677 lines
16 KiB
C
677 lines
16 KiB
C
/*
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* TCC runtime library for arm64.
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*
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* Copyright (c) 2015 Edmund Grimley Evans
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*
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* Copying and distribution of this file, with or without modification,
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* are permitted in any medium without royalty provided the copyright
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* notice and this notice are preserved. This file is offered as-is,
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* without any warranty.
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*/
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#ifdef __TINYC__
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typedef signed char int8_t;
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typedef unsigned char uint8_t;
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typedef short int16_t;
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typedef unsigned short uint16_t;
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typedef int int32_t;
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typedef unsigned uint32_t;
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typedef long long int64_t;
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typedef unsigned long long uint64_t;
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void *memcpy(void*,void*,__SIZE_TYPE__);
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#else
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#include <stdint.h>
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#include <string.h>
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#endif
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#ifndef __riscv
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void __clear_cache(void *beg, void *end)
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{
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__arm64_clear_cache(beg, end);
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}
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#endif
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typedef struct {
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uint64_t x0, x1;
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} u128_t;
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static long double f3_zero(int sgn)
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{
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long double f;
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u128_t x = { 0, (uint64_t)sgn << 63 };
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memcpy(&f, &x, 16);
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return f;
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}
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static long double f3_infinity(int sgn)
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{
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long double f;
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u128_t x = { 0, (uint64_t)sgn << 63 | 0x7fff000000000000 };
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memcpy(&f, &x, 16);
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return f;
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}
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static long double f3_NaN(void)
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{
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long double f;
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#if 0
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// ARM's default NaN usually has just the top fraction bit set:
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u128_t x = { 0, 0x7fff800000000000 };
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#else
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// GCC's library sets all fraction bits:
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u128_t x = { -1, 0x7fffffffffffffff };
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#endif
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memcpy(&f, &x, 16);
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return f;
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}
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static int fp3_convert_NaN(long double *f, int sgn, u128_t mnt)
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{
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u128_t x = { mnt.x0,
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mnt.x1 | 0x7fff800000000000 | (uint64_t)sgn << 63 };
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memcpy(f, &x, 16);
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return 1;
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}
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static int fp3_detect_NaNs(long double *f,
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int a_sgn, int a_exp, u128_t a,
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int b_sgn, int b_exp, u128_t b)
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{
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// Detect signalling NaNs:
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if (a_exp == 32767 && (a.x0 | a.x1 << 16) && !(a.x1 >> 47 & 1))
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return fp3_convert_NaN(f, a_sgn, a);
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if (b_exp == 32767 && (b.x0 | b.x1 << 16) && !(b.x1 >> 47 & 1))
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return fp3_convert_NaN(f, b_sgn, b);
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// Detect quiet NaNs:
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if (a_exp == 32767 && (a.x0 | a.x1 << 16))
