL>>12>>e;
+    if ((u.i & mask) == 0) {
+        *iptr = x;
+        u.i &= 1ULL<<63;
+        return u.f;
+    }
+    u.i &= ~mask;
+    *iptr = u.f;
+    return x - u.f;
+}
+
+float modff(float x, float *iptr) {
+    union {float f; uint32_t i;} u = {x};
+    uint32_t mask;
+    int e = (int)(u.i>>23 & 0xff) - 0x7f;
+
+    /* no fractional part */
+    if (e >= 23) {
+        *iptr = x;
+        if (e == 0x80 && u.i<<9 != 0) { /* nan */
+            return x;
+        }
+        u.i &= 0x80000000;
+        return u.f;
+    }
+    /* no integral part */
+    if (e < 0) {
+        u.i &= 0x80000000;
+        *iptr = u.f;
+        return x;
+    }
+
+    mask = 0x007fffff>>e;
+    if ((u.i & mask) == 0) {
+        *iptr = x;
+        u.i &= 0x80000000;
+        return u.f;
+    }
+    u.i &= ~mask;
+    *iptr = u.f;
+    return x - u.f;
+}
+
+long double modfl(long double x, long double *iptr) {
+    double d;
+    long double r = modf(x, &d);
+    *iptr = d;
+    return r;
+}

code/math/ieee754.c

@@ -4,12 +4,6 @@
 #include <stdint.h>
 #include <float.h>
 
-#include <_compiler.h>
-#if defined(_compiler_clang) || defined(_compiler_gnu)
-    #define just_do_it(t) __attribute__((unused)) volatile t
-#endif
-
-
 int _fpclassify(double x) {
     union {double f; uint64_t i;} u = {x};
     int e = u.i>>52 & 0x7ff;

code/math/round.c

@@ -5,13 +5,7 @@
 #include <float.h>
 #include <limits.h>
 
-#include <_compiler.h>
+#include "_util.h"
-#if defined(_compiler_clang) || defined(_compiler_gnu)
-    #define just_do_it(t) __attribute__((unused)) volatile t
-#endif
-
-#define asuint64(x) ((union {double f; uint64_t i;}){x}).i
-#define asdouble(x) ((union {double f; uint64_t i;}){x}).f
 
 double nearbyint(double x) {
     #pragma STDC FENV_ACCESS ON