100: Implement expm1 r=japaric a=Veykril ~~Closes 13~~, closes rust-lang/libm#18 and ~~closes 14~~. ~~I wasn't sure where to put `__expo2(x: f64) -> f64` so I left it in `src/math/cosh.rs` for now.~~ Moved the function into it's own module. Edit: Didn't see that `exp` was already done in a pull request, I'll take it out once rust-lang/libm#90 lands then. 103: implement fma r=japaric a=erikdesjardins closes rust-lang/libm#19 Co-authored-by: Lukas Wirth <lukastw97@gmail.com> Co-authored-by: Erik <erikdesjardins@users.noreply.github.com>
This commit is contained in:
bors[bot]
commit
f6bbea901b
5 changed files with 332 additions and 6 deletions
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@ -366,7 +366,6 @@ pub trait F64Ext: private::Sealed {
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#[cfg(todo)]
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fn signum(self) -> Self;
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#[cfg(todo)]
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fn mul_add(self, a: Self, b: Self) -> Self;
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#[cfg(todo)]
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@ -425,7 +424,6 @@ pub trait F64Ext: private::Sealed {
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(self.sin(), self.cos())
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}
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#[cfg(todo)]
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fn exp_m1(self) -> Self;
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fn ln_1p(self) -> Self;
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@ -485,7 +483,6 @@ impl F64Ext for f64 {
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fabs(self)
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}
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#[cfg(todo)]
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#[inline]
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fn mul_add(self, a: Self, b: Self) -> Self {
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fma(self, a, b)
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@ -604,7 +601,6 @@ impl F64Ext for f64 {
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atan2(self, other)
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}
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#[cfg(todo)]
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#[inline]
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fn exp_m1(self) -> Self {
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expm1(self)
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125
library/compiler-builtins/libm/src/math/expm1.rs
Normal file
125
library/compiler-builtins/libm/src/math/expm1.rs
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@ -0,0 +1,125 @@
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use core::f64;
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const O_THRESHOLD: f64 = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
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const LN2_HI: f64 = 6.93147180369123816490e-01; /* 0x3fe62e42, 0xfee00000 */
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const LN2_LO: f64 = 1.90821492927058770002e-10; /* 0x3dea39ef, 0x35793c76 */
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const INVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
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/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
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const Q1: f64 = -3.33333333333331316428e-02; /* BFA11111 111110F4 */
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const Q2: f64 = 1.58730158725481460165e-03; /* 3F5A01A0 19FE5585 */
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const Q3: f64 = -7.93650757867487942473e-05; /* BF14CE19 9EAADBB7 */
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const Q4: f64 = 4.00821782732936239552e-06; /* 3ED0CFCA 86E65239 */
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const Q5: f64 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
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#[allow(warnings)]
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pub fn expm1(mut x: f64) -> f64 {
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let hi: f64;
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let lo: f64;
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let k: i32;
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let c: f64;
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let mut t: f64;
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let mut y: f64;
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let mut ui = x.to_bits();
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let hx = ((ui >> 32) & 0x7fffffff) as u32;
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let sign = (ui >> 63) as i32;
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/* filter out huge and non-finite argument */
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if hx >= 0x4043687A {
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/* if |x|>=56*ln2 */
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if x.is_nan() {
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return x;
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}
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if sign != 0 {
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return -1.0;
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}
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if x > O_THRESHOLD {
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x *= f64::from_bits(0x7fe0000000000000);
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return x;
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}
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}
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/* argument reduction */
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if hx > 0x3fd62e42 {
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/* if |x| > 0.5 ln2 */
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if hx < 0x3FF0A2B2 {
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/* and |x| < 1.5 ln2 */
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if sign == 0 {
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hi = x - LN2_HI;
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lo = LN2_LO;
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k = 1;
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} else {
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hi = x + LN2_HI;
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lo = -LN2_LO;
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k = -1;
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}
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} else {
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k = (INVLN2 * x + if sign != 0 { -0.5 } else { 0.5 }) as i32;
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t = k as f64;
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hi = x - t * LN2_HI; /* t*ln2_hi is exact here */
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lo = t * LN2_LO;
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}
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x = hi - lo;
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c = (hi - x) - lo;
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} else if hx < 0x3c900000 {
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/* |x| < 2**-54, return x */
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if hx < 0x00100000 {
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force_eval!(x);
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}
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return x;
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} else {
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c = 0.0;
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k = 0;
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}
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/* x is now in primary range */
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let hfx = 0.5 * x;
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let hxs = x * hfx;
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let r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
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t = 3.0 - r1 * hfx;
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let mut e = hxs * ((r1 - t) / (6.0 - x * t));
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if k == 0 {
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/* c is 0 */
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return x - (x * e - hxs);
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}
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e = x * (e - c) - c;
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e -= hxs;
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/* exp(x) ~ 2^k (x_reduced - e + 1) */
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if k == -1 {
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return 0.5 * (x - e) - 0.5;
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}
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if k == 1 {
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if x < -0.25 {
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return -2.0 * (e - (x + 0.5));
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}
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return 1.0 + 2.0 * (x - e);
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}