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return fp3_convert_NaN(f, a_sgn, a);
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if (b_exp == 32767 && (b.x0 | b.x1 << 16))
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return fp3_convert_NaN(f, b_sgn, b);
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return 0;
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}
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static void f3_unpack(int *sgn, int32_t *exp, u128_t *mnt, long double f)
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{
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u128_t x;
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memcpy(&x, &f, 16);
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*sgn = x.x1 >> 63;
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*exp = x.x1 >> 48 & 32767;
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x.x1 = x.x1 << 16 >> 16;
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if (*exp)
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x.x1 |= (uint64_t)1 << 48;
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else
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*exp = 1;
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*mnt = x;
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}
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static u128_t f3_normalise(int32_t *exp, u128_t mnt)
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{
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int sh;
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if (!(mnt.x0 | mnt.x1))
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return mnt;
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if (!mnt.x1) {
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mnt.x1 = mnt.x0;
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mnt.x0 = 0;
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*exp -= 64;
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}
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for (sh = 32; sh; sh >>= 1) {
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if (!(mnt.x1 >> (64 - sh))) {
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mnt.x1 = mnt.x1 << sh | mnt.x0 >> (64 - sh);
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mnt.x0 = mnt.x0 << sh;
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*exp -= sh;
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}
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}
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return mnt;
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}
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static u128_t f3_sticky_shift(int32_t sh, u128_t x)
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{
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if (sh >= 128) {
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x.x0 = !!(x.x0 | x.x1);
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x.x1 = 0;
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return x;
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}
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if (sh >= 64) {
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x.x0 = x.x1 | !!x.x0;
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x.x1 = 0;
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sh -= 64;
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}
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if (sh > 0) {
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x.x0 = x.x0 >> sh | x.x1 << (64 - sh) | !!(x.x0 << (64 - sh));
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x.x1 = x.x1 >> sh;
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}
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return x;
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}
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static long double f3_round(int sgn, int32_t exp, u128_t x)
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{
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long double f;
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int error;
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if (exp > 0) {
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x = f3_sticky_shift(13, x);
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}
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else {
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x = f3_sticky_shift(14 - exp, x);
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exp = 0;
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}
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error = x.x0 & 3;
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x.x0 = x.x0 >> 2 | x.x1 << 62;
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x.x1 = x.x1 >> 2;
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if (error == 3 || ((error == 2) & (x.x0 & 1))) {
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if (!++x.x0) {
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++x.x1;
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if (x.x1 == (uint64_t)1 << 48)
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exp = 1;
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else if (x.x1 == (uint64_t)1 << 49) {
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++exp;
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x.x0 = x.x0 >> 1 | x.x1 << 63;
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x.x1 = x.x1 >> 1;
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}
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}
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}
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if (exp >= 32767)
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return f3_infinity(sgn);
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x.x1 = x.x1 << 16 >> 16 | (uint64_t)exp << 48 | (uint64_t)sgn << 63;
