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package math
import "base:intrinsics"
_ :: intrinsics
@(require_results)
fmuladd_f16 :: proc "contextless" (a, b, c: f16) -> f16 {
when IS_WASM {
return f16(fmuladd_f64(f64(a), f64(b), f64(c)))
} else {
foreign _ {
@(link_name="llvm.fmuladd.f16", require_results)
_fmuladd_f16 :: proc "none" (a, b, c: f16) -> f16 ---
}
return _fmuladd_f16(a, b, c)
}
}
@(require_results)
fmuladd_f32 :: proc "contextless" (a, b, c: f32) -> f32 {
when IS_WASM {
return f32(fmuladd_f64(f64(a), f64(b), f64(c)))
} else {
foreign _ {
@(link_name="llvm.fmuladd.f32", require_results)
_fmuladd_f32 :: proc "none" (a, b, c: f32) -> f32 ---
}
return _fmuladd_f32(a, b, c)
}
}
@(require_results)
fmuladd_f64 :: proc "contextless" (a, b, c: f64) -> f64 {
when IS_WASM {
return #force_inline fmuladd_slow_f64(a, b, c)
} else {
foreign _ {
@(link_name="llvm.fmuladd.f64", require_results)
_fmuladd_f64 :: proc "none" (a, b, c: f64) -> f64 ---
}
return _fmuladd_f64(a, b, c)
}
}
@(require_results)
fmuladd_slow_f64 :: proc "contextless" (x, y, z: f64) -> f64 {
@(require_results)
split :: proc "contextless" (b: u64) -> (sign: u32, exp: i32, mantissa: u64) {
MASK :: 0x7FF
FRAC_MASK :: 1<<52 - 1
sign = u32(b >> 63)
exp = i32(b>>52) & MASK
mantissa = b & FRAC_MASK
if exp == 0 {
shift := uint(intrinsics.count_leading_zeros(mantissa) - 11)
mantissa <<= shift
exp = 1 - i32(shift)
} else {
mantissa |= 1<<52
}
return
}
@(require_results)
mul_u64 :: proc "contextless" (x, y: u64) -> (hi, lo: u64) {
prod_wide := u128(x) * u128(y)
hi, lo = u64(prod_wide>>64), u64(prod_wide)
return
}
@(require_results)
add_u64 :: proc "contextless" (x, y, carry: u64) -> (sum, carry_out: u64) {
tmp_carry, tmp_carry2: bool
sum, tmp_carry = intrinsics.overflow_add(x, y)
sum, tmp_carry2 = intrinsics.overflow_add(sum, carry)
carry_out = u64(tmp_carry | tmp_carry2)
return
}
@(require_results)
sub_u64 :: proc "contextless" (x, y, borrow: u64) -> (diff, borrow_out: u64) {
tmp_borrow, tmp_borrow2: bool
diff, tmp_borrow = intrinsics.overflow_sub(x, y)
diff, tmp_borrow2 = intrinsics.overflow_sub(diff, borrow)
borrow_out = u64(tmp_borrow | tmp_borrow2)
return
}
@(require_results)
nonzero :: proc "contextless" (x: u64) -> u64 {
return 1 if x != 0 else 0
}
@(require_results)
zero :: proc "contextless" (x: u64) -> u64 {
return 1 if x == 0 else 0
}
@(require_results)
shl :: proc "contextless" (u1, u2: u64, n: uint) -> (r1, r2: u64) {
r1 = u1<<n | u2>>(64-n) | u2<<(n-64)
r2 = u2<<n
return
}
@(require_results)
shr :: proc "contextless" (u1, u2: u64, n: uint) -> (r1, r2: u64) {
r2 = u2>>n | u1<<(64-n) | u1>>(n-64)
r1 = u1>>n
return
}
@(require_results)
lz :: proc "contextless" (u1, u2: u64) -> (l: i32) {
l = i32(intrinsics.count_leading_zeros(u1))
if l == 64 {
l += i32(intrinsics.count_leading_zeros(u2))
}
return l
}
@(require_results)
shrcompress :: proc "contextless" (u1, u2: u64, n: uint) -> (r1, r2: u64) {
switch {
case n == 0:
return u1, u2
case n == 64:
return 0, u1 | nonzero(u2)
case n >= 128:
return 0, nonzero(u1 | u2)
case n < 64:
r1, r2 = shr(u1, u2, n)
r2 |= nonzero(u2 & (1<<n - 1))
case n < 128:
r1, r2 = shr(u1, u2, n)
r2 |= nonzero(u1&(1<<(n-64)-1) | u2)
}
return
}
UVINF :: 0x7ff0_0000_0000_0000
BIAS :: 1023
bx, by, bz := transmute(u64)x, transmute(u64)y, transmute(u64)z
switch {
case x == 0, y == 0, z == 0,
bx&UVINF == UVINF, by&UVINF == UVINF:
return x*y + z
}
if bz&UVINF == UVINF {
return z
}
xs, xe, xm := split(bx)
ys, ye, ym := split(by)
zs, ze, zm := split(bz)
pe := xe + ye - BIAS + 1
pm1, pm2 := mul_u64(xm<<10, ym<<11)
zm1, zm2 := zm<<10, u64(0)
ps := xs ~ ys // product sign
is_62_zero := uint((~pm1 >> 62) & 1)
pm1, pm2 = shl(pm1, pm2, is_62_zero)
pe -= i32(is_62_zero)
if pe < ze || pe == ze && pm1 < zm1 {
// Swap addition operands so |p| >= |z|
ps, pe, pm1, pm2, zs, ze, zm1, zm2 = zs, ze, zm1, zm2, ps, pe, pm1, pm2
}
if ps != zs && pe == ze && pm1 == zm1 && pm2 == zm2 {
return 0
}
zm1, zm2 = shrcompress(zm1, zm2, uint(pe-ze))
// Compute resulting significands, normalizing if necessary.
m, c: u64
if ps == zs {
// Adding (pm1:pm2) + (zm1:zm2)
pm2, c = add_u64(pm2, zm2, 0)
pm1, _ = add_u64(pm1, zm1, c)
pe -= i32(~pm1 >> 63)
pm1, m = shrcompress(pm1, pm2, uint(64+pm1>>63))
} else {
// Subtracting (pm1:pm2) - (zm1:zm2)
pm2, c = sub_u64(pm2, zm2, 0)
pm1, _ = sub_u64(pm1, zm1, c)
nz := lz(pm1, pm2)
pe -= nz
m, pm2 = shl(pm1, pm2, uint(nz-1))
m |= nonzero(pm2)
}
// Round and break ties to even
if pe > 1022+BIAS || pe == 1022+BIAS && (m+1<<9)>>63 == 1 {
// rounded value overflows exponent range
return transmute(f64)(u64(ps)<<63 | UVINF)
}
if pe < 0 {
n := uint(-pe)
m = m>>n | nonzero(m&(1<<n-1))
pe = 0
}
m = ((m + 1<<9) >> 10) & ~zero((m&(1<<10-1))~1<<9)
pe &= -i32(nonzero(m))
return transmute(f64)(u64(ps)<<63 + u64(pe)<<52 + m)
}
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