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ui = ((0x3ff + k) as u64) << 52; /* 2^k */
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let twopk = f64::from_bits(ui);
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if k < 0 || k > 56 {
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/* suffice to return exp(x)-1 */
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y = x - e + 1.0;
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if k == 1024 {
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y = y * 2.0 * f64::from_bits(0x7fe0000000000000);
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} else {
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y = y * twopk;
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}
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return y - 1.0;
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}
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ui = ((0x3ff - k) as u64) << 52; /* 2^-k */
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let uf = f64::from_bits(ui);
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if k < 20 {
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y = (x - e + (1.0 - uf)) * twopk;
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} else {
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y = (x - (e + uf) + 1.0) * twopk;
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}
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y
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}
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#[cfg(test)]
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mod tests {
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#[test]
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fn sanity_check() {
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assert_eq!(super::expm1(1.1), 2.0041660239464334);
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}
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}
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201
library/compiler-builtins/libm/src/math/fma.rs
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201
library/compiler-builtins/libm/src/math/fma.rs
Normal file
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@ -0,0 +1,201 @@
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use core::{f32, f64};
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use super::scalbn;
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const ZEROINFNAN: i32 = 0x7ff - 0x3ff - 52 - 1;
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struct Num {
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m: u64,
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e: i32,
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sign: i32,
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}
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#[inline]
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fn normalize(x: f64) -> Num {
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let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
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let mut ix: u64 = x.to_bits();
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let mut e: i32 = (ix >> 52) as i32;
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let sign: i32 = e & 0x800;
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e &= 0x7ff;
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if e == 0 {
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ix = (x * x1p63).to_bits();
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e = (ix >> 52) as i32 & 0x7ff;
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e = if e != 0 { e - 63 } else { 0x800 };
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}
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ix &= (1 << 52) - 1;
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ix |= 1 << 52;
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ix <<= 1;
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e -= 0x3ff + 52 + 1;
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Num { m: ix, e, sign }
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}
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#[inline]
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fn mul(x: u64, y: u64) -> (u64, u64) {
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let t1: u64;
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let t2: u64;
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let t3: u64;
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let xlo: u64 = x as u32 as u64;
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let xhi: u64 = x >> 32;
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let ylo: u64 = y as u32 as u64;
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let yhi: u64 = y >> 32;
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t1 = xlo * ylo;
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t2 = xlo * yhi + xhi * ylo;
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t3 = xhi * yhi;
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let lo = t1 + (t2 << 32);
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let hi = t3 + (t2 >> 32) + (t1 > lo) as u64;
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(hi, lo)
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}
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#[inline]
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pub fn fma(x: f64, y: f64, z: f64) -> f64 {
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let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
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let x0_ffffff8p_63 = f64::from_bits(0x3bfffffff0000000); // 0x0.ffffff8p-63
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/* normalize so top 10bits and last bit are 0 */
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let nx = normalize(x);
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let ny = normalize(y);
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let nz = normalize(z);
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if nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN {
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return x * y + z;
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}
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if nz.e >= ZEROINFNAN {
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if nz.e > ZEROINFNAN {
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/* z==0 */
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return x * y + z;
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}
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return z;
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}
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/* mul: r = x*y */
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let zhi: u64;
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let zlo: u64;
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let (mut rhi, mut rlo) = mul(nx.m, ny.m);
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/* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
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/* align exponents */
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let mut e: i32 = nx.e + ny.e;
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let mut d: i32 = nz.e - e;
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/* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
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if d > 0 {
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if d < 64 {
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zlo = nz.m << d;
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zhi = nz.m >> 64 - d;
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} else {
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zlo = 0;
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zhi = nz.m;
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e = nz.e - 64;
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d -= 64;
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if d == 0 {
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} else if d < 64 {
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rlo = rhi << 64 - d | rlo >> d | ((rlo << 64 - d) != 0) as u64;
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rhi = rhi >> d;
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} else {
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rlo = 1;
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rhi = 0;
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}
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}
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} else {
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zhi = 0;
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d = -d;
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if d == 0 {
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zlo = nz.m;
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} else if d < 64 {
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zlo = nz.m >> d | ((nz.m << 64 - d) != 0) as u64;
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} else {
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zlo = 1;
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}
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}
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/* add */
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let mut sign: i32 = nx.sign ^ ny.sign;
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let samesign: bool = (sign ^ nz.sign) == 0;