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memcpy(&f, &x, 16);
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return f;
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}
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static long double f3_add(long double fa, long double fb, int neg)
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{
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u128_t a, b, x;
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int32_t a_exp, b_exp, x_exp;
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int a_sgn, b_sgn, x_sgn;
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long double fx;
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f3_unpack(&a_sgn, &a_exp, &a, fa);
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f3_unpack(&b_sgn, &b_exp, &b, fb);
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if (fp3_detect_NaNs(&fx, a_sgn, a_exp, a, b_sgn, b_exp, b))
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return fx;
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b_sgn ^= neg;
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// Handle infinities and zeroes:
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if (a_exp == 32767 && b_exp == 32767 && a_sgn != b_sgn)
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return f3_NaN();
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if (a_exp == 32767)
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return f3_infinity(a_sgn);
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if (b_exp == 32767)
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return f3_infinity(b_sgn);
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if (!(a.x0 | a.x1 | b.x0 | b.x1))
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return f3_zero(a_sgn & b_sgn);
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a.x1 = a.x1 << 3 | a.x0 >> 61;
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a.x0 = a.x0 << 3;
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b.x1 = b.x1 << 3 | b.x0 >> 61;
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b.x0 = b.x0 << 3;
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if (a_exp <= b_exp) {
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a = f3_sticky_shift(b_exp - a_exp, a);
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a_exp = b_exp;
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}
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else {
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b = f3_sticky_shift(a_exp - b_exp, b);
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b_exp = a_exp;
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}
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x_sgn = a_sgn;
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x_exp = a_exp;
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if (a_sgn == b_sgn) {
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x.x0 = a.x0 + b.x0;
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x.x1 = a.x1 + b.x1 + (x.x0 < a.x0);
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}
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else {
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x.x0 = a.x0 - b.x0;
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x.x1 = a.x1 - b.x1 - (x.x0 > a.x0);
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if (x.x1 >> 63) {
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x_sgn ^= 1;
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x.x0 = -x.x0;
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x.x1 = -x.x1 - !!x.x0;
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}
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}
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if (!(x.x0 | x.x1))
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return f3_zero(0);
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x = f3_normalise(&x_exp, x);
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return f3_round(x_sgn, x_exp + 12, x);
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}
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long double __addtf3(long double a, long double b)
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{
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return f3_add(a, b, 0);
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}
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long double __subtf3(long double a, long double b)
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{
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return f3_add(a, b, 1);
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}
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long double __multf3(long double fa, long double fb)
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{
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u128_t a, b, x;
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int32_t a_exp, b_exp, x_exp;
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int a_sgn, b_sgn, x_sgn;
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long double fx;
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f3_unpack(&a_sgn, &a_exp, &a, fa);
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f3_unpack(&b_sgn, &b_exp, &b, fb);
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if (fp3_detect_NaNs(&fx, a_sgn, a_exp, a, b_sgn, b_exp, b))
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return fx;
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// Handle infinities and zeroes:
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if ((a_exp == 32767 && !(b.x0 | b.x1)) ||
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(b_exp == 32767 && !(a.x0 | a.x1)))
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return f3_NaN();
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if (a_exp == 32767 || b_exp == 32767)
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return f3_infinity(a_sgn ^ b_sgn);
