84 lines
1.9 KiB
C
84 lines
1.9 KiB
C
#include <stdint.h>
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#include <math.h>
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#include "libm.h"
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#include "sqrt_data.h"
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#define FENV_SUPPORT 1
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static inline uint32_t mul32(uint32_t a, uint32_t b)
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{
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return (uint64_t)a*b >> 32;
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}
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/* see sqrt.c for more detailed comments. */
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float sqrtf(float x)
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{
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uint32_t ix, m, m1, m0, even, ey;
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ix = asuint(x);
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if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
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/* x < 0x1p-126 or inf or nan. */
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if (ix * 2 == 0)
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return x;
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if (ix == 0x7f800000)
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return x;
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if (ix > 0x7f800000)
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return __math_invalidf(x);
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/* x is subnormal, normalize it. */
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ix = asuint(x * 0x1p23f);
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ix -= 23 << 23;
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}
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/* x = 4^e m; with int e and m in [1, 4). */
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even = ix & 0x00800000;
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m1 = (ix << 8) | 0x80000000;
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m0 = (ix << 7) & 0x7fffffff;
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m = even ? m0 : m1;
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/* 2^e is the exponent part of the return value. */
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ey = ix >> 1;
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ey += 0x3f800000 >> 1;
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ey &= 0x7f800000;
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/* compute r ~ 1/sqrt(m), s ~ sqrt(m) with 2 goldschmidt iterations. */
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static const uint32_t three = 0xc0000000;
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uint32_t r, s, d, u, i;
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i = (ix >> 17) % 128;
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r = (uint32_t)__rsqrt_tab[i] << 16;
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/* |r*sqrt(m) - 1| < 0x1p-8 */
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s = mul32(m, r);
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/* |s/sqrt(m) - 1| < 0x1p-8 */
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d = mul32(s, r);
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u = three - d;
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r = mul32(r, u) << 1;
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/* |r*sqrt(m) - 1| < 0x1.7bp-16 */
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s = mul32(s, u) << 1;
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/* |s/sqrt(m) - 1| < 0x1.7bp-16 */
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d = mul32(s, r);
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u = three - d;
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s = mul32(s, u);
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/* -0x1.03p-28 < s/sqrt(m) - 1 < 0x1.fp-31 */
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s = (s - 1)>>6;
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/* s < sqrt(m) < s + 0x1.08p-23 */
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/* compute nearest rounded result. */
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uint32_t d0, d1, d2;
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float y, t;
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d0 = (m << 16) - s*s;
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d1 = s - d0;
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d2 = d1 + s + 1;
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s += d1 >> 31;
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s &= 0x007fffff;
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s |= ey;
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y = asfloat(s);
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if (FENV_SUPPORT) {
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/* handle rounding and inexact exception. */
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uint32_t tiny = predict_false(d2==0) ? 0 : 0x01000000;
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tiny |= (d1^d2) & 0x80000000;
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t = asfloat(tiny);
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y = eval_as_float(y + t);
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}
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return y;
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}
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