/* This program is part of the TACLeBench benchmark suite. Version V 1.9 Name: isqrt Author: unknown Function: isqrt calculates the integer square root of a number Source: MiBench http://wwweb.eecs.umich.edu/mibench Original name: basicmath_small Changes: no major functional changes License: this code is FREE with no restrictions */ #include "basicmath_libc.h" #include "snipmath.h" // Wasm loop bounds #include "basicmath_libc.c" #include "wcclibm.c" __attribute__((import_module("__pragma"), import_name("loopbound"))) extern void __pragma_loopbound(unsigned int min_bound, unsigned int max_bound); #define BITSPERLONG 32 #define TOP2BITS(x) ((x & (3L << (BITSPERLONG - 2))) >> (BITSPERLONG - 2)) /* usqrt: ENTRY x: unsigned long EXIT returns floor(sqrt(x) * pow(2, BITSPERLONG/2)) Since the square root never uses more than half the bits of the input, we use the other half of the bits to contain extra bits of precision after the binary point. EXAMPLE suppose BITSPERLONG = 32 then usqrt(144) = 786432 = 12 * 65536 usqrt(32) = 370727 = 5.66 * 65536 NOTES (1) change BITSPERLONG to BITSPERLONG/2 if you do not want the answer scaled. Indeed, if you want n bits of precision after the binary point, use BITSPERLONG/2+n. The code assumes that BITSPERLONG is even. (2) This is really better off being written in assembly. The line marked below is really a "arithmetic shift left" on the double-long value with r in the upper half and x in the lower half. This operation is typically expressible in only one or two assembly instructions. (3) Unrolling this loop is probably not a bad idea. ALGORITHM The calculations are the base-two analogue of the square root algorithm we all learned in grammar school. Since we're in base 2, there is only one nontrivial trial multiplier. Notice that absolutely no multiplications or divisions are performed. This means it'll be fast on a wide range of processors. */ /* Forward declaration of functions */ __attribute__((always_inline)) static inline void isqrt_usqrt(unsigned long x, struct int_sqrt *q); __attribute__((always_inline)) static inline void isqrt_init(void); __attribute__((noinline)) __attribute__((export_name("entrypoint"))) __attribute__((noinline)) __attribute__((export_name("entrypoint"))) void isqrt_main(void); __attribute__((always_inline)) static inline int isqrt_return(void); __attribute__((noinline)) __attribute__((export_name("main"))) __attribute__((noinline)) __attribute__((export_name("main"))) int main(void); /* Declaration of global variables */ int isqrt_i; struct int_sqrt isqrt_q; unsigned long isqrt_l; unsigned long isqrt_checksum; /* Initialization function */ __attribute__((always_inline)) static inline void isqrt_init(void) { isqrt_l = 0x3fed0169L; isqrt_checksum = 0; } /* Return function */ __attribute__((always_inline)) static inline int isqrt_return(void) { if (isqrt_checksum == 53364) return 0; else return -1; } /* Main functions */ __attribute__((always_inline)) static inline void isqrt_usqrt(unsigned long x, struct int_sqrt *q) { unsigned long a = 0L; /* accumulator */ unsigned long r = 0L; /* remainder */ unsigned long e = 0L; /* trial product */ int i; __pragma_loopbound(32, 32); for (i = 0; i < BITSPERLONG; i++) { /* NOTE 1 */ r = (r << 2) + TOP2BITS(x); x <<= 2; /* NOTE 2 */ a <<= 1; e = (a << 1) + 1; if (r >= e) { r -= e; a++; } } basicmath_memcpy(q, &a, sizeof(*q)); } __attribute__((noinline)) __attribute__((export_name("entrypoint"))) __attribute__((noinline)) __attribute__((export_name("entrypoint"))) void isqrt_main(void) { /* perform some integer square roots */ __pragma_loopbound(1000, 1000); for (isqrt_i = 1; isqrt_i < 1001; isqrt_i += 1) { isqrt_usqrt(isqrt_i, &isqrt_q); isqrt_checksum += isqrt_q.frac; // remainder differs on some machines } isqrt_usqrt(isqrt_l, &isqrt_q); isqrt_checksum += isqrt_q.frac; } __attribute__((noinline)) __attribute__((export_name("main"))) __attribute__((noinline)) __attribute__((export_name("main"))) int main(void) { isqrt_init(); isqrt_main(); return isqrt_return(); }