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if (!(a.x0 | a.x1) || !(b.x0 | b.x1))
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return f3_zero(a_sgn ^ b_sgn);
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a = f3_normalise(&a_exp, a);
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b = f3_normalise(&b_exp, b);
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x_sgn = a_sgn ^ b_sgn;
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x_exp = a_exp + b_exp - 16352;
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{
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// Convert to base (1 << 30), discarding bottom 6 bits, which are zero,
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// so there are (32, 30, 30, 30) bits in (a3, a2, a1, a0):
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uint64_t a0 = a.x0 << 28 >> 34;
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uint64_t b0 = b.x0 << 28 >> 34;
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uint64_t a1 = a.x0 >> 36 | a.x1 << 62 >> 34;
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uint64_t b1 = b.x0 >> 36 | b.x1 << 62 >> 34;
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uint64_t a2 = a.x1 << 32 >> 34;
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uint64_t b2 = b.x1 << 32 >> 34;
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uint64_t a3 = a.x1 >> 32;
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uint64_t b3 = b.x1 >> 32;
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// Use 16 small multiplications and additions that do not overflow:
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uint64_t x0 = a0 * b0;
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uint64_t x1 = (x0 >> 30) + a0 * b1 + a1 * b0;
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uint64_t x2 = (x1 >> 30) + a0 * b2 + a1 * b1 + a2 * b0;
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uint64_t x3 = (x2 >> 30) + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
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uint64_t x4 = (x3 >> 30) + a1 * b3 + a2 * b2 + a3 * b1;
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uint64_t x5 = (x4 >> 30) + a2 * b3 + a3 * b2;
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uint64_t x6 = (x5 >> 30) + a3 * b3;
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// We now have (64, 30, 30, ...) bits in (x6, x5, x4, ...).
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// Take the top 128 bits, setting bottom bit if any lower bits were set:
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uint64_t y0 = (x5 << 34 | x4 << 34 >> 30 | x3 << 34 >> 60 |
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!!(x3 << 38 | (x2 | x1 | x0) << 34));
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uint64_t y1 = x6;
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// Top bit may be zero. Renormalise:
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if (!(y1 >> 63)) {
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y1 = y1 << 1 | y0 >> 63;
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y0 = y0 << 1;
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--x_exp;
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}
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x.x0 = y0;
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x.x1 = y1;
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}
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return f3_round(x_sgn, x_exp, x);
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}
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long double __divtf3(long double fa, long double fb)
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{
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u128_t a, b, x;
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int32_t a_exp, b_exp, x_exp;
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int a_sgn, b_sgn, x_sgn, i;
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long double fx;
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f3_unpack(&a_sgn, &a_exp, &a, fa);
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f3_unpack(&b_sgn, &b_exp, &b, fb);
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if (fp3_detect_NaNs(&fx, a_sgn, a_exp, a, b_sgn, b_exp, b))
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return fx;
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// Handle infinities and zeroes:
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if ((a_exp == 32767 && b_exp == 32767) ||
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(!(a.x0 | a.x1) && !(b.x0 | b.x1)))
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return f3_NaN();
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if (a_exp == 32767 || !(b.x0 | b.x1))
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return f3_infinity(a_sgn ^ b_sgn);
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if (!(a.x0 | a.x1) || b_exp == 32767)
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return f3_zero(a_sgn ^ b_sgn);
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a = f3_normalise(&a_exp, a);
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b = f3_normalise(&b_exp, b);
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x_sgn = a_sgn ^ b_sgn;
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x_exp = a_exp - b_exp + 16395;
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a.x0 = a.x0 >> 1 | a.x1 << 63;
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a.x1 = a.x1 >> 1;
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b.x0 = b.x0 >> 1 | b.x1 << 63;
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b.x1 = b.x1 >> 1;
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x.x0 = 0;
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x.x1 = 0;
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for (i = 0; i < 116; i++) {
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x.x1 = x.x1 << 1 | x.x0 >> 63;