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let mut nonzero: i32 = 1;
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if samesign {
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/* r += z */
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rlo += zlo;
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rhi += zhi + (rlo < zlo) as u64;
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} else {
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/* r -= z */
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let t = rlo;
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rlo -= zlo;
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rhi = rhi - zhi - (t < rlo) as u64;
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if (rhi >> 63) != 0 {
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rlo = (-(rlo as i64)) as u64;
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rhi = (-(rhi as i64)) as u64 - (rlo != 0) as u64;
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sign = (sign == 0) as i32;
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}
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nonzero = (rhi != 0) as i32;
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}
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/* set rhi to top 63bit of the result (last bit is sticky) */
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if nonzero != 0 {
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e += 64;
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d = rhi.leading_zeros() as i32 - 1;
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/* note: d > 0 */
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rhi = rhi << d | rlo >> 64 - d | ((rlo << d) != 0) as u64;
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} else if rlo != 0 {
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d = rlo.leading_zeros() as i32 - 1;
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if d < 0 {
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rhi = rlo >> 1 | (rlo & 1);
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} else {
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rhi = rlo << d;
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}
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} else {
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/* exact +-0 */
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return x * y + z;
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}
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e -= d;
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/* convert to double */
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let mut i: i64 = rhi as i64; /* i is in [1<<62,(1<<63)-1] */
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if sign != 0 {
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i = -i;
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}
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let mut r: f64 = i as f64; /* |r| is in [0x1p62,0x1p63] */
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if e < -1022 - 62 {
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/* result is subnormal before rounding */
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if e == -1022 - 63 {
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let mut c: f64 = x1p63;
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if sign != 0 {
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c = -c;
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}
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if r == c {
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/* min normal after rounding, underflow depends
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on arch behaviour which can be imitated by
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a double to float conversion */
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let fltmin: f32 = (x0_ffffff8p_63 * f32::MIN_POSITIVE as f64 * r) as f32;
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return f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * fltmin as f64;
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}
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/* one bit is lost when scaled, add another top bit to
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only round once at conversion if it is inexact */
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if (rhi << 53) != 0 {
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i = (rhi >> 1 | (rhi & 1) | 1 << 62) as i64;
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if sign != 0 {
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i = -i;
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}
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r = i as f64;
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r = 2. * r - c; /* remove top bit */
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/* raise underflow portably, such that it
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cannot be optimized away */
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{
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let tiny: f64 = f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * r;
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r += (tiny * tiny) * (r - r);
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}
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}
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} else {
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/* only round once when scaled */
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d = 10;
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i = ((rhi >> d | ((rhi << 64 - d) != 0) as u64) << d) as i64;
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if sign != 0 {
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i = -i;
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}
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r = i as f64;
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}
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}
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scalbn(r, e)
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}
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@ -16,12 +16,14 @@ mod exp;
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mod exp2;
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mod exp2f;
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mod expf;
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mod expm1;
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mod fabs;
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mod fabsf;
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mod fdim;
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mod fdimf;
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mod floor;
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mod floorf;
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mod fma;
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mod fmod;
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mod fmodf;
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mod hypot;
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@ -55,12 +57,14 @@ pub use self::exp::exp;
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pub use self::exp2::exp2;
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pub use self::exp2f::exp2f;
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pub use self::expf::expf;
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pub use self::expm1::expm1;
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pub use self::fabs::fabs;
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pub use self::fabsf::fabsf;
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pub use self::fdim::fdim;
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pub use self::fdimf::fdimf;
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pub use self::floor::floor;
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pub use self::floorf::floorf;
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pub use self::fma::fma;
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pub use self::fmod::fmod;
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pub use self::fmodf::fmodf;
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pub use self::hypot::hypot;
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|
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@ -705,7 +705,7 @@ f64_f64! {
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// cosh,
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exp,
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exp2,
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// expm1,
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expm1,
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floor,
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log,
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log10,
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@ -732,7 +732,7 @@ f64f64_f64! {
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// With signature `fn(f64, f64, f64) -> f64`
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f64f64f64_f64! {
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// fma,
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fma,
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}
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|
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// With signature `fn(f64, i32) -> f64`
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|
|
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