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x.x0 = x.x0 << 1;
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if (a.x1 > b.x1 || (a.x1 == b.x1 && a.x0 >= b.x0)) {
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a.x1 = a.x1 - b.x1 - (a.x0 < b.x0);
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a.x0 = a.x0 - b.x0;
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x.x0 |= 1;
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}
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a.x1 = a.x1 << 1 | a.x0 >> 63;
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a.x0 = a.x0 << 1;
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}
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x.x0 |= !!(a.x0 | a.x1);
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x = f3_normalise(&x_exp, x);
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return f3_round(x_sgn, x_exp, x);
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}
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long double __extendsftf2(float f)
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{
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long double fx;
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u128_t x;
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uint32_t a;
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uint64_t aa;
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memcpy(&a, &f, 4);
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aa = a;
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x.x0 = 0;
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if (!(a << 1))
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x.x1 = aa << 32;
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else if (a << 1 >> 24 == 255)
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x.x1 = (0x7fff000000000000 | aa >> 31 << 63 | aa << 41 >> 16 |
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(uint64_t)!!(a << 9) << 47);
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else if (a << 1 >> 24 == 0) {
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uint64_t adj = 0;
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while (!(a << 1 >> 1 >> (23 - adj)))
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adj++;
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x.x1 = aa >> 31 << 63 | (16256 - adj + 1) << 48 | aa << adj << 41 >> 16;
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} else
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x.x1 = (aa >> 31 << 63 | ((aa >> 23 & 255) + 16256) << 48 |
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aa << 41 >> 16);
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memcpy(&fx, &x, 16);
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return fx;
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}
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long double __extenddftf2(double f)
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{
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long double fx;
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u128_t x;
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uint64_t a;
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memcpy(&a, &f, 8);
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x.x0 = a << 60;
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if (!(a << 1))
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x.x1 = a;
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else if (a << 1 >> 53 == 2047)
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x.x1 = (0x7fff000000000000 | a >> 63 << 63 | a << 12 >> 16 |
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(uint64_t)!!(a << 12) << 47);
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else if (a << 1 >> 53 == 0) {
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uint64_t adj = 0;
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while (!(a << 1 >> 1 >> (52 - adj)))
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adj++;
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x.x0 <<= adj;
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x.x1 = a >> 63 << 63 | (15360 - adj + 1) << 48 | a << adj << 12 >> 16;
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} else
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x.x1 = a >> 63 << 63 | ((a >> 52 & 2047) + 15360) << 48 | a << 12 >> 16;
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memcpy(&fx, &x, 16);
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return fx;
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}
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float __trunctfsf2(long double f)
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{
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u128_t mnt;
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int32_t exp;
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int sgn;
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uint32_t x;
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float fx;
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f3_unpack(&sgn, &exp, &mnt, f);
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if (exp == 32767 && (mnt.x0 | mnt.x1 << 16))
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x = 0x7fc00000 | (uint32_t)sgn << 31 | (mnt.x1 >> 25 & 0x007fffff);
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else if (exp > 16510)
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x = 0x7f800000 | (uint32_t)sgn << 31;
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else if (exp < 16233)
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x = (uint32_t)sgn << 31;
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else {
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exp -= 16257;
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x = mnt.x1 >> 23 | !!(mnt.x0 | mnt.x1 << 41);
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if (exp < 0) {
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x = x >> -exp | !!(x << (32 + exp));
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exp = 0;
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}
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if ((x & 3) == 3 || (x & 7) == 6)
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x += 4;
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x = ((x >> 2) + (exp << 23)) | (uint32_t)sgn << 31;
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}
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memcpy(&fx, &x, 4);
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return fx;
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}
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double __trunctfdf2(long double f)
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{
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u128_t mnt;
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int32_t exp;
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int sgn;
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uint64_t x;
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double fx;
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f3_unpack(&sgn, &exp, &mnt, f);
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if (exp == 32767 && (mnt.x0 | mnt.x1 << 16))
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x = (0x7ff8000000000000 | (uint64_t)sgn << 63 |
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mnt.x1 << 16 >> 12 | mnt.x0 >> 60);
|
|
else if (exp > 17406)
|
|
x = 0x7ff0000000000000 | (uint64_t)sgn << 63;
|
|
else if (exp < 15308)
|
|
x = (uint64_t)sgn << 63;
|
|
else {
|
|
exp -= 15361;
|
|
x = mnt.x1 << 6 | mnt.x0 >> 58 | !!(mnt.x0 << 6);
|
|
if (exp < 0) {
|
|
x = x >> -exp | !!(x << (64 + exp));
|
|
exp = 0;
|
|
}
|
|
if ((x & 3) == 3 || (x & 7) == 6)
|
|
x += 4;
|
|
x = ((x >> 2) + ((uint64_t)exp << 52)) | (uint64_t)sgn << 63;
|
|
}
|
|
memcpy(&fx, &x, 8);
|
|
return fx;
|
|
}
|
|
|
|
int32_t __fixtfsi(long double fa)
|
|
{
|
|
u128_t a;
|
|
int32_t a_exp;
|
|
int a_sgn;
|
|
int32_t x;
|
|
f3_unpack(&a_sgn, &a_exp, &a, fa);
|
|
if (a_exp < 16369)
|
|
return 0;
|
|
if (a_exp > 16413)
|
|
return a_sgn ? -0x80000000 : 0x7fffffff;
|
|
x = a.x1 >> (16431 - a_exp);
|
|
return a_sgn ? -x : x;
|
|
}
|
|
|
|
int64_t __fixtfdi(long double fa)
|
|
{
|
|
u128_t a;
|
|
int32_t a_exp;
|
|
int a_sgn;
|
|
int64_t x;
|
|
f3_unpack(&a_sgn, &a_exp, &a, fa);
|
|
if (a_exp < 16383)
|
|
return 0;
|
|
if (a_exp > 16445)
|
|
return a_sgn ? -0x8000000000000000 : 0x7fffffffffffffff;
|
|
x = (a.x1 << 15 | a.x0 >> 49) >> (16446 - a_exp);
|
|
return a_sgn ? -x : x;
|
|
}
|
|
|
|
uint32_t __fixunstfsi(long double fa)
|
|
{
|
|
u128_t a;
|
|
int32_t a_exp;
|
|
int a_sgn;
|
|
f3_unpack(&a_sgn, &a_exp, &a, fa);
|
|
if (a_sgn || a_exp < 16369)
|
|
return 0;
|
|
if (a_exp > 16414)
|
|
return -1;
|
|
return a.x1 >> (16431 - a_exp);
|
|
}
|
|
|
|
uint64_t __fixunstfdi(long double fa)
|
|
{
|
|
u128_t a;
|
|
int32_t a_exp;
|
|
int a_sgn;
|
|
f3_unpack(&a_sgn, &a_exp, &a, fa);
|
|
if (a_sgn || a_exp < 16383)
|
|
return 0;
|
|
if (a_exp > 16446)
|
|
return -1;
|
|
return (a.x1 << 15 | a.x0 >> 49) >> (16446 - a_exp);
|
|
}
|
|
|
|
long double __floatsitf(int32_t a)
|
|
{
|
|
int sgn = 0;
|
|
int exp = 16414;
|
|
uint32_t mnt = a;
|
|
u128_t x = { 0, 0 };
|
|
long double f;
|
|
int i;
|
|
if (a) {
|
|
if (a < 0) {
|
|
sgn = 1;
|
|
mnt = -mnt;
|
|
}
|
|
for (i = 16; i; i >>= 1)
|
|
if (!(mnt >> (32 - i))) {
|
|
mnt <<= i;
|
|
exp -= i;
|
|
}
|
|
x.x1 = ((uint64_t)sgn << 63 | (uint64_t)exp << 48 |
|
|
(uint64_t)(mnt << 1) << 16);
|
|
}
|
|
memcpy(&f, &x, 16);
|
|
return f;
|
|
}
|
|
|
|
long double __floatditf(int64_t a)
|
|
{
|
|
int sgn = 0;
|
|
int exp = 16446;
|
|
uint64_t mnt = a;
|
|
u128_t x = { 0, 0 };
|
|
long double f;
|
|
int i;
|
|
if (a) {
|
|
if (a < 0) {
|
|
sgn = 1;
|
|
mnt = -mnt;
|
|
}
|
|
for (i = 32; i; i >>= 1)
|
|
if (!(mnt >> (64 - i))) {
|
|
mnt <<= i;
|
|
exp -= i;
|
|
}
|
|
x.x0 = mnt << 49;
|
|
x.x1 = (uint64_t)sgn << 63 | (uint64_t)exp << 48 | mnt << 1 >> 16;
|
|
}
|
|
memcpy(&f, &x, 16);
|
|
return f;
|
|
}
|
|
|
|
long double __floatunsitf(uint32_t a)
|
|
{
|
|
int exp = 16414;
|
|
uint32_t mnt = a;
|
|
u128_t x = { 0, 0 };
|
|
long double f;
|
|
int i;
|
|
if (a) {
|
|
for (i = 16; i; i >>= 1)
|
|
if (!(mnt >> (32 - i))) {
|
|
mnt <<= i;
|
|
exp -= i;
|
|
}
|
|
x.x1 = (uint64_t)exp << 48 | (uint64_t)(mnt << 1) << 16;
|
|
}
|
|
memcpy(&f, &x, 16);
|
|
return f;
|
|
}
|
|
|
|
long double __floatunditf(uint64_t a)
|
|
{
|
|
int exp = 16446;
|
|
uint64_t mnt = a;
|
|
u128_t x = { 0, 0 };
|
|
long double f;
|
|
int i;
|
|
if (a) {
|
|
for (i = 32; i; i >>= 1)
|
|
if (!(mnt >> (64 - i))) {
|
|
mnt <<= i;
|
|
exp -= i;
|
|
}
|
|
x.x0 = mnt << 49;
|
|
x.x1 = (uint64_t)exp << 48 | mnt << 1 >> 16;
|
|
}
|
|
memcpy(&f, &x, 16);
|
|
return f;
|
|
}
|
|
|
|
static int f3_cmp(long double fa, long double fb)
|
|
{
|
|
u128_t a, b;
|
|
memcpy(&a, &fa, 16);
|
|
memcpy(&b, &fb, 16);
|
|
return (!(a.x0 | a.x1 << 1 | b.x0 | b.x1 << 1) ? 0 :
|
|
((a.x1 << 1 >> 49 == 0x7fff && (a.x0 | a.x1 << 16)) ||
|
|
(b.x1 << 1 >> 49 == 0x7fff && (b.x0 | b.x1 << 16))) ? 2 :
|
|
a.x1 >> 63 != b.x1 >> 63 ? (int)(b.x1 >> 63) - (int)(a.x1 >> 63) :
|
|
a.x1 < b.x1 ? (int)(a.x1 >> 63 << 1) - 1 :
|
|
a.x1 > b.x1 ? 1 - (int)(a.x1 >> 63 << 1) :
|
|
a.x0 < b.x0 ? (int)(a.x1 >> 63 << 1) - 1 :
|
|
b.x0 < a.x0 ? 1 - (int)(a.x1 >> 63 << 1) : 0);
|
|
}
|
|
|
|
int __eqtf2(long double a, long double b)
|
|
{
|
|
return !!f3_cmp(a, b);
|
|
}
|
|
|
|
int __netf2(long double a, long double b)
|
|
{
|
|
return !!f3_cmp(a, b);
|
|
}
|
|
|
|
int __lttf2(long double a, long double b)
|
|
{
|
|
return f3_cmp(a, b);
|
|
}
|
|
|
|
int __letf2(long double a, long double b)
|
|
{
|
|
return f3_cmp(a, b);
|
|
}
|
|
|
|
int __gttf2(long double a, long double b)
|
|
{
|
|
return -f3_cmp(b, a);
|
|
}
|
|
|
|
int __getf2(long double a, long double b)
|
|
{
|
|
return -f3_cmp(b, a);
|
|
}
|